On the Effects of Resistive and Reactive Loads on Signal Amplification

The effects of reactive loads into amplification is studied. A simplified common emitter circuit configuration was adopted and respective time-independent and time-dependent voltage and current equations were obtained. As phasor analysis cannot be used because of the non-linearity, the voltage at the capacitor was represented in terms of the respective integral, implying a numerical approach. The effect of purely resistive loads was investigated first, and it was shown that the fanned structure of the transistor isolines can severely distort the amplification, especially for $V_a$ small and $s$ large. The total harmonic distortion was found not to depend on $V_a$, being determined by $s$ and the load resistance $R$. An expression was obtained for the current gain in terms of the base current and it was shown that it decreases in an almost perfectly linearly fashion with $I_B$. Remarkably, no gain variation, and hence perfectly linear amplification, is obtained when $R=0$, provided maximum power dissipation limits are not exceeded. Capacitive loads imply the detachment of the circuit trajectory from a straight line to an "ellipsoidal"-like loop. This implies a gain asymmetry along upper or lower arcs of this loop. By using the time-dependent circuit equations, it was possible to show numerically and by an analytical approximation that, at least for the adopted circuit and parameter values, the asymmetry induced by capacitive loads is not substantial. However, capacitive loads will imply lag between the output voltage and current and, hence, low-pass filtering. It was shown that smaller $V_a$ and larger $s$ can substantially reduce the phase lag, but at the cost of severe distortion.