**The RTP3 RIAA network**

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

where R_{A} 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:

where R_{1} is 50K (the two 25K anode resistors in series).

**Removing the LF high-pass filter**

The coupling capacitor C_{1} 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
C_{1} by a short circuit and then absorbing R_{5} into
R_{4}).

The resulting circuit looks like this:

and is now nice and straightforward to analyse.

**Analyis of the simplified single-ended circuit**

Let the RIAA time constants be t_{1} = 3180ms,
t_{2} = 318ms, t_{3} = 75ms and t_{4} = 3.18ms.
If this is to reproduce the required equalisation response, including
the extra time constant at 3.18us, we require that
R_{2}C_{2}=t_{2} and R_{3}C_{3}=t_{4}.

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

R_{1}//R_{4}=(t_{1}-t_{2}+t_{3}-t_{4})/(t_{2}/R_{2}+t_{4}/R_{3})

and

R_{1}//R_{4}=(t_{1}t_{3}-t_{2}t_{4})R_{2}R_{3}/(t_{2}t_{4}(R_{2}+R_{3}))

Equating the right-hand sides of these two equations gives

(R_{3}t_{2}+R_{2}t_{4})/(R_{2}+R_{3})=t_{2}t_{4}(t_{1}-t_{2}+t_{3}-t_{4})/(t_{1}t_{3}-t_{2}t_{4})=t_{s}=12.4924us.

So

R_{2}/R_{3}=(t_{2}-t_{s})/(t_{s}-t_{4})=32.807.

Substituting this above gives

R_{1}//R_{4}=(t_{1}t_{3}-t_{2}t_{4})((t_{2}-t_{s})R_{3}/(t_{2}t_{4}(t_{2}-t_{4}))

Note that this analyis only constrains the parallel combination of
R_{1} and R_{4} 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:

Alex Megann, December 2005