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A High-Resolution, Low-Frequency 
Spectrum Analyzer 

This dual-channel instrument uses digital computation with 
a microprocessor to make frequency-domain measurements 
in the 0-to-25.5-kHz range with bandwidths as narrow as 
20 mHz, and do it hundreds of times faster than conventional 
swept-frequency analyzers. At the same time, a number of 
other important capabilities are obtained. 

by Nixon A. Pendergrass and John S. Farnbach 

THE RECENT ADVANCES in large-scale inte- 
grated-circuit technology have brought substan- 
tial improvements to the performance of measuring 
instruments. In particular, microprocessor control of 
spectrum analyzers, recently described in these 
pages. 1 - brought significant advances in capability 
to this class of instrument. 

A microprocessor is used in a different way to 
achieve high performance in a new. moderately- 
priced dual-channel spectrum analyzer (Fig. 1) for 
use in the audio and subaudio frequency range (0.02 
Hz to 25.5 kHz). The digital technology used in this 
instrument. Model 3582A. provides greatly increased 
measurement speed and several measurements not 
available with analog techniques, such as true-rms 
averaging and a coherence function. 

The measuring bandwidth of the Model 3582A can 
be as narrow as 0.02 Hz in a 5-Hz frequency span 
anywhere in the 0.02-Hz-to-25.5-kHz range, and on 
the 0-to-l-Hz frequency span the bandwidth can be as 
narrow as 0.004 Hz. The instrument's dynamic range 
is more than 70 dB with full-scale ranges of +30 dBV 
down to -50 dBV (+30 V rms to 3 mV rms). 

The 3582A processes incoming signals digitally 
and stores the results for repetitive, flicker-free dis- 
play on a fully annotated, high-resolution CRT 
(Fig. 2). The method used to process the incoming 
signals, however, also derives phase information, a 
capability not normally associated with spectrum 
analyzers. Thus, besides obtaining spectrum dis- 
plays, this analyzer, with its two input channels and 
phase measurement capability, can be used to mea- 
sure transfer functions (Fig. 3). This is a measurement 
already familiar to electrical engineers and it is of 
growing importance to mechanical engineers, as in 
determining how a structure reacts to a forcing func- 
tion. The transfer function phase spectrum is particu- 
larly useful for pinpointing resonant frequencies. 
To enhance these capabilities, the analyzer has a 

built-in noise source that generates all frequencies of 
interest simultaneously for use as a measurement 
stimulus. This provides the user with a complete 
spectrum and network analysis instrument in a single 
compact package. 

Transient Capture and Averaging 

Because it uses digital storage, the 3582A can cap- 

Cover: Analysis of low-fre- 
quency sounds is but one of 
many uses for the Model 
3582A Spectrum Analyzer 
described in this issue. The 
spectrum analyzer's coher- 
ence function is being used 
here with a microphone and 
an accelerometer to find out 
which parts of a machine contribute to the overall 
sound level and what their contributions are. 

In this Issue: 

A High-Resolution, Low-Frequency 
Spectrum Analyzer, by Nixon A. Pen- 
dergrass and John S. Farnbach . . . page 2 

Window Functions for Spectrum Analysis, by 
Roger G. Cox. page 10. 

Designing Programmable Digital 
Filters for LSI Implementation, by Lynn 
A. Schmidt page 15 

Desktop Plotter 'Printer Does Both 
Vector Graphic Plotting and Fast Text 
Printing, by Majid Azmoon, Jaime H. 
Bohorquez. and Rick A. Warp page 24 

Plotter /Printer Interface Languages: HP-GL 
and ASCII, by Michael P Trego, page 26. 

Primed in u S A 2 ©HWtoWPflBtaW Company 19?8 

© Copr. 1949-1998 Hewlett-Packard Co. 

Fig. 1. Model 3582 A Spectrum 
Analyzer works with signals that 
have frequency components in the 
range between 0.02 Hz and 25 5 
kHz Digital processing with cus- 
tom integrated circuits provides 
high performance in a compact in- 
strument at moderate cost 

ture single-shot transient waveforms for subsequent 
display in a way similar to digital storage oscillo- 
scopes (Fig. 4). Also, with an appropriate trigger sig- 
nal, up to 256 repetitions of a waveform can be aver- 
aged, improving the signal-to-noise ratio of the 
waveform's time record by as much as 24 dB. Analysis 
can then be performed on the averaged waveform to 

JTERs 22.5 

5 82 H z 8.5 Hz/DIV 

0.22 Hz BW: 72.6 mHz 

Fig. 2. The fully annotated display ol Model 3582A has four 
lines ol alphanumeric information givingihe instrument's mea- 
surement conliguration The first two lines from the lop give 
vertical axis information, the bottom two give frequency infor- 
mation. A movable marker (bright dot) reads the frequency 
and amplitude of the indicated point with three-digit resolution, 
displaying either absolute or relative values 

derive amplitude and phase spectra. 

Alternatively, the 3582A can take the power aver- 
age (RMS AVERAGE) of up to 256 spectra to reduce un- 
certainties when characterizing signals that have 
random components. An exponential form of averag- 
ing can also be applied to reduce the contributions of 
older spectra as new spectra are added so changing 
spectra can be observed while being smoothed by 

Fig. 3. Model 3582A obtains transfer functions, both mag- 
nitude and phase, by relating the signal at the output of a 
device to the signal at the input The transfer function can be 
measured over frequency spans as narrow as 5 Hz anywhere 
within the 25-kHz range of the analyzer. 


© Copr. 1949-1998 Hewlett-Packard Co. 


ch ni + iedBv fs ledB^Div 


0 SECONDS .810 - 


- 0 Hz 

_ 25 KHz ' 
BW: 180 Hz 


An additional "averaging" mode, referred to as 
PEAK HOLD, retains the highest value encountered at 
each frequency as several successive spectra are pro- 
cessed. This allows the analyzer to be used with 
swept-frequency sources and to perform other tasks 
such as measuring the amount of frequency drift in a 


Model 3582A also has a COHERENCE function. Used 
with R.MS AVERAGING, this relates the power spectrum 
of a signal at the output of a device to the power 
spectrum of the input signal, giving an indication of 
how much of the output power is a result of the input 
(Fig. 5). At frequencies where the coherence function 
is 1.0 (top line of the CRT graticule), the output is 
caused entirely by the input. At frequencies where the 
coherence function is less than 1 .0. noise or distortion 
within the device is contributing to the output. This 
function is particularly useful for investigating causal 
relationships in multiple input systems because it can 
give a measure of how much each input contributes to 
the output while all inputs are active simultaneously. 
It also provides insight into the accuracy of transfer 
function measurements since it gives an indication of 
how much the measurement is disturbed by noise. 

Fig. 4. Transient waveforms can 
be captured tor display as an 
amplitude-vs-time record (lelt) 
The stored waveform can then be 
analyzed, such as finding the 
amplitude spectrum (right) 

harmonics, and other unwanted signals generated 
within the system being evaluated.' A 

Display Features 

The 3582A gathers input data in one block of 
read-write memory (RAM) and uses other blocks of 
RAM for processing and displaying the data. This 
allows the measurement function to be changed and 
the result displayed without the need to gather new 
data. This is important in an analyzer that has narrow 
resolution bandvvidths. since gathering one time re- 
cord for processing can take up to 250 seconds. 

With the exception of time functions, which are 
displayed singly, any two traces may be displayed at 
the same time. This enables amplitude and phase to 
be displayed simultaneously. In addition, any two 
traces may be stored for later recall. Thus, a newly- 
acquired transfer function amplitude curve may be 
compared against a stored curve. 

Considerable flexibility exists for display of 
amplitude information. The display may be linear in 
volts or gain, or it may be logarithmic in dBV or dB at 
10 dB/div or 2 dB/div. The AMPLITUDE REFERENCE LEVEL 
switch increases the display gain in 10-dB steps for 
convenient positioning of the displayed information. 
The reference level and the scale factor are displayed 
numerically on the CRT for ready reference. 

Fig. 5. The coherence function (right) gives a measure of the fraction of power at each frequency 
in the signal atlhe output of a device (center) that is caused by the signal at the input (left). Among 
other uses, this can indicate the validity of a transfer function measurement by showing how much 
output power comes from sources other than the driving signal. 


© Copr. 1949-1998 Hewlett-Packard Co. 

Phase information is displayed on a r200 c vertical 
scale, giving hysteresis at the ±180 : boundaries that 
prevents the phase trace from continually jumping 
between the top and bottom of the display if the phase 
measurement jitters across il80 c . To further prevent 
ambiguous displays, whenever the signal amplitude 
falls more than 65 dB below full scale where noise 
would obscure and confuse phase values, the phase 
measurement is suppressed and zero phase is dis- 

A marker in the form of a brightened dot may be 
placed on any displayed trace except time-function 
and recalled traces. The frequency and amplitude or 
phase at that point in the spectrum are displayed 
numerically on the CRT (see Fig. 2). Pressing the 
MARKER SET RET key stores the marker frequency and 
amplitude or phase as a reference. Then at any later 
time, pressing the marker REL key causes the present 
marker value relative to the stored reference to be 
displayed. If a point on the display is desired as either 
the START or CENTER frequency of a measured fre- 
quency span, placing the marker on that point then 
causes that frequency to be stored as the new START or 
center frequency when the SET I REQ key is pressed. 
Pressing the * VBW key gives a reading of spectral 
density at the marker position automatically nor- 
malized to a 1-Hz bandwidth for noise density mea- 

HP-IB Compatibility 

Model 3582A has an HP-IB* port, enabling remote 
control of the analyzer in automatic test systems. The 
HP-IB port also allows reading from and loading into 
memory, halting and continuing signal processing at 
specific points, and reading from and loading into the 
CRT alphanumeric display. It is possible, for exam- 
ple, to off-load the spectrum signature of a rotating 
machine onto magnetic tape through the HP-IB and at 
a later time reload it into the analyzer for comparison 
with the present signature. 

When controlled through the HP-IB port by an ex- 
ternal controller, such as the Model 0825A Desktop 

•HP-IB The HP Interlace Bus. Hewlett-Packard s implementation ol IEEE Standard 488-1975 and ANSI 
Standard MCI I 

Computer, the Model 3582A gains greatly enhanced 
signal analysis capability. With user-written 
software, the knowledgable user can apply the spec- 
trum analyzer'desktop computer combination to the 
computation and display of such quantities as auto- 
and cross-correlation functions, impulse responses, 
and cross-power spectra. 

Displayed traces are also converted to analog form 
and supplied to an X-Y recorder output. 

Internal Details 

A simplified block diagram of the Model 3582A 
Spectrum Analyzer is shown in Fig. 6. Each input 
signal initially goes through an attenuator and an 
amplifier that has programmable gain. This is fol- 
lowed by a low-pass filter. The signal then goes to an 
analog-to-digital converter (ADC), after which all 
processing is done digitally. 

The low-pass filter in each channel is required to 
prevent aliasing in the analog-to-digital conversion, 
i.e.. it removes high frequencies that would appear as 
low frequencies when sampled. The ADC sampling 
rate is 102.4 kHz. so high frequencies appear to be 
folded about 51.2 kHz. Unless filtered out. input sig- 
nals above 76.8 kHz would therefore appear on the 
display as below 25.6 kHz. 

The low-pass filtering is done by an active 
seventh-order, elliptic filter that has a cut-off fre- 
quency of 25.6 kHz and a 100 dB/octave roll-off. The 
stopband above 70 kHz is over 80 dB down while the 
passband ripple is less than 0.1 dB. 

The ADCs are 12-bit successive-approximation 
converters. To reduce the effects of quantization and 
associated nonlinearities lor low-level signals, an 
out-of-band 27-kIlz sine wave is injected as a dither 
signal into the signal path before each ADC at a level 
45 dB below full scale. Since the dither signal is not 
synchronized with the sampling, the noise it pro- 
duces is broadband. A small signal, that otherwise 
might fall between two quantization levels and not be 
detected, alters the statistics of the quantization noise 
so it is resolved by subsequent processing for display. 
Although the quantization noise is large relative to a 
-75-dB signal, it is broadband white noise so the 
narrow passband of the 3582A reduces it to well 
below -80 dB with respect to full scale, enabling the 
instrument to consistently detect signals at the 
-75-dB level. 

Digital Heterodyning and Filtering 

The outputs of the ADCs are applied to multipliers 
that digitally "heterodyne" the center of the fre- 
quency hand ol interest down to 0 II/.. Frequen cies 
outside the band of interest can then be removed by 
low-pass filters, This is the same technique used in 
the Model 5420A Digital Signal Analyzer to obtain 
band selectable analysis. - 


The last line on page 8 ot our August issue was missing Here it 15 in case you d like to copy H 
and paste it In 

mixer positive transition. The phase-locked loop has adjusted 

The complete section reads "The condition Oelore triggering 15 now reestablished, mat is. me 
reroth count is matched in time to the rimer positive transition The phase-locked loop has 
adjusted itselt to lock to the new peat Ireguency.' 

Also, on page 4 the last line Delore the title "Hysteresis Arming should read In t Tl ONLY 
the 5370A will not measure any time interval less than ten nanoseconds " The word not" was 
inadvertently omitted 

And on page 16. emitter-follower-iogic (EFl) should have read emitter-lunclion-logic 
(EFl).' There's a Big dirierence 


© Copr. 1949-1998 Hewlett-Packard Co. 










Fig. 6. Simplified block diagram ol the Model 3582A Spectrum Analyzer The entire signal- 
processing chain from the inputs through the ADCs is isolated electrically from chassis ground 
and the remainder ol the instrument to help eliminate ground loops 

Traditional analog heterodyning techniques for 
shifting a band of frequencies into a fixed bandpass 
filter have image-frequency problems that become 
increasingly severe as the band of frequencies ap- 
proaches 0 Hz where the images become very close to 
the desired frequency band. In band-selectable 
analysis, the samples of the input waveform are mul- 
tiplied digitally by samples of a complex waveform. 
cos27rf I .t-/sin27rf c t. instead of using a real multipli- 
cation by t:os277-f c t. The effect of this complex multi- 
plication is to slide the whole frequency spectrum to 
the left along the frequency axis so the selected center 
frequency (f r ) is at 0 Hz. h Frequencies that otherwise 
would become close-in image frequencies thus main- 
tain their relative positions with respect to the desired 
frequency band and are readily removed by low-pass 

The result of the multiplication is two data streams, 
one representing the real components of the 
frequency-shifted spectrum and the other represent- 
ing the imaginary components (for zero-start fre- 
quency spans that require no frequency shift, the 
LO inputs to the digital mixers are set to +1 in the 
3 582 A so the data streams pass unchanged through 
the multipliers). The two data streams are low-pass 
filtered in digital filters to obtain the desired fre- 
quency span and then stored in RAM where they are 
held for subsequent processing. The frequency- 
shifting and filtering thus enable a narrow band of 

frequencies anywhere in the analyzer's frequency 
range to be isolated for high-resolution examination. 

Each filter and associated multiplier (digital mixer) 
are integrated on a single 1C chip (see following arti- 
cle). Putting these complex circuits into integrated 
circuits reduced the parts count significantly and was 
a major factor in achieving compact size and moder- 
ate cost in this high-performance instrument. 

Digital Oscillator 

The samples of the waveform, cos2-f,.t-;'sin2<7-f c t. 
used as the "local oscillator" signal, are produced by 
a digital generator that uses cosine values from a table 
stored in read-only memory (ROM). Linear interpola- 
lion between stored values allows the table length to 
be confined to 1024 values. 

A block diagram of the generator is shown in Fig. 7. 
A binary representation of the selected center fre- 
quency is stored in a latch. This number determines 
the incremental phase angle between samples of the 
output cosine wave, and is added repeatedly to the 
total accumulating in the second latch to select the 
addresses of lfj-bit samples of a full cosine cycle 
stored in the cosine ROM. This ROM holds 1024 

Tor a given phase, both cosfl and -sinM are com- 
puted. Since for low frequencies the phase must be 
specified to a greater precision than 1 1024 of a cosine 
cycle, the computation of cos« is done by using the 


© Copr. 1949-1998 Hewlett-Packard Co. 


Choose t Cos. ♦ Sin 

Fig. 7. Block diagram o' the o>g>- 
lal oscillator instead of wave- 
torms. tr>is generator supplies 
digital words corresponamg to 
amplitude samples o> sine and 
cosine waveforms. 

first two terms of a Taylor series expansion: 

cosW = cos (<f>+e) = costi +e — cosd> = cos</>- esin<2>, 


where <b is a phase value in the cosine ROM. and £ is 
the error so d> + e = 0. The computation is in fractions 
of a cycle so e must he converted to radians. These 
conversions are stored in the interpolate ROM. 

The values of cosd>. e. and -sin(/> are latched at the 
outputs of the ROMs and the remainder of the compu- 
tation is done by a hardware multiplication and addi- 
tion lo produce cosft. A similar computation is used to 
obtain the -sinfl output. 

Processing the Data 

The filtered waveform samples stored in RAM are 
processed by a fast Fourier transform (FFT) algorithm 
(see box. next page). The result of the P'FT processing is 
a series of 512 values representing the real and imagin- 
ary parts of the input waveform spectrum at 256 points 
in the selected analysis band (128 points for each chan- 
nel in dual-channel measurements). These may then 
be presented on the CRT display as a plot of 
amplitude vs. frequency. The phase relationships of 
the frequency components with respect to the 
waveform reference are also derived from the real and 
imaginary data and may be presented as a graph ot 
phase vs. frequency. 

In effect, the 3582A functions as though the input 
waveform were applied to a bank of 256 narrow-band 
filters in parallel and the output of each filter were 
represented on the display by a discrete dot at the 
corresponding point on the display frequency scale. 
A line generator connects adjacent dots to obtain a 
continuous trace. The measurement can be made with 
256-line resolution within narrow frequency spans 
located anywhere in the basic 0-25.5 kHz range of the 
instrument when using the digital heterodyne 
technique to obtain band-selectable analysis 
("zoom"). This greatly enhances the analyzer's reso- 
lution. For example, the basic spectral line spacing 
with the 5-Hz frequency span is 0.02 Hz, and this span 
can be moved anywhere within the 0-25.5-kllz range 
of the Instrument. This gives the equivalent of a re- 
solution of 1.280.000 lines over the full 0-25.5-kHz 


Processing Speed 

FFT processing, display preparation, and averag- 
ing take somewhere between 350 and 600 ms to trans- 
form a time record into a displayed spectrum, de- 
pending on the instrument's operating and display 
mode. Thus, the spectrum can be presented almost 
immediately upon conclusion of data gathering. 
Furthermore, for frequency spans up to 500 Hz. the 
instrument has "real-time" operation, that is to say. 

Fig. 8. The ettect of the passband shape on spectrum dis- 
plays ol a single tone Displays in the column at left are the 
result ol tuning the input signal frequency to one ol the FFT 
spectral frequences Displays at right result from tuning the 
input frequency to a point hall way between two FFT spectral 
Irequencies where the window length is not an exact multiple 
ol the signal period In all cases, the input signal amplitude is 0 


© Copr. 1949-1998 Hewlett-Packard Co. 

The Fast Fourier Transform and 
the Model 3582A 

Digital processing of spectrum analyzer signals offers several 
advantages over analog approaches One of the most sigmli- 
cant is that filtering operations can be perlorrned with no drift 
and with high noise immunity Complicated arithmetic opera- 
tions that would be expensive or nearly impossible as analog 
tasks are readily implemented by digital techniques. 

The Model 3582A Spectrum Analyzer uses digital processing 
with the fast Fourier transform (FFT) to derive a complete 256- 
line spectrum from |usl one input record, an especially important 
capability in an analyzer with very narrow bandwidths For 
example, using the 0-1-Hz frequency span, Model 3582A takes 
250 seconds to obtain a single time record from wlncn it denves 
a spectrum with 0.004-Hz resolution. A swept-frequency spec- 
trum analyzer would take over 100 times as long to obtain a 
spectrum with that resolution 

As explained in the mam text, Model 3582A takes samples of 
the waveform to be analyzed and processes them digitally to 
obtain a sequence of words that correspond to samples of a 
low-pass or bandpass filtered version of the input waveform 
This sequence is then processed by an FFT algorithm to obtain 
another sequence of words that corresponds to the real and 
imaginary parts ot the frequency spectrum of the filtered input 

During the design of this instrument, considerable effort was 
devoted to deriving an FFT algorithm that could be performed 
by a microprocessor in a reasonable amount of time using a 
minimum ot memory 

Computing the FFT 

For a time record consisting of N amplitude samples x(n), 
where n=0,1.2 .N - 1 , the fast Fourier transform calculates the 
frequency spectrum X(k). where k=0,1,2,... N-1, at N frequen- 


X(k) = 2 x(n)e " 

To achieve the necessary processing speed, the FFT 
software in Model 3582A implements this calculation with in- 
teger arithmetic* The software was designed to achieve the 
highest possible processing speed without unreasonable re- 
quirements on the program memory space, and to minimize 
noise introduced by truncation and rounding without introduc- 
ing arithmetic overflow problems 

The FFT calculation is not affected by the selected frequency 
span. Since the digital filters produce data samples at a rate that 
is properly scaled for the selected frequency span, the FFT 
software needs to calculate spectra based only on the time and 
frequency indices n and k. The display processing software 
applies the proper scaling to the frequency axis of the display 
after the FFT processing 

■With integer arithmetic, sometimes teterred to as lued-point arithmetic, values ate represented 
by signed integer binary numoeis instead oi mantissas and exponents (scientific notationl The 
latter is often railed floating-point arithmetic 

there is no gap between the end of one time record and 
the beginning of the next. This is because the instru- 
ment can acquire a new time record while simultane- 
ously processing the previous record stored in mem- 

In the single-channel baseband mode, the time record con- 
sists of 1024 real samples that are formed into an array repre- 
senting a 512-point complex record by a process known as 
scrambling ' The complex FFT algorithm is then applied to this 
array followed by an unscrambling routine that derives the non- 
negative frequency components of the original time record This 
use of scrambling and unscrambling techniques avoids the 
wasted processing time associated with applying the FFT di- 
rectly to real data, which would result in calculating both the 
positive and negative frequency components ot a symmetric 

Further processing speed efficiencies were achieved in the 
FFT software by implementing the 512-pomt FFT as a base-8 
twiddle laclor algorithm 2 With this organization, most of the 
multiplications internal to the base-8 transform are by factors of 
±1 and =/. These do not actually take up processing time so do 
not slow overall processing speed 

The base-8 FFT organization, however, required significantly 
more program space than base 2. because considerations of 
speed required explicit programming of every internal step o< 
the base-8 transform However, this cost was minimized by 
using a Sande-Tukey algorithm for the base-8 transform, rather 
than a Cooiey-Tukey This structure provides an entry into the 
base-8 subroutine at a point where it performs a dual base-4 
transform. With this, a 256-point FFT could be programmed 
using a base 4x8x8 twiddle factor algorithm that used the 
same base-8 subroutine. The 256-pomt FFT algorithm is neces- 
sary for the dual-channel "zoom" mode where two independent. 
256-point, complex records are processed to give two 256- 
pomt complex spectra 

Also, because of the places in the Sande-Tookey algorithm 
where multiplications occur, truncation and rounding introduce 
less noise 

In Its final form, the FFT program package consists ot about 
1 100 program words, the bulk of which is devoted lo the base-8 
subroutine Much smaller portions are devoted to the control 
routines lor the 512- and 256-point transforms and an even 
smaller part is devoted to miscellaneous subroutines 

In the zoom mode, either single- or dual-channel, the digital 
heterodyning supplies the data samples to the FFT processing 
already in complex form, so the scrambling and unscrambling 
processes can be bypassed The FFT algorithm then produces 
a 512-point complex spectrum when the instrument is in the 
single-channel mode. 

in the dual-channel baseband mode, the lime record consists 
of two 512-point records containing real samples These are 
scrambled into a single 512-point complex record that is pro- 
cessed by the 51 2-pomt complex FFT algorithm, then unscram- 
bled to give the non-negative frequency components of the two 
input record spectra 


1 EO Bngham The Fasl Fou'ic TranslOTr Prentice>Hal! 1974. dc 163-169 

2 Ibid. PP 191-193 


One consequence of making an FFT measurement 
for a finite length of time is that the length of the time 
span or "window" during which the measurement is 
made affects the resulting spectrum. The mathema- 


© Copr. 1949-1998 Hewlett-Packard Co. 

tics of FFT processing deals with signals as though 
they were periodic: with a period equal to the window 
length. If the signal is indeed periodic, and if the 
length of the window is an exact multiple of the signal 
period, then the computed FFT spectrum is similar to 
the corresponding analog spectrum. When there is no 
Such relationship between the signal and the win- 
dow, a discontinuity exists that results in broadening 
the base of response peaks (see Fig. 8). Fortius reason. 
FFT analyzers offer a means of attenuating the begin- 
ning and end of the window so the signal is brought 
smoothly to the zero amplitude level at both ends. 
The modified signal waveform then has no discon- 
tinuity between the end of the acquired time record 
and the beginning of a hypothetical repetition of the 
same record. The results of FFT processing are 
thereby made to agree -more closely with the true 

The shape of the window affects the shape of the 
resolution bandwidth (see box. next page), so the 
3582A provides a user with a choice of three window 
shapes. In keeping with the spectrum analyzer orien- 
tation of the instrument, these are labeled PASSBAND 
SHAPE on the front panel. The three passbands offered 
are uniform, BANNING, and flattop. 

The UNIFORM passband is basic in that it allows the 
input signal time record to be treated with a constant 
gain factor during FFT processing. Since it does not 
alter the time record, it is used primarily for capturing 
transient signals. Many transients start at the zero 
level and decay to the zero level so no window shap- 
ing is necessary and the onset of a transient, which 
may contribute significantly to the spectral properties 
of the transient, can be left undisturbed (see Fig. 4). 
The UNIFORM passband provides the narrowest fre- 
quency resolution, so it is used whenever the 
periodicity assumption of the FFT can be satisfied 
without the end-point discontinuity problem. As will 

be explained below, the UNIFORM passband is also 
useful when the built-in noise source is used as a 
stimulus for the measurement. 

The flat TOP passband. developed especially for 
the 3582A. uses a window with a gain-vs-time charac- 
teristic that results in a filter response that is practi- 
cally flat across adjacent spectral lines. Thus, signal 
components that lie between FFT spectral lines suffer 
less than 0.1-dB amplitude degradation. This 
passband is useful for analyzing the spectra of dis- 
crete tones where amplitude accuracy is important. 
There is considerable overlap of adjacent passband 
responses, however, so it is more difficult to resolve 
fine frequency detail with this passband. 

The well-known MANNING passband, widely used 
in FFT analyzers, results in a passband width that is 
midway between the other two (adjacent responses 
overlap at -1.5 dB). The passband is narrower than 
the FLAT TOP passband while the stop-band lobes are 
at a lower level than the UNIFORM passband. Thus it is 
most useful where frequency resolution is important 
but high accuracy in amplitude measurement is not. It 
is often used lor measurements of noise-like spectra 
that have broad distributions of energy. 

The window or time record length is automatically 
selected with selection of the frequency span so the 
time record will encompass one complete period of 
the lowest frequency of interest. Passband shaping is 
implemented digitally by the microprocessor. In all 
cases, lime records are stored without window shap- 
ing, and windows can be changed without requiring 
the gathering of new data. 

Broad Spectrum Source 

The built-in signal source is a pseudorandom noise 
generator. The signal originates in a shift register 
using feedback taps to produce a two-level (binary) 
waveform that changes from one level to the other in 

Channel A 

Noise ► # 

ro 3582A Spectrum Analyzer 

Channel B 


9.995 kHz 

Fig. 9. Transfer function measurement (center) ol the admittance ot a 9.995-kHz crystal llett) 
using the "Finonc noise soiirce lor excitation and the 0 25 kHz frequency span Because the 
noise source's spectral lines are matched to the analyzer's, the measurement result is smooth 
even though averaging is not used Much greater detail shows up (right) when the measurement 
is made over a narrower span (50 Hz centered at 10 kHz) with band-selectable analysis . where 
both the source and analysis spectral lines are more closely spaced 


© Copr. 1949-1998 Hewlett-Packard Co. 

Window Functions for Spectrum 

by Roger G. Cox 

Window 'unctions are frequently used In conjunction with fast 
Fourier transform (FFT) analysis to minimize two of the limitations 
imposed by the FFT a limited lime record provided as input to 
the FFT, and a limited number of output frequency samples 
generated by the FFT 

The first limitation gives rise to what is known as the uniform or 
rectangular window. The uniform window always occurs by 
default since amplitude samples are taken only during a time 
interval T The continuous input signal thus appears to be multi- 
plied by the gating function 

G(t) = 1 for -T/2<t<T/2 and 0 for K-T/2 and T/2<t. 

The frequency response G(s) is the Fourier transform of G(t): 


G(s) = — — ^.wheres = fT 


Any continuous input signal spectrum will be convolved with 
G(s) such that when sinusoidal signals are input to the analyzer, 
instead of seeing a single impulse on the frequency display for 
each sinusoid, one observes a response with the shape of G(s) 
at each impulse location. This is why the window function in a 
FFT analyzer can be regarded as the equivalent of the IF 
passband in a conventional swept-frequency spectrum 

Window Shapes 

The uniform window (Fig. 1 ) can be thought of as a window 
consisting of a dc component ( = 1) multiplied oy the gating 
function G(l) All window functions must include ihe gating 
properties of G(t) If any other window shape is desired, it can be 
constructed by multiplying the uniform window function G(t) by 
an arbitrary continuous time function consisting of the sum of 
several cosine functions For example, the widely-used Hannmg 
window (Fig 2) consists of a dc term and a single cosine term: 

H(T) = G(t)(A 0 + 2A,cos27rt). where A 0 = 1 and A, = 0.5. 

The frequency response of the Manning window is the re- 
sult of the convolution of G(s) wit h three impulses, one at ac and 
a pair representing 2A|COs27rl. 

-1/2 T 


Uniform Window G(t) 

12 T 

Fig. 1. 

1 2 3 4 5 
Frequency (s = (T) 
Uniform Window G(s) 

-1/2 T 


Hanning Window H(t) 

1/2 T 

- 0 




31.5 dB 



) 4 5 

Frequency (s=fT) 
Hanning Window H(s) 

H(S) = G(S)* V A„ (S-k) 


To get other frequency response characteristics, more cosine 
terms can be used A Hal-top passband shape would be desira- 
ble because of the second FFT limitation, that of a limited 
number of frequency sample points being used to evaluate a 
continuous frequency function This flat shape is different from 

-1/2 T 


Flat Top Window F(t) 

1 2 T 

90.5 dB 

Fig. 3. 

Frequency (s=fT) 
Flat Top Window F(s) 


© Copr. 1949-1998 Hewlett-Packard Co. 

me rounded IF response ot most conventional spectrum 
analyzers, where a frequency component being measurea is 
always tuned to me too and center of the IF passband In a 
digital analyzer using the FFT the freauency spectrum is sam- 
pled only at discrete intervals This means that il accurate 
amplitude measurements are to be made on signals regardless 
of frequency, the window functions response must De essen- 
tially flat over one channel spacing of the FFT (-1/2<s<1 ; 2) 
The flat-top window m Mode 1 3582A is fiat withm ^% over one 
channel spacing (Fig 3) 

In addition to the Hat passband, accurate measurements over 
a wide dynamic range require that the response roll off rapidly to 
the maximum dynamic range of the analyzer The flat-top win- 
dow m Model 3582A has a rejection of better than 90 dB In me 
stop band, which occurs only five channel spacmgs from the 
center of the window 

To obtain these desirable characteristics, four cosine terms 
are needed 

F(t) = G(t)(A. 

•2 V Ai,cos2irl<!) 

!i = 1 

F(s) = G(s) * V A k 8(s-k) 


Ron Potter of Hewlett-Packard s Santa C ; ara Division pro- 
vided much valuable help m the derivation of the windows 

Roger G. Cox 

Roger Cox joined Hewlett- 
Packard s Loveiano Division in 
1 970, going to work on synthesizer 
circuits (one patent) and on a cal- 
culator HP-IB interface card One 
of the ongmal members of the 
3582A design team, he is respon- 
sible tor the instrument's basic ar- 
chitecture but left the project in 
1 976 to work on logic state analyz- 
ers at the Colorado Springs Divi- 
sion A native of St Louis. Mis- 
souri, Roger earned a BSEE de- 
gree at the University of Wisconsin 
m 1970 Leisure-time activities in- 
clude backpacking, ski touring and mountain climbing, and 
church volunteer work (counselling, visitations, etc ) 

coincidence with clock pulses, but not necessarily on 
every clock pulse. Changes from one level to the other 
occur in pseudorandom fashion, giving the waveform 
a frequency spectrum that approximates white noise 
over the analysis band. A low-pass filter with a cutoff 
frequency much lower than the clock rate limits the 
frequency band to the flattest part of the spectrum and 
shapes the output waveform to an approximation of 
Gaussian noise. 

Such a waveform is called pseudorandom because, 
although locally random in character, the pattern re- 
peats exactly. The spacing between spectral lines is 
inversely proportional to the length of the pattern 
(and proportional to clock rate). The 3582A provides 
the user with a choice of two pattern lengths. With the 
noise source switch set to periodic, the length of the 
pattern exactly matches the measurement window 
length. The spectral lines of the noise source then 
exactly match the spectral lines of the FFT measure- 
ment. The UNIFORM passband can then be used to 
achieve measurement accuracy without danger of 
spectrum smearing. Measurements can be made 
across the entire frequency span without frequency 
sweeping and without the averaging that is required 
with true random noise excitation, 

If the system has nonlinearities, errors can be intro- 
duced when using the PERIODIC noise source because 
harmonics of the waveform's spectral components 
fall exactly on other spectral lines. These errors can- 
not be reduced by averaging. The RANDOM noise 
source is useful in this situation. Although the RAN- 
DOM source is actually periodic and hence 
pseudorandom, the period of its waveform is over 
25(1,(100 limes as long as the PERIODIC waveform, so its 

spectral lines are far more densely packed and har- 
monics do not necessarily fall on the spectral lines. 
Measurement errors due to nonlinearities can there- 
fore be smoothed out by averaging. 

Because of the close spacing of the random 
source's spectral lines, an additional use for it is in 
situations where very high-Q resonances may be in- 
volved. With the less densely spaced excitation 
energy lines of the PERIODIC source, a high-Q reso- 
nance may fall between lines and the resonance may 
not be fully excited. 

With both types of noise, the noise bandwidth is 
matched to the selected frequency span. For mea- 
surements in the "zoom" mode, the noise source is 
mixed with the digital oscillator output, converted to 
analog form, so in all cases the noise spectrum covers 
the analysis band. Fig. 9 illustrates how this charac- 
teristic affects measurement resolution. 


Another pseudorandom source within the instru- 
ment supplies a calibrating signal to the signal chan- 
nels when the input SENSITIVITY controls are set tu the 
CAL position. This source generates a pseudorandom 
sequence 256 clock pulses long that repeats at a 1-kHz 
rate. This results in a frequency comb with 1-kHz 
spacing between frequency components and a sinx/x 
amplitude distribution. Since the first zero does not 
occur until 256 kHz, the comb is flat within ±0.2 dB 
up to 25 kHz. The calibrating signal is injected into 
the signal channels immediately after the input at- 
tenuators so that all of the amplifiers and filter 
passbands may be checked. 


© Copr. 1949-1998 Hewlett-Packard Co. 


Read Only 



Fig. 10. Block diagram of Model 3582A s control functions 

Instrument Control 

A block diagram of the 3582A control functions is 
shown in Fig. 10. Overall instrument control is han- 
dled by the microprocessor on the processor board, 
which also does the FFT calculations and display 
conditioning. This is the same 16-bit microprocessor 
that was developed for the Model 9825A Desktop 
Computer. 7 

General control of the instrument is accomplished 
over the processor I/O bus. a 16-bit. parallel, bi- 
directional bus with four additional control lines. The 
processor can interrogate the status of Ihe various 
boards over this bus and program them according to 
the operating mode of the instrument. 

Under local (front-panel) control, the processor in- 
terrupts its signal and display processing tasks about 
10 times per second to read (he status of the front- 
panel switches. When changes are detected, signal 
processing may continue with changed parameters, 
or may be discontinued and restarted depending on 
the nature of the change. The 10-Hz polling rate is fast 
enough to enable the instrument to appear to respond 
instantaneously to switch changes. 

Under remote control via the HP-IB. the only 
change in the control process is that the processor no 
longer interrogates the front panel. Instead, the HP-IB 
software routines interrogate the HP-IB board and set 
internal switch status registers to correspond to the 

programmed switch positions. 

To be able lo offer a high degree of HP-IB control, 
almost none of the front-panel switches are wired 
directly to the functions they control. For example, 
the rotary input sensitivity switches are not con- 
nected to the attenuator networks on the input boards. 
Rather, they are connected to a microprocessor I/O 
bus port, and the attenuators are switched by means of 
reed relays via a different port. In this way, the pro- 
cessor can program the input attenuators to agree 
with either the front-panel switches or the HP-IB 
selected sensitivity. 

The processor board is connected to the ROM and 
RAM boards by the memory bus. a bidirectional, 16- 
bit, parallel bus that is separate from the micro- 
processor I/O bus. The ROM and RAM memories are 
distinguished only by different high-order address 

The bulk of the ROM memory is stored in 16 mask- 
programmed ROM's, each storing 2K 8-bit bytes. To 
allow for last minute program improvements that in- 
evitably arise during development of any new pro- 
gram of this size, room was left in the ROM board for 
four "patch" ROM positions that can accept different 
types of fuse-link programmable ROMs, depending 
on jumpers on the board. The 16 mask-programmed 
ROMs cover the address space from 0100()0 H up 
while Ihe addresses below 010000 H are assigned to 
the patch ROM positions. 

The software is organized so that small program 
blocks are linked by addresses stored in the patch 
ROM. Most of the rest of the patch ROM address space 
is empty. Hence, to change a program block, it was 
only necessary to change the address link pointing to 
that block and write the new block in the blank space 
in patch ROM. This made it possible to begin instru- 
ment production while software revisions were being 
made without the delays that otherwise would have 
resulted from waiting for the generation of new 
masks. Thus. Ihe first production instruments were 
shipped with die correct software but without the 
need to equip the entire memory with expensive 
programmable ROMs. 

The RAM memory has 4 K 16-bit words stored in 16 
dynamic RAVI chips, each organized as 4K 1-bit 
words. Memory refresh is not performed by the RAM 
board itself, but rather by the interaction between the 
RAM board and the digital display driver. 

The RAM board is built as a two-port memory, with 
one port serving the processor over the memory bus. 
and the other port serving the digital display driver. 
To present a display, the processor formats both 
graphic and alphanumeric information into a special 
area ot RAM memory. The digital display driver then 
reads these words, separates graphic from al- 
phanumeric information, and draws this display on 


© Copr. 1949-1998 Hewlett-Packard Co. 

the CRT using the analog display driver. Since the 
rate at which the digital display driver reads words 
from the RAM board is sufficient to keep the memory 
refreshed, no additional refresh circuitry is needed on 
the RAM board. 


Cullen Darnell originally conceived of the Model 
3 582 A Spectrum Analyzer, and project manager 
Larry Whatlev contributed to the overall design with 
many helpful ideas. Besides those mentioned 
elsewhere in this issue, others involved in the design 
wereTomoyuki Akiyama, Mike LaMothe. Jerry Metz, 
Charlie Potter, and )im Saar. Industrial design was by 
Jim Berry. Gary Heimbigner and Chuck Kingsford 
Smith contributed marketing and applications re- 
search. 5 


1. S.N. Holdavvay and M.lJ. Humpherys. "The Next Gener- 
ation RF Spectrum Analyzer." Hewlett-Packard journal. 
|une 1978. 

2. R. Temple. "A Precision. Digitally-Controlled Spectrum 
Analyzer lor the 20-Hz-to-4U-MHz Frequency Range," 
Hewlett-Packard lournal. June 1978. 

3. N. Pendergrass. "Coherence Measurements." Elec- 
tronics, to be published 14 September 1978. 

4. "Measuring the Coherence Function with the 1 IP 3582 A 
Spectrum Analyzer," Hewlett-Packard Application Note 
number 245-2. 

5. R.H. Crote and H.VV. McKinney. "Advanced Digital Sig- 
nal Analyzer Probes Low-Frequency Signals with Ease and 
Precision," Hewlett-Packard lournal. October 1977. 

6. H.VV. McKinney. "Band-Selectable Fourier Analysis, " 
Hewlett-Packard lournal. April 1975. 

7. W.D. Eads and D.S. Maitland. "High-Performance 
NMOS LSI Processor." Hewlett-Packard Journal. |une 1976. 

Nixon A. Pendergrass 

Nick Pendergrass earned a 
degree at the University oi Mis- 
P^* sourl at Roila m 1967, and an 

jJ^^Hfe MSEE degree tn 1969 at Purdue 

University (Indiana) while serving 
as a graduate leaching assistant 
He then joined the U S An Force, 
graduating from Otticer Training 
School in 1969. While with the Air 
Force, he was involved in systems 
analysis ol communications sys- 
tems. Nick returned to the campus 
in 1972 as a research assistant al 
the University ol California al Ber- 
keley, where he earned a PhD de- 
gree in 1975 (his thesis involved digital fillers) He joined HP that 
same year Married and with one child, Nick is interested in 
photography and outdoor sports, including cycling, backpack- 
ing, and sknng 

John S, Farnbach 

John Farnbach obtained a BSEE 
degree al Princeton University in 
1965 He designed special- 
purpose instrumentation while 
earning an MSEE degree al the 
University of New Mexico. Relum- 
ing to Princeton in 1969, he ob- 
tained a PhD degree (1972) and 
Ihen laughi electrical engineering 
( m Span ish) for a year and a half at 
Ihe Universidad Iberoameri- 
cana in Mexico Hetheniomedlhe 
Seismological Lab al the Univer- 
sity of Uppsala. Sweden, where he 
did research on seismic signal 
processing He came lo HP in 1975, going to work on FFT 
soliware Married, and with two small children. John spends off 
hours renovaling the older home m which Ihey live, in picnicking 
and skiing, and playing volleyball in- regional competilions. 

Hewlett-Packard FFT Analyzers 

The Model 3582A Spectrum Analyzer described in Ihe pre- 
ceding is the newesl member of Hewlett-Packard's family of 
FFT-based analyzers The others are Ihe Model 5420A Digital 
Signal Analyzer and Ihe Model 545 1C Fourier Analyzer. 

The Model 3582A Spectrum Analyzer provides a low-cosi 
means of obtaining the advantages of FFT processing for signal 
analysis it can measure speclrum amphiude and phase, trans- 
fer functions, and coherence with frequency resolution as tine 
as 0 02 Hz over the entire 25-kHz frequency range It is op- 
timized for simplified operation, small package size and weight, 
and low cost while providing a powerful set of measuremenl 
capabilities It includes many convenience features, such as a 
choice of three windows and a fracking noise source that re- 
duces the averaging time usually required wilh random-noise 

The Model 5420A Digital Signal Analyzer, described in the 

October 1977 issue ol Ihe Hewlett-Packard Journal has addi- 
iionai measuremenl capabilities. It was designed for those who 
need auto- and crosscorrelalion functions, power and cross 
spectra and statistical analyses of signals, in addition lo 
frequency-domain measurements. Pre/posl-tngger delay is 
provided for acoustic. Iransient, and transfer function mea- 
surements, and Ihe analyzer may be operated Irom an external 
clock to adapt I] to rotating machinery studies. 

Model 5420A also provides very flexible display formatting 
thai can give Bode, Nyquisl, and Nichols plots as well as linear 
plots of resulls Digital storage lor measurement results is pro- 
vided by its buill-in magnetic tape unit Post-processing 
capabilities include such operations as integrating an accelera- 
tion speclrum lo a velocity spectrum, or calculating coherenl 
oulpul power and open-loop gain It has a built-in true random 
noise source lor stimulus-response measurements. The 


© Copr. 1949-1998 Hewlett-Packard Co. 

5420A's measurement frequency range extends from 25 kHz 
down to 0.008 Hz and its frequency resolution can be as fine as 
40 mHz. Its dynamic range is 75 dB 

The Model 5451C Fourier Analyzer, a further elaboration of 
Ihe Model 5451 A described In the June 1972 issue of the 
Hewlett-Packard Journal, offers a very flexible and powerful 
alternative that is capable of a full range of analysis functions, 
including the inverse Fourier transform It is a fully calibrated, 
multipurpose, computer-based system and can be obtained 
with a full range of computer peripherals such as disc 
memories. This combined with user-written programs allows 

each system to be tailored to specific applications it can also 
be obtained with up to four input channels and options for sucn 
tasks as vibration coniroi, modal analysis, and rolating- 
machinery signature analysis. Its frequency range extends from 
dc to 50 kHz and optionally to 100 kHz, and its dynamic range is 
75 dB. 

These three analyzers cover a wide range of applications in 
studies concerning mechanical vibrations, slrucfural dynamics, 
acoushcs, underwater sound, communications, and other in- 
vestigations involving audio and subaudio frequencies. 

HP Model 35B2A Spectrum Analyzer 



0-25 km SPAN Measurement is pertc-med over '«<") 'reounncy rang* 

0 Hi In US KM/ independent C FREQUENCY SPAN coiro" 
D-5TART '■ lea 1 ■ i f o*tK frequency long* demao oy 

FREQUENCY S"AN cenrt* wit\ lued itart Irequency ol 0 Hi 
SET CENTER Meuuiemenl ■ performed uvei i Ireojenci rangr wiH< t»i3lh 

aete-m.ned by FREQUENCY S"AN control aid center ireQjeney s« tiy 

ADJUST co"tm» *rth M« 
SET START Maaeuiemom ! w'o'mea «v#< a tieojency i»"ge *m Wflm 

deterrr ned By fHEChJENCY SPAN cinrlrui and sUrl lieauencY 591 0y 

ADJUST control - ll> 1*Hi 
FREQUENCY RANGE 0 0? Hi ro 25 5 kHz 
D START MODE ' Hi tjtl scale ;o 25 -Hi hi scale « t-a 5-5-10 sequence 
SET START OR SET CENTER MODE 5-mj span to 25 .Hi span in 1-2 5 5 '0 

FREQUENCY ACCURACY: - 0 003% o» aseay ceMer troqgoncy 
FREQUENCY RESOLUTION: Mailt*- resOuLun « ecual lu calculated ur>«t 

scoring lor 9«nCeG troq.ioncv ".pan and nunbrn zf ehanners |in TBfilt | 

Flal Too Manning Uniterm 

3-dB Bandwidth 

lingie-enaniWl l'«:0iis i05b- 005|N. 

of -.pan OtafaVI 

Snap- Factor , 2 6 - 
feO dB bandwdlhl 

. 3-dB band.**!mJ. 

10 35 * Q 0?p» 
ol suan 

FIAT TOP PASSBAND Sha d E rvovioW oor-mum amplitude accuracy UNI 
FORM PASSBAND SHAPE 19 npliniiied Idi use *>m Irensienla ana wlh lie 
tudB ^oquoncy rascArtron compmrnsa Mi general nose 



Equivalent Noise Bandwidth 







Flal Top 

Manning Uniterm 

1 Hi 


004 Hz 

14 5mHz 

6 00 mHi 4 TO mHz 

2.5 Hz 

100 a 


3* 3 mHz 

«4 0mHi iQOmHz 

9 Hi 


02 Hi 

72 6 mHi 

30G mHi 20 0 mHz 

!0 Hi 


04 Hz 

145 mm 

60 0 mHz 40 0 mHz 



1 Hi 

363 mr-j 

150 mHz 100 m-i 

SO Hz 

5 a 


726 n-f 

300 r»fi 200 mKr 

100 Hi 

2.6 b 

* HZ 

145 Hz 

600 mHi J CO mMi 

250 Hi 

1 HZ 

363 He 

>»Hi '00 hi 

500 Hi 

500 roe 


7 26 Hi 

3 00 Hi 2 00 Hz 

1 kHz 

250 ms 

a hi 

MS Hi 

6 00 Hi 4 00 Hz 

2.5 kKi 

10O ma 

ID Hz 

36 J l« 

16 0 tir 10.0 rw 

5 kHz 

50 ms 

20 HZ 

72 6 Hi 

30 0 Hi 200 hi 


25 ma 

40 HZ 

145 **r 

00 0 Hi Z0 0 >'z 

25 kHz 

10 ma 

100 Hz 

363 Hz 

150 Mz 100 hz 


ihm norawwin 

are round By dnuQ'ig calculated ton 

seating aid eouwa*". nafeM cendwidtn ana taking or* nail ih* time record lengt*' 

MEASUREMENT MODES MfJQinl amplttudo icwti »• mtaaurM 1" aiigia- 
ca-inelmoOe 1*0 129-poir'l s-mpltuda apeara are rtnuuia? in Dual cnannni 


LOO '■ -1.1. ' 1 ■ i:.r : . ■■ .-- 

LINEAR Contlanl .ollago mapr Qi*s*r> 

LOG CalOratM aKanuator langa . s - 30 dBV IC M flflV a^gle-lone rma 
rra»Tiu"i input lev«l i0-d3 -02 dB sleva Cunitnuriu» Hvmax picvroes 
- r ■ 1 'H ■ r -.- -f*r-r ■■ 

_INEAR Ca*nrai«d anenuaii" 'ange 4 > 30 V mia 10 3 mv vngi* tone "t>a 
ma«>mum irr»il r. 1-3- t&ieQuence V«tnm cnv^Mi coMmix^* co>e<aae 0e- 
■»e«fl lt*os AMPLITUDE REFERENCE LEVEL pronidw addtlirmal 'ang« 
doam lo d «v 'uD scale 

DISTORTION PRODUCTS^ -70 aB Doleo - ■ ■ • ...t «cu( 

SPURIOUS RESPONSES -TO dB Delo* "utii-rrjt. -io u | «rvf» 



-SO rJBV rangr 

Fiat Top ■-■•<•■■•• ■ - 

1 ail sou'ea impadancc 


- rma a.eragino. 
eacluaive at dc mponae 
25-kHi span 


DC RESPONSE: AD (J %iaDle 10 <(0 OS t*iO* manrnum xipul levfrt w.1li trunt- 

unnH rlc baiarxfr ad|uitmom 
AMPLITUDE ACCURACY '.O-.e-all accuracy 19 1'ie sum o- accuracy al pamoand 

nmrirr am *rtm accuracv) 



HANN'NG FILTER: -0 1 5 dB 

UNIFORM FILTER -0. 4 0 08 

LOG 0 1 dB All* rnarHor 

L I NEAR 3 Nlth mamar 

LINEARITY: -0 2dS --022% ol lull aca* 

AMPLITUDE CALIBRATOR: miemai calcawn s^iai 1% a »r* ip«lrum mlh 
no«wial 1-liHz liequency spaorg and r_ndamenuil levol ol 22r02 dBV on 
og acaias and 20r0 5 votI> pn linear Male 

LOG Overload occurs a* IM^Oirruji^m^pul level Mlicliraeaua.' to 'uliscaki 
*cen AMPLITUDE REFERENCE LEVEL ■ srrt lo NORMAL Wtcn overload 
occurs, vunous p<ooliOs nay D9 diealayed 
LINEAR Ce-fcad occurs at 'CO*, o" rripnum inpul tavru wnc" wpenoig 
un inpul arlonuaior] n ai SB or S-'E Ol lull acaie *rlien AMPLITUDE 
REFERENCE LEVEL .« gel lo NORMAL Wne- Overload Occurs sour^MB 
rmojcis may De oisfLayeo 

RMS fc oncti caic-a^tsd "nwunncv poim diulayed arrrphudn ■» 

V |1.'NjVA,SiH) ard phase >a ll.'Nl V^Hj. 
PEAK- For eacn ■- y<-: 1 -i, point OiptaveD anplitud* » 'AAX AuTi 

ana : 'I-.- is cofca pen ding value n* *etamed 1 • poml 
T)ME Fqi esc lime recvd poml ite amplitude ^ 1 1 Ni ^ A-|» 

The avo'agnd tmn record it "an Wormed In give correstanding ampMude an] 

NUMBER OF AVERAGES: 1 Ic ?M m amary sooi^nca ano e»pone"1ial E>- 
OOiemial averagrnB in 'ma mode gives runrmg a«erag4< -tin new wcjral 
Anrsnin.- I « and ive-'OJi 'eaul by 3 4 Eiccnenlial In pea* made give* ccm- 


MEASUREMENT MODES .V* poim pnasa specna »r* ^eaaure-J m *i»gle- 
criarmel mode Two 123-poini pnaae apedra we measureo ' dual*cnannel 

DISPLAY RANGE: -'0,r . 200 oec-ees B 200 Oeg-eet 

ACCURACY^ 1 10 degroec 


OSPLAV Mdogroos-ma|oro.*on 
MARKER I degree 

Transfer Function 

MEASUREMENT MODES ?ual-^>anne< I2a-pui"l lran*!er i^ncnota are 


I OQ AMPLITUDE '0 oB-major e*.'*o» and 2 dB magr di.ismi 
LINEAR AMPLITUDE Conslaffl noaiing-pont haciot majo* division 
PHASE Cnralam 50 dryeevmaior tPvoinn 
LOG AWPirTUDE Catoraied -angaa 0* • I600B 'uii sca«io 90 oB l»n scale 

al 10-dfl Woos Unca'dralad vomionj pra^oa cnrcmi04S sofa-age betwaen 


LINEAR AMPLITUDE Caiibraiod -angea ol 4 0 • 10* lull tceleio I O - 10 lull 
scale Mi 'acto'-eMO atepi ^icavDravd .e>*weTs pre>r-3» wme-unua cov«> 
age Uetwper aiepa 


WHASE -SdogreBi 

LOG AMPLITUDE 0 1 aB marker 

LINEAR AMPLITUDE 3-rJgit iDomrt.c noialion wrlh mar.ei 
P-ASE I degree «th mawrw 

Coherence Function 

MEASUREMENT MODE: Dual-channel i2fi-po*~l cone-ence lu-.ciiDn« a<e 

will- "TU !.•■■>-,, 1.] only 
RANGE: Soflom d-ipiay ine 15 0 0 and top Ina 19 1 C 

DISPLAY 0'25 ma|O>divt»-3n 

MARKER 0 01 


INPUT IMPEDANCE 'C-U 5 5"»lhunieoDv 60pFlrominputr.gniO>O"»tO'»!6 

man 75% reJaiivo humioty 
DC ISOLATION: IhojI low "lay be connected to chassis gruum: v l>9aled 141 to 

30 *ofls to 'Educe oriecis C ground Cops on me measure-r^nr 
INPUT COUPLING: ac o> oft LOar frequency 3-dB roi off ol ac couplng . • HI 

50 HZ -60 dB 

60 M2 -58 08 

INPUT CHANNEL CROSSTALK: - '40 dB nelrveen t^a-mels anlh 1 kll source 

1 - ■ r grivng one cnannoi *"1" otner cnannol terminated *i 1 alt 

FREE RUN New moaau-emenl *a initialed Cy eomplohon ol preview* moa- 

EXTERNAL Rear-panel awich alloo* nc* measurrmenlB to C* miliaiofl try 

e»tB"iai TTL svilses 
iN D uT Signal New meatmemeni rs imimled when -uui a^nal meets acec- 

tioa mgger condmon 
SIGNAL CONDITIONS Tnggonng can On Wectoo lo occur on DC&tive O 

"egetive gomg transilions throuon Ingge 'eve 1 - Tr^ger level * adjuBted 

c«r*nan time recoil overloac »n>t( Ov conntoou! vemiB- 
BINGLE. MULTIPLE TRIGGERS 5mgle-snol n^ganng 4 specif ec ny tak 

ode AHM control ! 
Ihe yno'e enoi mooe 

I til REPE1H 
atrumenr fo ia*o anwhc n 

VERTICAL 0 lo 5 25V - 5% 

PEN LIFT Comae cloture duimg s*eec 

PERiOO'C Rwudorandom noee iigrai "if apecuaii«etoaono»fnaimalcn 
calculBled poml spacing 'tx leleaed Iroouency span rasponse is 

- t aB *ah UNIFORM passunnd shape eno - 10 dBV level 
RANDOM Random roiw signal, noise loeclrurT 15 Band 'mrteo ana Dana 
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© Copr. 1 949- 1 998 Hewlett- Packard Co. 

Designing Programmable Digital Filters for 
LSI Implementation 

by Lynn A. Schmidt 

now becoming available through the use of large- 
scale integrated circuits is giving low-frequency spec- 
trum analyzers unprecedented flexibility and compu- 
tational power at relatively low cost. For example, the 
HP Model 3582A, described in the preceding article, 
derives much of its signal-processing capabilities 
from four single-chip LSI digital filters. This article 
describes how it was possible to implement these 
filters on LSI chips. 

The arithmetic, storage, and speed requirements of 
the digital filtering proposed for the Model 3582A 
presented formidable technical challenges. The re- 
quirement for doing three to six million multiplica- 
tions per second far exceeded the capabilities of 
available microprocessors. Additional complications 
were presented by the need for 18- to 21-bit precision 
in the computations. Thus, a dedicated hardware sig- 
nal processor of some kind appeared to be the only 
viable solution. 

This processor could have been built with off-the- 
shelf components, but the cost in terms of component 
count, board space, power, and reliability would have 
been high. Implementing the processor by large-scale 
integration (LSI), however, promised more than a 
80% hardware savings, coupled with lower power 
and higher reliability from the use of fewer compo- 
nents. The development of a custom NMOS digital 
filter chip was therefore undertaken. 

The underlying problem was how to design the 
filter processor with enough power to do the job 
within the confines of a reasonably sized chip. 

Digital Filtering in Spectrum Analysis 

The term "'digital filter" refers to a computational 
process by which a sequence of numbers, usually 
samples of an analog signal, is transformed into a 
second sequence of numbers (see box. page 17). In a 
spectrum analyzer this process corresponds to either 
low-pass or bandpass filtering. 

Digital filtering in a spectrum analyzer also pro- 
vides a practical means of implementing band- 
selectable analysis or "zoom" to analyze the spectrum 
of a narrow frequency band centered on any fre- 
quency within the range of the analyzer. The transla- 
tion of the frequency band to baseband needed for 

band-selectable analysis is possible by analog 
techniques but is often impractical because of the 
high cost of ensuring good gain and phase match 
between the real and imaginary signal channels. Two 
or more digital filters, on the other hand, can be 
matched in gain and phase exactly, regardless of 
temperature, aging, or production variations. 

Span Control 

Model 3582 A uses a particular type of digital filter 
called a decimation filter, a type that plays a funda- 
mental role in analyzers based on the fast Fourier 
transform (FFT). 

As explained in the box on page 7, the first step 
in FFT processing is the collection of N equally- 
spaced-in-time samples of the analog input during a 
measurement time interval T. The N samples are used 
in computing the discrete Fourier transform of the 
input signal. The result of the transform can be 
likened to the response of a bank of N narrow 
bandpass filters spaced at center frequencies of 1/T 
Hz. The responses of these filters are plotted on the 
analyzer's CRT to generate the amplitude-vs- 
frequency display. 

An important characteristic of the FFT frequency 
analysis is that the frequency span width and resolution 
is directly proportional lolhesamp!ingrate(f s = N/T). 
In accordance with sampled-data theory, the input 
signal must be band limited to less than f s /2 to avoid 
aliasing but because of practical filter limitations, the 
input signal bandwidth is usually limited to some- 
thing between fJ4 and f s /3. 

Spectrum analyzers need to change their frequency 
span over a broad range to accommodate a variety of 
input signals. Model 3582A, for example, has four- 
teen spans ranging from 1 Hz to 25 kHz in a 1-2.5-5 
sequence. Providing fourteen sample rates poses no 
problem, but providing an analog anti-aliasing filler 
with fourteen programmable bandwidths does. In the 
Model 3582A, digital filters following the A-to-D 
converter limit the bandwidth to the frequency span 
desired. The input signal to the A-to-D converter is 
band-limited to 25.6 kHz by a fixed, analog, low-pass 
lilter regardless of the frequency span desired, and 
samples of the input are taken at a fixed rate of 102.4 
kl Iz. Sample words at the output of the digital fillers 
are selectively discarded to effect a resampling at a 


© Copr. 1949-1998 Hewlett-Packard Co. 





Low-Pass Filter 

25.6 kHz 
02.4 kHz 

Programmable f c 

— O »— Output 
Bandwidth=f c 
Sample Rate=4f c 

0 dB 

-80 dB 

3 f c 


4 U 


Sample Rate 

102 kHz 

Sample Rate 
(Input Bandwidth= 
25.6 kHz) 

Fig. 1. Specifications tor the bana-iimiting litters to be used in 
the Model 3 582 A Spectrum Analyzer. The litter is to have 14 
programmable cut-oil frequencies (t c ) ranging Irom 25 kHz 
down to 1 Hz 

lower rate of four times the desired frequency span. 

This process of simultaneous digital low-pass fil- 
tering and sample rate reduction is called decimation 
filtering. Only the band to be analyzed is presented to 
the FFT processor. Since the resample rate tracks the 
span width, the FFT algorithm remains the same re- 
gardless of the selected span. 

Choosing a Filter 

The basic requirements for Uie digital filters in the 
Model 3582 A are shown in Fig. 1. The passband 
corner frequency, since it sets the frequency span of 
the analysis, needs to be variable from 25 kHz (no 
filtering] down to 1 Hz in a 25-10-5-2.5 sequence. To 
provide proper anti-aliasing, the stopband needs to 
start at three times the cut-off frequency and should 
be at least -80 dR relative to the passband to assure 
that aliased signals are suppressed to an undetectable 
level. The passband ripple, however, can be on the 
order of ±0.5 dB since the effects of ripple can be 
compensated for by weighting the spectral frequency 
components after the FFT analysis. This compensa- 
tion is accomplished simply by multiplying the spec- 
trum by the inverse of the ripple function. Phase non- 
linearities introduced by the filter can be removed in 
an identical fashion. 

It soon became obvious that it was impractical to 
meet these requirements with a single filter. The 
higher reduction ratios (input bandwidth/output 
bandwidth) that would be needed for the narrow span 
widths would require coefficient word lengths great- 
er than 30 bits if a recursive infinite-impulse- 
response (IIR) low-pass filter were used. If a non- 
recursive finite-impulse-response (FIR) filter were 
used, the number of coefficients required would be 
greater than 100.000. 

Coefficient words get very long with IIR filters be- 
cause the poles of the transfer function in the z plane 
group closer and closer to the unit circle at z = +1 as 
the bandwidth is reduced. The relative positions of 
these poles must be maintained precisely to preserve 
both stability and the desired transfer function. With 
finite arithmetic, the poles can only assume certain 
quantized positions so, to obtain the desired transfer 
function as the bandwidth is made narrower, the pre- 
cision of the arithmetic needs to be increased. 

With FIR low-pass filters, the transfer function is 
determined by zeros in the z plane. The order of the 
filter, or equivalently the length of its impulse re- 
sponse, grows in size inversely with bandwidth. The 
order (number of multiplication coefficients) re- 
quired for the 1-Hz bandwidth is about 10.000 times 
that required for the 10-kHz bandwidth. 

LSI chip area relates directly to the complexity of 
the processing algorithms for the LSI filters, so a re- 
duction in processing complexity was a major goal for 
this project. The solution was to implement the filter 
as a cascade of several filters with interstage decima- 
tion of the sample rale, a common practice with deci- 
mation filtering. Each filler stage then needs to ac- 
complish only a modest sample rate reduction with a 
consequent reduction in the complexity of the filter 

Input Samples 



| 3 

Fig. 2. Interleaved processing scheme tor the digital litter. 
Two complete litter computations are performed during each 
input sample period, one tor the lirst titter stage, and one tor 
one of the downstream filters according to this example 


© Copr. 1949-1998 Hewlett-Packard Co. 

stage. In addition, the downstream filters in the cas- 
cade compute at reduced sample rates, further 
simplifying computational requirements. 

Interleaved Multiplications 

In the final filter design, a cascade of eight filters in 
series is used with the output selected from any of the 
eight. Each filter stage is allowed to compute either a 
decimation by two or a decimalion by five, giving 
overall decimation ratios of 2 m X 5" where m + n «8. 
This easily satisfies the requirement for the 14 fre- 
quency spans with decimation ratios ranging from 1 
to 25000. 

An interesting aspect of this filter structure is found 
upon examination of the total computational re- 
quirements. Consider the case where all eight filters 
are each performing a decimation by 2. The first filter 
computes at the input sample rate. The second filter, 
however, needs to compute at only one-half the rate 
because of the sample rate reduction. In like manner, 
the third filter computes at one-fourth the rate, the 
fourth at one-eighth the rate, and so on. forming a 

geometric series, l + l /2 + '/4+ 1 /8 + that converges on 

2. This means that the total computational require- 
ment of all eight filter stages can be satisfied by a 
single processor operating at twice the rate required 
by the first filter stage. Actually, hardware is needed 
for only one filter stage. The processor has eight 
channels of memory to store intermediatestates of the 
filters but only one set of arithmetic: hardware. Fig. 2 
illustrates how the processing steps are scheduled so 
the eight filter stages can timeshare the hardware. 

IIR or FIR? 

Much has been written in the literature about the 
virtues of both IIR and FIR filters. The primary differ- 
ences between these two classes of fillers as far as 
decimation is concerned are listed below in Table 1. 

Evidently the advantages of FIR filters have resulted 
in more decimation filters being implemented with 
FIR approaches than IIR. but in our case the necessity 
to implement the filters in LSI required some special 

Table I 


Only need lo compult' at 

output rate 
Linear phase 
More storage 
4-8 multiplications/input 
N= 16 to 38'per stage 

Mori: coefficients 
Less noise'bit 


Must compute every input 

Not linear phase 
Less storage 

B-12 multiplications input 
5th order strui turcper 

Fewer coefficients 
More noiseibit 

In making the choice between FIR and IIR. let us 
consider the elements that require chip area in an LSI 
digital filter. By far the largest consumer of chip area 
would be the multipliers. For example, a 12xl6-bit 
multiplier requires nearly 10 6 square micrometres of 
chip area. A second consumer is memory. Dynamic: 
memory takes less space than static, and serial shift 
registers take much less space than random access 

A third large consumer of chip area is interconnect. 
We have found that about 40% of the area of most LSI 
chips is devoted to simply interconnecting the vari- 
ous active devices. Serial arithmetic structures bring 
an advantage here since only a single interconnect is 
needed to transfer a 24-bit word. This, however, is at 
the expense of the total transfer time. 

We chose to use serial arithmetic: to minimize inter- 
connects, and dynamic shift-register memory. I low- 
ever, the key element by far in our design strategy 
became the multipliers and associated coefficients. 

What is a Digital Filter? 

Digital filtering is a computational process or algorithm by 
which a sampled signal or sequence of numbers, acting as an 
input, is transformed into a second sequence of numbers called 
the output. The computational process may correspond to 
high-pass, low-pass, bandpass, or bandstop filtering, integra- 
tion, differentiation, or something else The second sequence 
can be used lor further processing, as in a last-Founer- 
transform analyzer, or it can be converted lo an analog signal, 
producing a liltered version ol the original analog signal. 

The digital approach offers many advantages over analog 

• Changes resulting from variations in component values — 
normally associated with filter capacitors and resistors as a 
result of temperature or aging— are non-existent 

• Periodic calibration is eliminated 

• The perlormance from unit lo unit is stable and repeatabie 

• Great flexibility is available since filter response can be al- 

tered by changing arithmetic coefficients 

• Arbitrarily high precision can be achieved, limited only by the 
number ol bits involved 

• Very small size, low power, and low cost are possible by 
large-scale integration 

An Example 

Let us consider the following practical situation, the need to 
reiect very strong 60-Hz interference contaminating a 10-Hz 
signal of interest The obvious solution is to build a bandstop or 
notch tiller that rejects Ihe 60-Hz component while passing the 
10-Hz signal with little or no alteration. 

First a familiar analog RC notch filter will be examined A 
commonly used RC notch filter network is the "twin-T" shown in 
Fig 1 (next page) This familiar network derives its bandstop 
characteristics from a pair ol transmission zeros located in the 
s plane on the imaginary axis at 60 Hz II also has two poles on 


© Copr. 1949-1998 Hewlett-Packard Co. 

the negative real axis, but they hardly attecl the bandstop 
characteristics Applying the wavelorm shown in color in Fig 1 
to the notch filter results in the output shown in black As can be 
seen, the twin-T circuit reacts all ot the 60-Hz interference and 
leaves the desired 10-Hz signal 

Changing the center frequency of the notch requires changes 
m the values of all three capacitors, all three resistors, or the Iwo 
shunt elements. FT and C, together The position and depth of 
the notch is very sensitive to parameter changes in the compo- 
nents of the twm-T. so precision components must be used In 
building the filter if good reaction at exaclly 60 Hz is to be 

The Digital Filter 

The digital filter solution to this problem is simple yet just as 
effective as the linear filter and is consideiably more flexible In 
this case the input signal is sampled by an analog-to-dlgital 
converter at a rate of 500 samples per second That is. the input 
signal level is measured at intervals of 2 ms and the result forms 
the input sequence to our digital filter 

Fig. 2 shows the digital counterpart lo the twm-T notch circuit 
This filter is made using two registers, a digital multiplier, and a 
3-input adder As the difference equation in Fig. 2 shows, the 
current output sample word [y(n)] is formed by summing the 
current input sample word [x(n)] with the previous input 
[x(n -1 )] multiplied by the constant - 1 46, and with the second 
previous input [x(n-2)] When this filter is fed sample words at 

20 Log |H(S)| (S=j27rf) 


-20 - 

-40 - 

10 Hz 60 Hz 


^— Input Signal 

-Output Signal 

a rate of 500 samples's, 60-Hz components in the analog input 
signal will be eliminated from the regenerated analog output 

Just as the Laplace transform can be used to analyze linear 
filters. Ihe z transform can be used to analyze digital filters. The 
filter shown in Fig 2 derives its bandstop characteristics from a 
pair of transmission zeros located in the z plane on the unit circle 
at a point corresponamg to 60 Hz No poles are indicated in this 
transfer function but these can be implemented when desired 

Fig. 2 also shows two cycles of the sampled 10-Hz input 
signal (in color) which is contaminated as before by 60-Hz 
interference Passing this input sequence through the digital 
bandstop filter results in the output sequence shown in black It 
is evident that the filter has rejected all of the 60-Hz interference 
leaving the desired 10-Hz signal (It is a simple exercise on a 
calculator or computer to generate this input signal and com- 
pute the output sequence y(n) according to the difference equa- 
tion shown in Fig. 2). 

One advantage that the digital filter has in this application is 
that the position and depth of Ihe bandstop notch will remain 
constant and will not drift with temperature or age 

The notch center frequency can be changed in two ways The 
first way is simply to change the multiplication coefficient. For 
example, changing the - 1 46 coefficient to - 1 .62 changes the 
notch center frequency to 50 Hz 

The second way is to change the sample rate In this particu- 
lar example, the notch center frequency is 12% of the sample 
rate Reducing the sample rate to 417 Hz reduces the notcn 
center to 50 Hz. 

In summary, for certain applications digital fillers offer advan- 
tages in terms of flexibility, stability, and simplicity of control 
when compared to their analog counterparts. 





y(n) Output Sequence 
y(n)=x(n)-1.46 x(n-1)+x(n-2) 

H(z)=^iJ=1-1.46z-'+ Z - J 






■5 0 



Fig. 2. 

10 Hz 60 Hz 


Input -Ml— 2 ms 


Output '*: Cf , 




© Copr. 1949-1998 Hewlett-Packard Co. 

Sparse «D 

1.0 1.5 2.0 

With reference to Table I. we found that FIR filters 
require fewer multiplications but these involve more 
coefficients. IIR filters require less storage but longer 
coefficients. Linear phase was not of prime impor- 
tance because the analyzer would have the ability to 
correct for both gain and phase after the FFT ana lysis. 

To achieve the required multiplication rate with 
NMOS circuits, several multipliers operating in 
parallel would have to be included on the chip. 
Minimizing the number of coefficients that each mul- 
tiplier had to work with would further simplify the 
circuitry. Some further space-saving developments 
with respect to IIR coefficients, to be described next, 
occurred. Thus an IIR filter design was chosen. 


The usual bi nary coefficients can be represented by 
the expression: 

X = V x,2 i . 


a weighted sum of B powers of 2 where the weights, x, 
or bits as we know them, can take on the values 0 or 1. 

Another method of representing coefficients, 
called canonical signed digits (CSD). allows the bits 
to take on the values 0. 1. and 1 (-1). During the 
1950's in the early days of computers, this code was 
discussed in many publications with reference to fast 

It has been shown that for any integer X. there exists 
a unique representation in CSD code in which no two 
consecutive bits are non-zero, 1 Furthermore, the CSD 
representation has the least number of non-zero bits. 
For example, decimal 31 becomes 011111 in binary 
but in CSD it is 100001 — only two non-zero bits as 
compared to five in binary. 

It can be shown that CSD representation generally 
requires 33% fewer non-zero bits than binary. This bil 
minimization feature of CSD was very important to 
the realization of the LSI filter. Consider the operation 
of multiplication. Although there are many multipli- 
cation algorithms , the fundamental technique in- 
volves shifting and adding. CSD requires fewer addi- 
tions than straight binary because an add is needed 
only for the non-zero bit positions in the multiplier 
word. Although using a CSD multiplier and a binary 

Fig. 3. Comparison o' discrete 
.a/ues Between 0 and 2 available 
mm 7-t»t binary code and wth 
canonicai-signed-digit code lim- 
ned to tnree Of 'etver nonzerobits 

multiplicand requires a capability for subtraction, 
this is just as easy to do as addition. (These techniques 
result in mathematical operations closely related to 
the well known Booth's algorithm for multiplication.) 

This bit-minimization feature along with further 
developments to be discussed allowed the implemen- 
tation of separate multiplier circuits for each of the 12 
coefficients in the filter structure. 

Modified CSD s 

Further reductions in multiplier complexity are 
possible by limiting the number of non-zero bits in 
each CSD word to three, a representation we chose to 
call sparse canonical signed digits. This means, of 
course, that certain values cannot be represented. 
However, it turns out that this is not a severe restric- 
tion. Fig. 3 indicates all the CSD numbers with three 
or fewer non-zero bits available between the values of 
0 and +2 compared to 7-bit binary (fractional powers 
of two are present and restricted to no smaller than 
2~ h ). An identical set exists for the range -2to0. Most 
IIR digital filters are designed using second-order 
sections having coefficient values between +2 and 
— 2, a result of the necessity to keep the poles and 
zeros on or within the unit circle in the z plane. Thus, 
very few coefficient values would be missed by using 

Poles al re~ 
Where r = Vb 

«=cos"'(^f ) 

Fig. 4. Second-order canonic digital filler section. The boxes 
labelled z~' are storage registers that delay output sample 
words by one sample period. 


© Copr. 1949-1998 Hewlett-Packard Co. 

p 0 Unit Circle ^ ^ Unit Circle 


Z-Plane Z-Plane 

f 2 

1 I 

i-5 j.5 

.5 Real 1.0 ° 

(a) (b) 

CSD code restricted to three non-zero bits. 

Let us now examine the distribution of poles avail- 
able with sparse CSD in a f ilter design. Fig. 4 indicates 
the configuration of a second-order canonic digital 
filter section (canonic meaning that this structure has 
the least number of memory elements with respect to 
other second-order structures: it also involves the 
least number of multiplications). 

The pole and zero locations can be found by sub- 
stituting all possible sparse CSD values for coeffi- 
cients a and b in the equations of the z-transform 
transfer function in Fig. 4. Fig. 5a shows the location 
of the poles in the first quadrant resulting from this 
substitution. Since this analysis simply involves find- 
ing the root positions of a second-order polynomial. 
Fig. 5a also shows the location of available zeros. 
Zeros useful for shaping the stop band of the filter all 
fall on the unit circle. The missing bands correspond 
to the missing digits in sparse CSD. as indicated in 
Fig. 3. 

In this analysis the number of non-zero digits was 
restricted to three and the maximum shift positions to 
eight, giving the least-significant digit a weight of 
±2~ 7 . The density of pole locations can be increased 
by allowing more shift positions. Fig. 5b shows the 
result of allowing an additional shift position but 
still only three non-zero bits, where the least signifi- 
cant digit has a weight of 2:2"". 

Which Poles and Zeros? 

The problem now was to find appropriate filter 
transfer functions using the available pole and zero 
positions of Fig. 5b. An iterative procedure was used. 
Initially, a prototype analog filter was selected from 
one of the filter design handbooks. Using the bilinear 
z-transform, the transfer function H(s) of this filter 
was converted to H(z). Then, with the aid of an HP 

Fig. 5. (a) Discrete poles realiza- 
ble wth 8-bit canomcal-signed- 
dtgit code limited to three non-zero 
bits m the filter of Fig 5. (b) Poles 
realizable with CSD code limited to 
three non-zero bits when nine shift 
positions are allowed, 

21l)U disc-based computer system, the pole positions 
of the z transform were iteratively adjusted to the 
neighboring sparse CSD positions of Fig. 5b and the 
resulting frequency responses evaluated. The optimi- 
zation strategy was directed towards keeping the 
stopband rejection to greater than 80 dB while 
minimizing the passband ripple. Equal positive and 

l rt Frequency 3 f 5 , e f«i 

'««o 3 f 5 , 2 o Frequency ( WJ 

Fig. 6. Transfer functions of the decimation filter selected with 
the help of a computer iterative procedure. The procedure 
derived the functions using pole-zero positions selected from 
those plotted in Fig 5b 


© Copr. 1949-1998 Hewlett-Packard Co. 

negative excursions of the ripple were desired in both 
the pass- and stopbands. 

This procedure resulted in finding sparse CSD coef- 
ficients that contain an average of 1.7 non-zero bits 
(2.3 for poles. 1 . 1 for zeros). This compares to the 4 to 
7 non-zero bits that normally would be required for 
conventional binary. 

The chosen transfer functions are shown in Fig. 6. 
The decimation-by-5 filter requires a fifth-order ellip- 
tic algorithm having five poles and five zeros and the 
decimation-by-2 filter uses a fourth-order elliptic al- 
gorithm. Although the latter has a less-than-optimum 
transfer function, it was chosen for reasons to be 
explained later. 

Scaling and Word Lengths 

Two other items were considered as an integral part 
of the design of the filter structure. One concerns 
overflows at the internal summing nodes. Not only 
does an overflow cause distortion in the output, but in 
recursive digital filters an overflow can cause the 
filter to go into an oscillatory mode that is sustained 
by repeated overflows. Called overflow oscillation, it 

is well documented in the literature. 

The usual way of dealing with this problem is to 
scale the signal levels between filter sections to keep 
the arithmetic values within bounds. The scale fac- 
tors can be included as part of the feed-forward coeffi- 
cients that define the zeros. We chose the so-called 
safe scaling, a conservative approach wherein the 
theoretical maximum value attainable at each node is 
determined and the scaling factors are adjusted to 
keep these values within bounds. Other strategies are 
available but they require additional overload detec- 
tion and limiter circuits to prevent oscillations. Safe 
scaling also insured that no input signal regardless of 
shape or crest factor could cause overloads in the 
internal structure of the filter. 

Secondly, analysis of the effects of rounding or 
truncation played a fundamental role in the design. 
For example, a 27-bit product results from multiply- 
ing a 16-bit data word by a 12-bit coefficient. Ordinar- 
ily, the product would be trimmed back to 16 bits to 
conserve storage and chip area but internal noise is 
generated in filters at every point where this trim- 
ming occurs. These noises are summed at the output 



12 ,6^ 

Output 1r \i \r 



z ' Memory 

ft ft 










I 1 I* 

Select 1 of 8 

Fig. 7. Block diagram nl the 
selected iiller 7 ins one structure 

isvtmsftamas? tttm&ytti implied 

lilter sections. Eight channels ot 
memory m each z ' block store 
results from tht: various tiller sec- 
lion computations 


© Copr. 1949-1998 Hewlett-Packard Co. 

to form the total self noise of the filter. Analysis and 
simulation showed that to keep this self-noise at an 
insignificant level compared to the signal, an in- 
terstage word length of 21 bits would be required. 

Optimum Structure 

The final structure of the filter is related to both the 
self noise and the scaling. The decimation filter has 
two second-order zeros, two second-order poles, one 
first-order zero, and one first-order pole. We chose to 
implement the filter as three cascaded sections: two 
second-order and one first-order. 

The relative positions of these sections can be per- 
muted within the filter structure, and the poles and 
zeros can be paired in many combinations. The rela- 
tive noise-power figures for the various permutations 
were derived theoretically (and verified once the fil- 
ter was completed). The quietest structure could then 
be determined. Actually, the next-to-quietest struc- 
ture was chosen instead of the quietest because the 
simpler coefficients used with the non-optimum 
decimation-by-2 algorithm, mentioned previously, 
could be formed as a subset of the decimation-by-5 
coefficients. This allowed a single processor to be 
used for both the decimation by 2 and the decimation 
by 5. Savings in chip area was the reason for this 

The resulting arithmetic structure is shown in Fig. 7. 
The two second-order sections are followed by the 
first-order section. The multiplier at the filter input 
multiplies the 12-bit ADC output with the 16-bit 
"local oscillator" sample to perform the frequency 
translation for band-selectable analysis (zoom). 

The data word length is 21 bits. Of these, 17 bits are 
necessary tor a single filter's operation, an average of 
lVi bits are necessary for the combined insertion loss 
of the eight cascaded filters, and IV2 bits compensate 
for the accumulated self noise. One bit is added for 
timing considerations. 

As shown in Fig. 7. each memory block has eight 
shift-register memories to serve as the z~' (sample) 
delays for the internal nodes of the filters. The feed- 
back memory collects and saves filter outputs to be 
used as inputs to the subsequent downstream filler 
operations in the cascade. 

Software Emulation 

A bit-for-bit model of the filter structure was pro- 
grammed in software and exercised extensively on 
the computer to determine the filter's true perfor- 
mance. Roundoff noise was studied and it agreed 
with predicted performance. Overloading was tested 
with worst-case inputs. 

Probably the most important outcome of this por- 
tion of the design was the discovery of small signal 
limit-cycle problems. These are non-zero outputs 

even though the input is zero, a consequence of the 
truncation or rounding of the results of arithmetic 
operations. Since the normal sample-to-sample 
changes in the filter input are large compared to the 
rounding error, the effect is simply the addition of 
noise, as previously discussed. The limit-cycle non- 
zero outputs can be either a constant value (dead- 
band), or oscillatory in nature and they are well- 
documented in the digital-filter literature. 

During early investigations of the filter algorithms, 
analysis indicated that the data word lengths were 
sufficient to keep the limit-cycle amplitudes at ac- 
ceptable levels. However, in experiments with the 
software model, more severe limit cycles appeared. 
Investigation revealed that several filters in the cas- 
cade would limit cycle in a "synchronous" manner 
such that the limit-cycle output of the last filter in the 
cascade was well above the noise level. 

Rather than increase the data word length to reduce 
the limit cycle amplitude, we chose to inject a low- 

Fig. 8. Shift register memory cell used in the LSI implementa- 
tion of the digital filler A Dit is stored in parasitic capacitance 
C1 when clock <&2 occurs, and it is transferred to capacitance 
C2 on clock *' 

+ 7V 


a ill 


Metal — » 




ii i 

— 1 — 

i » \ i 


56 M 


r— r---,v 


+ 7V 





© Copr. 1949-1998 Hewlett-Packard Co. 

level dither signal into the rounding input of the 
summation nodes of the two second-order sections. 
The dither variance is sufficient to break up the limit 
cycles but low enough to be invisible compared to the 
signal. As a further precaution, the dominant spectral 
energy of the dither signal was placed in the filter's 
transition band. 

Hardware Simulation 

The digital filters were then simulated in hardware. 
This required about 450 TTL IC's per filter, this many 
being required because the simulated filters were de- 
signed to be as close as possible to the proposed LSI 
design. Many of the details and problems of the dis- 
tributed control and timing system were debugged 
and improved with the aid of these filters. Along with 
the debugging performed with the software model, 
this proved the integrity of the design before the LSI 
design was complete. 

The simulated filters also enabled lab prototypes of 
the spectrum analyzer to be built and evaluated long 
before the filter LSI filter chips became available. 

LSI Implementation 

The final design was implemented in LSI with the 
Hewlett-Packard NMOS-II process. 2 Typical of the 
kind of circuits used is the one-bit memory cell shown 
in Fig. 8. This design was chosen because it uses less 
chip area and loads the clock less than other designs. 
Twenty-eight of these are cascaded to form each of the 
eight circulating shift-register memories in each 
delay element shown in Fig. 7. These registers oper- 
ate at a 6-MHz clock rate. 

Other circuits on the chip include full adders, 
counters. R-S flip-flops. D-latches. ROMs, and as- 
sorted logic gates. A key element in the design phase 
was the inclusion of about seventy-five 20>m-square 
test pads at critical points. During the debug phase, 
digital sequences at these points resulting from a test 
input were compared to sequences generated by the 
software simulator. Debugging could therefore be 
performed in a manner similar to signal tracing. This 
saved a substantial amount of time during the chip 
turn-on phase. 

The final chip is shown in Fig. 9. Of special interest 
here are the areas devoted to multipliers. All of the 
arithmetic required to perform the decimation-by-2 
and decimation-by-5 algorithms is located in the 
central portion of the chip. They perform the equiva- 
lent of 13 multiplications every 5 /xs. using the sparse 
canonical signed digits. By contrast, the input 
"mixer" (multiplier) at the lower left of the chip is of 
standard design, it performs one 12 x 16 multiplica- 
tion every 5 /xs. 


No IC is designed without the help of many people 
and the full support of an organization. My thanks to 
all. Special thanks go to Lou Scheffer who performed 
most of the chip device design and layout, to Yvette 
Norman and other members of the LID computer- 
aided artwork department for their expert help in 
managing the multitude of rectangles that went into 
the chip design, and to Dick Toftness and |ohn Stan- 
back of the IC engineering department for their pro- 
cess and design guidance, 2 


1. G.W. Reitweisner. "Binary Arithmetic, - ' Advances in 
Computers) Vol, 1, Academic: Press 19(>(). 

2. I.E. Deweese and T.R. Ligon. "An NMOS Process for 
High-Performance LSI Circuits." Hewlett-Packard Journal. 
November 1977. 

Fig. 9. Digital titter chip contains about 16.500 transistors and 
measures 4 73 x5 27 mm 

oak turmture tor his home He 
in Loveland, Colorado 

Lynn A. Schmidt 

A native of Colorado, Lynn 
Schmidt did his undergraduaie 
work at Rensselaer Polytechnic 
Institute and the Rochester (N Y ) 
Institute of Technology, earning a 
BSEE degree at the latter In 1969 
He then worked in sonar signal 
processing, obtaining an MSEE 
degree at Syracuse University 
along the way ( 1 972) Lynn joined 
HP in 1974 and did some circuit 
design in voltmeters and signal 
sources before |ommg the 3582A 
proiecueam His outside interests 
include skiing and making solid 
and his wife and three children live 


© Copr. 1949-1998 Hewlett-Packard Co. 

Desktop Plotter/Printer Does Both Vector 
Graphic Plotting and Fast Text Printing 

This HP-IB desktop hardcopy unit has a bidirectional 
paper drive for long-axis plots and unattended plotting. 
It offers user unit scaling, graph rotation, printer capabilities, 
seven dashed-line fonts, English and European character 
sets, and user-definable characters. 

by Majid Azmoon, Jaime H. Bohorquez, and Rick A. Warp 

computer-generated data use two separate in- 
struments, a vector plotter for graphics and a printer 
for reports or program listings. Now there is a cost- 
effective alternative. A new microprocessor-con- 
trolled desktop hardcopy unit, Model 7245A Plotter/ 
Printer (Fig. 1). has both capabilities. Thus it can not 
only replace two separate instruments, but also 
imbed text in graphics and combine reports and plots 
on a single sheet of paper (Fig. 2). 

Operating as a plotter, the 7245A has most of the 
features of Models 9872 A and 7221 A X-Y Plotters. 1 - 2 - 3 
These include absolute and relative plotting, internal 
drawn-character generation for labeling plots, 
dashed-line fonts, and point digitizing. Five drawn- 

character sets are standard. The plotter/printer also 
has automatic page advance, long-axis plotting capa- 
bility, and user unit scaling. Option 001 adds circle 
and axis generation. 

In addition to these plotter features, the 7245A 
operating in plotter mode can print 7x9 and 14x9 
dot-matrix characters in four orthogonal directions 
for fast plot labeling (Fig. 3). In fact, it can do every- 
thing in plotter mode that it can do in printer mode, as 
described in the next paragraph, except that it cannot 
do tabbing in plotter mode, and the interface lan- 
guage is different. Operating as a plotter, the 7245A 
accepts instructions over the HP Interface Bus* in 
HP's standard graphics language. HP-GL (see box. 

■The HP-IB is Hewlett-Packard's implementation ol IEEE standard 48B-1975 (ANSI standard MCI II 

Fig. 1. Model 7245 A Plotter/ 
Printer combines the features ol a 
last thermal dot matrix printer with 
the capabilities of an X-Y plotter 
that can produce long-axis plots 
Its 61 -metre roll ol paper allows it 
to operate unattended lor long 

© Copr. 1949-1998 Hewlett-Packard Co. 

POMA t •« 

— . \ 

\ / 
\ / 

'C 1 



✓ "**~* 

1 1 

t*a-ralaa .eato-rn 

1 1 — 1 — 1 . 1 1 — 

Fig. 2. The plotter/printer can imbed text in graphics and 
combine reports and plots on a single sheet ol paper Plots 
can be labeled with either drawn characters or dot matrix 

page 26). In this respect, it is software compatible 
with the 9872A. 

Operating as a printer, the plotter/printer accepts 
standard ASCII line-printer codes for such functions 
as form feed, font change, and control of margins and 
tabbing. It prints 7x9 dot-matrix characters at 38 
characters per second. Characters can be underlined 
while they are being printed, and 88 columns can be 
printed across the 216-mm-wide paper. A larger 14x9 
dot matrix is used to print titles at 19 characters per 
second in a 44-coIumn format. Option 001 adds a 

Either of these 


r s 








•jnomim jo 





Fig. 3. For last plot labeling, the plotter '.printer can punt dot 
matrix characters in lour orthogonal directions 

132-column font and the ability to reproduce a 720- 
bit-wide raster-scan picture from the HP-IB (Fig. 4). 
Standard dot-matrix character sets include a 128- 
character ASCII set and special characters for six 
European languages. 

The 7245A has a bidirectional paper drive that can 
produce plots as long as five metres and return to the 
starting point from any point in any direction with a 
repeatability of 0.25 mm. The highest plotting speed 
is 0.25 m/s (10 in/s) on each axis. A moving thin-film 
thermal printhead serves for both matrix printing and 
vector plotting. The thermally-sensitive paper comes 
in rolls 61 m (200 ft) long, adequate for many unat- 
tended applications. Self-test features and a 120- 
character buffer are built-in. 

Model 7245A Plotter/Printer is expected to find ap- 
plications in engineering design, production testing, 
data acquisition, process monitoring, and business 
and medical plotting. 

Design Considerations 

The perceived applications for a product with both 
printing and plotting capability demanded consider- 
able mechanical capability. In a production test envi- 


. Sfti.ES _ 



~^rZ z -~' PROF I TS 

1— A 

r in* iwt .»:• iifi i«r» m. mi 

Fig. 4. Option 001 adds the ability to reproduce a raster scan 
CRT display Irom the HP Interlace Bus. 


© Copr. 1949-1998 Hewlett-Packard Co. 

Plotter/Printer Interface Languages: HP-GL and ASCII 

by Michael P. Trego 

The standard 7245A Plotter' Printer is interlaced via the HP 
Interface Bus. or HP-IB (IEEE standard 488-1975). and de- 
codes incoming eight-bit data m two modes In plotter mode the 
data consists ot ASCII' characters forming a language called 
HP-GL (Hewlett-Packard Graphics Language) In printer mode 
the data are also ASCII characters decoded as a line printer 
would lor last character printing with escape sequences used 
for control functions. If Option 001 is installed a raster function 
may be accessed through the printer mode with additional 
escape sequences The raster function allows control of a 720- 
bil-wide picture 

■ The Plotter/Printer function is controlled by two methods. 

■ Two listen addresses The rear-panel HP-IB address 
switches select the plotter address and the printer address is 
the next higher address 

■ Escape sequences. All data is sent to the address selected 

by the rear-panel address switches To enter printer mode 

send _ 
esc % @ 

To leave printer mode (return to plotter mode), send: 
esc % A 


The Hewleti-Packara Graphics Language, or HP-GL. came 
into being when the 9872A X-Y Plotter' was In the planning 
stage The new plotter was to have the capability to send data 
as well as to receive it This would make possible such mea- 
surement functions as point digitizing The HP- IB was chosen 
as the input/output system. The proiect offered an opportunity to 
create a new graphics language Requirements for the lan- 
guage were: 

■ That the elements of the language be ASCII typing charac- 
ters lor ease of calculator or computer generation and for 
ease of debugging at the interface 

■ That commands be in some mnemonic form for ease of 
remembering and yet be consistent with minimizing the 
number of transmitted characters 

■ That the number of commands be expandable tor use in 
future products 

■ That default conditions be as consistent as possible 
One-letter instruction mnemonics did nol permit enough m- 

' ASCII = American Standaid Code 'o» information Intefcnange 

structions Three-letter and variable-length mnemonics gave a 
good representation of words, along with a large number of 
combinations for instructions, but were difficult to store and 
parse In a 16-bit processor Fixed-length, two-lelter instructions 
seemed to be an optimum compromise in that they gave lair 
representation, were well suited to processing in a 16-bit ar- 
chitecture, and provide over 600 combinations for instructions 
A choice ol upper or lower-case representation was added for 
ease of software generation in some desktop computers 

Commas for delimiters and ASCII numbers for parameters 
are commonly used and therefore seemed natural for HP-GL 
An "end-ot command" symbol was necessary because of the 
variable number of parameters in some of the commands. This 
was specified as a semicolon or line-feed, because line-feeds 
are olten generated automatically in desktop computers and 
the semicolon is a familar typing character. 

7245A Plotter Language 

The plotter language for the 7245A Printer/Plotter was to be 
compatable with 9872A HP-GL and add scaling capability 
These goals were met by expanding the parameter format to 
include tloating-pomt numbers and adding the scale instruc- 
tion A rear-panel switch is used to set either 9872A mode when 
scaling is done externally or scaled mode for internal scaling. 

A list of the HP-GL commands for the two machines is given in 
Table 1 . HP-GL is intended to be an expandable language As 
new products use the language, new instructions can be 
created and parameter definitions specified to fit the need. The 
7245A is a good example. New instructions such as pg (page) 
and sc (scale) were added 

Parameters for the 9872A are required lo be in two ranges, 
t 32767 oi ±127.99, because of the 16-bit internal representa- 
tion The 7245A expands the range of the parameters to 
±1x10"" with its internal floating-point representation. The 
7245A also has some two-letler parameters, for example, fa 
ioo 300.LL , where ll means lower left Yet the 7245A is compati- 
ble with the 9872A. 


1 T H, Daniels and L W Hennetsee. "Easy-to-use Interlace Language Comrois 
HP-IB Plaller Hewielt-Pauka'a Journal. Seplembe' '977 

Table 1. 9H7ZA and 7245A HP-GL Instructions 

9B72A X V Plotter 

r— 7245A Plotter/Printer 




Input Pi and P2 
input window 





Read memory 

Select alternate character se 







Scale & rotation 



Label enhancement 




Absolute character size 


o Arc absolute 



Label origin 




Absolute character slant 



' Automatic pen pickup 




Line lype 




Symbol mode 


o Arc relative 



Output actual position and pen 



Select pen 


• Beep 




Outpul current position and pen 




Relative character size 



• Designate alternate set 




Output digitized point and pen 


Size user units 


o Circle 




Output e"or 




Tick length 



• Character plot 



Output scale lactors 




User detined character 



• Designate standard set 



Outpul identification 



Adaptive velocity 



• Digitize clear 



Output options 



Normal velocity 



• Default values 




Output Pi and P2 



Velocity selection 



• Direction Absolute 




Output status 



Write memory 



• Digitize point 




Plot absolute 



X axis 



• Direction relative 



Position cursoi (pa) 




X-axis nek 


• Detme terminator 




Pen down 



Y axis 


O Direction user units 







Y-axis nek 


• Enable memory 




Plot relative 



• Input mask 




Pen up 

■ NOP instruction 



• Initialize 



Read curse position 4 pen (oa) 

O In 

option only 


© Copr. 1949-1998 Hewlett-Packard Co. 

ronment. tor instance, an unattended plotting capa- 
bility is desirable, so the characteristics of a product 
can be reported and plotted, then automatically re- 
peated for the next product. This requires the ability 
to advance pages automatically. In making Gant 
charts for project management, plots may be many- 
pages long to account for the many time periods in- 
volved, and this requires a machine that can make a 
plot with one very long axis. It also means that the 
machine must be able to return to a given position on 
the plot from perhaps three meters away with the 
same accuracy as if it had come from 20 mm away. 
These requirements for unattended and long-axis 
plotting put significant constraints on the develop- 
ment of the paper drive for the 7245A. 

In developing the 7245A Plotter/Printer and the 
9872A and 7221A X-Y Plotters, many pieces of 
technology development were shared. For instance, 
the step motors and the microstep drive used in the 
7245A are identical to those used in the 9872A and 
the 7221A. 4 The microprocessor systems are the 
same, and the language is the same as the 9872A's, 
with some extensions to account for the increased 
capability of the 7245A. 

In addition, some new technologies were required 
for the dual capabilities of printing and plotting. A 
thermal printhead was developed to achieve both the 
plotting quality demanded and a printing speed 
reasonable for the applications. It was also essential 
that a bidirectional paper drive be developed to pro- 
vide the long-axis and unattended plotting 

While the plotter/printer is a vector device when 
plotting, it is a raster device when being used as a 
printer. That is. it prints horizontal rows of dots on the 
paper to form characters. 12 rows at a time. This 
Capability can be generalized to any dot-matrix in- 
formation. With Option 001 . the 7245A has the ability 
to accept general raster information from the HP-IB. 
The first products to make use of the 7245A in this 
mode are the HP 2647A and 2648A Graphics Termi- 

With the increasing number of instruments that 
have built-in intelligence, the question arises whether 
an instrument can drive a graphics device on the 
HP-IB without any other controller in the system. The 
7245A provides for this with a listen-only mode. The 
instrument need only send the appropriate graphics 
commands in HP-GL to the 7245A. It does not have to 
address the 7245A as a listener on the HP-IB. This can 
significantly decrease the cost of the customer's solu- 
tion, since no controller is needed to do plotting. The 
7245A*s scientific input format and internal scaling 
capability enhance the usefulness of this feature. 

Thin-Film Plotter/Printer Printhead 

The 7245A Plotter/Printer uses a single thin-film 

printhead for dot-matrix printing, vector plotting, 
and drawn characters. Heat generated when thin-film 
resistors are energized is applied to areas of heat sen- 
sitive paper, causing a reaction that changes the color 
of the paper at the point of applied heat. By constant 
application of heat, continuous lines can be produced 
to form drawn characters or plotted lines. If instead 
the resistors are pulsed, independent dots can be 

The 7245A prints a standard half-shifted 7x9 dot 
matrix character set. By printing each vertical row 
twice, a 14x9 matrix font is generated that can be 
used for printing titles. The expanded font is of the 
same height, but twice the width of the standard 
characters, giving the printing a bold appearance. 
Expanded characters can be printed at 19 characters 
per second and standard characters can be printed at 
38 characters per second. Option 001 adds a 132- 
column 5x7 dot matrix character set printed at 64 
characters per second. 

Text can be printed in any of the four orthogonal 
directions with or without underline. An example of a 
lower-case s. underlined to show orientation, is 
shown in Fig. 5. The configuration of the text printing 
resistors is shown in the center of Fig. 5. This array is 
the equivalent of a diagonal line of resistors and is 
used because a true diagonal line was difficult to 
reproduce photolithographically. An array of this 
type allows the resistors to be placed without an ap- 
parent gap between resistors. The diagonal array al- 
lows text printing in two directions, and by appro- 

Fig. 5. Dot matrix printhead resistors are arranged in a 
diamond pattern to allow printing in any ol the lour orthogonal 
directions, with or without underline. 


© Copr. 1949-1998 Hewlett-Packard Co. 

priate addressing of the print elements, text can be 
printed in four directions. 

The design of the thermal printhead was dictated 
by several requirements. The primary requirement 
was for the printhead to be capable of high-quality, 
fast, high-accuracy plotting. To achieve a high- 
quality plotted line, the heat element has to have high 
and constant heat transfer to the surface of the paper. 
High thermal efficiency guarantees that, during con- 
tinuous plotting, the printhead assembly temperature 
does not rise above the thermal paper threshold. 
These requirements for the plotting element are met 
by using relatively thick thermal insulating material 
(glass) to support the thin-film resistors. 

A secondary requirement was for the thermal 
printhead to be capable of fast text printing. To print 
dot-matrix characters quickly the thermal time con- 
stant of the print resistors has to be very short. This 
requirement for the matrix printing elements calls for 
a very thin glaze that allows rapid heating and cool- 
ing of the printing elements. Early in the project the 
decision was made to assure that the 7245A was an 
excellent plotter even at the sacrifice of very fast text 
printing. The glaze thickness was selected to achieve 
a high-quality plotted line with acceptable printed 

As shown in Fig. 6. the thin-film printhead has an 
alumina (aluminum oxide) substrate 10 mm by 16 
mm. The substrate is 1 mm thick and is coated with 70 
micrometres of glass as the insulating layer. The glaze 
is etched to leave raised areas that act as mesas for the 
thin-film resistors. The 10-micrometre-high mesas 
improve the contact between the heating elements 
and the surface of the paper. The resistor film (tan- 
talum aluminum) and the conductor film (alumi- 

Al Conductor (3 j<m) 

TaAl Resistor 

Al20 3 
Wear Layer 
(6 fim) 

Character Dot 
(300 ^m) 
Analog Dot 
(400 ,<m) 

7 fim 

Thermal Isolation 
(70 /xm) 


10 /im 

Al,0 3 
(900 ,jm) 


Resistance = 2511 

Analog 2.3 w 
Character 4.0 W 

Temperature. 400"C 


Analog. 3.25 km 
Character: 10 M 

Fig. 6. Cross-section ol the thin-lilm thermal printhead. 

Fig. 7. Photograph ot the thermal printhead. showing the 
array ol dot matrix printing resistors and the single, larger 
plotting resistor. 

num) are then vacuum-deposited by sputtering. Pat- 
terns are etched using conventional photolitho- 
graphic techniques. A protective layer of aluminum 
oxide is sputtered to provide both chemical and 
mechanical protection of the thin-film printhead. 

Fig. 7 is a photograph of the printhead showing the 
array of dot-matrix print resistors and the separate 
plotting resistor. Each printing resistor is approxi- 
mately 340 micrometres square and the plotting resis- 
tor is 450 micrometres square. Mounted on the print- 
head is a clear plastic sight with crosshairs. This 
cursor can be used to position the printhead with 
pinpoint accuracy. 

The thermal paper used by the 7245A employs the 
two-component dye color reaction method of image 
formation. The two component compounds are pul- 
verized to a diameter of several micrometres, mixed 
with a binder, and coated on the paper surface. The 
completeness of the color-change reaction depends 
on the temperature reached by the heat sensitive 
layer. During plotting, the power to the resistor has to 
be modulated as a function of velocity. To insure 
rapid temperature rise, the power is increased during 
initial turn-on or during rapid acceleration. 

Because of the compromise glaze thickness, a more 
complicated method of power modulation had to be 
used for the printing resistors. Each individual power 
pulse is modulated to insure rapid temperature rise 
without excessive surface temperature that might 
prove damaging to the resistor elements. Modulation 
of the power envelope minimizes the effects of the 
gradual heating of the printhead assembly during a 
continuous power pulse train. Print element power 
modulation is shown in Fig. 8. Two different modula- 
tion time constants are used: t u is the individual 
power pulse modulation time constant and t, is 


© Copr. 1949-1998 Hewlett-Packard Co. 


Maximum Operating Temperature 


Time Constant = t 0 

Time Constant = ti 

"7- i 


Fig. 8. Power to the printhead resistors is modulated to insure 
rapid temperature rise without excessive temperatures. The 
individual power pulses and the envelope ol the pulses are 
both modulated 

the power envelope modulation time constant. This 
type of power modulation has been shown to improve 
print quality and printhead reliability. 

Printhead Gimbal 

One of the factors affecting printing quality is con- 
tact between the head and the paper. Maintaining 
good paper-resistor contact over a large area is a prob- 
lem. Not only must all the resistors touch the paper, 
but ideally each resistor should see an identical force. 
The total force from all resistors is called the head 

A rubber roller can be compressed to provide a flat 
area of contact, but the force gradient from center to 
edge is very severe and print consistency is far from 
adaquate. A flat platen, with perfect alignment be- 
tween head and paper, could provide equal force on 
each element, but practically speaking, perfect 
alignment is very difficult, if not impossible, to 

In this machine the head is free to move in two axes, 
thus making it self-align to a rigid flat platen. This 
method has its own set of problems, because the rota- 
tion or gimbal point is above the surface of the paper. 
Friction forces produced by the head on the paper 
introduce moments about the gimbaling point and 
these moments are counteracted by an unequal force 
distribution between head and platen (Fig. 9). 

The ideal situation would be to have the gimbal 

point on the surface of the paper. A four-bar linkage 
can accomplish this, but involves quite a few moving 
parts, creating manufacturing and reliability prob- 
lems. The 7245A does not use a four-bar linkage. 
Instead, the gimbaJ point is arranged as close to the 
surface of the paper as possible and then the moments 
about this point are minimized by offsetting the gim- 
bal point from the center of the printhead. In this way 
it was possible to optimize printing in the left-to-right 
direction. Experimental compromises were then 
made to obtain adequate printing in the other three 

The optimum horizontal position for left-to-right 
printing is computed as follows (see Fig. 9). Assume a 
linear force distribution w(x). that is, 

w(x) = a + bx. 

Equating vertical forces, the head force F H is 

= J w(x)dx = J 

Balancing the moments about the gimbal point, 
-F f d = J (ql-x)w(x)dx -J (x-ql)w(x)dx 

-F f d = I (ql-x)(ax+b)dx 

where F f is the friction force, d is the minimum possi- 
ble distance from the gimbal point to the paper sur- 
face, and 0<q<l. Solving for a and b. the coefficients 

Fig. 9. Printhead gimbal point location is optimized to main- 
tain good paper-resistor contact and equalize the forces seen 
by the individual print resistors. 


© Copr. 1949-1998 Hewlett-Packard Co. 

of the linear force distribution. 

6F„q 4F„ 6F f d 

a = + + 

1 1 P 

tZFfd 12qF H 6F H 

b = + 

13 [? P 

For no force gradient, b = 0. 

12F f d 12qF H 6F H 

+ =0 

P P P 

Solving for q in this equation gives the optimum 
horizontal position for left-to-right printing. 

1 F,d 

Bidirectional Paper Drive 

The bidirectional paper drive represents a vital 
contribution to this product. This technology, com- 
bined with the thermal printhead, provides vector 
graphics, long-axis plotting, and unattended plot- 
ting, as well as high-quality printing. 

For high-quality plotting and printing, a head force 
of 150 grams is needed to maintain good contact be- 
tween the printhead and the paper. This head force 
gives the paper a tendency to buckle. In the 7245A. 
the buckling problem is overcome by using a vacuum 
system that tensions the paper uniformly in both di- 
rections along the paper length. 

One conventional means of moving a sheet of paper 
is the friction drive, as in a typewriter. A similar 
friction paper drive was investigated for the 7245A. 
Essentially, this system consisted of two rubber roll- 
ers driving the paper, a writing platen in the middle, 
and a few spring-loaded idlers to keep the paper on 
the rollers. 

The problems encountered with this system were 
reliability of the drive in a wide environmental range 
and accuracy and repeatability in long-axis plotting. 
Any side-to-side variations in a roller's diameter or 
any variation in idler forces during the paper move- 
ment created a tendency for the paper to move toward 
one side or the other, resulting in gross inaccuracies 
in long-axis plotting or complete failure of the drive. 
To avoid this problem in a friction drive means 
balancing a number of large vector forces, trying to 
resolve them into a small force to cause the paper to 
track precisely. This is extremely difficult if not im- 
possible to obtain in a wide range of environments. 

Repeatability, accuracy, and reliability were 
achieved by using a sprocketed drive system driven 
by a step motor (Fig. 10). This system has two sets of 

sprockets, front and rear. The front set consists of two 
sprockets and a stationary platen in the middle and is 
driven directly for better accuracy. The rear set is a 
sprocketed drum and is driven by a belt from thesame 
step motor. The two sets of sprockets are synchro- 
nized to provide identical surface velocities. 

The continuous sheet of paper wraps around the 
bottom of the drum, then around the platen and back 
to the top of the drum, forming a chamber in which a 
vacuum is drawn by a centrifugal fan (Fig. 11). Re- 
gardless of the direction of paper movement, the vac- 
uum acts evenly on both sides of the platen, tension- 
ing the paper uniformly to overcome the frictional 
drag from the head force and the stationary platen. 
The tension in the paper is linearly related to the 
vacuum pressure, which in this design is 0.2 inch of 

Changes in humidity and temperature markedly 
affect the strength and dimensional stability of paper. 
This paper drive is capable of operating at 40°C and 
95% relative humidity as well as at 40°C and 15% 
relative humidity. 

Fa per movement on the stationary platen results in 
enough friction to make the system over-damped. 
Consequently, this axis of the drive, unlike the other 
axis, does not need a mechanical damper to reduce 
the amplitudes of resonances. The mechanical 
damper used on the other (X) axis is the same as the 
one used in the 9872A X-Y Plotter. 4 

When the sheet of paper is driven back into the 
machine, it is stored in a paper chamber instead of 
being rolled back onto the supply roll. Five metres of 
paper can be stored in this chamber and driven out 
and back many times. This mechanism is not so com- 
patible with z-fold paper as with rolled paper, primar- 

Fig. 10 Sprocketed drive system provides accuracy re- 
peatability, and reliability The drive is bidirectional, papercan 
back up as much as five metres Repeatability is 0.25 mm from 
any point in any direction. 


© Copr. 1949-1998 Hewlett-Packard Co. 


Fig. 11. /4 vacuum in the chamber formed by the paper and 
the drums tensions the paper uniformly to overcome the fric- 
tional drag from the head force and the stationary platen 
Acceleration buffer helps the relatively small motor accelerate 
the large roll of paper. 

ily because the static charge created in the paper by 
paper movements on the stationary platen causes the 
folded sheets to stick to each other in the paper 
chamber. When this happens, extra sheets of paper 
may move through the sprockets. Using a roll of paper 
eliminates this problem. However, the step motor 
does not have enough torque to accelerate a full roll of 
paper. To make use of the available torque without 
reducing tin; paper acceleration, an acceleration buf- 
fer is placed between the roll and the drum (Fig. 11). 
This device is basically a shaft thai swings in an arc 
against a spring force. When the paper is pulled by the 
drum, the shaft is displaced, allowing the roll of paper 
to accelerate at a lower rate than the rest of the system. 
The roll then continues to accelerate until the accel- 
eration buffer returns to its stable position and the roll 
has caught up with the rest of the system. 


It is diff icult to lhank the many people to whom we 
are indebted on a project this large, but here goes. 
Norm iohnson's leadership of the firmware group and 
help in product definition kept us on the right path. 
His group made the hardware sing. They were Mark 
Allen. Tom Halpenny. and Larry Hennessee. Dave 
Shelley was a contributor in every discipline on the 
project. The power supply was done by Dave. Myron 
Son. and Dave Ellement. It was packaged by Dick 
Kemplin and cooled by Dave Perach. Steve White 
implemented our processor, memory, and drive elec- 
tronics, while Hal Beach conceived ihe power mod- 
ulation scheme on the printhead drive. Terry Flower 
and John Morton did much of the paper drive. John is 
now keeping the 7245A alive and well in production 
engineering. Bill Sperry did the development and 
characterization of the thin-film process and thin- 
film sputtering systems. Bill Fbert of I IF Laboratories 

and Beth N'idzieko transferred the process from HPL 
to San Diego. Terry Siden and Tom Young of our 
tooling and process group logged many miles and 
hours obtaining tooled parts for the project. Their 
expertise was vital. Pat Fobes became virtually a part 
of the lab project learn with his contributions as our 
product marketing engineer. S 


1. L.G. Brunetti. "A New Family of Intelligent Multi-Color 
X-Y Plotters." Hewlett-Packard lournal, September 1977. 

2. T.H. Daniels and L.VV. Hennessee. "Easy-to-Use Interlace 
Language Controls HP-IH Plotters." Hewlett-Packard lour- 

Majid Azmoon 

Maj Azmoon was responsible lor 
Ihe paper Onve, head drive and 
writing system mechanics for Ihe 
7245A plotter/printer and Ihe 
mechanical characterizaiion and 
line quality tor the 9872A four-color 
ploiler With HP since 1973, Ma| 
was named inventor on the patent 
for the 7245A bidireclionai paper 
drive and is currently project 
A leader for development of a new 

^2 j plotter He graduated from 

m California Polytechnic University in 
H -A 1969 with a BSME degree and 

^5? *m went on to get his MSME degree in 

1971 from the University ol Southern California Since gradua- 
tion in 1 97 1 , he has done additional graduate study in mechani- 
cal engineering at USC Born m Tehran. Iran, Ma| now lives in 
Poway, California, with his wife and son (age nine months) in the 
house thai he built himself His favorite pastimes are swimming, 
cooking, landscaping, racquetball. woodworking and building 

Jaime H. Bohorquez 

An HP employee since 1973, Jim 
Bohorquez was protect manager 
tor the development ol the thin-lilm 
process, facility and tnermal print- 
head for the 7245A plotter/printer 
Before |ommg HP. Jim designed 
several types of integrated cir- 
cuits, ranging from low-power 
linear circuits to a (amily of sub- 
nanosecond mainframe logic cir- 
cuits Originally from Bogota. Co- 
lombia, Jim received his BSEE 
degree from University of Califor- 
nia at Berkeley He was a United 
States Navy oflicer lor four years, 
has taught courses in eleclronics and integrated circuit design 
and is named inventor on two patents Jim lives in EscondidO, 
California, with his wife and two daughters, ages nine and lour 
In his leisure time, he enjoys family outings, photography, and 
restoring his classic Porsche 356C 


© Copr. 1949-1998 Hewlett-Packard Co. 

nal, September 1977. 

3. D.A. Bones and M.L. Patterson. "Remote Terminal Plotter 
Offers Simple Programming and Efficient Communica- 
tions," Hewlett-Packard lournal. September 1977. 

Rick A. Warp 

Rick Warp is a Stanford University 
graduate who received his BSME 
degree and MSME degree simul- 
taneously m 1971 He was proiect 
manager for the 7245A plotter/ 
printer and also did mechanical 

P. .L^^^Jitf designonthe7155Bportabiestnp 
* ^BDJ J chart recorder. A seven-year HP 
' "■ ' employee. Rick is now product 
marketing engineer at San Diego 
Division and is named inventor on 
two patents related to the 7245A 
Originally from Tacoma, Wash- 
* tngton. Rick now makes his home 

' ■wil^ML in San Diego, California, with 
his wife and their six-month-old daughter. He »s "addicted" to 
tennis and enjoys woodworking, home improvement and 
"watching his daughter grow " 

4. M.L. Patterson, R.D. Haselby.and R.M. tvemplin, "Speed. 
Precision, and Smoothness Characterize Four-Color Plotter 
Pen Drive System," Hewlett-Packard Journal. September 

Michael P. Trego 

Mick Trego was born tn Gillette. 
Wyoming, and received his BSEE 
degree in 1962 and MSEE degree 
m 1 963. both from the University of 
Wyoming He was responsible for 
the design of the HP Interlace Bus 
hardware and software for both 
the 7245A plotter/printer and the 
9872A four-color plotter He also 
designed the read head for the 
7260A and 7261 A optical mark 
card readers. Before joining HP in 
1 971 . Mick did aerospace work for 
another firm, primarily m digital 
design Mick lives m San Diego, 
California, with his wife, daughter. 15. and son, 13, and when 
he snot water skiing, snow skiing ordunebuggymg, he's active 
taking photographs, camping with his family and repairing his 


MAXIMUM '88 urn - 5 m (7.a in - 16 4 fl> -It" M< Ddoei iBtum 

IBB mm • SI ffi |7 « - 200 II w"nool lull NOW lefcun 
ENGLISH PAGE IB" ■ 279 mm (7* - 11 m\ 
METRIC PAGE -88 • 299 5 mm |7 4 - 1 1 7! MM 
ADDRESSABLE DYNAMIC RANGE {1 10* imtitii un4» 
PLOTTING ACCURACY- - 03** ol deflection r0.35 mm |:00'4 m Inclines 

Unenrdy and lepMtttMUy 
REPEATABILITY- 0.25 mm <Q0- tn) hom my given potnl 
MOTOR RESOLUTION: 0 016 mm 1 0 000ft in) 

ACCELERATION 4 40 nvp (14 7 K't'l 

Pen OH 513 mnV»(20?in-t| Mi* 
725 mm * |J9 6 Hlttg ai 49! v«e 
Pan On 256 mm'i (10 1 mat M •■Ol 

363 mns (14 3 mil « 4V angle 


HP Model 7245A Plotter, Printer 

WiTll A* ROW AND FAS' BUTTONS 965 mn\» r3 76 m»l 
CHARACTER PRINTING SPEED: 7 i 9 oo\ malm tnaiftCle- ai 38 chai.'t 14 ■ 

Odot mom» cNwacte H 19 Char s. *im opboi 001 5- 9 dot mafti cnaractet al 

63 CMris. 2 5 mm (0 I mi chatadet lypca*i. rVtw" at 3 Qia>'» 
OFF-SCALE PLOTTING- When of ui» data * ntcexed Dy (I* 7245A. me gnfl 

«n aulomAKiov calculate me mecnamui "mi) mtwcert ot inai •ecim and 

A'OCMd. to mat poinl Ai BsMtaMl a" scale Oala ^ :ec»ved Ihe 72«A will 

TtvvKV the location o* fits data ai*J 'W^w ptoRmo; once nn >na# ;a-a t 
Dv aga-n . il ■■ ; the new mecfianc* lm»l and piling 

itam Rial limit to me on scale data porni Pion>nd. accu'acy a no (eoeo'3T>»ty 

Bpecilicauoni are ?«WvN 
PRiNTHEAD CONTROL: Local conni* Sy dom-tan" s*unea c 'emole comrui 

&. HP a cont(o«et cogiam commands 
OPTIONS' 00' CRT Baiter Outno and HP-GL Eviancementi 

SOURCE 100V 10%. -5-w 

120V 10V -5% . : 

240V in% • t\ 

•20V<Z 5A 
«0V ij* 
300 W mat 
RELATIVE HUMIDITY 5% to 95% (M4e> 40 Cj 
DIMENSIONS 201 mm H . 44i' mm W ■ 4B3 mm D {' B - 17 4 i || *>, 
WEIGHT. 19 1 kg [42 IB I 
CUBE: 0 11 m> (396 n't 
PRICES IN U.S-A.i Model 7245A. 5*60000 

OpUonKM 1260 00 

I63&9 Wej; Dam*do Onve 

San D.»ga CaHomd 92127 USA 

Hewlett-Packard Company. 1501 Page Mill 
Road. Palo Alto. California 94304 


SEPTEMBER 1978 Volume 29 • Number 13 

Technical Information trom the Laboratories of 
Hewlett-Packard Company 

newion-Facparti Cen»,n Mjj'mr. Depititm* 
VdnHetivftn GoeilhartiLian 121 
A«nweiveer>- 1 1 3.1 The Neti'eV-onds 
»o«o>>awa -Hewlett Packard i to SuQIflBRlf 
Tokyo t&8 Japd" 

Editorial Director a Howard L. Roberts 
Managing Editor • Richard P Dolan 
Art Director. Photographer • Arvid A. Danielson 
Illustrator • Susan E Wright 
Administrative Services. Typography • Anne S LoPresti 
European Production Manager • Dick Leeksma 


Bulk Rate 
U.S. Postage 



LAUREL MO 20810 — 

o mange you' aoaiesi Of MM youf nama Hom our rrwiling lisi please *»oa us .c-' ola sid'ess Uitxl ill pools 0"i 
eoa cnanrjes 10 Howiell-Pac»n'a Journal. '50i Page Mi« Road Palo Alio CMMM »*30'i US* Alio* 60 aavs 

© Copr. 1949-1998 Hewlett-Packard Co.