1152 PROCEEDINGS OF THE IEEE A ugust

a diode which shows the excess current to dominate a t a total current which is 3.5 times its peak current. If the injection cur- rent component is 15 percent of the total current a t the measurement point, it is 10-4 times the total current a t the peak point. Although this may still be sufficient to cause degradation, it would be more likely if this were a substantially larger fraction of the total current a t the peak point. The work of this writer indicates that, for diodes with Ip/Iv220: 1, the excess current and thermal current components become comparable in magnitude a t current levels on the order of the projected peak current level.

R. D. GOLD Electronic Components and Devices

RCA Somerville, N. J.

Fig. 2 (&low). A class of two-ports with com- plementary transistors.

I -

o

Fig. 1 (left). Negative impedance converter.

A Class of Transistorized Two-Po~~s

impedance converters (NIC) is described by A transistorized circuit realizing negative

Yanagisawa [l ] and by Drew and Gorski- Popiel [2]. The circuit (Fig. 1) has the ad- vantage of dc-coupling throughout. The "hook" combination of transistors in Fig. 1 can be used to form a class of six different two-ports. The circuits and their a-matrices (using ideal transistors) are shown in Fig. 2. The a-matrix is defined as f3

According to Fig. 2 :

1) is a current-inversion NIC if det Z=O

2) is a current-inversion NIC if det Z=O

3) is a voltage-inversion NIC if det Z=O

4) is a voltage-inversion NIC if det Z=O

and Za = 2 1 2 .

and 211 =&I.

and 2 2 1 = ZB.

and ZU = 212.

Y J

If circuit 5) is connected between two exter- nal impedances we get the a-matrix of Fig. 3.

The circuit of Fig. 3 is recognized as a negative impedance inverter (NI I ).

By cascading a NIC with a NII we get a gyrator. If the circuit of Fig. 3 is cascaded with circuit 3) of Fig. 2 we get a dc-coupled gyrator with only four transistors. A transis- torized gyrator has previously been pub- lished by Ghausi and McCarthy [3], but it is rather complicated with six transistors and four floating batteries. Also, it is not dc- coupled.

The circuit 5) of Fig. 2 has an interesting property. If we calculate the Y-matrix we get :

+ - 11

"1 -7 I 1

d e t Z - zl 1z12z21

I '

Z -21 z22

zll z12z 22 d e t Z

0

-22 Z

z12

0

-- z21 z1 1

0

1

0

1

- z21

-- z21 z1 1

- z22

-- z22 z12

Manuscript received June 1, 1965. d e t Z = z1 1 22 - z12z21

1965 Correspondence 1153

k E Z k E 3

I

+ E l

i f Z12 = ZZ1

= z,

-zoj 0

z = z21 z o ’ 2 2 2

Z 2 = z12 zo z1 1

det Z = z l l z12222 20

Fig. 3 (abow). Segative impedance inverter.

Fig. 4 ( le f t ) . Circulator.

Fig. 5 ( b e l a ’ ) . Practical NIL

0

I t is, thus, possible to realize a Y-matrix if only the elements l‘11, and so on, are realiz- able and the resulting circuit is stable. If we combine three SIC’S as in Fig. 4, we get a circulator. By using the S I C in circuit 1) of Fig. 2 we get a dc-coupled circulator.

An example of the circuit of Fig. 3 is shown in Fig. 5. The values of the elements of the a-matrix are close to their theoretical values. The zeros are in fact less than 0.01 a t 100 kc/s. The useful frequency band ex- tends from dc to above 1 Mc/s. 4 practical

An Extension of the Lagrangian Formalism to the Electro- mechanical Mode of Propagation in Plasmas

In a recent communication, the author showed that the Lagrangian formalism is useful in studying wave propagation in inhomogeneous plasma waveguides [l I. The Lagrangian is formulated by stationarizing the difference of the “pseudo” magnetic and electric energies [2]. In this note, we extend this technique to find the field distribution in a homogeneous, anisotropic plasma wave- guide when the “electromechanical” mode is propagating [ 3 ] . I n this case, the energy interchange is essentially between the elec- tric energy and the kinetic energy of the particles. This mode is characterized in that it allows propagation beneath the plasma frequency together with a phase velocity less than that of light. The application of the Lagrangian technique to this problem aids in its physical interpretation.

NIC has also been built and tested. The ele- ments of the a-matrix deviate less than 0.01 from their ideal values of 100 kc/s. The com- bination of a S I C and a S I 1 to a gyrator works equally well.

INGEMAR INGEMARSSON Dept. of Elec. Engrg.

Chalmers Inst. of Tech. Gothenburg, Sweden

REFERESCES T. Yanagisawa, ’RC active networks using cur- rent inpersion type negative impedance con- verters, IRE Trans. on Circuit Theory, vol.

A. J. Drew and J. Gorski-Popiel. “D;Uectly coupled CT-4. PP. 140-144, September 1957.

I E E (London). vol. 1 1 1 , P. 1282, July 1964. negative impedance convertor, Proceedings

M. S. Ghausi and F. D. McCarthy. “A realiza-

Sdid Sfate Tech. vol. 7, no. 10, pp. 13-17, October tion of transistor gyrators, Semicond. Prod. and

1964.

2 ” I Fig. 1.

Consider in Fig. 1 that the TMOl mode of propagation is excited in the homogeneously filled plasma waveguide with metal walls at r = R . The magnetic field will assume the form .

He = + ( T ) E + ~ ’ (1)

where 4 7 ) is the unknown but to be de- termined cross-sectional field distribution and the time dependence eiut is understood. I l i th the infinite magnetic field oriented in the direction of propagation, the plasma may be represented as a tensor 2

where 02 = Nqz/meo. From Maxwell’s equation, curl g=iuiE,

one can determine the components of elec- tric field E, and E, to be

Manuscript received June 4, 1965.