358 THE RADAR RECEIVER 



To obtain a low conversion loss, the voltage applied to the diode by the 

 local oscillator signal is very large so that there is negligible conduction 

 during one half of the local oscillator cycle. The signal voltage is much 

 smaller than the local oscillator voltage. 



A current flows through the IF impedance which can be described by the 

 multiplication of the signal and local oscillator voltages by the transfer 

 characteristic of the mixer. The transfer characteristic can be expressed as a 

 power series in the applied voltage. Because of the magnitude of local 

 oscillator voltage a large number of terms are required to describe the 

 mixer behavior. 



Thus 



/ - E a.E- (7-9) 



n=0 



where E is the input voltage 



/ is the current flowing in mixer 



an are the coefficients of the power series describing the mixer; 

 these are dependent on the local oscillator signal level 



n is an integer 0, 1, 2, 3, ... . 



Normally E consists of the sum of two voltages, the signal voltage and 

 the local oscillator voltage. In general the input may be 



E=Y,Ar cos CO./ (7-10) 



r=l 



with the condition that Ai cos coi/ be the local oscillator signal and Ai )$> ^2, 



If the signal is a single frequency C02 and the IF center frequency is 

 (coi — CO 2), the desired output spectrum from the mixer is the intermodula- 

 tion term K cos (coi — C02)/. An expansion of the expression for the current 

 in the IF impedance yields terms of the form 



Ij, = jJa.J, + ~ a,A,' + - + ^r^,2^ll^y^^ ^2„^i(-^"-^' + 



cos (coi — C02)/, r 9^\. (7-11) 



for the IF outputs incident to mixing of the signal frequencies with the local 

 oscillator frequency. The term in the brackets is a constant for a particular 

 value of local oscillator voltage, and the mixer thus produces an IF output 

 which can be expressed as 



Itf = KA.. r9^\. (7-12) 



