Using the Jacobian matrix and Excel/Matlab to solve for RIAA network values

The point of this really is to reproduce the recording without degrading it any further, and that IMO is a valid goal. I aim for +/-0.1dB RIAA accuracy in my designs but generally can't achieve that at the bottom end. My newest design hopes to address that issue.
 
Is anyone going to pay your work? Aren't there enough online riaa network calculators? Are they bad calculators that need more precision?
You can't probably get a better job at applying riaa than reversing a Neumann real network.I think someone should care to measure the precision of antiriaa action of a real Neuman Ortophon or Scully cutting machine first...Same argument was made for lowering turntable's rumble orders of magnitude below the cutter's own rumble ....
It was academic -- Ellis did not do a very good job (at all) of describing the error terms, miniscule as they are.

And yes, I have read Self.

R3, R6 are spec'd as "0" in the article.
 
Your test equipment (RIAA decoder) should have x10 better accuracy than the DUT (the LP).
Why? You're not measuring thd, you're trying to get a linear response by reversing the anti riaa action of the cutter working on a real world material.You won't get a 0.05db accurate reproduction of the input musical program by applying a 0.05 db riaa preamp to a +-0.5 dB off vinyl. You'll still be 0.45...0.55db off the musical program input.
Nobody talks about the other processes that results in you buying a copy of the real master which is even more degraded...
I aim for +/-0.1dB RIAA accuracy in my designs but generally can't achieve that at the bottom end.
There's a reason for that and that's the result of using the Neumann or other simillar machine by itself .
Check lathetrolls forum cause they have good explanations for that.You cannot fix it with a fixed riaa, you need either a tonestack eq or a variable riaa as EMT does. The guys there can't even settle on the subject and they are real owners of Neumann and Orthophon cutters:
https://www.lathetrolls.com/viewtopic.php?t=1762
https://www.lathetrolls.com/viewtopic.php?t=1417
Unless you have a cutter yourself you'll never get to listen to the real master accuracy.
 
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It's not really clear to me what is being optimized here and why.

As long as the op-amp is ideal and as long as you want to place the poles at -1/(3180 us) and -1/(75 us) and the first zero at -1/(318 us), it is straightforward to find analytical expressions for all the component values and for the extra zero. You can then correct for the extra zero with a first-order low-pass somewhere further down the chain if you want to.

Is the trick here to correct for finite op-amp gain or to tweak the pole and zero locations in order to minimize the effect of the extra zero over a given frequency range (without needing an extra first-order low-pass)?
 
Why? You're not measuring thd, you're trying to get a linear response by reversing the anti riaa action of the cutter working on a real world material.You won't get a 0.05db accurate reproduction of the input musical program by applying a 0.05 db riaa preamp to a +-0.5 dB off vinyl.

The error is not the same from one cutter to another.
You want to be on the peak of the bell curve, not down one side.

The number of people who would (or want to) properly use a variable phono eq is vanishingly small.
I would definitely not include myself in that small number.
 
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Is the trick here to correct for finite op-amp gain or to tweak the pole and zero locations in order to minimize the effect of the extra zero over a given frequency range (without needing an extra first-order low-pass)?

Some have tried, but the open loop response has too much variability.

Conrad-Johnson had a tube preamp with an open loop response primarily defined by an inter-stage RC network,
which then could be taken into consideration in the NFB RIAA calculations.
 
There's a reason for that and that's the result of using the Neumann or other simillar machine by itself .
Check lathetrolls forum cause they have good explanations for that.You cannot fix it with a fixed riaa, you need either a tonestack eq or a variable riaa as EMT does. The guys there can't even settle on the subject and they are real owners of Neumann and Orthophon cutters:
https://www.lathetrolls.com/viewtopic.php?t=1762
https://www.lathetrolls.com/viewtopic.php?t=1417
Unless you have a cutter yourself you'll never get to listen to the real master accuracy.
You are being way too literal, I get all of that, but that is not at all what I was talking about or indeed is the matter discussed in this thread which is simply the conformance to the theoretical playback curve, AKA the standard RIAA playback curve.

I have no control over what is cut into the grooves of any particular recording I play, likewise I have pretty limited control over the cartridge performance other than purchasing that provides matches the expected velocity response as closely as my budget allows.

The discussion here is about optimizing the pre-amplifier response as closely as possible to the RIAA playback curve. In the particular case I referenced response deviation referred to is between the theoretical ideal and the measured response of my pre-amplifier - which practically speaking has a first order roll off where one should not exist.due to a long ago decision to optimize gain over extreme accuracy in the LF. Today I have a system that plays down to below 20Hz so adherence to the theoretical electrical response down to 20Hz seems a worthwhile goal - even if practically speaking it matters not at all. I think I've mentioned that my enthusiasm for analog and vinyl in particular has waned greatly with the arrival of truly affordable killer dacs from a variety of sources. So for me this is just fun, not much invested emotionally in the technology or any discussion related to it.
 
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The network has to be built with standard 1% resistors and 2% capacitors (standard values or combinations thereof).
Ed
No it doesn't. Much tighter tolerance parts (excluding supply chain issues) have been available off the shelf for years. I have made the conversion to mostly SMD resistors which are readily available in 0.1% tolerance at 10ppm at reasonable cost. You can buy 1% capacitors from Vishay, and you can select/match/trim to tiny fractions of a percent if you have high accuracy LCR meter. This is all comparatively easy for an experienced diy'er, manufacturers of bespoke phono stages at least in some cases do the same. Not practical in cost effective, mass produced gear, but binned parts are available at a premium from some passive component suppliers for manufacturers that want to guarantee somewhat tighter conformance to the standard.
 
I'm always litteral with reproducing real vinyls on real turntables with real cartridges using real phono preamps that we listen with real ears on real speakers in real rooms ...I just can't be other than lazy at learning anything about a technology that's been develloped for 6...7 decades.
I simply want quick results that are good enough for listening a totaly unpredictable vinyl copy made by a real company that needs to deliver hundreds of thousands of them without too much quality controll that I buy from a real store who looks for the best bargain while selling it to me for the price of a good indian replica of an Audemars Piguet or Rolex watch...