Phono Termination Calculations and Calculator
Posted in here as a lot of people don't appear to check the software thread often !
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Why would someone wish to model the LCR response? In most cases it will be swamped by the mechanical response, so in most cases it will lead people seriously astray.

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If one 'optimises' LCR response in isolation, then overall response, ie what matters, is near certain to be nonoptimal. This is because there is typically an audioband mechanical system response, which is independent of the electrical response, so cartridge designers work LCR and mechanical systems together for an overall result. LD 
A further comment: any such model assumes inductance is ideal, whereas in practice it often isn't IME. Losses might vary with level, frequency and/or slew rate of programme material, and I found some evidence a few years back that inductance itself might effectively vary with such parameters. I eventually formed the view that is all part of the character of the cartridge, and perhaps vinyl sound, after some fairly hairbrained schemes to use a 'passive' or dummy cartridge as part of termination as a means to avoid such effects.
Halcyon days ! LD 
Change f_o from 22kHz to 2.122kHz and le voila, you have 75uS pole  but you would want to optimize R_L from f_o.

Jack: spooky, this is something I posted on couple of days ago as looking at the 'damped RIAA' that Bob Cordell put forwards. As in all things it may be more complex that first imagined, although the VST V laminated cores and the split pins in Ortofons suddenly make sense.

His formula for the electrical Q is wrong. I sent him an email with the correct derivation of the formula for Q. I will find the email and post it.

His model is wrong as well, Magnetic Phono Pickup Cartridges

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I seem to recall that a Mr. Halgren (?) proposed a more complicated model than the simple low pass filter in the JAES in the 1970s. He added some additional resistors to account for other losses. A respondent pointed out that the calculated results using the complicated model weren't much different than the results of the simple model so there was no big rust to use the complicated model.
Here is the correct derivation of the formula for the cartridge electrical Q assuming the simple low pass filter model. Line 1 is the transfer function and Rs is the cartridge resistance and Rl the load resistor. Line 2 is just some definitions and these definitions are put in the transfer function in line 3. The second term in the denominator contains some time constants and the inverse of a time constant is a frequency. Line 4 shows what the frequencies are. Line 5 shows that Qs sum like resistors in parallel and finally we get line 6. You then equate the second term in the denominator of line 6 to the second term in the denominator of line 1. After some manipulation you have line 7 which is the correct formula for the Q. You can obtain several formulas depending on the substitutions used, so why is this formula the correct one? If you solve the line 7 formula for C you have to solve a quadratic. However every case I've tried, the denominator is just a little larger than 1.0, it might be 1.02 or 1.05 so usually you can ignore the denominator and solve the formula in line 8 for the approximate Q. That formula is so simple I can do it on my fingers, if I don't have to count above 10. Line 9 is the formula for the cutoff frequency where the response is down 3 dB. 
Bjorn Hallgren 1975. Somewhere I have the actual paper reference, but didn't feel need to pay $33 for the paper. The model Rod Elliot proposed I believe is more advanced than the Hallgren model.
https://linearaudio.net/sites/linear...lte_vol3_1.pdf second letter has a bit of analysis looking at it from the point of cancelling the mechcanical resonance with an inverse filter. Of course all this t*rd polishing is only of interest if you don't like the idea of a peaked response with 4th order roll off. And if you have the right cartridge then you are flat to over 20kHz provided you have a low enough input C on your phono preamp. Many don't and complain a cartridge is bright when in fact its just wrongly loaded. 
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