Hi all, thank you for reading,

I have been an assignment to design a "double zobel" network.

The first image is Part 1 of the assignment. It's instructions are to prove the Z(in) is purely resistive for the circuit shown. Based on the fact that R=8 ohms and L =400uH, I have calculated C to be 6.25uF.
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I believe I have done part 1 circuit analysis correctly. I was able to show Z1 as (8-8i) and Z2 as (8+8i), indicating resonant frequency. I also calculated Z(in) to be 8ohms and purely resistive. If anyone sees any problem with my work in Part 1, please let me know.
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The third image I have shown is the LTspice build of the circuit. Along with the circuit build, i have run an ac analysis using a 1A current, in and have measured for V(in). My assumption was that since Z=V/I, if I sent I=1, then Z=V, so whatever I measured for the input voltage would equal my impedance, which shows at 8V, same as the 8ohm impedance. Is there a way to run the spice analysis at resonant frequency so that I can show a purely real result?
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Part 2 is where I am struggling. I really honestly don't even know where to begin other than plugging random numbers into LTspice. The purpose is to design a network based on the circuit shown and the values given that would result in a purely real and purely resistive input.
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My first problem with this circuit is how you would even go about determining a resonant frequency, given that you have so many unknown values, and I don't know which values of L and C to plug into the formula, because there is more than one L and more than one C. I have played around in LTSPice, and came up with a circuit that appears to be purely resistive, and Vin is close to Vout, but it is not purely real, and I don't know how to make it both without simply guessing. Is there a way to use circuit analysis to solve this problem?
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Thank you for reading. I will be here all day to take advise.

 

Here is ESP's Passive Crossover Network page that has Zobel Networks with speaker models. You should pick up some ideas there. http://sound.westhost.com/lr-passive.htm

And here is another resource https://www.trueaudio.com/st_zobel.htm

 

Here is ESP's Passive Crossover Network page that has Zobel Networks with speaker models. You should pick up some ideas there. http://sound.westhost.com/lr-passive.htm

And here is another resource https://www.trueaudio.com/st_zobel.htm

Thanks for the links. They haven't provide much information on how to solve for the 4 unknowns though.

 

You can simply pick L1 and R2 value for example L = 400μH and R2 = 8Ω and then find C1 and R1 in similar way as you did in Part 1.

 

You can simply pick L1 and R2 value for example L = 400μH and R2 = 8Ω and then find C1 and R1 in similar way as you did in Part 1.

That doesn't work. First off, the alignments of the L1, R2, R1, C1 are different than in the 1st problem. If that worked, you could just enter the exact same values as the first problem. That is not the solution. In that case, the whole circuit is not purely real or purely resistance. The whole circuit has to be, including the given values. Not just that one part.

 

Can you identify which two are Zobel networks and which two are being compensated on your diagram?