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 comming 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?

 

[piercas]

I understand the challenge you are facing in designing a circuit to undo the effects of a "black box" on a signal. Based on the information you have provided, it seems like you have already made some good progress in your design by using a simple inverting op amp circuit and a series combination of inductors and resistors. However, the limitation of only being able to use 1mH inductors and the DC gain of 1 may be causing some difficulties in achieving the desired results.

One suggestion I have is to explore using capacitors in your circuit design. Capacitors are often used in circuits to alter the frequency response and can be a useful tool in this situation. By introducing capacitors into your design, you may be able to achieve the desired frequency response and phase shift more effectively.

Another approach could be to use a combination of inductors and capacitors in your circuit design, known as a "Twin-T" or "bridged T" circuit. This type of circuit is commonly used for pre-emphasis and de-emphasis in audio applications and may be helpful in your situation.

Additionally, it may be helpful to simulate your circuit design using software such as SPICE to test different configurations and see how they affect the frequency response and phase shift. This can save time and resources in the design process.

Overall, it seems like you are on the right track and with some adjustments and experimentation, you should be able to find a solution to your circuit design challenge. Keep exploring and don't hesitate to reach out for further assistance if needed.