I have gone through the derivation of the transfer function of this transistor-based amplifier, including the dc-block capacitors and the two parasitic contributors. Needless to say that without the fast analytical circuits techniques or FACTs, it would be a nightmare to get to the result that I obtained without writing a single line of algebra, just inspecting small sketches.
You start by determining the gain at dc, for \$s = 0\$, and then turn the input source off to obtain all the time constants. There are four capacitors with individual state variables which means a fourth-order transfer function:
It looks intimidating but it's not, just carefully draw these little sketches with proper labeling and they will help you fix a wrong time constant if necessary. This is the cool thing here: if you spot a deviation between what you obtain with the FACTs and the brute-force transfer function, not need to restart from scratch. Just identify the guilty sketch, fix the associated time constant and there you go.
For the zeroes, I have chosen the generalized formula which means I have to determine high-frequency gains. As it is usually the case, many of these gains are zeroed by the shorting of capacitors across the signal path so, in the end, only one remains:
Once you have these contributors, assemble them and check the magnitude and phase response between all the transfer functions. In the end, the difference in magnitude and phase between the brute-force expression and the FACTs should be in the solver noise, at the pico level. This is what I have here:
This is how the FACTs lead you to the results here, in this 4th-order circuit. Further work would be necessary - further factoring this expression - but I'm done for the day : ) If you are interested by the approach, I invite you to take a look at my last book on the subject.
