Single-stage active RIAA correction with second- or third-order Butterworth high-pass included

Hi all,

While thinking about ways to speed up the settling of a single-supply single-op-amp RIAA amplifier, see https://www.diyaudio.com/community/...upply-phono-preamp-design.413571/post-7702435 , I found a way to include a second- or third-order Butterworth high-pass filter. As it may be useful outside the context of single-supply circuits, I give it a separate thread.

When you just look at the topology and ignore the component values, this is a rather conventional RIAA amplifier (you could make it even more conventional by connecting R7 in parallel with C5, that doesn't matter much for the principle):

RIAAEV3tussenstap.png


Normally, C8 is used to cause roll-off in the subsonic region and the network R7...R9, C5, C6 realizes the RIAA poles and zero. In this case, however, I use C8 to realize the lowest RIAA pole at -1/(3.18 ms) and R7 to get subsonic roll-off.

Note that C8/C5 = 1000, meaning that without the subsonic roll-off, the DC gain would be 1001, a very ordinary value for a moving-magnet amplifier (1 kHz gain roughly 40 dB).

With everything ideal, at the value of the Laplace variable s where the impedance of C8 cancels the impedance of R12, the feedback disappears and the gain goes to infinity. This means that there is a pole at exactly -1/(R12C8), so if this has to be the first RIAA pole, one needs R12C8 = 3.18 ms. It's actually 3.196 ms in the schematic, pretty close.

The disadvantage of using C8 for the first RIAA pole is that C8, which has a relatively large value, needs to be accurate to get an accurate first RIAA pole. The advantage is that you can include better subsonic filtering in the loop by adding two more resistors and a capacitor.

As an intermediate step, suppose you could add an ideal inductor with a huge value between the output and the negative input of the op-amp, chosen such that it resonates with C5 at the desired subsonic roll-off frequency, and that you chose R7 such that it damps the LC circuit to a quality factor of 1/2 √2. The subsonic response would then be very close to second-order Butterworth. That's because the gain of the RIAA correction amplifier is one plus the ratio of the feedback impedance to the impedance from the negative op-amp input to ground, and that "one" is quite negligible at low frequencies. Mind you, R8 and R9 contribute to the damping of the LC circuit, but not by much. You could also choose a quality factor of 1 and design the AC coupling at the input for the same cut-off frequency. The combined response is then third-order Butterworth.

Such an ideal inductor is totally impractical, but it can be approximated with a T network consisting of two resistors with values much smaller than R7 and a capacitor to ground at the point where they are connected, see this figure:

RIAAEV3.png


The transfer from the voltage going into R11 to the current coming out of R10 rolls off at a first-order rate from some very low frequency onwards, like would be the case with an inductor.

I haven't found any simple exact equations for any of the values except R12C8 = 3.18 ms. In fact, I've been very lazy and just calculated approximate values for the other components, and then used a pole-zero extraction program to fine-tune the values.

Regarding those approximate calculations:
R12C8 = 3.18 ms to get the first RIAA pole at the right spot.

The DC gain would be 1 + C8/C5 without subsonic roll-off, so C8/C5 = 1000 gives you a midband gain of roughly 40 dB.

At s = -1/((R8 + R9)(C5 + C6)), the impedance of the network R8, R9, C5, C6 goes to zero and the gain of the circuit becomes 1. As a gain of 1 is pretty close to 0, this must be close to the location of the RIAA zero. That is,

(R8 + R9)(C5 + C6) ≈ 318 μs

At s = -1/((R8 + R9)C6), the impedance of the parallel connection of C6 and R8 & R9 goes to infinity. The impedance of the whole feedback network remains finite due to the other branches R7 and R11, C7, R10, but it does get pretty large. That means the second RIAA pole must be close, so we get the extra criterion

(R8 + R9)C6 ≈ 75 μs

The (theoretical) inductance L is chosen to resonate with C5 at the required subsonic roll-off frequency and R7 is chosen to get the desired quality factor. R10 and R11 get convenient values much smaller than R7 with R10 also much greater than R12. We then have

C7 = L/(R10R11)

Best regards,
Marcel
 
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Is it possible to use several ceramic capacitors in parallel for C8 instead of electrolytic? I have just tried using the box of cheap Chinese capacitors. I got to 6.8 uF with just three of them in parallel. As a rule of thumb, their values may jump around in the same batch, especially for higher ones. Their relatively high-temperature dependence is not very significant in this application: warming them up to a body temperature from the regular room conditions moved the capacitance from 6.83 down to 6.79, which should be acceptable, I believe.
 
A film capacitor would be the best option, and it would be quite feasible at 6.8 μF. With a 5 % tolerance, capacitor inaccuracies could cause an error of about 0.4 dB well below 50 Hz, if you have the bad luck that you get the worst capacitors that pass the production test. Example of a suitable film capacitor: https://www.reichelt.de/mks4-pet-kondensator-6-8-f-5-63-vdc-rm-15-mks4-63-6-8--p172806.html This is MKT; polypropylene would be even better, but much larger.

Bipolar electrolytics are used all over the place in loudspeaker crossover filters, so they should be reasonably stable - loudspeaker crossover filters cross over in the middle of the audio band, where deviations are probably more noticable than at 50 Hz and below. They are generally less accurate than good film capacitors, though.

I wouldn't use ceramic capacitors, as they are bound to be class 2 at these values. Maybe you could get away with the nonlinearity because of the low signal level across C8, but there is also microphony, long-term drift (ageing) and temperature dependence, and the initial tolerance isn't very good either.

C7 is less critical, as it mostly affects the subsonic response, and C3 is not critical at all, as it only affects the deep subsonic response.
 
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I believe production tolerance is not a big issue unless the goal is batch production. For a single-device design, one may pick the capacitor with a value slightly below the nominal and use one or two film capacitors of a smaller value to get the exact match.
 
I believe production tolerance is not a big issue unless the goal is batch production. For a single-device design, one may pick the capacitor with a value slightly below the nominal and use one or two film capacitors of a smaller value to get the exact match.

Yes, of course. If you have the equipment to accurately measure capacitance and resistance, you can measure R12, calculate C8 = 3.18 ms/ R12 and aim for that value, rather than the rounded value of 6.8 μF.
 
I wouldn't use ceramic capacitors, as they are bound to be class 2 at these values. Maybe you could get away with the nonlinearity because of the low signal level across C8, but there is also microphony, long-term drift (ageing) and temperature dependence, and the initial tolerance isn't very good either.

Forgot one thing: there is a DC bias voltage across C8, which would reduce its capacitance if it were a ceramic class 2 capacitor.
 
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That could very well be, I tend to unintentionally reinvent things. For example, I came up with a distortion cancellation scheme for differential pairs in the 1990's and read a few months ago on this forum that the basic idea was already used in valve amplifiers in the 1950's.

The resistor-capacitor-resistor T-network was quite common in discrete transistorized RIAA amplifiers of 50 or so years ago, but I don't know if realizing the 3.18 ms time constant with R12 and C8 was ever done back then. Is that how it was done in the Radford (?) amplifier?
 
What do you mean by T6?
T6 is the final zero introduced by the series-feedback configuration due to the gain never falling below 1, so T5=75uS cannot continue downwards at 6dB/octave forever (Lipshitz numbering). In this circuit it is given by C5C6/(C5+C6)*R12 = 0.781uS ~= 200kHz, which is high enough not to worry about. If it gets below 100kHz you need to add an extra passive pole at the end to compensate for it. See Lipshitz passim, especially Table 1(b).

Your scheme models pretty well under the Lipshitz calculations. I'm unclear how exactly interchanging the lower LP and HP poles and frequencies can work, but it does.