FREQUENCY CONVERSION BY A NONLINEAR ADMITTANCE 1405 



it may be expressed as an even function of time, we may write 



7 = 



(1) 



where coo/27r is the local oscillator frequency /o and the Fourier coeffi- 

 cients Gn are real. Similarly the charge on the nonlinear capacitor is a 

 function of the applied voltage. The derivative of this function is the 

 capacitance as a function of the applied voltage. The application of the 

 local oscillator thus causes the capacitance to vary at the local oscillator 

 frequency so that it also may be expressed as a Fourier series. The ca- 

 pacitance K is real, and assuming it may be expressed as an even function 

 of time, we have 



+ Cae"''""' + Cre~'"'' + Co + Cie^""' + C^e'^"'' + 



(2) 



It is assumed that the current and charge functions are single valued and 

 that their derivatives are always positive. 



When a small signal voltage v is apphed to the nonlinear resistor, the 

 signal current through the resistor is given by yv. When it is applied to 

 the nonlinear capacitor the charge on the capacitor is kv. The total cur- 

 rent i which flows through the two nonlinear elements connected in 

 parallel thus becomes 





(3) 



V of course must be small and not affect the value of 7 and k. 



Fig. 1 shows a heterodyne conversion transducer made up of a non- 

 linear resistor and a nonlinear capacitor in parallel driven by an internal 

 local oscillator, /i is the signal frequency at the terminals 1-2, and 7/1 is 

 the external admittance connected to these terminals. The signal fre- 

 quency at the terminals 3-4 is /2 , and y2 is the external admittance. 



Fig. 1 — Heterodyne conversion transducer. 



