How do you calculate the output impedance and current gain of a common-emitter BJT amplifier?
1 Answer
To calculate the output impedance and current gain of a common-emitter Bipolar Junction Transistor (BJT) amplifier, we need to analyze the small-signal model of the circuit. The small-signal model simplifies the amplifier circuit, assuming that the input signals are small enough to be considered as small variations around the DC operating point. Here are the steps to calculate the output impedance and current gain:
Small-signal model of the common-emitter BJT amplifier:
In the small-signal model, we represent the BJT with a small-signal current source (i.e., gm * Vbe), a small-signal voltage source (rπ * ib), and an output resistance (Ro). Here:
gm: Transconductance of the BJT (Ic/Vt), where Ic is the DC collector current and Vt is the thermal voltage (k * T / q, where k is Boltzmann's constant, T is the temperature in Kelvin, and q is the charge of an electron).
rπ: The small-signal base-emitter resistance (referred to as rπ or rbe).
ib: The small-signal base current.
Output impedance (Ro):
The output impedance (Ro) is the impedance seen at the collector of the BJT when the input signal source is shorted. To calculate Ro, you need to determine the resistance between the collector terminal and the ground in the small-signal model. It is usually equal to the parallel combination of the BJT's collector resistance (Rc) and the Early voltage (VA) divided by the collector current (Ic).
Ro = (Rc || VA) / Ic
Current gain (β):
The current gain (β) is the ratio of the small-signal output current (ic) to the small-signal input current (ib).
β = ic / ib
In a common-emitter BJT configuration, the current gain (β) is approximately equal to the ratio of the collector current (Ic) to the base current (Ib). Hence,
β ≈ Ic / Ib
Keep in mind that β is a ratio of DC values, and the actual current gain for small-signal AC analysis will be slightly different.
To summarize, to calculate the output impedance and current gain of a common-emitter BJT amplifier, you will need the values of the transconductance (gm), the small-signal base-emitter resistance (rπ), and the DC collector current (Ic). These values can be obtained from the BJT datasheet or through appropriate circuit analysis and transistor biasing calculations.
Small-signal model of the common-emitter BJT amplifier:
In the small-signal model, we represent the BJT with a small-signal current source (i.e., gm * Vbe), a small-signal voltage source (rπ * ib), and an output resistance (Ro). Here:
gm: Transconductance of the BJT (Ic/Vt), where Ic is the DC collector current and Vt is the thermal voltage (k * T / q, where k is Boltzmann's constant, T is the temperature in Kelvin, and q is the charge of an electron).
rπ: The small-signal base-emitter resistance (referred to as rπ or rbe).
ib: The small-signal base current.
Output impedance (Ro):
The output impedance (Ro) is the impedance seen at the collector of the BJT when the input signal source is shorted. To calculate Ro, you need to determine the resistance between the collector terminal and the ground in the small-signal model. It is usually equal to the parallel combination of the BJT's collector resistance (Rc) and the Early voltage (VA) divided by the collector current (Ic).
Ro = (Rc || VA) / Ic
Current gain (β):
The current gain (β) is the ratio of the small-signal output current (ic) to the small-signal input current (ib).
β = ic / ib
In a common-emitter BJT configuration, the current gain (β) is approximately equal to the ratio of the collector current (Ic) to the base current (Ib). Hence,
β ≈ Ic / Ib
Keep in mind that β is a ratio of DC values, and the actual current gain for small-signal AC analysis will be slightly different.
To summarize, to calculate the output impedance and current gain of a common-emitter BJT amplifier, you will need the values of the transconductance (gm), the small-signal base-emitter resistance (rπ), and the DC collector current (Ic). These values can be obtained from the BJT datasheet or through appropriate circuit analysis and transistor biasing calculations.