On this page I want to give some background on active filter design for RIAA amps. Some time ago I decided to build some amplifiers according to the principles of "less is more". Of-course this was nothing new, since almost every tube based amplifier is built around that concept. But in this case I was inspired by the gainclone principles, building amplifiers with monolithic power Opamps and a matching phono amp using opamps as well.

On this page I want to give some more background based on my experience with building the PhonoClone and GainPre phono amplifiers that were built with opamps. Both Phonoclone and GainPre have hybrid filtering: Part of the RIAA filter is included in the feedback loop and the highest pole is passive in between the first and the second Opamp stage. Of-course the active filtering (or negative feedback) principle is usable for tube projects as well. In fact, the Hounddog amplifier was based on the same principle of feedback. Anyway, I'll describe the principle using opamps.

The idea behind the feedback is as follows, design an amplifier with more gain (and bandwith) than necessary and use the feedback loop to the amplifier to selectively reduce amplification. Apart from filtering unwanted frequencies, feedback loops have a positive impact on noise and distortion as well.

These unwanted signals could be certain frequencies.

On the right is a figure with a basic amplifier circuit for opamps. In this
case`the amplification of this design is given by *V
= 1+R2/R1. (* see OpAmp background
article for relevant formulas) *as it is a non-inverting
design. In this example all frequencies on the output of the opamp are equally
fed back to the negative input and therefore the resulting amplification factor
is equal for all frequencies resulting in a flat curve.

By changing R_2 from a fixed resistor to whatever type of impedance that is
dependent on frequency, we construct a filter.

A simple way of building an active filter is to replace the single feedback resistor R1 with the right mix of filter components such as resistors and capacitors. In figure 3.2 on the left, the feedback resistor R1 is put in parallel with a capacitor C1 resulting in a low-pass filter. Since a RIAA filter is a combination of two low-pass filters this basic filter is very important and needs to be used well in designs that use feedback.

Even without looking at the formula it is easy to understand the behaviour of the amplifier at low frequencies. As the capacitor will have a high impedance for low frequencies, probably much higher than R1, we would expect the impedance of Z1, the parallel impedance of R1 and C1 in the feedback loop to near to R1 and the gain will reach it's maximum at: 1 + ( R1 / R0 ). For very high frequencies, the capacitor will have an impedance that might be much lower than the feedback resistor R1 resulting in a total feedback impedance Z1 much lower than R1 and thus a lower gain as well. The resulting impedance for a capacitor in parallel to a resistor is given by the following formula:

In the formula, when substituting 0 for w (the frequency component) the formula
for Z1 will be simplified to R1. For higher frequencies the nominator changes.In
fact, when simplifying the formula for higher frequencies R1 has disappeared
from the feedback impedance and it is dependent on *w*
and *C1* only.

Similarly, we can create a hi-pass filter by bypassing the resistor R0 with
a capacitor. Since I did not need a high-pass filter in my RIAA amp, I will
not further discuss this filter here but I hope the principle is clear.

A low-pass filter is not sufficient for building a RIAA phono amplifier. After all, it makes the curve break at a timepoint t =1/( 2 * pi * freq ) which is 50Hz/3180 uSec and 2120Hz/75uSec for reproduction. These point on the RIAA curve where it breaks down are called "poles". Unfortunately, we cannot build our amp with low-pass filters alone. We also need points on the frequency curve where it breaks and bends up again. These -3dB points are at 500Hz/318uSec and for the hidden 4th time constant at 50kHz/3.18uSec, and these breakpoints on the curve are called "zero's".

Therefore, in the next section we will deal with these filters.

Figure
3.3 contains a typical pole-zero filter that is used in RIAA filter designs.
For the moment, do not pay attention to the values in the figure as there are
numerous combinations of sensible values for *R0, R1, R2 and C1*, all depending
on where you want your curve to break ( up or down). In this section I want
to have a second look at such a filter and determine based on the time constants
*t1* and *t2* where t1 determines where we want the curve to bend
up (the so-called pole) and t2 determines where we want it to flatten again
(the so-called zero).

Figure 3.3 contains a part of the PhonoClone design (the actiev filter for 50/500 Hz breakpoints), and therefore the values for the components are not chosen random. on page 5, the design of PhonoClone is documented extensively but the formulas in this section are needed for a better understanding of page 5.

When we want to use formula 3.2 and for example check the values in figure 3.3, we have to use the right time constants for t1 and t2. Since it's part of PhonoClone, I used the RIAA time constants for 50 Hz and 500 Hz, 3180 uSec resp. 318 uSec.

It is relatively easy to find the transfer function of a pole-zero filter (we'll do so in a minute) and put it in a spreadsheet to calculate the filter behaviour. It is even simple to compare the output of the filter against the ideal RIAA curve or any other. But in order to avoid lot's of try-and-error in order to find the best values for resistors and capacitor in the filter we'll better find the pole and zero in the transfer function and calculate the best values from there.

In the formulas above it is easy seen that the product of R1 and C1 gives t1=3180e-6.
Therefore, pick either R1 or C1 and the other will follow. With the last formula
for calculating R2 (who did expect that it was so easy after all) it is possible
to find a matching value for R2 to the values of R1 and C1 already found.

Be careful to choose R1 and R2 such that the amplifier gives enough gain, even in the filtered frequencies. Not all opamps like to work with unity gain or a gain below 5, so choose your components such that over all frequencies the gain is acceptable to the opamp.

Finally, for those building amps with inverted configuration, here are the formulas for calculating the component values for pole-zero (t1, t2). In general the pole-zero values for timeconstants t1 and t2 will be 3180e-6 and 318e-6 sec for the 50 and 500 Hz breakpoints. However, the formula below is also usable for breakpoints 2122 and 50000 Hz when using timeconstants t1= 75e-6 and t2= 3.18e-6 sec.

It's good to know that building an active RIAA filter with two Opamps is so simple to calculate. On page 5, a template for building a complete phono amp based on these formulas is found.

It
is also possible to build a complete RIAA filter as part of a feedback loop.
in this case we need to have two poles and two zero pairs included in the loop.
This is why we need R4 as part of the loop. The figure on the left shows the
schematics for such an amplifier. In the figure, R2 and C2 make the filter for
the 50Hz pole and R3 and C3 for the 500 Hz pole (* pole
1 at 50 Hz for R2 * C2 = 1/w , and pole 2 at 2122 Hz for R3 * C3 = 1/w*
)

The formulas for calculating the gain are as follows:

Based on formulas 3.3, it is possible to calculate the exact gain for each frequency.
This is work for a computer, and the formulas can be easily entered in a spreadsheet
program.

When looking closer to formula 3.3 its behaviour for the low-end and high-end
frequencies is relatively easy to see. For very low frequencies (value dependent
on the capacitor values used), formula 3.3 equals *(
R1 + R2 + R3 + R4 ) / R1* which is equal to the standard gain formula
of non-inverted opamps: *1 + ( R_feedback / R1 )*.
For higher frequencies the terms with R2 and R3 will become smaller and ultimately
the gain formula could be determined by *( R1 + R4 )
/ R1* equal to *1 + ( R4 / R1 )*.
In this case, effectively R4 would be the only remaining feedback resistor,
R2 and R3 would be shorted by the capacitors for higher frequencies.

Of course, whether these extremes play a role will be determined by the value of the capacitor caps. And let's not forget that their value must be chosen such that the RIAA reproduction is as good as possible and the extremes in the audio range of 20-20kHz are between the -20dB and +20dB (relative to 1kHz=0dB).

Formula 3.4 describes the formulas that can be entered in a spreadsheet. (I have one available for those interested, but it's in draft).

For those interested I put together a spreadsheet for calculating your own 1-pass active filter.

It is important to remember however, that these formulas do not take into account
the output impedance of the opamp itself nor the input impedance of the next
stage in the ampification (integrated or preamp) as well as the cabling between
the output and the next stage. It is possible of course to make a model for
calculation of these values as well, but probably it is better to make your
life easier and use values in the filter such that the influence of these additional
parasitic components is neglectible.

For opamps, this is relatively easy to accomplish, as output impedance of opamps is low in general, and input impedance of opamps are really high. For tube amps hoewever, output impedance is a factor to take into account and the value of R_4 should be calculated with the output impedance in mind.

Also, being able to compute the correct values for resistors and capacitors will bring joy in the life of a technicia, it will however not mean that the resulting amp will sound good at all. Selection of the right components, good capacitors and resistors with 1% or better tolerance, a well designed power supply etc. are necessary to make up a good sounding amp.

A combination of partly active filtering and passive filtering is often used when building a phono amp with opamps. I call it the Hybrid RIAA filter, by lack of a better word for now. The RIAA filters for PhonoClone and GainPre are built using this principle. Below is the final (hmm) version of the PhonoClone amplifier . R1, C1 and R_2 are part of the filter in the feedback loop. This filter manages the 50 Hz pole and 500Hz zero. The second filter dealing with the higher frequencies is defined by R3, C3 and Rx. This passive filter makes the 2122Hz (75uSec) pole and the 50kHz zero.

The design of such a hybrid amp is discussed in (much) more detail on page
5, on the example page for Opamp RIAA amps.

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Page 1: Introduction << Page 2: Passive RIAA filters |
Page 4: Tube examples >> |

Page last modified: October 31, 2006