How Can I Design a Circuit to Counteract a Black Box Signal Alteration?

[samurye]

I have to design a circuit that will undo the effects on a signal passed through a "black box". I have already determined that I have a pole at 500rad/s and a zero at 2000rad/s and a max phase shift of ~ -37* at ~950rad/s. It has a DC gain of 1 and a HF gain of ~0.25. The input signal is a sine wave of between 0 and 20k Hz. I have attached the gain and phase diagrams. We can only use 1mH inductors and 741 op amps but a range of resistors and caps are available.

I have designed a circuit (between the buffer amp to prevent loading and the inverting amp gain -1 to send it positive again) just using a simple inverting op amp circuit and a series combination of L and R for each the Zf and Zi that will undo this (same R, L in Zf 4* L in Zi), but the problem is that I thought I had much larger inductors (100mH) to work with. Doing it this way the ratio of R to L is only 2000:1, which gives values of R about 10 Ohms, less that the output impedence of the 741.

There has to be an easier way that is just eluding me! I have tried working out transfer functions for all manner of simple amps using just L and R values in the impedences that determine gain, but I'm coming to a dead end. Perhaps I need to use a voltage divider before the input to the amp? I've tried some of those too but still to no avail.

Help me please!

I've just found out that we can use capacitors and edited the post, now on to try again!

 

[samurye]

Ok, so with the availability of caps I have got what seems the perfect solution. I've got a non inverting amp with an Rf of 15k and a Zi consisting of a series 100nF cap and a 5k resistor. Solved! With an ideal op amp this seems perfect.

The only problem I can see is that when I run it in spice with the u741, there is an HF phase shift into the negative, crossing zero at about 10kHz. Our signal is bounded within DC and 20kHz so all I need to do is null the small phase shift that occurs between 10k and 20kHz.

Is there anything I can do to avoid changing the transfer function and the rest of the phase portrait that will just account for the HF phase shift?