Analysis of a Four Quadrant Ring Multiplier with General No-Memory Bridge Arm Impedances

An analysis is made of a four-quadrant ring multiplier in which the currents in the bridge arm inpedances are represented as general, no-memory functions of the arm impedance voltages. Application of Kirchoff's current and voltage laws to the ring circuit yields an implicit functional relationship between the output and drive voltages of the bridge that involves the bridge load resistor and the general arm impedance functions. The form of the Taylor's series expressing the output voltage as a function of the drive voltages is developed for the special but important case in which the ring consists of four identical arm impedance functions. General formulas are derived for the first three nonzero coefficients occurring in this series. An evaluation is made of circuit performance for the case in which 1N72 junction diodes serve as the bridge arm impedances. A direct comparison is made between predicted and measured bridge output voltage for this case with the ring circuit used to square a sinusoidal signal. Finally, an analysis is made of the bridge drive voltage rejection capabilities for mismatched arm impedances. Numerical values of rejection (in db) are computed for each drive voltage from measured parameter values of the 1N72 junction diodes used in the tests.