140G THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956 



A, B and C are ideal frequency selective networks whose admittances 

 are zero at /i , f^ and /o respectively, and infinite at all other frequencies. 

 This circuit permits the application of the local oscillator voltage to the 

 nonlinear elements but permits signal voltages to develop across them 

 at /i and f^ only. Similarly, signal currents at frequencies other than /i 

 and /2 encounter no external impedance, so they cannot alter the signal 

 voltage or contribute to the external power. This, of course, assumes that 

 if the nonlinear element is a point contact rectifier the spreading resist- 

 ance normally present is negligible. 



If /i is a frequency less than half the local oscillator frequency /o (it is 

 generally very much less), the network B can be selected to make /2 

 either /o + /i , or fo — fi ■ To distinguish between the two cases, we will 

 call the former a noninverting conversion transducer since an increase 

 in one signal frequency causes an increase in the other. The latter will 

 be called an inverting conversion transducer since an increase in one 

 signal frequency results in a decrease in the other. When yi contains 

 the generator and 2/2 the load, the device becomes a modulator. When 2/2 

 contains the generator and yi the load, it is a converter. 



The real part of the signal voltage may be written 



V = Vie''^'' + Vi*e~'"'' + V^e'"'' + ¥2*6-'"'' (4) 



where V* is the complex conjugate of V and w = 27r/, Similarly, the real 

 part of the signal current may be written 



• ^ j^^J-it _|. /^*e-i"i« + 72gi"2t ^ /2*e~'"=^' (5) 



If we multiply equations (1) and (4) and retain only those terms con- 

 taining /i and /2 we obtain, in the case of the non-inverting conversion 

 transducer where /2 = /o + /i , 



(6) 

 + [GoV,* -f G,V2*]e~'"'' -f [GiFi* + GoV2*]e~'"'' 



Similarly, if we multiply (2) and (4) we get an expression like (6) with 

 the G's replaced by C's. If we differentiate this expression we get 



~ M = jcci [CoVi + CV^le'"'' + MiCiVi + C0V2W'''' 



at (7) 



- jcoiiCoFi* -f CiF2*]e-^"^ ' - icoslCiFi* + C,V2*]e 



■joi2 t 



When we perform the addition indicated by (3) and compare the result 

 with (5) we obtain 



/i = [Go + icoiColFi -f [G, -f jmCi]V2 



(8) 

 h = [Gi + ic^CJFi + [Go + JCC2C0W2 



