Tube DIY Asylum: How to design a passive single-network RIAA (two tubes) by Kurt Strain

To calculate the correct values for this RIAA phono preamp equalizer, except for using 6922 triodes to make a different case, I developed the following formulae for anyone wishing to implement this single network two-tube topology. I hope the work is appreciated.

The things you need to know beforehand (gather the data):

For the 6922:
mu = 33, rp = 2.9K, gm = 11.5 ma/V, Cgp = 1.4 pF

The amplifier is not loaded with a CCS, but a 20K plate resistor. For simplicity I bypassed the cathode resistor. If you unbypass it then the plate resistance will go up considerably and needs to be recalculated. If you battery bias it with a small resistor left unbypassed in the cathode, again recalculate the effective plate resistance of the new circuit. This version creates an output impedance, Ro, from V1, the driving 6922, equal to:

Ro = rp || 20K plate resistance = 2.9K || 20K = 2.5K ohms.

The output resistance of V1, Ro, is something you need to add to R1 in order to get the total series resistance from a modeled voltage source, called Rs, that precedes the shunt capacitor node on the other side of R1.

Now that the preliminaries are out of the way, Iâ€™m not going to derive the complete transfer function here because you donâ€™t need to know. You want to plug and chug and get a real good passive RIAA going.

First choose C1, a value that makes sense. The one criterion that C1 should meet is that it should be much larger than [3*Cgp*(mu+1)] + 20pF using V2â€™s parameters, a good rule of thumb to avoid inaccuracy due to input capacitive loading from V2 and some stray capacitance. For the 6922, this value is [3*1.4pF*(33+1)]+20pF = 163pF. â€œMuch largerâ€ means 50 times larger to avoid an error of about 2%, or you can simply add the amount of capacitive loading to C2 later for greater accuracy. Neglect that in this example.

Iâ€™m going to try one I know works here. Set C1 = 0.033uF, which is 200 times more capacitance than my rule of thumb says, 163pF. I can forget about adding the loading capacitance to C2 with that much room to spare.

Now calculate the exact value for R2. It happens that R2 calculates directly from the transfer function when C1 is known:

R2 = 318usec / C1 = 318E-6 / 0.033E-6 = 9640 ohms, or 9.64K.

This one gets the 318 usec breakpoint, a frequency of 500.5 Hz. Only two more values left!

Rs = series resistance talked about earlier = 6.877*R2. Thatâ€™s a known constant I calculated out that works every time, derived by iterative process:

Rs = 6.877*R2 = 6.877*9640 = 66300 ohms, or 66.3K.

From here calculate R1 necessary to get Rs = 66.3K:

R1 = Rs â€“ Ro = 66.3K â€“ 2.5K = 63.8K ohms.

Now we need to check if this value for R1 makes sense. It needs to be less than 500K to avoid isolating the drive of V1 output to the input of V2 and overcoming the effect of the 1M grid resistor on V2 (maximize this grid resistance!). It also needs to be larger than Ro so that V1â€™s importance is not critical, as this varies over time and with different 6922â€™s. Well, R1 is 25 times that of Ro and less than 500K, which is not bad. Some movement over time and variance in rp of the 6922 is to be expected, but this can work fine without a significant error. Larger ratios of R1 to Ro might be a good choice, and since we have a large ratio of C1 to the loading capacitance we might choose a lower value for C1 and try again, which will raise R2 and hence R1. Thatâ€™s something you can try.

The last value to pick is C2:

C2 = C1 / 2.915 (where 2.915 is another calculated constant that works all the time)

And so:
C2 = 0.033uF / 2.915 = 0.0113uF.

The other time constants, 3.18 msec and 75 usec, are now in place.

In summary we have our values already as:
R1 = 63.8K
R2 = 9.64K
C1 = 0.0330uF
C2 = 0.0113uF

...to 3 significant figures. If you choose Caddock values for resistors and standard capacitor values, the following choices are close:

R1 = 64.9K
R2 = 9.76K
C1 = 0.033uF
C2 = 0.01uF + another 0.001uF in parallel = 0.011uF.

Choose close tolerance parts, +-1 percent or better for the resistors and +-5 percent or better for the capacitors should be sought. But really itâ€™s better to select measured capacitors for even closer values for better precision than 5%, 2% being much more desirable.

With this circuit you can get the standard RIAA to be within +-0.5 dB without trying hard, or trim values to get them closer for better accuracy.

For further enhancement, itâ€™s possible to add in a rumble filter of -6dB/octave at around 20 Hz and maybe even a â€œhidden time constantâ€ at 3.18 usec where it stops attenuating above about 50KHz. For the 20Hz rumble filter, set the coupling cap values to do this job. For the 3.18usec hidden breakpoint (where recordings on average stop increasing treble boost), you can add a small resistor, R3, in series with C2, where R3*C2 = 3.18usec. In this case, that would make R3 = 3.18E-6 / 0.011E-6 = 289 ohms, and a 301 ohm Caddock would be close enough. The difference is a small approximately 0.6 dB boost at 20KHz.

Kurt