I have the following circuit: (which should represent a "new" design for preemphasis block in a FM transmitter circuit)
I need to calculate the transfer function H(s) and draw a Bode plot. My question is, how to do it fast and efficient with respect to time since I won't have a computer to use in my exam.
Here's an example from NI Multisim bode plot:
I need help to calculate the H(s) and bode plot manually. Thanks.
If you want to be fast and be efficient to determine transfer functions, there is no other way than resorting to the fast analytical circuits techniques or FACTs that I describe in my book on the subject. However, and it could be the issue for an exam, I am not sure if the person who reviews your contribution will recognize it as a valid method as he/she perhaps expects the classical KVL/KCL approach.
The methods relies on determining the time constants when the stimulus - \$V_{in}\$ - is reduced to 0 V or replaced by a short circuit. You first start with \$s=0\$ and opens the caps (and short the inductors if any), just like what SPICE does during its bias point analysis. You determine the dc gain \$H_0\$ in this mode. Then, you temporarily remove each capacitor and "look" through its connecting terminals to determine by inspection (no equations) the resistance \$R\$ you see. Then, multiply the resistance by the involved capacitor to form the time constant \$\tau=RC\$. So determining the transfer function is mostly about splitting the circuit into small drawings that you individually solve and eventually fix if you spot a mistake in the end.
Once you have the natural time constants, you can form the denominator. For the zero, you have to identify a specific impedance in the circuit which could block the stimulus propagation if tuned at the zero frequency. As highlighted in the below picture, it is when the parallel combination of \$C_1\$ and \$R_1\$ would become infinite. And this is true for \$s=s_z=-\frac{1}{R_1C_1}\$.
This is it, we have everything to be happy and a Mathcad sheet can check these results. I usually build a high-entropy expression obtained with Thévenin in this case and make sure both answers are rigorously similar in magnitude and phase. This is the case here. As I said, should you spot a small deviation, then review the individual sketches and fix the guilty one without restarting from scratch as any other analysis would require:
Because the roots are real in this circuit (the quality factor is low), you can try to model the transfer function with two cascaded poles and a zero. As shown in the below plots, all three expressions deliver the exact same response:
If I count the time needed to determine the expression using FACTs, it does not exceed a few minutes. Should I now expand the Thévenin expression, first it's likely that I make mistakes while expanding the equations but, second, I will need more time to format the expression in a nice low-entropy format.
