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](/images/midbandgainformula.jpg)
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](/images/actransistorcircuit2.jpg)
Below is the equivalent AC Equivalent Circuit of the schematic above:
![AC Transistor Equivalent of Circuit](/images/actransistorcircuit1.jpg)
AC Analysis
Solve R1||R2 (which is RB)
The first thing to do is solve for RB:
Solve for RB|| RB' Next, after you get the value for RB, solve for RB', which is RB||rπ:
![Rb prime formula](/images/rbprimeformula.jpg)
Solve for Output Resistance RL'
Next, we solve for the output resistance of the transistor circuit, RL', which equal to r0 || RC || RL.
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](/images/vpiformula.jpg)
Once we have these calculations, we can reduce the above circuit to the one below:
![Ac Transistor analysis](/images/actransistoranalysisfinalcircuit.jpg)
Now we can solve for VOUT and then the gain of the transistor, AM:
![Vout formula of a transistor](/images/Voutoftransistor.jpg)
We now solve for the midband gain of the transistor circuit, AM:
![Midband Gain Am of a Transistor](/images/midbandgainamoftransistor.jpg)
The Midband Gain calculated in dB:
![Midband gain formula of transistor in db](/images/midbandgainindb.jpg)