After building three phono equalizers (tube amps of-course) I realized some weeks ago that the (translated: site did not yet contain much information on RIAA equalization.

And even now, I'm sure there are somewhere on the net much better sources of information, but at least I could not find them, therefore I created these pages which contains the following information:

Well, anyway I hope the information on this page is at least useful to someone else. It better be for me, since I'm planning to build yet another phono equalizer based on either ECC83 or 12SL7GT tubes that will be based on experience with Tweety, yet will contain a filter setup as in Scratch.

What is RIAA equalization?

During the recording process, not all frequencies are recorded the same. Coding/Recording lower frequencies require most space on Vinyl, since the lower the frequency the wider the groove. This could result in difficulties for the stylus to follow the groove without jumping out and at the same way it reduces the recording time on the record (which is not fixed but dependent on the number of grooves that fit on one side). The solution was to reduce the amount of lower frequencies during recording and reverse this process (amplify lower frequencies) during playback.

Higher frequencies are amplified before putting them on the record, and corrected during playback. Since noise is for a large part present in the higher frequencies, so this process makes the signal to noise ratio a lot better.

In the 50's, there was no standard for the correction process mainly because record companies had not standardized the recording equalization. Amplifiers in that time therefore allowed their owner to adjust the equalization parameters. In the 60's the RIAA curve became the standard for recordings.

Please read the Wikipedia page on RIAA equalization which is quite extensive in explaining the history of the RIAA equalization

RIAA curve explained

The picture below is the very well know RIAA reproduction curve, which is found everywhere on the web. Although it is easy to find this figure, it is less easy to find how the RIAA curve is defined and how you can check your own designs against the definition. On the RIAA plot it is easy to see that the curve bends down at the 50Hz point, goes up at 500Hz and down again at 2122 Hz. At 1000 Hz there is the 0 dB point which is the reference for all other frequencies: Relative to this point, lower frequencies are amplified (> 0 dB) and higher frequencies are attenuated (<0 dB). The mid-band, between 500-2122 Hz is critical since voices are all in this band and our ears are sensitive to these frequencies.

Of-course, when building a RIAA filter in an amplifier the notion of "amplification of low frequencies" is nonsense. The filter in between two amplifier stages will not amplify AT ALL, it will merely filter higher frequencies stronger than the lower ones. It doesn't matter since it is relative anyway, since we assume that the 1000 Hz point is our 0dB point and the "amplification"-factor of other frequencies are relative to this 0-dB point.

In the spreadsheet output above, clearly is shown the RIAA curve in blue and the asymptotic lines in red that are responsible for the curve: At 50 Hz, 6 dB per octave , between 500 and 2122 Hz a flat response and after 2122 Hz the curve falls again with 6 dB per Octave.

But as explained above, since this is a reproduction curve, it means that it shows how to correct the frequencies of a phono cartridge during playback such that over the frequency band all frequencies are correctly reproduced. Normally this means that RIAA correction is done with a filter that is built-in in an amplifier. And therefore it doesn´t really matter what the absolute values are for the RIAA curve that we or you use, as long as the relative values over the frequency band match. For example for 20Hz it needs to be nearly 20dB more than for the 1000Hz point. The curve is often plotted between 20 and 20000 Hz, with the 0dB point at 1000 Hz. Of course the curve also works for frequencies lower than 20 Hz (especially with today's DC coupled amps) and for frequencies higher than 20000 Hz as you can read below.

How to calculate

The standard RIAA reproduction filter has one zero (t3) and two poles (t1& t2):

With the formulas given above it is very easy to plot the RIAA correction for every frequency desired or for a range of frequencies. Of-course I did so, and the results are available in an Excel file for those interested, or comparison of your own projects against the RIAA standard.


Frequently Asked Questions on above Formula 1.1

1. Why does the formula above, and your spreadsheet, provide different results form the tables found on the web and in books?

Please keep in mind that for this calculation the 1000 Hz point should be at 0 dB and therefore you will have to subtract the value for 1000 Hz from every value you calculate with the formula. In most cases, therefore 20 dB is added to these results in order to have the 0dB around 1000 Hz. Please do the math with the spreadsheet and add 20 dB to all calculated values and you´ll find that the results are the same as found in those tables.

2. So why would we need the spreadsheet?

Well if you don´t need it, please don´t use it and use a standard table. For me it was important to calculate the correct formulas myself and build a spreadsheet file.
On the web, I always find the same table which gives the RIAA calculations for a limited set of frequencies ranging from 20 Hz - 21000 Hz. And for my projects I need to work with both lower and higher frequencies, I want the 1000 Hz point calculated and I need to use frequency values that are equal to the values that are exported in simulation software. And these software packages use completely different values and were therefore not usable.

3. How come that your calculated values do not match exactly with the tables I find?

That is because most sources calculate the RIAA curve and correct 20 dB to get the 0 dB point for 1000 Hz. Unfortunately the correct calculated value for 1000 Hz is 19.911 dB and therefore the correction of 20 dB may be used but is strictly spoken not correct (my feelings). the difference of 0.09 dB is by the way far to small to be audible. So, since the calculated value for 1kHz is -19.911dB, subtract this value from all other calculated RIAA values and you will reproduce the perfect RIAA curve.

4. So you say that the formula above is equal to the one found on other places, except that you have to add 20 dB to get the 0 dB point at 1000 Hz?

This is because LOG calculations are difficult in nature. Let me illustrate by a few calculations in the section below yielding formula 1.1.b.

Alternative RIAA Formula 1.1.b

Below I did some calculations on the formula 1.1 as described above. Let me prove that Formula 1.1 when corrected for the 0dB point at around 1000 Hz can be rewritten such that the formula produces exactly the RIAA curve but still most people would think it is a totally different formula. If have used some colors in the text below to easily group certain fomulas and explain my point. Please pay attention to the values of 20 dB in red.

So as you can see in the calculations above the formulas as found on websites such as Bonavolta are first of all correct but are really the same formulas as formula 1.1 only corrected with 20 dB. But please be careful, I found a lot of formulas that look very similar to the one above but are not correct, some of them contain writing errors others use incorrect values for t1, t2, t3.


The "improved" IEC version of RIAA

Years after publishing the standard RIAA reproduction curve described above, an enhanced version was proposed. Reason for this proposal was (according to literature) that amplifier equipment at that time was more and more using DC-coupled which meant that low frequencies (turntable rumble) would be reproduced better than before.

The solution was simple: define a 4th timeconstant on the curve and define it as a hi-pass filter. This would make the curve ramp up from 20 Hz and have it's maximum value around 31Hz instead of 20 Hz for the standard curve.

Please add 20dB to the output of the formula above to get the output corrected for and relative to the 1 Hz frequency point.

The following figure contains the plot for the IEC RIAA curve for 20-20kHz. Clear is to see how the lowest frequencies are filtered compared to the standard curve.

Still, the IEC version has not become very popular, as most manufacturers seem to think that turntables, arm and cartridge combinations should be of such high-quality that the problem should not arise in the first place.


Enhancing the RIAA Reproduction Curve

But there is a better way for improving the good'ol RIAA curve. Today, there are many people that deliberately add a second zero timeconstant to the RIAA curve. This is because the cutter of the records will beyond a certain point not be able to get higher frequencies on the record with an extra amplification of 6dB/octave. Record cutter manuals seem to specify 50kHz as a roll-off value. As a result, there must be a fourth timeconstant at 50 kHz that defines how the RIAA curve should flatten out.

For comparing our own phono amplifiers against this "enhanced" reproduction curve, it would be so nice if our spreadsheet would enable comparison against both the standard reproduction curve and the enhanced one.

OK, let's see what happens if we put this formula in a spreadsheet and plot the resulting transfer function in a chart. It is too early to tell what the effect of such a fourth time constant is on the sound of my phono preamps. In the designs for Lookie, Jerry, PhonoClone and GainPre I have included a fourth time constant in the design, but I did not stick to the definition but made the amps behave in between the standard and the enhanced RIAA curve.

As shown in the chart (in purple line), around 10kHz the curve will slowly "bend" making sure that higher frequencies are no longer filtered 6dB/octave. Hopefully, implementing this enhanced curve will reveal details in your recordings that did not appear with your "old" phono preamplifier.

Phase Response

According to literature for a transfer function phase shift is defined as the arctangent of the real part divided by the imaginary part of the equation.

The phase of Loekie, PhonoClone is similar to this ideal phase curve. For filter designs based on the standard RIAA curve without the 4th time constant the phase curve differs for the higher frequencies.

Above you find the resulting phase plot of the enhanced RIAA curve in an Excel chart. For each of the time constants the phase contribution is plotted separately and the total phase shift in plotted in bold (purple).


Passive or Active Filtering

In order to reproduce the signals from our turntable as meant during recording, we have to use a reverse RIAA filter (=RIAA reproduction filter) on the signal. A filter is according to Webster defined as:

A filter is a device that passes electric signals at certain frequencies or frequency ranges while preventing the passage of others.

There are basically two ways for constructing a RIAA filter:

  1. The first method is the power method: Build an amplifier with enough gain and construct a filter on it's output (or between two stages of an amplifier) such that the resulting transfer function equals the RIAA reproduction curve. Enough gain in practice means 60-70dB gain for a MC cartridge at 1 kHz. And since the RIAA curve at 20Hz is about 20dB higher, it means that we'll have to construct an amplifier with 90dB gain at 20Hz. Of course, for MM cartridges this is about ten times (=20dB) lower but still a very high amplification factor. Potential difficulties include: Noise management, oscillation etc. This way of filter construction is called passive filtering.
  2. The second way to construct the filter is using negative feedback to the amplifier itself (whether this is a tube based amp or an opamp based one). In this case, the filter is built in the feedback loop and makes the amplifier alter it's amplification factor based on the feedback received from the filter; The more feedback, the less the amplification for that frequency.
  3. And of-course there is a third one in case of a RIAA filter; A mix of active and passive filtering is often used, where the lower frequencies are for example actively filtered and the 75 uSec pole passive.

Nowadays, active filtering is amongst audiophiles often considered an inferior way of filtering. However, when working with integrated components such as opamps, there is always feedback involved and therefore in my opinion it is a matter of preference and design. Therefore, use whatever

On the next two pages filter construction is explained for both types of filtering. Page 2 describes the passive filtering design and Page 3 describes active filtering which is often used in opamp designs.

References and Links

  1. Look at the Wikipedia RIAA Equalization page for some background information and history of the RIAA curve
  2. Bonavolta Site with the RIAA formula (see formula 1.1.b above) which is corrected with 20dB
  3. TriodeDick: Scratch bouwbeschrijving (Dutch)
  4. Tweety, Loekie, Jerry and PhonoClone projects
  5. Ultranalog: Odeion III project (Link removed since it links to adult sites today)
  6. Rainer zur Linde: Buizenversterkers, Toepassingen voor Hifi en Gitaar, ISBN 90-5381-011-0, 1992
  7. Rainer zur Linde:
  8. Thorsten Loesch: El Cheapo Phono Pre (© Analog Addicts 1997/98)
  9. Menno van der Veen: Moderne High-End Buizenversterkers (Book also available in English), ISBN 90-5381-089-7, 1999
  10. George Rose: Electronica Formules, Kluwer 1975, ISBN 90-2010-798-5
  11. Ron Mancini (Texas Instruments): Opamps for Everyone, Texas Instruments SLOD006B (free download on TI site)
  12. Hagerman Technology RIAA calculator and some background
  13. Andreas Hunebeck, "Zur theorie der Schallplattenentzerrung"
  14. and many, many others


^^ Back to the Background page

Page 2: Passive RIAA Filtering >>
Page 3: Active RIAA filters >>
Page 4: Tube Examples >>
Page 5: OpAmp examples >>
Page 6: Reversie RIAA circuit >>

©, May 2002
Page last modified: December 23, 2009