How can you calculate the small-signal output resistance of a common-emitter BJT amplifier?
1 Answer
Calculating the small-signal output resistance of a common-emitter BJT (Bipolar Junction Transistor) amplifier involves analyzing the small-signal equivalent circuit and finding the output resistance. Here's a step-by-step guide to the process:
Obtain the Small-Signal Equivalent Circuit:
To calculate small-signal parameters, you need to start with the small-signal equivalent circuit of the common-emitter BJT amplifier. This circuit consists of small-signal models of the transistor and the surrounding components while assuming that the DC operating point remains fixed.
Identify the Components in the Small-Signal Equivalent Circuit:
The small-signal equivalent circuit for a common-emitter BJT amplifier typically contains the following components:
The small-signal model of the BJT (pi-model or T-model).
Input resistance (ri): The resistance seen by the base terminal when looking into the amplifier.
Output resistance (ro): The resistance seen by the collector terminal when looking into the amplifier.
Transconductance (gm): The change in collector current with respect to the change in base-emitter voltage.
Short Circuit the Input:
To find the output resistance, we need to turn off all independent sources (current and voltage sources) and then short-circuit the input signal source.
Replace the Transistor with Its Small-Signal Model:
For the common-emitter configuration, the small-signal model of the BJT can be approximated as a current source (gm * Vbe) in parallel with a resistance (ro). The transconductance (gm) represents the change in collector current for a given change in base-emitter voltage (Vbe).
Apply Test Signal:
Apply a small test voltage (Vtest) across the output terminals (collector and emitter) of the amplifier. This test voltage is usually a voltage source in series with the output resistance (ro).
Calculate the Output Current (Iout):
Using the test voltage Vtest and the output resistance ro, calculate the output current (Iout) flowing through the test voltage source.
Calculate the Small-Signal Output Resistance (ro):
The small-signal output resistance (ro) is the ratio of the change in output voltage (Vtest) to the output current (Iout) when the input signal source is shorted. It can be calculated using Ohm's law:
ro = ΞVtest / Iout
The output resistance (ro) is a critical parameter for analyzing the stability and loading effects of the amplifier.
Keep in mind that the actual calculations depend on the specific small-signal model used for the BJT, and the values of components in the amplifier circuit. For a more accurate and detailed calculation, you will need the small-signal model parameters of the BJT, which can be obtained from the datasheet or through characterization.
Obtain the Small-Signal Equivalent Circuit:
To calculate small-signal parameters, you need to start with the small-signal equivalent circuit of the common-emitter BJT amplifier. This circuit consists of small-signal models of the transistor and the surrounding components while assuming that the DC operating point remains fixed.
Identify the Components in the Small-Signal Equivalent Circuit:
The small-signal equivalent circuit for a common-emitter BJT amplifier typically contains the following components:
The small-signal model of the BJT (pi-model or T-model).
Input resistance (ri): The resistance seen by the base terminal when looking into the amplifier.
Output resistance (ro): The resistance seen by the collector terminal when looking into the amplifier.
Transconductance (gm): The change in collector current with respect to the change in base-emitter voltage.
Short Circuit the Input:
To find the output resistance, we need to turn off all independent sources (current and voltage sources) and then short-circuit the input signal source.
Replace the Transistor with Its Small-Signal Model:
For the common-emitter configuration, the small-signal model of the BJT can be approximated as a current source (gm * Vbe) in parallel with a resistance (ro). The transconductance (gm) represents the change in collector current for a given change in base-emitter voltage (Vbe).
Apply Test Signal:
Apply a small test voltage (Vtest) across the output terminals (collector and emitter) of the amplifier. This test voltage is usually a voltage source in series with the output resistance (ro).
Calculate the Output Current (Iout):
Using the test voltage Vtest and the output resistance ro, calculate the output current (Iout) flowing through the test voltage source.
Calculate the Small-Signal Output Resistance (ro):
The small-signal output resistance (ro) is the ratio of the change in output voltage (Vtest) to the output current (Iout) when the input signal source is shorted. It can be calculated using Ohm's law:
ro = ΞVtest / Iout
The output resistance (ro) is a critical parameter for analyzing the stability and loading effects of the amplifier.
Keep in mind that the actual calculations depend on the specific small-signal model used for the BJT, and the values of components in the amplifier circuit. For a more accurate and detailed calculation, you will need the small-signal model parameters of the BJT, which can be obtained from the datasheet or through characterization.