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JUNE 1971 

© Copr. 1949-1998 Hewlett-Packard Co. 

The Routine 
Rotational Microwave Spectrometer 

For the first time, it's now a simple matter to get high-quality 
data using this 30-year-old technique. A new spectrometer makes the centimeter- 
wavelength region of the spectrum available for routine analytical work. 

By Howard W. Harrington, John R. Hearn, and Roger F. Rauskolb 

Spectroscopy — the study of how matter interacts with 
the electromagnetic spectrum — has for over a century 
been providing scientists with solutions to some of the 
knottiest problems of physics and chemistry. The ultra- 
violet and visible segments of the spectrum were the first 
to be used routinely. Scientists didn't thoroughly under- 
stand the exact nature of the interaction between the 
radiation and the sample, but spectrometers were easy 
to build and operate, and they provided a wealth of data 
from which useful empirical rules were deduced. As tech- 
nology advanced, the infrared and X-ray portions of the 
spectrum began to be used for spectroscopy, and again 
routine use preceded a complete understanding of the 
interaction between the radiation and the sample. Abun- 
dant, easy-to-aequire data, combined with the ingenuity 
of the scientist-detective, yielded useful solutions to 
analytical problems. Understanding of the interactions 
developed gradually. 

Quite a different story applies to rotational microwave 
spectroscopy, which uses the centimeter-wavelength 
region of the electromagnetic spectrum. Here there exists 
a nearly complete understanding of how gas molecules 
which have unsymmetrical electric-charge distributions 
will, at low pressures, absorb microwave energy at highly 
distinctive frequencies as they increase their rates of 
rotation. 1 -' ' Measurements of the frequencies and in- 
tensities of the absorptions yield detailed information 
about molecular structure and serve to identify mole- 
cules beyond a shadow of a doubt, even when they're 
parts of complex mixtures. This kind of spectroscopy 
is thirty years old and has reached a certain maturity as 
a research technique. Yet unlike ultraviolet, visible, or 
infrared, the absorption spectroscopy of low-pressure 


polar gases in the centimeter-wavelength region hasn't 
become a routine analytical tool. Why not? The chief 
reason is that recording microwave absorption spectra 
hasn't been a routine matter. Most spectrometers have 
been home-made, narrow-band instruments. Building 
and operating one successfully has typically called for 
considerable engineering skill. Only a small portion of 
the available wavelength range could be examined at 
any one time, and gathering any significant amount of 
data required constant tuning of the microwave source 



© Copr. 1949-1998 Hewlett-Packard Co. 

Cover: Rotational micro- 
wave spectroscopy, operat- 
y — ing in the centimeter-wave- 
length region ot the electro- 
«^t355^^ magnetic spectrum, gives 
* exact information about the 

structures of molecules. But 
spectrometers haven't been 
as easy to use as those for 
other regions of the spectrum. Hence there's 
been a gap, but it's now bridged by the HP 
8460 A MRR Spectrometer described in this issue. 

In this Issue: 

The Routine Rotational Microwave 
Spectrometer, by Howard W. Harring- 
ton, John R. Hearn, and Roger F. 
Rauskolb page 2 

Everything You Always Wanted to 
Know About Rotational Microwave 
Spectroscopy page 4 

An Easy Way to Analyze Graphs, by 

Dean Millett and Ivar Larson page 13 

and detector. All of this served to defer the interest of 
many potential users. 

This story is about to change. A new spectrometer, 
incorporating the latest microwave and solid-state tech- 
nology, makes rotational microwave spectra as easily 
accessible as spectra in other wavelength regions of the 
electromagnetic spectrum. With the HP 8460A MRR* 
Spectrometer (Fig. 1 ), no engineering skill is required 
to observe, measure, and reproduce spectra over a wave- 
length range of 3.75 to 0.75 centimeters. For the first 
time, therefore, the unique sensitivity, resolution, and 
specificity of rotational microwave spectroscopy are 
available for routine use. 

But that isn't the whole story. As often happens when 
an advanced instrument is developed, the new spectrom- 
eter has begun to change our notions of what microwave 
spectroscopy is. An important recent development that 
wouldn't have been possible without this sensitive, broad- 
band instrument is the discovery that rotational micro- 
wave spectra exist for many large molecules that weren't 
previously thought to have such spectra. These 'band 
spectra' can only be seen easily with a spectrometer 
that's capable of sweeping wide frequency ranges rap- 
idly, something early spectrometers couldn't do. Also 

* 'MRR' stands for molecular rotational resonance, a term comes by HP mainly because 
it's descriptively accurate, and it's a lot easier to write and say 'MRR' than 'rotational 
microwave soectroscooy.' MRR also has the interesting property that molecular 
moment of inertia, to which MRR is especially sensitive, has the same units (I — mr-')! 

Fig. 1. New HP 8460 A MRR 
Spectrometer is the lirst rota- 
tional microwave spectrometer 
that's really easy to operate. 
'Table tops.' which hold all the 
microwave circuitry already 
mounted and ready for use, 
make it easy to change fre- 
quency bands. 

new and significant are improved methods for measur- 
ing absorption intensities. Accurate intensity measure- 
ments are essential for quantitative mixture analysis. 
Much of the work on band spectra and intensity mea- 
surements has been done by HP. 

What Makes a Rotational Microwave 
Spectrometer Routine? 

Development of a routine spectrometer wasn't a sim- 
ple matter. The low-pressure gas samples have absorp- 
tions ranging from narrower than 0. 1 MHz to wider than 
100 MHz.* Samples may have only a few absorptions 
or hundreds of absorptions in a particular wavelength 
range. These can be very weak, absorbing only 1 0 5 per 
cent of the incident microwave radiation, or they can be 
as much as 10" times stronger. Absorption lines can be 
as close as a few MHz or separated by tens of thousands 
of MHz. The routine spectrometer has to observe and 
measure these absorptions quickly, accurately, and re- 

Like any spectrometer, a rotational microwave spec- 
trometer has four basic parts (Fig. 2 ) : a source of radia- 
tion (microwave in this case), a sample cell in which 
the radiation interacts with the sample, a detector to 

• In the microwave region one generally refers to freouency rather than wavelength 

[frequency = '' e " Ki,, °' h|ht l. A frequency of 30,000 MMj or 30 GHz has a wave- 
1 wavelength 1 

length of one centimeter. 

© Copr. 1949-1998 Hewlett-Packard Co. 

Everything You Always Wanted To Know About 
Rotational Microwave Spectroscopy 

Rotational microwave spectrometers detect and record the 
absorption spectra of low-pressure gases or vapors at mi- 
crowave frequencies. A spectrum recorded by one of these 
instruments is a graphic plot of the electromagnetic energy 
absorbed by the sample as a function of the frequency of 
the energy. The processes which lead to the absorption of 
radiation by the sample are governed by quantum-mechan- 
ical laws, and as a consequence a given substance will ab- 
sorb energy only at discrete frequencies. A typical spectrum, 
therefore, consists of many very narrow peaks called ab- 
sorption lines. 

In general, microwave energy affects the slow end-over- 
end rotation of the molecules of the sample. When a mole- 
cule absorbs energy its rate of rotation increases. But its 
rotational energy is quantized — only certain energies are 
allowed. Absorptions occur when the frequency » of the 
microwave energy and the energy difference -*E between 
two allowed rotational energies satisfy the quantum rela- 
tionship -iE = hi 1 , where h is Planck's constant. 

For a molecule to absorb radiation, the radiation must 
exert a force on the molecule. With few exceptions, this 
force is a torque exerted by the electric-field component 
of the radiation on a permanent electric dipole moment 
fixed in the molecule. A molecule has such a dipole mo- 
ment if the centroid of all of its negative electric charges 
doesn't coincide with the centroid of all of its positive elec- 
tric charges. The electric field exerts forces in opposite 
directions on opposite electric charges and thereby applies 
a torque to the molecule Not all molecules have permanent 
electric dipole moments, although most do, including many 
common air pollutants, which are mostly small, light gas 
molecules. Sulfur dioxide (SO:), for example, has a micro- 
wave spectrum. Carbon dioxide (CO.-), on the other hand, 

The general features of a rotational spectrum are deter- 
mined by the moments of inertia of the molecule. The 
moment of inertia I about any axis of rotation is a func- 
tion of the masses m of the atoms in the molecule and the 
distances r of the atoms from the axis of rotation, that is. 
I = imr'. Rotational spectra are extremely sensitive to 
changes in a molecule's moments of inertia. Substitute for 
one of the atoms an atom of a different isotope of the same 
material and the spectrum changes radically. Change the 
angle of one bond or the distance of one atom from the 
axis and you get a totally different spectrum. This sensitivity 
makes rotational microwave spectroscopy a valuable tool 
for determining exact molecular structure, that is, the exact 
angles of interatomic bonds and exact interatomic dis- 
tances Take for example a simple linear molecule like 
carbonyl sulfide (OCS). which looks like 

O = C = S 

Knowing the masses of the three atoms from other experi- 
ments, microwave spectroscopists have measured the fre- 
quencies of absorption lines in the rotational spectrum of 
OCS and have determined that the distance between the 
O and C atoms is 1.1552 x 10 ' centimeters and the dis- 
tance between the C and S atoms is 1.5653 x 10 1 centi- 

How is this done? Spectroscopists calculate quantities 
called rotational constants from microwave spectra. For a 
linear molecule the rotational constant is B = h/8-'l. The 
laws of quantum mechanics show the allowed rotational 
energies of such a molecule to be E = hBJ(J + 1), where 
J is an integer (0, 1, 2, . . .) called the principal rotational 
quantum number. Because of quantum-mechanical restric- 
tions, or selection rules, the microwave radiation can induce 
transitions only between energies whose values of J differ 
by one unit. The transition frequencies, the frequencies 
where absorptions occur, are then i'(J— J + 1) = 2B(J + 1). 
This equation describes the rotational spectrum of a rigid 
linear molecule. It's a series of equally spaced lines start- 
ing at a frequency 2B and occurring at higher frequencies 
at intervals of 2B. Thus it's easy to determine B by measur- 
ing the frequency difference between lines. One measure- 
ment, of course, isn't enough to determine two distances. 
But two measurements, made on the very different spec- 
tra of two different isotopic combinations. *0 C'-'S and 
<0"C'-'S, are quite sufficient and lead to the values given 
above for the bond distances. 

Normally the situation is more complex than it is for 
the rigid linear molecule. Three moments of inertia are 
needed to describe the rotation of rigid asymmetric non- 
linear molecules. Sometimes computers are needed to help 
interpret the observed spectra. But the mathematics are 
highly developed and it's a straightforward task, following 
along the lines of our linear example. For many molecules, 
extensive tabulated data are available. 

Also complicating the situation is the fact that no mole- 
cule is truly a rigid rotor. To a spectroscopist, however, 
deviations from the rigid-rotor spectrum are often the most 
important aspects of a spectrum, since they provide addi- 
tional fundamental information about molecular properties. 

An untapped application area with great potential is 
analysis of complex mixtures by rotational microwave spec- 
troscopy. The high-resolution absorption lines are extremely 
narrow. They occur at absolutely constant frequencies and 
lines for different molecules almost never overlap. Thus this 
kind of spectroscopy is highly specific. A molecule's spec- 
trum is a distinctive fingerprint which identifies it beyond 
a shadow of a doubt, even when it's part of a complex 
mixture. With an easy-to-use instrument like the HP 8460A, 
quantitative as well as qualitative mixture analysis is 

For more Inlormatlor about theory and applications than It's been 
possible to give In this necessarily brief and elementary discussion, we 
suggest the following: 

1. G. M. Barrow, Introduction to Molecular Spectroscopy.' McGraw- 
Hill Book Co.. Inc., 1962. This Is suitable for general reading. The 
other four books are more advanced. 

2. T. M. Sugden and C. N. Kenney, 'Microwave Spectroscopy of Gases.' 
D. Van Nostrand Co . 1965. 

3. A. L. Schawlow and C. H. Townes. 'Microwave Spectroscopy.' 
McGraw-Hill Book Co . Inc.. 1955 

4. J, E. Wollrab, 'Rotational Spectra and Molecular Structure.' Aca- 
demic Press. Inc., 1967 

5 W Gordy and R. L. Cook. 'Microwave Molecular Spectra.' Inter- 
science, 1970. 


© Copr. 1949-1998 Hewlett-Packard Co. 

Fig. 2. Like all spectrometers, the HP 8460A has tour 
basic parts: a source of radiation, a sample cell where 
the radiation interacts with the sample, a detector to 
monitor the power absorbed by the sample and a re- 
corder to plot absorbed power versus frequency. 

monitor the power absorbed in the sample cell, and a 
recorder to plot the absorbed power as a function of 
frequency. In a microwave spectrometer the sample cell, 
or absorption cell, must function well as a microwave 
transmission line in addition to holding the low-pressure 
sample (sample-cell pressures arc typically 10 ' to 10 ' 
atmospheres ) . 

Design of such an instrument is primarily a microwave 
measurement problem. This is HP's business, of course, 
or a large part of it. Yet it's safe to say it challenged 
HP's microwave technology to build this instrument. 
Here are the high points of how it was done. 

The Microwave Source 

The source of microwave radiation must have con- 
siderable versatility to cope with the wide variety of 
absorptions expected. Formerly, klystron tubes were 
the most commonly used sources. These tubes generate 
sufficiently monochromatic microwave radiation, but 
have to be tuned manually to cover a wide frequency 
range. Also, it isn't a simple matter to measure their 
frequencies precisely; yet precise knowledge of the fre- 
quency of the source is necessary for accurate measure- 
ments of absorption frequencies. 

The source in the new spectrometer is a backward- 
wave oscillator (BWO). which is electronically tuned. 
For stability, the BWO is continuously phase-locked to 
a harmonic of a stable 400-420 MHz reference oscil- 
lator; this ensures an output sufficiently close to mono- 
chromatic. The stability of the reference oscillator comes 
from a 10 MHz crystal. Reference frequencies of 400 
to 420 MHz are synthesized digitally from the crystal 
frequency, and therefore have the same percentage sta- 
bility and frequency accuracy as the crystal. 

Because its outputs are synthesized, the reference 
oscillator's output frequency can't be tuned continuously. 
Instead, it's programmed in 1-Hz steps. To cover the 
spectrometer's frequency range of 8.0 to 40.0 GHz. 
reference-oscillator harmonic numbers of 20 to 100 arc 

used, and this means that the BWO frequency is varied 
in steps of 20 to 100 Hz. These steps are small com- 
pared to the narrowest absorption lines expected, and 
the stepping rate is fast enough so the effect approaches 
a continuous sweep. 

Four BWO's are needed to cover the entire 8.0 to 
40.0 GHz range. BWO's are changed by exchanging 
plug-in modules in the source power supply mainframe. 
Each BWO corresponds to a standard microwave band 
(X, P, K. and R). 

The user will find the spectrometer source easy to 
operate. All of the control settings are of the fingertip 
type and are located on the front panel of the micro- 
wave source sweep control unit (Fig. 3). The operator 
can select arbitrary frequency limits in 0.001 MHz steps 
merely by dialing them on thumbwheel switches. These 
limits. Fl and F2. can enclose any part or all of a par- 
ticular microwave band. The user can also select one 
of 13 different scan rates between 10 MHz per second 
and 0.001 MHz per second, and he can rest assured 
that the sweep rates will be linear because the source 
is digitally controlled. He can also read the frequency 
continuously with 0.001 MHz resolution from the digi- 
tal display on the control unit. 

Fig. 3. The HP 8460A has a specially designed source, 
sample cell, and detector, which don't require any engi- 
neering skill to operate. This is the source control unit, 
used tor setting sweep limits and sweep rates. The 
display reads the instantaneous microwave trequency. 

There's additional flexibility in the choice of operat- 
ing modes. In the CW mode the output frequency will 
be Fl and will be stable within less than 5 parts in 10" 
per day. In the UP mode the source will sweep from 
Fl to F2 linearly at the specified sweep rate and stop 
at F2. In the U/D mode the source will sweep from Fl 
to F2 and back to Fl and stop. Again, this will be at 
the specified sweep rate. The auto mode will produce 
a back-and-forth sweep between Fl and F2. 

The operator can change the sweep rate at any time 
during a scan without affecting the frequency. In the 
event that some interesting spectral feature is discovered 

© Copr. 1949-1998 Hewlett-Packard Co. 

during a sweep, the sweep can be interrupted by chang- 
ing a front-panel toggle switch to STOP. The region 
above and below the frequency where the sweep was 
interrupted can then be investigated by pressing a fre- 
quency rocker switch. The operator can then return 
the toggle switch to its original position and the sweep 
will continue. For convenience, frequency markers with 
selectable spacing will be printed on the record chart. 

Quite a bit of advanced microwave technology had 
to be applied to make this specially designed source this 
easy to operate. Yet there are no unnecessary frills. All 
these features arc necessary if it's to be a routine matter 
to obtain accurate and reproducible spectral data. 

A feature of the source that isn't absolutely necessary 
but is often convenient is compatibility with computers 
or other remote control units. The source can be re- 
motely controlled by way of a rear-panel connector. 

The Absorption Cell and Stark Modulator 

While the 8460A user will be required to set the 
various sweep conditions himself, he will find that he 
all but ignores the absorption cell. The same cell is used 
for all four microwave bands. No tuning or other adjust- 
ments are required while operating in any of these bands. 

Nevertheless, the cell is a critical spectrometer com- 
ponent and required considerable design effort to assure 
its performance in the dual role of sample chamber and 
microwave transmission path. As a sample holder, it 
must be air tight because the sample pressure is gen- 
erally between 10 and 100 millitorr (7.6 x 10' millitorr 
is atmospheric pressure). There also must be minimum 
interaction between the surface of the absorption cell 
and the sample. To that end, the entire inside of the 
8460A absorption cell is gold plated. The cell must also 
be a high-performance microwave transmission device; 
this is essential for uniform sensitivity over the 8.0 to 
40.0 GHz frequency range. Microwaves can be tempera- 
mental. Unless great care is taken in the design and 
manufacture of the transmission path there will be re- 
flections and significant losses which will degrade the 
performance of the spectrometer. 

Complicating the microwave design problem is the 
spectrometer's use of the Stark modulation technique 
invented by Wilson at Harvard in 1947.' This tech- 
nique greatly improves spectrometer sensitivity. The 
Stark effect, that is. the dependence of molecular ener- 
gies on an electric field, is used to modulate the mo- 
lecular microwave absorption process. An electric field, 
sometimes as high as 4.000 volts per centimeter, is 
applied across the sample and switched on and off (at 

a 33.333 kHz rate in the 8460A). When the field is 
applied, rotational quantum levels are shifted and split. 
What is observed is that a single absorption line with no 
field applied is shifted in frequency in the presence of 
the field, or more often, is split into separate lines called 
Stark components. Whenever the spectrometer is being 
swept through an absorption, whether zero-field or a 
Stark component, the microwave power will be modu- 
lated at the Stark modulation rate because the absorp- 
tion frequency is being shifted by the presence and 
absence of the applied electric field. The spectrometer 
detection system is tuned exactly to this modulation fre- 
quency. In the 8460A a synchronous detection system 
is used. A reference signal from the modulator is applied 
to the synchronous detector, which sees only signals at 
the 33.333 kHz rate and rejects spurious noise. 

New HP Division for Physics 
and Physical Chemistry 

The Hewlett-Packard Scientific Instruments Group is a new 
organization formed by the combination of two major proj- 
ects from Hewlett-Packard Laboratories and the former 
scientific inslruments group of the Microwave Division. Its 
function is to design, manufacture and market measuring 
instruments in the fields of physics and physical chemistry. 
It operates in conjunction with the Avondale Division, which 
produces a range of routine analytical and research instru- 

The 8460A MRR Spectrometer was the new group's first 
product. It has been followed by the 8330A/8334A Radiant 
Flux Meter and Detector, the 5930A Mass Spectrometer and 
the 5950A ESCA X-Ray Photo-Electron Spectrometer. Watch 
these pages for more articles from this new HP division. 

All of this adds another dimension to the Stark cell 
microwave transmission path design problem. First, the 
Stark electrode, or septum, is inside the Stark cell and 
runs the entire length of the cell. The septum must be 
insulated from the cell body. Furthermore, the high 
alternating Stark fields can produce mechanical distor- 
tions in the cell body if the walls are not reinforced, 
and such distortions are a source of synchronous noise. 
These problems have been minimized in the 8460A. and 
the Stark cell is a smooth transmission path over the 
8.0 to 40.0 GHz range. 

In the 8460A there are two Stark cells, each three 
feet in length. Thus the total length is six feet. Since 
spectrometer sensitivity increases with increasing ab- 
sorption-path length, the Stark cells were made as long 
as possible within the limitations of the machining proc- 
esses necessary to guarantee that the cells have good 

© Copr. 1949-1998 Hewlett-Packard Co. 

transmission characteristics. So important are these trans- 
mission characteristics that the 8460A has better broad- 
band sensitivity than some spectrometers with Stark 
cells 15 feet or more in length. 

The Stark cells are constructed with care to keep 
reflections to a minimum. The cells are basically three- 
foot pieces of 8 GHz waveguide, but they have walls 
several times thicker than regular waveguide so mechan- 
ical motions that might cause errors arc minimized. The 
insides are broached to give precise internal dimensions 
and to create grooves to hold the septum. The septum 
is inserted in the grooves with a small piece of teflon 
tape around the edges for high-voltage insulation. Mica 
windows at the ends of each Stark cell act as vacuum 
seals, but allow microwave power to pass through. Two 
windows spaced approximately one-quarter wavelength 
apart are used at each end of each cell; this minimizes 
reflections. Transition pieces adapt the same Stark cells 
for use in different frequency bands. The total volume 
of the two Stark cells is approximately 500 cc. 

The modulator itself plays an important role in in- 
suring uniform sensitivity. Some absorptions are very 
sensitive to the applied field, shifting over wide fre- 
quency ranges for relatively small applied fields. In these 
cases, the off portion of the applied Stark field must be 
very close to zero or these first-order lines will be greatly 
distorted or missing altogether. The sensitivity of the 
system will be significantly degraded no matter how 
good the source or the Stark cell or the detector may- 
be. The 8460A solid-state Stark modulator unit has a 
special circuit which insures adequate zero-basing over 
the complete range of modulating voltages. 

The Microwave Detector 

Like the absorption cell, the 8460A detector requires 
little or no operator attention. The detector requires 
no tuning at all. It's a rugged, selected, high-efficiency 
point-contact silicon crystal diode mounted in a broad- 
band ridged-waveguide configuration. In the past, spec- 
trometer detectors required manual tuning every few 
MHz and, in spite of this tuning, their performance was 
highly frequency dependent. Such tuning and frequency 
dependence are not characteristic of the 8460A detector. 

For maximum sensitivity the microwave crystal 
detector output is synchronously detected to eliminate 
random noise. W hen absorption occurs, there is a 33.333 
kHz component in the rectified crystal output due to 
the Stark modulation. The crystal output is fed into a 
tuned preamplifier, which is followed by a crystal filter 
that narrows the noise bandwidth. After the filter comes 

Fig. 4. This is an absorption line only 80 kHz wide at a 
center frequency ol about 36,489 MHz. That's a resolu- 
tion ot about two parts per million— orders ol magnitude 
higher resolution than infrared spectroscopy. 

Fig. 5. HP 8460A can resolve two absorption lines only 
90 kHz apart at microwave frequencies. 

the synchronous detector, synchronized with the 33.333 
kHz Stark modulation. This detector rejects spurious 
noise that isn't synchronous with the modulation rate. 

The Total Spectrometer 

Model 8460A MRR Spectrometer requires only a 
low level — a few milliwatts — of microwave radiation, 
which doesn't degrade the sample or pose a health haz- 
ard to the operator. Very small samples — a few micro- 
grams — are needed. If a liquid, the sample is injected 
into the spectrometer with a microliter syringe. If a gas. 
it's introduced through a half-inch quick-connect input 
port. The Stark cell is purged with a single small me- 
chanical pump and an ion pump, both of which are 
standard parts of the instrument. 

A unique, removable table-top design makes it easy 
to change waveguide systems when going from one of 
the four frequency bands to another. The table-tops con- 
tain all the microwave circuitry — except the Stark cell, 
which isn't changed* — already mounted and ready for 
use. Three of the waveguide systems — those for fre- 
quencies above 12.4 GHz — come in two versions, one 
a standard 'in-line' system for measuring absorption 
frequencies and unsaturated intensities, and the other a 
• The low-cressure sample can even Jlay in the Stark cell when changinj table-tops. 

© Copr. 1949-1998 Hewlett-Packard Co. 

microwave bridge system with more intensity-measure- 
ment capability. For the 8-to-I2.4-GHz band, only the 
standard in-line type of system is available. The bridge- 
type waveguide system makes it possible for the user to 
vary the power in the Stark cell and keep the crystal 
detector current constant at the same time. This is re- 
quired for absolute intensity measurements and intensity- 
law measurements. 

What the Routine Spectrometer Can Do 

Centimeter-wavelength measurements made easily 
available by the HP 8460A MRR Spectrometer fall into 
three categories. High-resolution spectroscopy includes 
all the more traditional applications. Exact molecular 
structure determination (bond angles and bond dis- 
tances), studies of intramolecular forces (vibration- 
rotation interaction, nuclear quadrupole interactions), 
and dipole-moment determination from the Stark effect 
arc all in the high-resolution category. Qualitative mix- 
ture analysis also belongs in this category. Fast-scan 
spectroscopy is the study of band spectra. This recent 
development is used for characterizing molecules larger 
than those generally considered suitable for study by 
microwave spectroscopy. The third category, intensity 
measurements, includes all applications that call for the 
precise measurement of the microwave absorption rate. 
Uses range from spectral assignment and line-shape 
studies to quantitative analysis of complex mixtures. 

High-Resolution Spectroscopy 

High-resolution rotational microwave spectroscopy 
has produced a wealth of very detailed, accurate infor- 
mation which has helped to clarify many puzzling situa- 
tions.' Its contributions include exact molecular 
structural determination, accurate dipole-moment mea- 
surements, analysis of internal rotation barriers, specifi- 
cation of various molecular conformational preferences, 
and structure analysis of new molecules. Since this tech- 
nique looks at the molecule between collisions, isomeric 
forms which interchange on collision can be caught and 
studied in stop action. The data generated in this field 
has been drawn on by theorists to test their models of 
chemical bonding. It is safe to predict that as more and 
more rotational absorption data become available, the 
impact on chemistry will be enormous. 

How high is high resolution? Fig. 4 shows an absorp- 
tion line that's only 0.08 MHz wide at a center fre- 
quency of about 36.489 MHz. The energy in this par- 
ticular transition can be measured to better than 10 " 
wave numbers. Compare this with infrared spectroscopy. 

Fig. 6. Mixture analysis— qualitative and quantitative — is 
an important application of high-resolution rotational 
microwave spectroscopy. For example, given the indi- 
vidual spectral lingerprints ol these lour compounds it's 
easy to spot them in the mixture. 

© Copr. 1949-1998 Hewlett-Packard Co. 

for example, which typically gives measurements to 
within one wave number or so. How far apart must two 
peaks be before they are distinguishable? Fig. 5 shows 
a trace of two peaks separated by about 0.090 MHz. 
These traces were recorded on a standard 8460A with 
no manual tuning of the source, cell, or detector. 

Qualitative Mixture Analysis 

Here is a largely untapped application area with sig- 
nificant potential. Once a molecule has been finger- 
printed by rotational microwave spectroscopy, it can 
always be recognized no matter what kind of mixture 
it's in. The peak frequencies of the narrow absorption 
lines do not depend on the mixture composition, that 
is. these frequencies have no solvent effects. The full 
impact of this statement is easy to underestimate. Imag- 
ine being able to dial in the fingerprint-frequency of 
a molecule to a few parts in 10' and being certain to 
find an absorption if the molecule is present. If one re- 
quires even more evidence, he can dial in another known 
frequency to double check: molecules generally have 
several absorptions in a given microwave band. With 
the 8460A, it's as easy to dial in a frequency thousands 
of megahertz away as it is to check an absorption line 
which is only a few MHz away. 

Other advantages of this technique arc the low level 
of microwave radiation (milliwatts) which prevents 
degradation of the sample, the very low sample pres- 
sures which minimize chemical interactions between 
mixture components, and the fact that rare and valu- 
able samples can easily be recovered. 

Fig. 6 shows the absorption spectra of four organic 
molecules — formaldehyde, acrolein, propionaldehydc, 
and methanol — and the spectrum of a mixture of these 
substances. These traces cover only a small portion — 
27,000 to 29.000 MHz — of the microwave R-band 
region. Yet it's easy to see what's in the mixture. 

Suppose a mixture contains various istopically sub- 
stituted combinations of the same molecule. For exam- 
ple, there might be DH,C-CH = CH,, H,C-CD = CH ; .. 
H,C-CH = CHD. and so on. Each of these can be indi- 
vidually identified in a mixture. They are distinguish- 
able because their moments of inertia are different, even 
though they have the same chemical formula. C H-,D. 
Isomeric forms of a molecule arc also easily distinguish- 
able for the same reason, even though they're impossible 
to separate chemically. 

Fast-Scan Spectroscopy 

This new technique greatly expands the scope of rota- 
tional microwave spectroscopy. If the 8460A is swept 

in its fastest scan rate, 10 MHz per second, and the 
spectra arc compressed into about three feet of recorder 
chart paper, then a surprising number of organic mole- 
cules show spectra like those shown in Fig. 7. These are 
band spectra for three bromoethylbenzene molecules 
which have the same empirical chemical formula, 
CH.,Br. Band spectra have been observed in the past 
but only for a few molecules. Now it turns out that they 
exist for many types of molecules, including fairly asym- 
metric types. 

Quick inspection of these traces reveals an orderly 
series of strong bands which are broader — 50 to 100 
times broader — than the usual high-resolution absorp- 
tion lines. One quickly notices that these band patterns 
arc simple in appearance, and there is obviously a sig- 
nificant pattern change as the bromine atom is relocated 
in the ethylbenzene molecule. One also quickly notices 
that the bands appear in doublet pairs, each member 
having the same shape and intensity, at least qualita- 
tively. This is especially clear in the 1 -bromoethylben- 
zene and p-bromoethylbenzene spectra. 

Fig. 7. These are band spectra, recorded by scanning a 
broad frequency range quickly. The absorption bands 
here are 100 times wider than high-resolution absorp- 
tion lines like those ot Fig. 6. Such spectra have been 
tound to exist lor many more molecules than were pre- 
viously thought to have them. 

© Copr. 1949-1998 Hewlett-Packard Co. 

The intensity and simplicity of the appearance of band 
spectra is initially surprising to the spectroscopist. A 
general rule of thumb is that the more atoms a molecule 
has, the greater the number of individually weaker lines. 
But instead we find that a large number of large mole- 
cules — we have nearly 100 examples so far — give sig- 
nificantly stronger, simpler-appearing spectra than this 
rule of thumb predicts. These bromoethylbenzene spec- 
tra are good examples. 

Interpretation of band spectra isn't difficult. Each of 
the three shown in Fig. 7 consists of two regular scries 
of bands separated in frequency by Av = B*(J -|- 1 ) 
where Ai is the frequency difference between any two 
consecutive band members. J is the angular momentum 
quantum number, and B* is an average rotational con- 
stant which contains the molecular structural informa- 
tion. In the case of the 1 -bromoethylbenzene, there are 
two B*'s, one for each of the two bromine isotopes. 
51 Br and 7 'Br. These two isotopes are nearly equal in 
natural abundance and account for the doublet band 
structure. This slight molecular mass difference alters 
the moment of inertia enough to cause the large fre- 
quency difference between members of each doublet. 
Relocating the bromine atom in the molecule has an 
even more noticeable effect on the spectrum. The num- 
ber of bands changes significantly. Hence even though 
these bands are broad, the isotope effect and isomeric 
forms are still easily visible. 

How useful arc these spectra? Glance at Fig. 8. the 
band spectrum of crotonic acid, a solid material yet 
with sufficient vapor pressure to observe the rotational 
spectrum at room temperature. Two sets of bands are 
observed and two B*'s can quickly be evaluated from 
the spectrum. Drawing upon the structural data (bond 
angles and distances) of past high-resolution microwave 
research, one can calculate the Cartesian coordinates 
for the atoms of crotonic acid, then calculate the B* 



Fig. 8. The two conformations of crotonic acid shown 
here are impossible to separate chemically, but the band 
spectrum clearly shows two series of bands, one tor each 
conformation. This is why rotational microwave spec- 
troscopy is valuable tor determining molecular structure, 
its principal use to date. 

associated with that particular geometry and compare 
this with the measured B*'s. In this way. we can con- 
clude that the two band scries of crotonic acid arise 
from the s-trans and s-cis isomeric forms. This is a sim- 
ple way to characterize these two inseparable confor- 

The fast-scan mode can also be a real time saver for 
the high-resolution spectroscopist. This is elegantly illus- 
trated in the spectrum of N-methylaniline, Fig. 9. The 
fast-scan spectrum shows a series of bands with con- 
siderable fine structure, but if an 80-MHz part of the 
center of the band at 38,000 MHz is examined under 
high-resolution conditions, there is no recognizable pat- 
tern. Twenty minutes of time invested in scanning the 
spectrum in the fast-scan mode makes sense out of an 
apparently meaningless spectrum. 

Quantitative Analysis 

Microwave absorption intensity-coefficient measure- 
ments contain valuable molecular information. However, 
the intensities of the absorption lines have historically 
been difficult to measure accurately. 7 No other consid- 
eration has affected the design of the HP 8460A as 
much as an intensity-measurement requirement. 

While work is still in progress on the intensities of 
band spectra. HP has investigated in depth the intensity 
of high-resolution absorptions with the objective of 
quantitatively analyzing mixtures like that of Fig. 6. 
This is a three-fold problem. One. relating the observed 
spectrometer signal to an intensity coefficient. Two. in- 
terpreting the intensity coefficient in terms of the partial 
pressure of the molecules absorbing the radiation. Three, 
determining the percentage of each constituent from a 
total sample pressure measurement. 

HP has done considerable investigation on the first 
two stages of this problem. There arc accurate pressure 
gauges available commercially which operate in the mil- 
litorr region and which satisfy the third requirement. 

A simple measurement of the spectrometer output 
corresponding to a peak in the spectrum doesn't neces- 
sarily yield the information that's needed, which is the 
partial pressure of a particular component in the mix- 
ture. The area under a peak under low-power conditions 
is a measure of the partial pressure which is independ- 
ent of the mixture composition, but this area is diffi- 
cult to measure except for strong absorption lines, 
the reason being that with low incident power one ap- 
proaches the noise level where accuracy is a problem. 

Several years ago HP investigated the possibility of 
intensity measurements at a single microwave frequency. 


© Copr. 1949-1998 Hewlett-Packard Co. 

Fig. 9. The band spectrum (top) often makes sense 
when the high-resolution spectrum doesn't. Both can be 
recorded with a sensitive, broadband spectrometer like 
the HP B460A. 

the peak frequency, which would be proportional to the 
partial pressure of the absorbing species and independ- 
ent of the sample composition. The results of this re- 
search have been published elsewhere. s " An intensity 
coefficient was found which had the required quantita- 
tive properties. It's defined as r=APg/LP„' "-, where 
APg is the power absorbed by the sample, L is the length 
of the sample cell, and P,, is the incident power. It was 
discovered that P varied with the incident microwave 
power P 0 as shown in Fig. 10. The maximum in this 
curve is directly proportional to the partial pressure of 
the absorbing molecular species. What's more. r,„ u , is 
constant for a given concentration of the absorbing spe- 
cies, independent of the remaining mixture components. 

The observed spectrometer output signal is directly 
proportional to 1" provided the crystal detector current 
is kept constant while P,„ the incident power to the 
sample cell, is varied. The crystal current can be kept 
constant using an optional microwave bridge arrange- 
ment on the 8460A. This capability is possible between 
12.4 and 40.0 GHz. 

This investigation was carried a step further. It was 
found that a plot of log f versus log P„ (and when using 
the microwave bridge, log S versus log P„. where S is 
the observed spectrometer output signal ) gives a curve 
shape that depends only on the microwave power den- 
sity distribution in the sample. The incident power level, 
the mode of microwave propagation, reflections, and 
the absorption-cell insertion loss all affect this power 
distribution. The 8460A Stark cell has been designed 
to minimize moding and reflections over its operating 
microwave range. However, there can be variations in 
the cell insertion loss with frequency. This insertion loss 

is measured by the operator using standard microwave 
power measurement techniques and an intensity mea- 
surement is easily corrected for it. Thus accurate infor- 
mation from intensities is readily available. 

There are many applications of intensity measure- 
ments. Mixture analysis is only one. Intensities can be 
an aid to spectral assignment. Another use is exempli- 
fied by the spectrum of conformations such as axial and 
equatorial cyclohcxyl fluoride. From a measurement of 
the relative intensities of lines from each of these species 
one can calculate the energy difference between the two 
conformations. '"Another application is line-width studies 
from which intermodular effects can be determined. 

Fig. 10. Intensity coefticient V..., readily measured with 
an HP 8460A MRR Spectrometer bridge option, is a 
measure ol the partial pressure ol a mixture component 
independent ol mixture composition. It's useful for 
quantitative mixture analysis. 


We gratefully acknowledge the invaluable contribu- 
tions of many members of the HP Microwave Division. 
Among them, to mention just a few. are Howard Poulter. 
Paul Ely. Nick Kuhn. Rich Bauhaus. Dec Humpherys, 
and Jim Smith. Special thanks go to John Shanahan and 
his group, for their unselfish efforts in the design of the 
digital source. In the HP Scientific Instrument Division. 
Bruno Bienenfeld, Marvin Higgins, Ned Kuypers. and 
Dave Stead arc prominent among the many who con- 
tributed to the design of the 8460A, and Stu Armstrong 
has been heavily involved in marketing and manufactur- 
ing. To the many practicing rotational microwave spec- 
troscopists who have contributed their interest, advice, 
and comments, we express our appreciation. Finally, 
thanks to Lee Scharpen. responsible for rotational micro- 
wave spectroscopy applications, who reviewed the manu- 
script of this article and wrote the material on page 4.8 

© Copr. 1949-1998 Hewlett-Packard Co. 


(1) . E. B. Wilson, Jr.. 'Microwave Spectroscopy in Chem- 
istry: Science, Vol. 162, page 59, 4 October 1968. 

(2) . D. R. Lidc, 'Chemical Information from Microwave 
Spectroscopy! Surveys of Progress in Chemistry. Vol. 5. 
page 95. 1969. 

(3) . H. D. Rudolph. 'Microwave Spectroscopy! Annual Re- 
view of Physical Chemistry, Volume 21, 1970 (H. Eyring, 
ed.). Annual Reviews Inc. 1970. 

(4) . V. W. Laurie, 'Studies of Internal Molecular Motions 
and Conformation in Microwave Spectroscopy! Accounts 
of Chemical Research. Vol. 3, page 331, 1970. 

(5) . R. H. Hughes and E. B. Wilson. Jr.. 'A Microwave 
Spectrograph! Physical Review. Vol. 71. page 562. 1947. 

(6) . K. B. Mc Afee. Jr.. R. H. Hughes, and E. B. Wilson, 
Jr.. 'Stark-Effect Microwave Spectrograph of High Sensi- 
tivity! Review of Scientific Instruments. Vol. 20. page 821. 

(7) . A. S. Esbitt and E. B. Wilson, Jr., 'Relative Intensity 
Measurements in Microwave Spectroscopy! Review of Sci- 
entific Instruments, Vol. 34, page 901, 1963. 

(8) . H. W. Harrington. On the Separation of the Broaden- 
ing-Relaxation Time and Molecular Concentration from 
Pure-Rotational Spectroscopic Intensity Data! Journal of 
Chemical Physics. Vol. 46. page 3698. 15 May 1967. 

(9) . H. W. Harrington. 'Intensity Law for Microwave Spec- 
troscopy: Theoretical and Experimental! Journal of Chemi- 
cM Physics, Vol. 49. page 3023. 1 October 1968. 

(10) . L. H. Scharpen. 'Axial-Equatorial Energy Difference 
in Cyclohexyl Fluoride from Rotational Transition Intensity 
Measurements! to be published. 

Howard W. Harrington 

Howard Harrington has to be one 
of the world's most enthusiastic 
microwave spectroscopists. 
He came to HP in 1 962 to 
Initiate the rotational microwave 
spectrometer project out o( 
which has come the 8460A. 
He's the author of several 
fundamental papers on micro- 
wave spectroscopy and holder 
of two patents. He's now 
product manager tor the 8460A. 
Howard received his AB degree 
in chemistry from Hope College 
in 1957 and his PhD degree in 
physical chemistry in 1962 from the University of California 
at Berkeley. He's a member of several scientific 
organizations. Art collecting is another of his passions; 
music and skiing are for relaxation. Lately, Howard's been 
spending much of his spare time helping his wife fill 
orders for an ecology handbook she helped organize for 
the American Association of University Women. 
So far. 40,000 copies have been sold in five months. 

HP 8460A 
MRR Spectrometer 

PRICE. 8460A prices depend on the options ordered. A 
standard in-line spectrometer for one band is 
approximately 550,000. Standard conversion kits 
(BWO and table-top) vary from about $7,000 to 
about S1 4,000 depending on the band. Conversion 
kits including the microwave bridge option cost 
about twice as much as the standard kits. The 
bridge option can be added at any time. 


1601 California Avenue 
Palo Alto, California 94304 

John R. Hearn 

John Hearn, engineering 
manager of the HP Scientific 
Instruments Group, is a 1956 
graduate of the University of 
Southhampton with a B.Sc. 
(Honours) degree in physics. 
When he joined HP in 1961 he 
was the first development 
engineer at Hewlett-Packard 
Limited in the United Kingdom. 
Later he was chief engineer 
there. He transferred to the 
HP Microwave Division in 1966 
as a project leader and assumed 
his present position in 1968. 
John is a member of the Institute of Physics and the 
holder of several patents. As for diversions, John says he 
likes 'travel, good cars, and steam railways!' 

Roger F. Rauskolb 

< ^tJHBHJfPHnn R °9 er Rauskolb received his 

1.1 rllT Diplom Ingenieur degree from 
the Technical University of 
Darmstadt in 1961 and his MSEE 
degree from Stanford University 
in 1965. At HP since 1962, he 
put together the first of HP's 
highly successful automatic 
network analyzer systems. He 
was project leader for the 8460A 
and is now group leader for 
the 5950A ESCA Spectrometer. 
He's published three papers in 
Germany. Roger enjoys music, 
photography, and skiing, but 
more important to him are the discussion groups he and 
his wife lead with the objective of helping to make the 
world better through awareness of its problems. 


© Copr. 1949-1998 Hewlett-Packard Co. 

An Easy Way to Analyze Graphs 

By Dean C. Millett and Ivar W. Larson 

Data from strip charts. X-Y plots, oscilloscope 
photos and even contour maps can be converted into 
digital form and fed to the Model 9100 desktop calcu- 
lators for analysis. The Hewlett-Packard Model 9 107 A 
Digitizer, Fig. 1. a new calculator peripheral, has three 
main components: a hand-held cursor, the digitizing 
surface, and the electronics package. The free-moving 
cursor contains a transmitting coil and is used to trace 
the graphic material. Graphs or charts are mounted on 
a platen, or digitizing surface, which contains a precise 
grid of conductive strips. An audio-frequency ac field 
produced by the cursor coil induces voltages in the 
matrix. Circuitry in the electronics package converts 
the signals from analog to digital. These digital signals 
arc the X and Y coordinates of the cursor position on 
the platen. 

Resolution of the Digitizer is 0.01 inch (0.25 mm). 
Tracing speed can be up to 150 inches per second. When 
set in the continuous sample mode, the Digitizer can 
feed up to 100 pairs of points per second to the calcu- 
lator. However, this rate may be limited if a printer or 
plotter is used. Either a keyboard command or program 
control of the calculator initiates transfer of coordinate 
data to the X and Y registers of the calculator. 

Four operating control buttons are on the cursor. An 
(O) button enables the operator to set the origin any- 
where on the digitizing surface, for four-quadrant digi- 
tizing. Single points may be sampled by pressing the 
single sample (S) button. Continuous sample mode (C) 
is used when tracing lines or curves for analysis. The 
fourth button on the cursor (H) sets the hold. 

Any flat non-magnetic material less than 0.025 inch 
(0.63 mm) thick may be used as graphic media for 
digitizing without loss of accuracy. The cursor may be 

lifted 0.04 inch ( I mm ) above the platen before data 
lockout. If this happens, a small 'beep' notifies the user 
that lockout has occurred. 

The 'beep' is also programmable and may be used 
to give the operator an audible indication that a pre- 
determined condition has been met. For example, the 
operator may not remember the starting point when he 
is tracing around an irregular shape to determine the 
area. The digitizing system may be programmed to 
'beep' when the operator reaches the starting point. 

The HOLD button can be used to translate the ori- 
gin. When HOLD is pressed, and the cursor is moved 
to a new point, and HOLD is pressed again, the new 
point assumes the coordinate values of the last point 
digitized. Using this technique, charts larger than the 
17x17 inch area of the digitizing area can be analyzed. 

Applications of the Digitizer 

Strip Chart Recordings 

Strip chart recorders have been used for many years 
to provide permanent records for various phenomena. 
The reduction of this data into useful form has pre- 
sented the recorder user with a tedious and time con- 
suming task, particularly if the recording is not linear 
in either axis. The digitizer may be used to transform 
the recording in almost any manner, limited only by the 
imagination of the user. 

For example, an accelerometer response curve might 
be digitized and replotted to a different scale as the first 
step in the data reduction. The digitizer is then used to 
retrace the curve. Plotting the first and second integrals 
will yield the velocity and displacement diagrams re- 

© Copr. 1949-1998 Hewlett-Packard Co. 

Fig. 1. In using the Model 91 07 A Digitizer , the graphic 
data to be analyzed is placed on the platen. The cursor 
is placed over the chart and the curves traced as shown. 
Coordinate pairs under the cross hairs are automatically 
entered into the X and Y registers ot the Model 9100 

Analysis of X-rays 

For example, the determination of cardiac output and 
ventricular volume has presented the cardiologist with 
several data reduction problems. An accurately mea- 
sured quantity of an opaque (to x-rays) dye is rapidly 
injected into the heart. A high speed (about 50 frames 
per second) x-ray camera records the heart in various 
states of expansion (diastole) and contraction (systole). 
One technique used to determine the ventricular volume 
is the length-area method. The ventricle is approxi- 
mated by an ellipsoid of revolution. 

The x-ray is digitized to determine the area and the 
length of the major axis. The mathematical relation- 
ship between length of the major axis and area gives 
the length of the minor axis. The volume is easily com- 
puted by revolving the resulting eilipsc through 180 
degrees. The program calculates systolic volume, dia- 
stolic volume, stroke volume, ejection fraction, and 
heart muscle mass. 
Photo Analysis 

Photographs including oscilloscope photos may be 
easily analyzed with the digitizer. The photograph is 
placed directly on the digitizing surface. Calibration to 
allow for photographic distortion may be incorporated 
into any program by digitizing the known distance be- 
tween two points to obtain a scale factor. Since 
the digitizer always reads the X, Y coordinates directly 
in inches, the scale factor will be applied to all input 
values. Additional scaling can also be used to plot on 
any graph paper. 

Typical Applications 

Statistical Analysis of Data 

Curve fitting — regression analysis 

Analysis of strip-chart recordings 

Histogram analysis — probability density functions 

Mathematical models of families of curves 

Analysis of Irregular Shapes 

Calculate areas within or under irregular shapes 
Calculate centroid 
Calculate moments of inertia 

Determine distance between points over irregular path and 
lengths of curved and irregular lines 

Analysis of Irregular Waveforms 

Harmonic analysis — determine Fourier coefficients 
Find area under curves 

Transient analysis from oscilloscope photos or plots 

Teaching Mathematical and Statistical Concepts 

Illustrate integration and differentiation by plotting on cal- 
culator plotter as curve is traced 

Contour Maps 

Determine volumes of earth that must be moved for road 
building or site planning 

Scaling with Plot 

Trace curve and plot to different scale 

Change from logarithmic plot to linear or vice-versa 

Coordinate Transformation 


Fourier Analysis 

A periodic signal can be defined mathematically by 
the following equation. Because the waveform repeats 
itself at regular intervals: 

f(,) = j(t+nT) n=l,2,3... 

where T is the time required for one complete cycle. 
Periodic signals can be rewritten as 

1(0= f + £ (fl.CO.^ +^)(l) 


f t„ + T 

2 1 Itlrrt . ... 

dn = Y J HO COS ~Y~ dt (2) 


f'" +r 

b, = J- J /(/) sin dt (3) 


Now, f(t) is sampled at discrete values of t over a com- 
plete cycle. The next task is to evaluate the coefficients 
a„ and b„ by carrying out the integrations of Eqs. 2 
and 3. 


© Copr. 1949-1998 Hewlett-Packard Co. 

Fig. 2. The time function (A) is digitized, and the frequency spectrum (B) is the resulting 
plot of the Fourier analysis. Plotting the reconstructed f(t) from the computed coef- 
ficients gives an approximation of the original time function (C). 

Fig. 3. Contour map used for preliminary studies of most 
economical freeway route AB. Alternatives may be in- 
vestigated without sending surveying crews into the field. 

A Fourier series analysis associated with a time func- 
tion may be performed with the 9100A/B digitizer sys- 
tem to obtain up to 35 sine and cosine coefficients. The 
waveform in Fig. 2(A) is traced with the cursor to ob- 
tain the discrete f(t) values for given t values. The pro- 
gram computes the coefficients and plots the frequency 
spectrum as shown in Fig. 2(B). The representative 
Fourier series may be expressed as Eq. 1. This function 
is reconstructed and plotted. Fig. 2(C), using the derived 
coefficients, and may be compared to the original func- 

Contour Map Analysis 

Highway road building and subdivision layout almost 
always involve moving volumes of earth. Earth volumes 

can be calculated from contour maps and surveying data 
with the digitizer and calculator combination. 

Preliminary cost and time studies may be performed 
using the digitizer, plotter and extended memory. The 
proposed roadway ccnterline is drawn on the conlour 
map as shown by the line AB in Fig. 3. The map scale 
and contour interval, as well as the desired scale for 
horizontal and vertical distance to be plotted, are en- 
tered into the calculator by the operator. The digitizer 
is then used to enter data at each point where the cen- 
terline of the roadway crosses a contour line. This data 
is scaled in the calculator and is used to plot the exist- 
ing profile shown in Fig. 4. The proposed grade is drawn 
on the same plot thus indicating the vertical distance to 
the existing ground level in either cut or fill at any point 
along the roadway. 

Fig. 4. Profile section shows areas of cut and till. Suc- 
cessive sections are used to compute the volume of 
earth to be moved. 

Stations are taken at desired intervals along the cen- 
tcrline and existing elevations are recorded. Successive 
end areas, or cross-sections, are used to determine the 
total amount of cut and fill required. 


The Model 9 107 A is manufactured for Hewlett- 
Packard by Bcndix Computer Graphics, an operating 
section of the Bendix Corp's Advanced Products 

© Copr. 1949-1998 Hewlett-Packard Co. 

We should like to give credit for technical assistance 
in designing the Calculator-Digitizer interface to Mr. 
Robert E. Childs of Bendix and Mr. Edward L. Miller 
of Hewlett-Packard. S 

Ivar W. Larson 

Ivar is a graduate of the 
University of Colorado with a 
B.S in Applied Mathematics 
Engineering. He received his 
MSEE from Bradley University 
in 1967. 

Ivar joined the Hewlett- 
Packard Loveland Colorado 
Division In 1967 and has worked 
on the design and development 
of advanced calculators and 
equipment. He is presently 
■ Applications Engineering 
•^Y ^^t^^H Manager. 

I^BC ■ *a »f I A member of Phi Kappa Phi, 

Ivar's hobbies include woodworking, hunting, fishing 
and painting. 

Dean C. Millett 

Dean has had extensive 
experience in the field of mass 
spectrometry, thin-film 
deposition equipment and 
programmable calculators before 
joining Hewlett-Packard. 
He joined HP in 1968 in 
calculator sales, and transferred 
to the Loveland, Colorado 
Division as applications engineer 
early in 1970. He is now Product 
Manager for calculator 

Dean has a BSME from Heald 
Engineering College. San 
Francisco, 1961. He also attended the University of 
California at Berkeley. 
His hobbies include fishing and raising quarter horses. 


HP Model 9107A 

ACTIVE DIGITIZING AREA: An area of 17 x 17 Inches (431,8 x 431,8 mm) 
RESOLUTION: 0.010 Inch (0,254 mm) 

ACCURACY: ±0.010 Inch (±0.254 mm) per axis from 15'C (59"F) to 

30-C <86"F) 

±0.030 Inch (—0.762 mm) per axis from 30"C (86'F) to 
50'C (122'R and 0"C I32°F) lo 15*C (59'F) 

ORIGIN: Can be placed anywhere on the digitizing surface 

MAXIMUM TRACING SPEED: 150 Inches (3810 mm) per second 

RECORD MOOES: Single (SI — Digitizes one point at a lime 

Continuous (C) — Digitizes up to a mlxlmum of 110 
points per second 

LOCKOUT: Cursor may be lifted 0.040 Inch (1.0 mm) above platen before 
data lockout. Data lockout is Indicated by an audible tone of approx- 
imately 0.75 second. 

HOLD: Pressing Ihe hold button locks In the coordinates of the last 
digitizer position on the platen. These coordinates may become the 
initial coordinates lor a subsequent cursor position on the platen by 
locating the cursor over the new coordinates and pressing the hold 
button again. Coordinates digitized thereafter continue from the 
locked-ln coordinates. 

COMPATIBILITY: Operates with all HP 9100A/B Calculators and 

GRAPHIC MEDIA: Flat non-magnetic material less than 0.025 Inch 
(0.64 mm) thick may be digitized without loss of accuracy. 

POWER: 50-60 Hz. 75 Volt Amps. 115/230 V, ±10% 


Electronics Package: 
514 Inches high (139.7 mm) 
17 Inches wide (431,8 mm) 
18*/2 Inches deep (469,9 mm) 

22 Inches deep (558,8 mm) 
22 inches wide (558,8 mm) 
2 Inches high (50,8 mm) 


Electronics Package: 
24 lbs. (10.9 kg) 

13 lbs. (5.9 kg) 
PRICE: $5900 

OPTIONS: 001 Digitizing System — Includes 9107A Digitizer and 9100A 

Price: $9850 

002 Digitizing System — Includes 9107A Digitizer and 9100B 

Price: $10,800 

Loveland, Colorado 80537 

HEWLETT-PACKARD JOURNAL § JUNE 1971 Volume 22 • Number 10 

Hewlett-Packard S A 121 7 Meynn - Geneva. Switzerland • Yokae* we- Hewlett-Packard Ltd., Shtbuya-Kg. Tokyo 151 Japan 

EdiiQf R H Snyder Edttonai Board R P H L Roeert* L 0 SnefOalt* *»! D-recic Arvtd A □■meteon Aimtam Mendel Jordan 

© Copr. 1949-1998 Hewlett-Packard Co.