PROCEEDINGS LETTERS

critical dependence of the circuit behavior on T is quite interesting to observe.

In Fig. 3 (a), ten traces of the output are displayed with T varying from 1.0 to 1.9 in 0.1 step. It is seen that when the input is of suffi- cient strength, the flip-flop switches at around t = 1.5. But while T = 1.0 does not produce switching, T = 1.1 does, eventually. Fig. 3 (b) shows output waveforms with T varying from 1.00 to 1.09 in 0.01 step. It is seen that the circuit remains in the indefinite region (metastable region) longer and switching eventually OCCUIS if T > 1.03. Fig. 3 (c) shows the output waveforms when T varies from 1.021 to 1.031. The step is 0.0002 if T is between 1.024 and 1.026, otherwise T varies in step of 0.001. For some values of T , it appears that the circuit would remain in the metastable region for a long time and could not settle until much beyond the normal switching time. By carefully selecting the parameter T , the output waveform can be made to remain in the “metastable” region much longer than what has been shown in these figures. It is interesting to note the similarity of these waveforms with trace Q of Fig. 1 in [ I ] .

In conclusion, we have presented here an alternative explanation to the purely probabilistic one advanced by Couranz and Wann concerning the behavior of synchronizers operating in the metastable region. In reality, the detailed operation of the flip-flop should probably take into consideration both the probabilistic and the deterministic behaviors.

REFERESCES [ 1 1 G. R. Couranz and D. F. Wann, “Theoretical and experimental

behavior of synchronizers operating in the metastable region,” ZEEE Trans. Comput., vol. C-24, no. 6, pp. 604-616, June 1975.

On Resistor Loops m Hybrid Circuits S. C. DUTTA ROY .ASD V. G. DAS

Absrmct-A simple method is presented for measuring the individual resistances in a loop of resistors without breaking the loop. Such a problem is often encountered in hybrid integrated circuits. Our method is exact and noniterative, in contrast to an alternative method recently suggested in the literature. Also, it requires n number of measurements for an n-resistor loop and hence is canonic.

In hybrid integrated circuits, a problem often encountered is that of measuring the individual resistors in a closed loop of n resistors. Swart and Van Wyk [ 11 have recently proposed two methods for solving the problem, both of which involve iterative techniques and the use of a digital computer. In this letter, a simple, yet exact, method is given for such measurements, which does not require any iteration or the use of a computer.

Consider a loop of n resistors r l , rz . . r,, as shown in Fig. 1. Let the n nodes be denoted by N , , N , * N,, with the resistance ri be- tween the nodes Ni-, and N i , and let gi = l / ~ . First consider the case when n is odd, n = 1 cannot form a loop, so let n 2 3. The measure- ment procedure is as follows. Short-circuit nodes N , and N , and measure the conductance (G , ) between nodes N , and N , ; obviously, G, = g , + g, . Similarly measure G,, G 3 , . G,. Where Gi = gi + gi+l is the conductance between the node Ni and the common node ob- tained by short-circuiting nodes Ni-, and Ni+,.. In the last measure- ment, viz. that of G,, t h i s common node is obtamed by short-circuiting Nn-l and N , . Let S denote the sum of all Gi’s; then

n n

s s & . = 2 2 g i . i=l i=l

Let So be the sum of Gi for all odd values of i ; then

From (1) and ( 2 ) , we get the value of g , as

g , = so - s / 2 .

Manuscript received August 6, 1976. The authors are with the Department of Electrical Engineering, Indian

Institute of Technology, New Delhi-110029, India.

Nn 1

Nn- I

\ N 2

\ \

I I

Fig. 1. A closed loop of n resistors.

The other gi’s, i = 2 to n, can be obtained simply as

g, = G, - g ,

g3 = G2 - g,

gn = Gn-1 - gn-1. (4) Thus all the n resistances can be obtained from n measurements only.

We next consider the case in which n is even. When n = 2 , it is im- possible to measure the individual resistances without breaking the loop. Let n = 4; if we follow the procedure discussed above, we measure G 1 = g l + g z , G 2 = g z + g 3 , G 3 = g 3 + & and G 4 = g , + g , . The last measurement is however redundant because G4 = G, + G , - G,. This difficulty can be obviated by a simple modification as stated below for a general even n 2 4. Short-circuit one of the resistances, say the nth one, and proceed exactly as in the previous case to determine the n - 1 resistors from the same number of measurements. Finally, remove the short circuit across r,, short circuit the nodes N1 and N,- , , and measure the conductance G, across N , and N,. Obviously G, = g, t g , . Since gl is known, g, can now be determined. In this case, a g m , exactly n measurements are needed.

REFERENCES [ 11 P. L. Swart and J . D. Van Wyk, “Resistor loops in hybrid circuits,”

Microelectron. J . , vol. 7, pp. 53-55, Mar. 1976.

Comments on “The Active Medium Propagation Device’’ B. G. BOSCH

In the above letter,’ P. L. Fleming asserted that “a novel microwave solid-state device is described in which the RF signal propagates trans- verse to the direction of electron flow. No prior art appears to exist for this c o n f ~ t i o n . ”

Manuscript received August 10, 1976. The author is with the Institut fur Elektronik. Ruhr-Universitat.

‘P. L. Fleming, Roc. IEEE (Lett.), vol. 63, pp. 1253-1254, Aug. D-4630 Bochum, F. R. Germany.

1975.

584 PROCEEDINGS OF THE IEEE, APRIL 1977

The purpose of this letter is to point out that, contrary to P. L. Flem- ing’s belief, a resonable amount of preceding work on the subject exists as reviewed in [ l ] though, admittedly, his dual slot-he arrangement constitutes a certain advancement. Major prior proposals and experi- mental contributions concerning this “traveling electromagnetic wave amplifer”-a term coined by Thim [ 21 -are found in [ 31 -[6] . In par- ticular, Chawla et al. [ 31 investigated the amplification experienced by a TEM wave propagating in n-type GaAs transversely to the electron drift velocity, with the semiconductor biased into its negative differen- tial conductivity (NDC) region. Baynham [4] used a microstrip arrange- ment principally similar to that described in Fleming’s letter and demonstrated the feasibility of TEM wave amplification in NDC n-type Ge, whereas Baynham and Colliver (61 obtained selfsustained micro- wave emission when providing an appropriate mismatch at the end planes of their NDC GaAs sample contained in such a microstrip configuration.

Traveling electromagnetic-wave amplifiers suffer from lack of unidi- rectivity-unless additional measures employing ferrites are taken-and thus are liable to breaking into oscillations [ 6 ] . This is in contrast to the GaAs traveling space-charge-wave amplifier, e.g., [ 71 and [ 81 ,where any backward traveling spacecharge wave is heavily attenuated and a possible fast backward electromagnetic wave exercises only a second- order influence [ 1 ] , [ 81 .

Both types of transferredelectron traveling-wave amplifiers have a relatively low-power efficiency in common. If ohmic contacts are used in devices of a subcritical doping-length product (as in Fleming’s letter) or a subcritical doping-width product for preventing dipoledomain formation, the dc electric bias field within the semiconducting layer is highly nonuniform. For some distance the dc field in front of the cathode remains below the threshold for the transferredelectron effect [9] so that no NDC is available there. In addition, the dc field, particu- larly in planar devices, may reach such high values in front of the anode, e.g., [ l o ] , that the available NDC is greatly reduced. In consequence, only a limited part of the GaAs material exhibits pronounced NDC properties.

Experiments performed with spacecharge-wave amplifiers have shown that the dc field can be made fairly homogeneous by using Schottky- barrier coatacts, instead of ohmic contacts, for the cathode [ 11 ] , [ 121 and for the anode [ 10) , [ 131 . It might, therefore, be worthwhile apply- ing these techniques also to the traveling transverseelectromagnetic- wave amplifier.

REFERENCES [ 1 1 B. G. Bosch and R. W. H. Engelmann, Gunn-effect Electronics.

London: Pitman Publishing, 1975, p. 307. [ 2 ] H . W. Thim., “Gunn amplifiers,” in: Solid State Devices. London

and Bristol: The Institute of Physics, Conf. Ser. no. 12, 1971,

[ 3 ] B. R. Chawla, D. J. Bartelink, and,D. J. Coleman, “Transverse p. 8 7 .

electromagnetic-wave amplification m n-GaAs,” presented at the

NY, Mar. 1969; and Bull. Amer. Phys. SOC., vol. 11/14, p. 747, Symp. on Instabilities in Semiconductors, Yorktown Heights,

1969. (41 A. C. Baynham, ‘Wave propagation in negative differential con-

ductivity media: n-Ge,” IBM J. Res. Dev., vol. 13 , pp. 568-572,

151 -, “Emission of TEM waves generated within an n-type Ge Sep. 1969.

[ 6 ] A. ,C: Baynham and,,D. J. Colliver, “New mode of microwave cavitiy,”Electron. Lett., vol. 6 , pp. 306-307, May 14, 19.70.

emlsslon from GaAs, Electron. Lett., vol. 6 , pp. 498-500, Aug. 7, 1970.

[ 7 ] P. N. Robson, G. S. Kino, and B. Fay, “Two-port ,microwave am- plification in long samples of gallium arsenide, IEEE Trans. Electron Devices (Lett.), vol. ED-14, pp. 612-615 , Sep. 1967.

[ 8 ) W. Frey, R. W. H. Engelmann, and B. G. Bosch, “Unilateral trav- elling-wave amplification in ,Gallium arsenide at microwave fre- quencies,” Arch. Elekron. Ubertragung., vol. 2 5 , pp. 1-8, Jan.

[ 9 ] D. E. McCumber and A. G. Chynoweth, “Theory of negftive- 1971.

valley semiconductors,” IEEE Trans. Electron Devices, vol. condu,ctance amplification and of Gunn instabilities in two-

[ 101 W. Frey and R. W. H. Engelmann, “On the pq?ential profile of ED-13, pp. 4-21, Jan. 1966.

overcritically biased thin epitaxial GaAs layers, Arch. Elektron. obertraggung., vol. 27 , pp. 284-285, Jun. 1973.

[ 1 1 1 R. H. Dean and P. M. Schwartz, “Field profile in n-GaAs layer biased above transferredelectron threshold,” SolidStute Elec- tron.,vol. 15, pp. 417-429, 1972. R. H. Dean, “A practi:al technique for controlling field profile in thin layers of n-GaAs, IEEE Trans. Electron Devises, vol. ED-1 9 ,

W. Frey, R. Becker, R. W. H. Engelmann, and K. Keller, “CW operation of GaAs travelling-wave amplifiers for x band frequen- cies,’’ Arch. Elektron. Ubertragung., vol. 2 7 , pp. 245-252, June, 1973.

pp. 1144-1148, NOV. 1972.

Reply’ by P. L. Fleming3

Dr. Bosch is correct in pointing out the prior art on the “traveling transverse electromagnetic-wave amplifier,” especially the early work of Baynham [ 1 ] . However, my work refers to a coplanar geometry on GaAs for which there is no prior art. This view is supported by the US Patent Office which has issued Patent No. 3 975 690 on this device [2] . This document cites the prior workof Baynham [3] -[5] as background to the invention.

I would like to point out that the coplanar h e is capable of both even- and oddmode propagation. This is not the case in previously considered parallel plate or microstrip structures. These modes have to be taken into account in developing a noise theory to cover all the pos- sible experimental situations.

At the present time, I would like to augment the experimental data reported previously with some recent CW results:

- f Noise Figure Chip Gain

16.25 GHz 10.7 dB 3.0 dB

We are working toward improving this result. It should be pointed out that the lowest reported noise figure [6] for a GaAs transferred elec- tron amplifier is 10.5 dB at 13.0 GHz.

REFERESCES 11 A. C. Baynham, ‘Wave propagation in negative differential con-

ductivity media: n-Ge,” IBM J. Res. Dev., vol. 13, pp. 568-752, Sept. 1969.

21 P. L. Fleming, US Pat. No. 3 9 7 5 6 9 0 , “Planar transmission line comprising a material having negative differential conductivity.”

31 A. C. Baynham, US Pat. No. 3 796 964 , “Negative conductivity amplifiers and oscillators.”

41 -? “Emission of TEM waves generated within an n-Type Ge cav~ty,”Electron. Lerr.,vol. 6 , pp. 306-307, May 14, 1970.

51 A. C. Baynham and D. J. Colliver, “New mode of microwave emis- sion from GaAs,” Electron. Lett., vol. 6 , pp. 498-500, Aug 7 ,

(61 P. N. Robson, “Low-noise microwave amplification using trans-

no. 10, Oct. 1974. ferred-electron andBmmdevices,” Radio Electron. Eng., vol. 4 4 ,

1970.

‘Manuscript received October 22, 1976. ’The author is with the Device Physics Department, COMSAT Labo-

ratories, Communication Satellite Corporation, Clarksburg, MD 20734.

Harmonic Oscillation Using A-Shaped Negative Resistance Device

HIROMITSU TAKAGI ASD GOTA KANO

Abststmct-The oscillator performance of A-shaped negative resistance devicea is numerically analyzed. The most distinguished feature re- vealed is that the A -shaped device shows a monotonic increase of out- put power with increasing bias voltage. A maximum oscillation efficiency as high as 94 percent is predicted.

Since the publication of a new type of voltagecontrolled negative resistance device [ 11-[3], a wide field of promising applications has been found. The device is characterized by its I-V curve, where the current is practically zero at and above a valley voltage Vu in contrast to the tunnel diode. As a result, it is expected that the new device will show an excellent oscillator performance with an extremely small para- sitic loss.

In this letter, the harmonic oscillation due to the A-shaped I-V characteristic is described in terms of the amplitude, the output power, and the efficiency, which are obtained though a mathematical analysis of the nonlinear differential equation. For comparison with the tunnel diode, the analysis includes a hypothetical case in which there is an exCe5 current proportional to the voltage above V u .

Manuscript received August 20, 1976. The authors are with The Research Laboratory, Matsushita Elec-

tronics Corporation, Takatsuki, Osaka, Japan.