628 BELL SYSTEM TECHNICAL JOURNAL 



N, the voltage ratio of a perfect transformer, is usually complex. The 

 impedance ratio A^A^* is real. If we are not interested in the relation of 

 output phase to gap phase, we may disregard the phase angle of N, and 

 deal only with the impedance ratio, the absolute value of A^ squared, which 

 we will call N . Thus, using this equivalent circuit and disregarding the 

 phase of A^ we can for our purposes reduce the number of independent 

 parameters from the usual 6 for a passive 4 terminal network to 4, 

 Y(= G + jB), 7V^ and R. This reduction can greatly simplify the algebra 

 and arithmetic of microwave problems. The circuit of Fig. 118 has an 

 additional advantage; if we choose our impedance reference point on the 

 output line or guide to be the suitable point nearest to the actual output 



TRANSDUCER 



LINE OR 

 WAVE-GUIDE 



Fig. 117.— A 4-terniinal transducer is the most general connection between the oscilla 

 tor gap and a line or wave guide. 



I 



SPECIAL POINT 

 ALONG LINE 



O 



Fig. 118. — One circuit which will represent all the properties of a general 4-terminal 

 transducer. This circuit consists of an admittance Y shunting the gap, a perfect trans- 

 former of complex ratio N and a series resistance R. 



loop or iris, the circuit represents fairly accurately the frequency dependence 

 of the output impedance if we merely take Y as 



Y = C;« + ico(C - 1/coL) (a21) 



Near resonance we may use the simpler form. 



I' = Gh + jlMAco/coo (a22) 



Something has already been said in a general way about the evaluation of 

 L and C" in terms of the electric and magnetic field distribution in a resonator. 

 It is completely outside of the scope of this paper to consider this subject 

 at any length; the reader is referred to various books. ' ' The discon- 

 tinuity calculations of Whinnery and Jamieson are also of great value in 



" Electromagnetic Waves, S. A. Schelkunoff, Van Nostrand, 1943. 

 *" Fields & Waves in Modern Radio, Ramo & Whinnery, Wiley, 1944. 

 " Microwave Transmission Data, Sperry (lyroscope Company, 1944. 

 " J. R. Whinnery and H. W. Jamieson, Ecjuivalcnt Circuits for Discontinuities in 

 Transmission Lines, Proc. I.R.E., i2, 2, pp. 99-114. 



