# Calculating the Gain in an Amplifier circuit

Having some issues calculating the gain in circuit below, it is apparently 1802, but I can't seem to arrive at this answer. If anyone could help explain how to get this answer I'd be very appreciative!

Edit: My Working

• Show your work and others will help you spot the mistake. But currently your question is just going to be closed because no initial effort is shown. – Bence Kaulics May 30 '16 at 18:10
• Sorry about that, my working is here, thank you for the advice – ohkneel May 30 '16 at 18:21

## 2 Answers

The gain A of a single transistor amplifier stage is given by $$A = -g_m r_{out}$$ For two stages in cascade it's the product of the gains.

The gm can be found using $gm = I_C/V_T$.

The output resistance is $R_C$ in parallel to everything else that loads the output node.

OK, here my calculation:

gm1 = 100e-6 *  q/(k*T)
gm2 = 1e-3 *  q/(k*T)
rpi2 = 100 /gm2
RC1 = 47e3;
RC2 = 4.7e3;
A1 = -gm1 * 1/(1/RC1 + 1/rpi2)
A2 = -gm2 * RC2
gain = A1 * A2


which gives the following results

gm1 =  0.0039571
gm2 =  0.039571
rpi2 =  2527.1
A1 = -9.4897
A2 = -185.98
gain =  1764.9

• I also get around 1800 times gain in a quick calculation. – Bimpelrekkie May 30 '16 at 18:49
• @FakeMoustache - Yes, and even if there is same mistake in the calculation it should be easy to fix it. – Mario May 30 '16 at 18:51

To confirm Mario's answer, I get gain:

$G = +\frac{I_{C1}I_{C2}R_{C2}}{V_T^2(\frac{1}{R_{C1}}+\frac{I_{C2}}{\beta V_T})}= +1766$

where $V_T = kT/q = 25.26\text mV$