BJT 2 stage amplifier
Each transistor runs near 5mA, thus reac ( 1/gm) is near 5 ohms. The collector resistors are each 1Kohm, thus maximum gain is 1,000 / 5 = 200.

Total maximum gain, ignoring Re of stage1, and the loading upon stage1 by stage2, etc, will be 200 * 200 = 40,000.

Now for the realities. Finite beta, assume 100, and the low reac of 5 ohms, tells us the Rin is at most 5 * 100 = 500. This is ignoring the biasing resistors. Gain drops by (500 || 1,000) / 1,000 =  0.333x. We are still ignoring the discrete Re1a of 3 ohms. Gain now has dropped by 67% in each stage,
thus total gain is 40,000 * 1/3 * 1/3 = 40,000/9 = 4,444x.

Now the non-zero Rsource, and the non-zero Re1a, get included in your gain.

By the way, given the 2nd order and 3rd order Intermodulation Intercepts for a bipolar (at any bias current, assuming non-saturated) are both near -10dBv (+- some dBv, but we'll approximate both wrongly as -10dBv), that -10dBv being a peak number used in a Taylor Series model of the emitter diode nonlinearity, and -10dBv is 0.316 volts, and given the 3rd order products drop 20 dBc for every 10dB dropoff from the Intercept Point (that -10dBv), to have 0.1% distortion which is 3 factors of 20dB you need to be 3*10dB below -10dBv IP3.

Thus for 0.1% distortion IM3, you need an input of about the size -10dBv IP - 3*10dB = -40dBv. Which is 0.01 volts input peak. Scaled by gain of 5,000, the output is 50 volts peak. Thus a whole nother world exists when you care about distortion.

Here is log-log plot of signal_in and signal_out levels, to illustrate distortion







simulate this circuit &ndash; Schematic created using CircuitLab