Intermodulation analysis of crystal mixer

An expression for the amplitude of the intermodulation products and harmonics produced in a crystal mixer is derived using the coefficients of the power series expansion of the device. Using this expression and an exponential approximation of the current through a diode [i = i
0
(ε
^αv
- 1)], the amplitude of intermodulation produced in a crystal mixer is found to be 2i
0
ε
^αV0
R
0
I
s
(αV
1
)I
b
(αV
2
). I
n
(x) is an nth order modified Bessel function of the first kind. The quantities s and b are the signal harmonic and the oscillator harmonic, R
0
is the output resistance, and V
0
, V
1
, and V
2
are the bias, signal, and oscillator voltages, respectively. The quantities i
0
, α, R
0
, and V
2
are found from the dc E-I diode characteristics, the mixer bias current, and the loss in the desired signal. Experimental tests on a mixer operating from 450 Mc to 850 Mc show that the signal input power necessary to produce a given intermodulation output power can be predicted within 6 db.