2nd order high pass filter with two real poles

Question

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?

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):

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):