Cross-modulation figure of merit for transistor amplifier stages

This article concerns itself with comparison of transistor amplifier configurations in relation to their cross-modulation distortion characteristics. Only the base-emitter junction nonlinearity is considered, since this nonlinearity is considered to be the most significant contributor to cross-modulation distortion. For this case investigations have shown that since cross modulation occurs because of a third-order nonlinearity, the cross-modulation distortion is therefore proportional to the square of the interfering voltage which appears across the base-emitter junction. In this article the cross modulation of the transistor stage is analyzed from its equivalent circuit rather than from the theoretical device characteristics, It is assumed that the transistor stage gain and input impedance remain relatively constant with small signal voltage excursions. Using these hypotheses, a figure of merit factor is derived for comparison of transistor and transistor amplifier configurations with respect to their cross-modulation distortion characteristics. This figure of merit factor is then used to compare the relative cross-modulation susceptibility of the common collector, common emitter, and common base configurations. All three configurations are compared in the hypothetical voltage-generator and short-circuit load case. The derivation of the equations is shown in Appendix I. For this case it is shown that the three configurations have equal figures of merit. The latter two configurations are then analyzed and compared for the more practical matched input and matched output (maximum power transfer) case. Familiar formulas for transistor gain and input impedance in the low-frequency equivalent model are used for this analysis. Derivations of the equations are shown in Appendix II. The effect of feedback on the cross-modulation figure of merit is then analyzed using both degenerative and regenerative types of feedback. It is then shown that by use of the analysis of the low-frequency model, together with the analyses of the effects of feedback, a high-frequency analysis of cross-modulation figure of merit can be made. This analysis is most applicable to wide-band VHF amplifiers, such as used in Community Antenna Television trunk cascades. A convenient means for analysing cross modulation in the more complicated high-frequency circuit is thus described. Other types of stages, such as push-pull and parallel outputs, are also discussed in regards to the defined cross-modulation figure of merit. A set of conclusions concerning the defined cross-modulation figure of merit is then reached.