Phono equalisation in the RTP3

The RTP3 RIAA network

The RIAA equalisation network in the RTP3 differential phono stage looks like this:

RTP3 RIAA EQ schematic

where RA is the 25K anode resistor on each of the input valves, and the resistor across the outputs is equivalent to the parallel combination of the 1M grid leak resistors and the 50k W volume pots (doubled up, of course).

An equivalent single-ended network

For ease of analysis we can consider this equivalent single-ended circuit:

SIngle-ended equivalent RTP3 RIAA EQ

where R1 is 50K (the two 25K anode resistors in series).

Removing the LF high-pass filter

The coupling capacitor C1 gives DC isolation between the phono input stage and the line stage (and provides a little rumble filtering), but introduces a high-pass filter at around 7Hz that is not specified by the RIAA standard. We may approximate the response over most of the audio range replacing C1 by a short circuit and then absorbing R5 into R4).

The resulting circuit looks like this:

Simplified RIAA EQ schematic and is now nice and straightforward to analyse.

Analyis of the simplified single-ended circuit

Let the RIAA time constants be t1 = 3180ms, t2 = 318ms, t3 = 75ms and t4 = 3.18ms. If this is to reproduce the required equalisation response, including the extra time constant at 3.18us, we require that R2C2=t2 and R3C3=t4.

Pushing through the algebra(I can give more detail if you like), we end up with

R1//R4=(t1-t2+t3-t4)/(t2/R2+t4/R3)

and

R1//R4=(t1t3-t2t4)R2R3/(t2t4(R2+R3))

Equating the right-hand sides of these two equations gives

(R3t2+R2t4)/(R2+R3)=t2t4(t1-t2+t3-t4)/(t1t3-t2t4)=ts=12.4924us.

So

R2/R3=(t2-ts)/(ts-t4)=32.807.

Substituting this above gives

R1//R4=(t1t3-t2t4)((t2-ts)R3/(t2t4(t2-t4))

=227.8R3

Note that this analyis only constrains the parallel combination of R1 and R4 and not the individual values. This means we can choose these to give any required DC gain, or - as Allen has done here - match the network to the anode loads of the valves.

Choosing component values

Allen states that his RTP3 circuits have a measured RIAA error of less than 0.1%. This is, of course, with all the parasitic capacitances and inductances resulting from a real-world hard-wired layout. We can, all the same, check his values against what the theory would predict in an ideal world.

The procedure is then:

  • Choose a value for C2 to start with: Allen uses 75nF.
  • Use R2C2=t2 to get R2 (this gives 4,240R: the RTP3D has 4,216R).
  • Use R2/R3 = 32.807 to get R3 (this gives 129R: the RTP3D has 150R).
  • Use R3C3=t4 to get C3 (this gives 24.61nF: the RTP3D has 24.68nF).
  • Use R1//R4=227.8 R3 to find the required parallel impedance of the anode load resistors, the grid leak resistors, the LF correction resistors and the volume control pots (this gives 29,441R).
  • Since all of the above resistances are prescribed apart from the LF correction resistors, we can subtract the parallel combination of the other three to get the latter. The anode load resistance is 50K, and this in parallel with the pots and grid bias resistors is 32,787R. The parallel resistor that is then needed to get a total of 29,441R is then 288.5K, which is a little lower than Allen's 660K
  • Alex Megann, December 2005