Radio Frequency Circuit Design, 2nd Edition

CHAPTER ELEVEN

RF Mixers

11.1 NONLINEAR DEVICE CHARACTERISTICS

A typical mixer is a three-port circuit that accepts two signals at two different frequencies and produces at the third port a signal that is the sum or difference of the two input frequencies. Production of a new frequency or frequencies requires a nonlinear resistance device. The two most common semiconductor nonlinear characteristics are of the form e^qV(t)/kT as found in pn junction diodes or bipolar junction transistors and of the form I_DSS[1 − V (t)/V_t]² as found in field-effect transistors. Schottky barrier diodes are not described here since they are mostly used out of necessity for low-noise high-microwave-frequency applications.

When a pn junction is excited by two signals (plus a dc term):

(11.1)

The device current is of the form

(11.2)

where the thermal voltage, V_T, is defined as kT/q, k is Boltzmann’s constant, T is the absolute temperature, and q is the magnitude of the electronic charge. It is known, however, that this can be simplified by expressing it in terms of modified Bessel functions because

(11.3)

where I_n(z) is the modified Bessel function of order n and argument z [1]. The Bessel function has the ...