Passive Filter construction

How to make a good RIAA filter? This is a tough one to answer, as every component modifying the signal is in effect a filter, intentionally or not. However, for RIAA equalization just a few simple components are enough to alter the signal significantly: Two capacitors and four resistors are all it takes (sometimes a few more components). Unfortunately, there are many factors other than these capacitors and resistors involved which makes all the difference, especially with a RIAA filter network such as the parasitic capacitance of wiring.

Capacitors are components best suited to make a (RIAA) filter, although we could use other components such as coils etc.

Let's assume we would like to make a RIAA filter and we have chosen (based on preference or tolerance etc.) a 22nF capacitor for the 50 & 500Hz point and a 8.2 nF capacitor for the 2,122Hz (and possibly the hidden 50KHz) point.

The picture on the left contains a simple filter which is constructed of two resistors and a capacitor.

Here V-out= V-in * Z(R2+C1)/( R1 + Z(R2+C1) ) where Z(R2+C1) is the series impedance of a resistor and a capacitor and is calculated as R2 + 1/j*w*C1. Filling everything in gives formula 2.1 which is found below.

Based on this formula it is now possible to calculate the values for the remaining components of the filter. After all, the numerator part defines the pole, and the denominator defines the zero.

That means that for a capacitor value of 22nF, the value of R2 will be 14,454 Ohm for the zero (500Hz point), and 144,545Ohm (R1+R2) for the pole (50 Hz) which since R2 is computed above means that R1 is 130,091 (=144,545-14,454) Ohm.

A similar design can be used for the 2,122Hz pole of the RIAA curve, which can if desired be combined with a zero at the 50kHz point. The same idea can be used, only the values will be different for the 2,122 Hz point on the RIAA curve: Typical values for C2 range from 220pF to 8.2nF.

In practice however, it is a good idea to try to stick to standard resistor values where possible since resistors introduce additional noise (and capacitors do not). Therefore, final filter adjustments be better made with capacitors than resistors.

In order to make spreadsheet calculations with this model some further work on the equation needs to be done, the effective value of numerator and denominator is defined by the square roots of their products. The following formula makes calculations much more easy:

Most of the times, and especially when comparing the output of RIAA filters to the original RIAA curve, we need to calcutate the gain in dB relative to the 1kHz point.

With the above formula it is easy to calculate the filter gain in dB, and by calculating the value for 1kHz and using this value to normalise all other frequencies it is easy to get someting which should resemble the RIAA curve.

Combining two filters

Two of these filter networks would together be able to implement a RIAA network.
In theory, both filter networks can be easily combined, where the V-out of the first filter is the input for the second filter stage. Such a setup is described in figure 2.2. However, when put right behind each other in the same amplifier stage both parts of the filter will interact and influence the RIAA significantly especially if the value of R3 is small.

In this case, maybe a smaller value for C2 would have resulted in a larger value for R3 and thus decoupling of the two filter sections, however you may not want to have too much of a resistor in the signal path.

This is why many designers use a two step filtering method: The first filter is applied between the input tube and the second stage, the second filter between tube 2 and tube 3 where tube 3 is the driver for the preamplifier.

Scratch and Tweety use a one-step filter between the first stage and the SRPP. This means that special care must be taken when choosing the values for the various components. These are the moments where I really appreciate software like SuperSpice. It is easy to understand that there may be an influence between both filter sections, after all the impedance of the second section is in parallel with the series impedance of C1 and R2, but it is very difficult to compute this exact on a piece of paper. Only when R3 would be significantly higher in value, it's influence on the R2 would be neglectible.

Aren't we forgetting something?

Apart from the influence between the two filter sections, there are more parts in the design that influence the RIAA filter. For example, the output impedance Ru of the first amplifier stage is when using tubes large enough to be of influence on R1. Also, the Miller capacity will influence the second filter section in the higher frequencies. The figure below displays the components we have to take into account if we build a one-pass passive RIAA filter that is put between the input and driver section of a phono equalizer.

In short, it does not make sense to use very expensive caps, calculating everything in 5 decimals if after all that work your R1-value is off by 10K.

Other components now taken into account are:

The schematic above does not include the signal capacitor. I assume it's value is high enough not to influence the low frequencies too much. In Example 2, "Jerry", I have modelled the signal capacitor also which gives better results for smaller values of the signal capacitor and thus for the lower frequencies.

My conclusions

There are a couple of things I will keep in mind when designing the next phono amp:



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Page 4: Examples with Tubes >>
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Page last modified: October 31, 2006