136

The solution of the differential equation (lb) is found and discussed in [ 5 ] . The result for the modulated mode is analyzed at ( b x / h ) < 1 * e ( t ) = arctan [Bout(w)/G,ut(w)l

+ 2 arctan kl - -tan ""1 (2) kz

[ Aw 2 where

kl = (hrnax/Aw)

and kt = [(Aw)' - (Awm,,x)*]l'*.

Since (2) is a periodical function of time t , one obtains a discrete frequency spectrum of the oscillator-output signal

v ( t ) = v sin [wit + e@)]. Substituting (2) in dt), we obtain

v ( t ) = V sin (wit + ka)p(t) + V cos (w1t + ko)zc(t)

where

p ( t ) = cos [z arctan (k l - - tan - Aw 2

ko = arctan (B,,,t(w)/G,,,t(w)). Functions p ( t ) and u(t) are developed in a

power series where terms higher than four are omitted. After a tedious mathematical manipulation, we obtain the following.

PROCEEDINGS OF THE IEEE, JANUARY 1972

u' Z W

W I I

I , a, &U-jo 10 W b 4 f M k J

Fig. 1. Experimental results shown for Af 'versus Af.

where

Stable frequency fl =w1/27 represents the reference signal of the frequency spectrum from (3). The following results are obtained.

1) Frequency spectrum is without the line p .

2) When Aw is approaching kl becomes unity. The magnitude of thefl com- ponent increases in respect to the adjacent lines. In the meantime. the interval Af' = k , / 2 ~ decreases and approaches zero when h becomes 4wmax.

3) There is an asymmetry in frequency spectrum. The amplitudes on the right side of fl are higher in respect to those on the left side for h = ( w l - w 0 ) < 0 and vice versa.

The above results were checked with an avalanche diode oscillatol. A perfect agree- ment was found in respect t o the frequency separation of components and relative ampli- tude distribution.

For & approaching hmax, the accuracy of calculation could be improved if terms higher than four are taken into account in (3). In Fig. 1, experimental results are shown for Af' versus L'J In addition to these results, the calculated lines based on (3) and Stover's relation [6] are drawn.

JANEZ DEKLEVA Prometni Institut Ljubljana, Yugoslavia I . ZANCHI Sveutiliste u Zagrebu ETF Split, Yugoslavia

R!ZFERENCES [l] A. J. Vi'erbi, Principles of Coherent Communicaiion.

[2] R. Adler, "A strdy of locking phenomena in oscil- New York: McGraw-Hill, 1966.

[3] L. J. Paciorek "Injetion locking of osdllators," lators," hoc. IRE, vol. 34, pp. 351-357, June 1946.

[4] J. C. Slater, Microwace Electronics. Princeton. Proc. I€€€ , vol. 53, pp. 1723-1727, Nov. 1965.

N. J.: Van Nostrand, 19%. [ 5 ] I. Zanc%, Master's degree thesis, ETF Split, 1971. 16) H. L. Stov.: . "Theoretical explanation for the out-

put spectra cf unlocked driven oscillators." Proc. r€€E (Lett.), vol. 54, pp. 310-311, Feb. 1966.

Transistor Stark Modulator Abstract-A transistor Stark modulator for

microwave spectroscopy i s reported. This is a description of a reliable Stark modulator which i s easily constructed from commercial compo- nents. The output i s a high quality 1000-V square wave at IO kHz. Minor modifications permit operation to 50 kHz or higher voltages.

Vacuum tubes and thyratrons used in high- voltage switching circuits have limited life- times and dissipate excess power. Vacuum

was supported by the National Science Foundation. Manuscript received August 5, 1971. This research

PROCEEDINGS LETTERS 137

2N2646 2N3563 *15"

2N3904 2N3906

Fig, 1. Driver circuit. The 100-K potentiometer adjusts the frequency. Capacitances Icn, than 1 are in microfarads and capacitances greater than 1 are in picofarads. Terminals C and D are the outputs.

Fig. 2. Stark modulator circuit. Capacitors in micro- farads unless o t h d i e specified. Unspecified diodes are IN%. Transformers T1 and R FREED-MPT- 2OC (see text).

tubes have comparatively high "on" resis- tance and the turnoff time of thyratrons limits operation frequency. A Stark modulator em- ploying many transistors connected in series to achieve the desired voltage rating was re- ported by Britt.' This unit requires 14 power transistors in the output section and special transformers must be constructed. A Stark modulator employing SCRs was reported recently by Baron and Harris.' We have had difficulty preventing cross triggering with various other SCR circuits, particularly when SCRs are stacked.

The present circuit employs Delco high- voltage transistors to obtain a relatively simple and reliable Stark modulator. Special precau- tions are taken to insure that the square wave is zerebased. The possible load capacitance is limited only by the desired rise and fall times for the square wave. With 100-pF load capacitance this is approximately 0.3 ps. A drive circuit is included which produces a square wave with highly symmetrical on-off cycles. The current pulses used to turn on the switching transistors are provided by blocking oscillators.

The driver circuit is shown in Fig. 1. The

Rev. Sci. Instr., vol. 38, Oct. 1967, pp. 1496-1501. 1 C. 0. Britt. "Solid state microwave spectrometer,"

modulator for microwavespectroocopy," Reo. Sci. Instr., f P. A. Baron and D. 0. Harris, "A solid state stark

vol. 41, Sept. 1970, pp. 1363-1365.

(C)

Fig. 3. Waveforms for Stark modulator. (a) Output from pulse transformer(25p/cm).(b) Output square wave (IO kHz). (c) Output square wave (0.1 @/an).

unijunction transistor relaxation oscillator provides a series of pulses at 20 kHz to trigger the bistable multivibrator. The frequency is adjusted by the 100-K potentiometer. The 2 N W transistors are used as buffers to im- prove the quality of the square wave from the multivibrator. The outputs of these buffers may also be used to operate a lock-in detector. The outputs switch between + 4 and + 15 V.

The output circuit is shown in Fig. 2. The blocking oscillators are G. E. circuits.a The output pulse shape is determined primarily by the characteristics of the pulse transformers T1 and T2. The waveform obtained using Freed Transformer Co. MFT 20C is shown in Fig. 3(a). The rise time is 1 ps and the pulsewidth is 5 ps. The 100-0 resistors in the collectors of the DTS-802 transistors limit the current to 10 A. The rise and fall time of the

era1 Electric Co., Syracuse, N. Y.: 1967, p. 85. 8 F. W. Gutzwiller, Ed., SCR Mrmunl, 4th ed.. Gen-

output square wave is limited by the driving current on the output transistors and these resistors in combination with the load ca- pacitance. The diode (A1000) and 3-V bias battery insure that the output waveform will be zero based. Output waveforms are shown in Fig. 3(b) and (c). Another possible tran- sistor for the output circuit is Delco DTS 704. With the DTS-802 the unit should operate up to 1400 V in the present form and putting two switching transistors in series should allow much higher voltage operation. M in Fig. 2 is a monitor terminal.

There are no tuned circuits in this system and the frequency can be changed easily. The fact that the average power dissipated in the switching transistors is proportional to fre- quency must be taken into consideration when raising the frequency. Faster pulse transformers must be used at frequencies above 30 kHz.

ACKNOWLEDGMENT The author would like to thank Miss

Penny Graves for drawing the circuits. D. J. Ruben provided help with the circuits.

STEPHEN G. KUKOLICH Dept. of Chem. Mass. Inst. Tech. Cambridge, Mass. 02139.

Microwave Holography by Synthetic Aperture

Abstract-A simple method for constructing a microwave hologrom is described. In this method, a common antenna is employed for both transmitting and receiving, while the rotation of this antenna results in the generation of a synfhetic aperture in the angular direction. The behavior of this type of hologram is explained easily by that of a "concave zone plate."

Recently, many investigations have been reported on various techniques for recording a microwave h~logram.l-~ This letter presents an entirely different approach to the construc- tion method of a hologram, in which a com- mon rotating antenna is employed both to illuminate the object and to receive the scat- tered waves from it. Hence it will be shown that the hologram under consideration is con- structed on a concave plane, and its radius of curvature is determined by the locus of the antenna. The experimental arrangement and the diffraction geometry are shown in Fig. 1, where a two-dimensional setup is considered.

tember 20, 1971.

(Corresp.), vol. 53, pp. 1733-1735, Nov. 1965.

warn." U.S. Patent 3 284 799.

Manuscript recdved July 21. 1971; revised Sep-

1 R. P. Dooley, "X-band holography," Proc. IEEE

: E. L. Rope and G. P. Tricoles, "Microwave holo-

"Microwave holography," Proc. IEEE (Lett.), vol. 57, - * R. W. Larson. E. J. Johansen, and J. S. Zelenka,

pp. 2162-2164, Dec 1969.