I want to implement an active analog high pass filter, which behaves as a high pass filter implemented by a capacitance, an inductance and a resistor in the following way:


simulate this circuit – Schematic created using CircuitLab

Which gives the follwing transfer function:

$$G_{hp} = \frac{CLs^2+RCs}{CLs^2+CRs+1}$$

Usually second order high pass filters are build up by Sallen-Key elements.


simulate this circuit

But the transfer function of these filters is given by $$G_{hp2}=\frac{\frac{s}{\omega_g}^2}{\frac{s}{\omega_g}^2+s\cdot a\cdot\frac{s}{\omega_g}+1}$$ $$\omega_g=\frac{1}{RC}$$

In this transfer function there is only a conjugated complex zeros. But what I want to have is a zero at 0 and R/L.

Does some one know a circuit, which will give me an active filter, which is build up by an op-amp, capacitors and resistors, which behaves as the LCR filter?


1 Answer 1


You could implement a grounded inductor with a GIC and add a resistor and capacitor (swapping the resistor and inductor will make no difference to the output in this case). The GIC takes two op-amps, a capacitor and several resistors (in this case).

GIC (image from Wikipedia): enter image description here

Alternatively, a gyrator takes only one op-amp and two resistors to simulate a grounded inductor with a resistor in series. There are probably differences in the behavior between GIC and gyrator, especially near resonance if your op-amp(s) don't have a lot of GBW compared to the signal. Also if your resistor RL is relatively low value.

Gyrator (image from Wikipedia):

enter image description here

  • 1
    \$\begingroup\$ See "The Art of Electronics", section on "Generalized Impedance converter". The 3rd edition shows the equation for realizing an inductor and also shows how the opamp gain-bandwidth degrades performance. If the GIC oscillates, add equal valued compensation capacitors across Z2 and Z3. By adding two compensation capacitors, the effects cancel out which doesn't affect the inductance (BBC took a patent out on this using one compensation capacitor and back-pedaled on how it affected the characteristics). \$\endgroup\$
    – qrk
    Commented Apr 25, 2023 at 18:54
  • \$\begingroup\$ I had the idea of a gyrator as well, but the problem is, that I need still a second op-amp top get a low impedance output port. This is the nice thing on the Sallen-Key circuit, it has already a low impedance output. So this does not solve my problem entirely. \$\endgroup\$
    – stefan
    Commented Apr 26, 2023 at 9:21

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