To determine the small-signal output resistance of a common-emitter Bipolar Junction Transistor (BJT) amplifier, you typically perform an AC small-signal analysis. This analysis helps you understand how the circuit responds to small changes in input signals and provides insights into its characteristics. The small-signal output resistance, often denoted as "ro," reflects how the output voltage changes in response to a small change in output current.
Here are the steps to determine the small-signal output resistance of a common-emitter BJT amplifier:
Identify the Circuit Configuration: The common-emitter BJT amplifier consists of a BJT transistor in a common-emitter configuration, along with resistors for biasing and other components. This configuration amplifies the input signal.
DC Biasing Analysis: Perform a DC biasing analysis to determine the operating point of the BJT. This involves calculating the DC voltages and currents at various nodes in the circuit. The DC biasing establishes the Q-point (quiescent point) of the transistor.
Small-Signal Model: The small-signal model represents the circuit using small-signal equivalent components. Replace the DC voltage sources with short circuits and replace the DC bias currents with equivalent small-signal current sources.
Apply AC Signal: Apply a small AC input signal to the input of the amplifier. This signal is often represented as "vin" (voltage in) or "iin" (current in).
Calculate Small-Signal Parameters: Calculate the small-signal parameters of the circuit. The parameters you need to calculate include:
Transconductance (gm): This represents the change in output current with respect to the change in input voltage. It's given by the formula gm = ΔIc / ΔVin, where ΔIc is the change in collector current and ΔVin is the change in input voltage.
Dynamic Output Resistance (ro): This represents the change in output voltage with respect to the change in output current. It's given by the formula ro = ΔVout / ΔIout, where ΔVout is the change in output voltage and ΔIout is the change in output current.
Calculate Output Resistance: The small-signal output resistance (ro) of the BJT amplifier is essentially the inverse of the dynamic output resistance (ro) calculated in the previous step. So, you can calculate it as ro = 1 / ro_dynamic.
Account for Load Resistance: If the output of the amplifier is connected to a load resistor (R_load), you need to consider its effect on the output resistance. In this case, the total small-signal output resistance (ro_total) is the parallel combination of the intrinsic ro and the load resistance ro_total = (ro * R_load) / (ro + R_load).
Remember that these calculations assume that the signal variations are small enough to be considered linear. The actual small-signal output resistance can vary based on the specific characteristics of the transistor and the circuit components.