How can you calculate the small-signal input resistance of a common-collector BJT amplifier?
1 Answer
To calculate the small-signal input resistance of a common-collector (CC) BJT (Bipolar Junction Transistor) amplifier, you can follow these steps:
Draw the Small-Signal Equivalent Circuit: Start by drawing the small-signal equivalent circuit of the common-collector amplifier. The small-signal equivalent circuit simplifies the original circuit to focus only on the small variations in voltage and current around the operating point. In this circuit, you replace the BJT with its small-signal model, which typically includes the transconductance (gm) and output resistance (ro).
Apply AC Analysis: Once you have the small-signal equivalent circuit, you can apply AC analysis by considering the small-signal variations in voltage and current sources. For input resistance calculations, you'll be looking at the input side of the amplifier.
Set DC Sources to Zero: Since you are calculating small-signal parameters, set all DC sources (voltage and current sources) to zero. This is because you are interested in the linearized behavior around the operating point.
Apply Test Signal: For input resistance calculation, apply a small AC test signal at the input. Typically, it's a small voltage source (vtest) connected at the input terminal.
Calculate the Input Current (i_in): Determine the small-signal input current flowing into the base terminal of the transistor due to the applied test signal. You can find this current using Ohm's law: i_in = vtest / Rin, where Rin is the small-signal input resistance you want to calculate.
Calculate the Transistor Transconductance (gm): The transconductance (gm) is the small-signal parameter representing the change in collector current concerning the change in the base-emitter voltage. It is usually provided in the datasheet of the transistor or can be calculated using the formula gm = ΔIc / ΔVbe, where ΔIc is the change in collector current, and ΔVbe is the change in base-emitter voltage.
Input Resistance Calculation: Finally, calculate the input resistance (Rin) using the formula Rin = ΔVbe / ΔIb, where ΔVbe is the change in base-emitter voltage due to the test signal, and ΔIb is the corresponding change in the base current, given by ΔIb = gm * vtest.
So, the complete formula for the small-signal input resistance (Rin) of a common-collector BJT amplifier is:
Rin = ΔVbe / ΔIb = ΔVbe / (gm * vtest)
It's worth noting that Rin will depend on the specific biasing conditions of the BJT amplifier and the transistor's small-signal parameters (gm). Additionally, practical input resistance may be influenced by external circuit elements.
Draw the Small-Signal Equivalent Circuit: Start by drawing the small-signal equivalent circuit of the common-collector amplifier. The small-signal equivalent circuit simplifies the original circuit to focus only on the small variations in voltage and current around the operating point. In this circuit, you replace the BJT with its small-signal model, which typically includes the transconductance (gm) and output resistance (ro).
Apply AC Analysis: Once you have the small-signal equivalent circuit, you can apply AC analysis by considering the small-signal variations in voltage and current sources. For input resistance calculations, you'll be looking at the input side of the amplifier.
Set DC Sources to Zero: Since you are calculating small-signal parameters, set all DC sources (voltage and current sources) to zero. This is because you are interested in the linearized behavior around the operating point.
Apply Test Signal: For input resistance calculation, apply a small AC test signal at the input. Typically, it's a small voltage source (vtest) connected at the input terminal.
Calculate the Input Current (i_in): Determine the small-signal input current flowing into the base terminal of the transistor due to the applied test signal. You can find this current using Ohm's law: i_in = vtest / Rin, where Rin is the small-signal input resistance you want to calculate.
Calculate the Transistor Transconductance (gm): The transconductance (gm) is the small-signal parameter representing the change in collector current concerning the change in the base-emitter voltage. It is usually provided in the datasheet of the transistor or can be calculated using the formula gm = ΔIc / ΔVbe, where ΔIc is the change in collector current, and ΔVbe is the change in base-emitter voltage.
Input Resistance Calculation: Finally, calculate the input resistance (Rin) using the formula Rin = ΔVbe / ΔIb, where ΔVbe is the change in base-emitter voltage due to the test signal, and ΔIb is the corresponding change in the base current, given by ΔIb = gm * vtest.
So, the complete formula for the small-signal input resistance (Rin) of a common-collector BJT amplifier is:
Rin = ΔVbe / ΔIb = ΔVbe / (gm * vtest)
It's worth noting that Rin will depend on the specific biasing conditions of the BJT amplifier and the transistor's small-signal parameters (gm). Additionally, practical input resistance may be influenced by external circuit elements.