# Identify zeroes of circuit by inspection

In a circuit, we can approximate the poles of the transfer function by calculating the AC Resistance and Capacitance at every node. For every node we get a pole so a change of slope in the Bode plot by -20db/dec. Is there a similar way of approximating the zeroes of the transfer function, so we get a clearer picture of the circuits frequency response?

• Just look for notch filters and high pass filters in the schematic. Jan 16 at 17:59

If you place $$\L_1\$$ in its high-frequency state (open-circuit it) while $$\C_2\$$ is kept in its dc state (open-circuited), you see that if you apply a stimulus at $$\V_{in}\$$ then you can follow the signal which through $$\R_2\$$ finds its way to the output node: you have response if you open-circuit $$\L_1\$$. It means that this element contributes a zero in the transfer function. Now, place $$\C_2\$$ i its high-frequency state (short-circuit it) and check if the stimulus still makes it to the output while $$\L_1\$$ is back in its dc state (a short circuit). Yes, you have a response then a second zero.
Now, where are these zeroes located? To find where they are, you have to find the impedance condition in the circuit where, for a certain stimulus frequency, you null the response. In other words, for a given frequency - the frequency of the zero you want - , the stimulus is blocked somewhere in the circuit. Either a series impedance becomes an infinite value or a branch is shunted to ground. In the below circuit, when $$\Z_1\$$ approaches infinity, the stimulus is lost and when $$\Z_2\$$ becomes a transformed short, there is no current in $$\R_4\$$ and the output is nulled. Both of these conditions reveal where the zeroes are located: