Spectrometer for the Frequency Range 100 to 300 McRichard Conley La Force Citation: Review of Scientific Instruments 32, 1387 (1961); doi: 10.1063/1.1717259 View online: http://dx.doi.org/10.1063/1.1717259 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/32/12?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Modified Robinson Type Spectrometer for the NQR Study of 14N Nuclei in the Range 0.5–6 Mc Rev. Sci. Instrum. 38, 1331 (1967); 10.1063/1.1721096 Measurement of Ultrasonic Wave Velocities for Solids in the Frequency Range 100 to 500 Mc J. Acoust. Soc. Am. 34, 404 (1962); 10.1121/1.1918141 Measurement of Elastic Moduli by Means of Ultrasonic Waves in the Frequency Range 100 to 500 Mc/sec J. Acoust. Soc. Am. 33, 1673 (1961); 10.1121/1.1936702 Electronic Equipment and Transducers for Pulse Measurements in the Frequency Range 500 cps to 10Mc J. Acoust. Soc. Am. 31, 120 (1959); 10.1121/1.1930155 A Resonance Curve Method for the Absolute Measurement of Impedance at Frequencies of the Order 300mc/Second J. Appl. Phys. 10, 27 (1939); 10.1063/1.1707238

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THE REVIEW OF SCIENTIFIC INSTRUMENTS VOLUME 32, NUMBER 12 DECEMBER, 1961

Spectrometer for the Frequency Range 100 to 300 Mc

RICHARD CONLEY LA FORCE

Department of .lnneral Technology, University of California, Berkeley, California

(Received August 28, 1961)

A spectrometer of the marginal oscillator type has been designed and constructed to operate over the range 100 to 300 Mc. The salient features of this spectrometer are that it may be frequency swept over a wide band, it is frequency modulated, and the extraneous amplitude modulation, often known as "potato," is kept to a minimum and made largely independent of frequency. The spectrometer has been used with considerable success to study the nuclear resonance of CO·9 in various ferromagnetic environments.

INTRODUCTION

THE discovery of nuclear resonance! in ferromagnetic C059 and the subsequent observation of detailed

structure in the nuclear resonance spectra of C0 59 in dilute alloys2 has engendered interest in rf spectrometers covering the range 100 to 300 Me.

Spectrometers for the particular problem of observing nuclear resonance in ferro magnets and the more general problem of directly observing zero field splitting must possess two basic characteristics. They must continuously sweep frequency over a wide band, a sweepable bandwidth of 25% of the central frequency is desirable, and they must be frequency modulated. The marginal oscillator appears best adapted to these requirements.

DESIGN CONSIDERATIONS

The mechanical problem of sweeping frequency may most conveniently be solved by using an oscillator circuit of the Hartley type. The design considerations shall, there­fore, treat this type of circuit. The Hartley circuit is shown schematically in Fig. 1. One may, by solving the loop equations, neglecting the distributed grid-cathode and plate-cathode capacitances and assuming that no grid cur­rent flows, derive the following conditions for oscillation3 :

(1)

where L=L1+L2 • Assuming Gm LIR2 and G",L2R 1 negli­gible, one obtains

1 ( RI) w2=- 1+~ , CL Yp

(2)

and to the same approximation,

_ C(R1+R2)L G =-------

m LIL{l+(Rl/rp)J+RlR~' (3)

1 A: C. Gossard and A. M. Portis, J. Appl. Phys. 31, 205S (1960). 2 RIchard C. La Force, S. Frederick Ravitz, and Gene F. Day,

Phys. Rev. Letters 6, 226 (1961) . . 3 F?r a list of the symbols and a general discussion of oscillation

cntena see S. Seely, Electron Tube Circuits (McGraw-Hill Book Company, Inc., New York, 1950), 1st ed., p. 244.

1387

where am is defined as t:.i p / t:.cg • In the limit of high Q circuit elements, Rl is negligible, R2 the sample losses if the sample is placed in the grid circuit, and Eq. (3) becomes

(4)

The explicit relation of am to oscillation amplitude will be discussed directly. The important point is, however, that if the marginal oscillator is frequency modulated by slightly varying the value of C at an audio repetition rate, then an amplitude modulation of the oscillator may also be expected. It is this extraneous amplitude modulation that must be minimized by the design or at least made fre­quency independent if the oscillator is to be a useful broad­band device. By differentiating Eq. (4) with respect to C, expressions may be obtained for the extraneous amplitude modulation and the amplitude modulation due to the sample resonance.

The ratio of signal to extraneous modulation is

1 aR2 --w. 2R2 aw

(5)

(6)

(7)

Equations (5) through (7) do not include the effect of fre­quency dependent nonresonance losses in the sample. These losses may be important under some conditions, particularly in the case of metal samples. Equation (5) indicates that the extraneous variation in Gm is frequency independent, except of course when C becomes small and the distributed capacitances are no longer negiigible. Because the amplitude modulation is detected by observ-

FIG. 1. Schematic" dia­gram of the Hartley oscil­lator circuit.

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1388 RICHARD CONLEY LA FORCE

OF 6SN7

3'DIA.

MODULATI~ DIODES

1----- 10' ------+--- 4'

FIG. 2. Semischematic representation of the marginal oscillator as actually constructed.

ing changes in the average oscillator plate current, am must be related explicitly to the vacuum tube parameters. a m is defined as 6.i p/6.eg. Expanding i p as a power series in ea,

(8)

and writing eg as eo cosw! one obtains, to third order, the following expression for am

(9)

Equation (9) clearly shows the dependence of am on the oscillation amplitude.

The sensitivity of the oscillator is defined as the change in average plate current (ip>av for a given change in am. The plate current average is to be taken over a time much greater than 1/w but much less than a period corresponding to the repetition rate of the frequency modulation. The following expression for a(ip>av/ aam may be obtained from Eqs. (8) and (9).

(10)

The expansion coefficients in Eq. (8) may be expressed in terms of the conventional vacuum tube parameters. ao establishes the dc operating point and al is the trans­conductance Gm • The following expressions relate a2 and ag to the transconductance:

(11)

For maximum sensitivity, Eqs. (10) and (11) imply that an operating point should be chosen for which aGm/ aeg

has a large value and a2G.,J aeg2 a small value. Further­

more, in order to maintain the extraneous amplitude modu­lation frequency independent, it is necessary that the ratio of a2 to ag be independent of changes in am. That am must change as the frequency is swept is clear from Eq. (4). If the tube characteristics (ip vs ep for constant eo) are straight lines and if the average grid bias egO, is held fixed, then as the plate voltage on the tube is changed all ex­pansion coefficients in Eq. (8) are changed by the_same factor. Thus, the ratio of a2 to ag is independent of Gm • In

the practical construction of this oscillator circuit, the grid bias is maintained constant by a feedback loop. Since the characteristics of all triodes tend to be linear for small plate voltage and small grid bias, it is desirable to operate under these conditions. But this is also the region of low Gm and consequently low am, which means that the circuit param­eters appearing in Eq. (4) should be adjusted to minimize the value of am required for oscillation. In other words, Ll should equal L2 and C should be as small as possible for any given frequency range.

CONSTRUCTION AND OPERATION OF THE APPARATUS

Figure 2 shows a semischematic drawing of the oscillator. The inductances in the grid and plate are supplied by shorted coaxial lines less than l wavelength long in the frequency range of interest. The inductance of these lines may then be suitably approximated by the following expression

L=27r-lc-160 In (b/a) , (12)

where 1 is the length, b the outer conductor radius, and a the inner conductor radius. c is the velocity of light. The plate inductance is varied by a sliding short and the grid inductance by changing the diameter of the center con­ductor. The sample, one or two grams of powdered metal contained in a plastic bag, is ordinarily placed nearlthe shorted end of the grid line. The capacitance C is supplied by a butterfly condenser. The stators of the butterfly are connected one to the grid circuit, the other to the plate,

OUTER SHIELD OF r-------/ OSCILLATOR , , I I

470k 20'

LEVEL

I I

·>00"1",0. ADJUSTMENT

+300v.

(a)

.300.

Ik

TO OSCILLATOR

PLATE

.... _______ -,._+ 300 •.

FROM 0.11" 30 CYCLE --I

OSCILLATOR

33k

3300

(b)

TO MODULATION DIODES

lOOk

FIG. 3(a) Schematic diagram of the level control circuit. (b) Sche­matic diagram of the bias circuit for the variable capacitance diodes.

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100-300 Me SPECTROMETER 1389

while the rotor is connected to a motor drive by an insu­lated shaft. This method of construction eliminates the flow of rf current through a sliding contact and thereby materially decreases the noise level. The frequency modula­tion is obtained by voltage modulating two silicon diodes which are themselves connected in series and then placed in parallel with the tuned circuit. These diodes must be biased as far as possible in the back direction to increase their Q. The oscillator triode is a 955 acorn tube placed between the plate and grid coaxial lines as shown in Fig. 2. This allows complete shielding of the oscillator and keeps distributed inductance and capacitance to a minimum. The grid operating point is maintained fixed by a feedback amplifier that samples the grid current and changes the plate voltage to keep this current constant. The tube is generally operated with about a lO-JLa grid current flowing through a 68-k grid resistor. Schematics of the pertinent circuits are given in Fig. 3. The frequency modulation is at a 30-cps repetition rate and the resultant amplitude modu­lation is amplified in a narrow band 30-cps amplifier and synchronously detected for display on a strip chart recorder.

RESULTS

The extraneous amplitude modulation in this circuit is substantially frequency independent except near the high frequency end of the sweep where it may be shown that distributed capacitance in the vacuum tube is expected to cause it to depart from a constant value. Figure 4 shows the nuclear resonance spectrum of one gram of Johnson­Matthey cobalt powder of about 99.999% purity.

.-~~~--'--" ~------

-~-~~~~- ,-~~~~--I--I.-~-~~~.~-'

'" -w

\

-F==;;~L:=r::::-=-=----_~c:\-\l----___ -._-\- 4-----------;--·---·-~~~-;;--~--~-__+l4~-~~~__;;r___-

, " ,\, 228 224 220 216 212 208

:: fAfOllfNC't IN MEGACYCI ES

FIG. 4. The nuclear resonance spectrum from 1 gram of about 99.999% pure cobalt taken at room temperature. Because of the frequency modulation, this curve is a derivative of the absorption spectrum.

Because a ferromagnetic sample cannot be considered as a small perturbatioin on the oscillator, removing it from the oscillator is not always an unambiguous way to check the reality of an apparent resonance. The oscllator has proved to be remarkably free of spurious resonances however.

ACKNOWLEDGMENTS

It is a pleasure to acknowledge the support of this work by the National Science Foundation. I am also indebted to my colleague, S. Frederick Ravitz, for many helpful suggestions.

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