How to Calculate the Midband Gain of a Transistor Circuit

The formula to calculate the Midband Gain, AM, of a transistor circuit is:

Midband Gain Formula for Transistor Circuit

However, in order to calculate this midband gain, complete AC analysis must be done.

Below is a transistor circuit which we will find the midband gain for:

Ac Transistor Analysis

Below is the equivalent AC Equivalent Circuit of the schematic above:

AC Transistor Equivalent of Circuit

AC Analysis

Solve R1||R2 (which is RB)

The first thing to do is solve for RB:

How to Calculate RB of a Transistor

Solve for RB|| RB' Next, after you get the value for RB, solve for RB', which is RB||rπ:

Rb prime formula

Solve for Output Resistance RL'
Next, we solve for the output resistance of the transistor circuit, RL', which equal to r0 || RC || RL.

RL prime formula of a transistor

Solve for Vπ
Next, we solve for Vπ, which is the voltage that drops across rπ. This is important for other calculations in the AC analysis.

formula for vpi of a transistor

Once we have these calculations, we can reduce the above circuit to the one below:

Ac Transistor analysis

Now we can solve for VOUT and then the gain of the transistor, AM:

Vout formula of a transistor

We now solve for the midband gain of the transistor circuit, AM:

Midband Gain Am of a Transistor

The Midband Gain calculated in dB:

Midband gain formula of transistor in db

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