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

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.
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But that's not the topic being discussed here as I have pointed out elsewhere. I understand your viewpoint, but like doing my own thing regardless, even if it is just reinventing the wheel, I think (almost) everyone else here would agree with me.
 
I have not read the article. Rayma has a good point that the rest of the circuit may not be ideal enough to ignore.

Your passive RIAA equalization driven by a current source shouldn't have those particular limitations.
Tube RIAA circuits with global NFB are unworkable for this reason. But there are alternative topologies.
 
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All of my tube phono stages have been passively equalized, but a cascode into conventional common cathode amplifier stage buffered by CF or white CF that would provide sufficient loop gain for fairly good performance with global NFB. (80dB or more OLG can be achieved based on limited experience.)
 
I use 6S3P in the bottom and 6S4P in the top, this gets me around 46dB of gain in the first stage, the second stage adds a further 34dB (ccs loaded) - this in a passively EQ'd design. I can squeeze a bit more gain out of the first stage cascode, but requires higher voltage to accommodate the larger plate resistor. I have considered a hybrid cascode with a FET on the bottom and a tube on top, but thus far have not. Probably should since I use LOMC.. 🙂
 
This is my variant: first part with flat gain set by the mu of the triode-connected EF86, second part an inverting amplifier with RIAA correction (hence no + 1 term), low noise input termination by shunt feedback across the first part, works quite well with AC heater supply, built-in second-order Butterworth high-pass at 6.05 Hz. Disadvantages: maximum Miller effect in the first stage (about 90 pF of input capacitance with all switches off), ECC83 last stage can't deliver much current.

Measured frequency response compared to an ideal RIAA response + second-order 6.05 Hz Butterworth high-pass, 20 Hz to 20 kHz:

-0.29 dB ... +0 dB left with 10 kohm load
-0.17 dB ... +0.02 dB left with 1 Mohm load
-0.23 dB ... +0 dB right with 10 kohm load
-0.15 dB ... +0.12 dB right with 1 Mohm load

No idea how much of that is due to the measuring set-up (CD player with test CD, resistive attenuator, 1:1 probe and Hameg HM 1505 scope) or to tolerances.


Figure3.png
 
First of all 90pF still leaves enough capacitance for the input cable for most carts, second few consider miller effect adding to circuit's stabililty and better noise performance these days .Tubes can easily pick up all the phones around you.90pF will kill the Big Bang noise too.I wonder if V2A and first tube bootstrap was really necessary.With tubes the input series resistor of V3 and riaa network inpedance can be much larger than with the usual opamps used in phono preamps due to their native grid currents being so low.Lowering those values add to SNR, but having one more tube fillament noise(V2) to deal with is annoying.Probably using D3A or other higher transconductance tube for V1 and V3 would remove entirely the need for V2.When builders reffer to darker triode wired D3A sound, they actually pimpoint the lack of high frequency oscillations and associated microphonics as I could measure 25khz sqw on such a triode wired d3A.I don't know EF86 FT parameter, but withD3A you don't want 110Mhz bandwidth in open loop circuits honestly.
 
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The catch is that the actual circuit's open loop gain will vary more than is implied.
The model of a fixed constant gain, with one fixed pole, is not an adequate approximation
of open loop gain for this purpose. He should have done some Monte Carlo calculations
of response deviation due to random component variations in the open loop amplifier circuit,
especially including the active devices.
 
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Oh that’s quite tricky! I’ve done lots of continuous function optimisation before (finding the minimal with large number of parameters) and I’ve done integer optimisation before (where things are on or off). Is seems to mix both. The standard value part sounds a bit integer-like and minimising the error sounds continuous.

I’m interested to know more about the equations and methods if they are known!?
 
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You guys aren't remotely dealing with Ellis' recommendations for calculation of RIAA components. That was the point when I started this thread.

@jackinnj As you have read Ellis' article, could you answer this question about it:

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)?
 
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)?
Ellis proposes an optimization scheme for the cases in which R(0) in figures 2 and 3 of Lipzhitz is not equal to zero.
 
Here's a chart which illustrates the difference, using the "Ellis" values from the AudioXpress article, then using R1 of 92.152k Ohm as a seed value for the "Lipshitz" values. Gain error is adjusted to 0dB @1kHz. In both cases, R(0) = 100 Ohms.
 

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I thought I had a copy of Lipshitz's article in the attic, but I just had a look, and I actually only copied Baxandall's Letter to the Editor in which he politely explains why he finds Lipshitz's analysis unnecessarily complicated (Journal of the Audio Engineering Society, vol. 29, no. 1/2, January/February 1981, pages 47 ... 53).
 
Jack informed me that Lipshitz's figure 3 is essentially a standard non-inverting RIAA circuit. As the gain is an impedance ratio plus one, or more generally plus some constant, the gain fails to drop to zero when the frequency approaches infinity.

If I understand it correctly, Lipshitz just places the RIAA correction poles and zeros at their ideal locations and then gets an error due to the extra zero caused by the + 1 term (and explains how to get rid of it with an extra first-order filter, if desired), while Ellis tweaks the RIAA correction poles and zeros to more or less compensate for the effect of the + 1 over the audio band.
 
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