# RA15

## RIAA equalization filter.

### Introduction.

RA15 is an accurate RIAA equalization filter I built in order to be able to measure noise on a linear moving coil pre-amplifier.
The design is very straight-forward, should be easy to trim (I did not need to), but the component count is not minimal (series or parallel coupling is used for components in order to get non-standard values).

### Amplifier.

Fig.1: RIAA equalization plots.

Lime: Equalization used for recording.
Blue: Equalization used for playback.
t3, t4 and t5 are the corner frequencies specified in the RIAA standard.
t2 is an additional time constant specified by the IEC. It is a simple rumble filter at 20 Hz and is only used for playback.
t6 is a time constant that exist in all recording equalizers as the gain can not increase to infinity. Depending on the recording equipment this is typically 50 kHz to 500 kHz. It has been suggested to use a similar time constant for playback, but as you do not know the frequency most people prefer not to.
t2: 7950 µs (20.02 Hz)
t3: 3180 µs (50.05 Hz)
t4: 318 µs (500.5 Hz)
t5: 75 µs (2122 Hz)
To convert between time constant and frequency:
f= 1 / ( 2 * π * t ) or
t= 1 / ( 2 * π * f )

Fig.2: RIAA recording equalizer.

This is shown for reference only. I have not had any use for this circuit, but the math is the same as for the playback equalizer.

Fig.3: RIAA playback equalizer.

R1 and R2 loads the DUT (Device Under Test) with 47 kΩ.
C1 is input AC coupling. 100 µF is used because the value is used for power supply decoupling already. 10 µF is sufficient to decouple the input current noise of a NE5532.
C2, R4 and R5 sets the gain for the input stage. For 20 dB gain:
C2=1000 µF
R5=1 kΩ
R4=111.11 Ω (113 Ω // 6.65 kΩ).

2. stage is used for the time constants t3 and t4 (3180 µs and 318 µs) and the 3. stage for t5 (75 µs) and optionally t6.
I used 100 nF for both C10 and C20. Noise can be decreased by using a larger value for C10, but I did not have that.
The capacitor values are measured (I have shown the values with 4 digits, but I do not actually know what the measurement accuracy is):
#1: 99.47 nF
#2: 99.87 nF
#3: 99.87 nF
#4: 99.03 nF
As I do not want t6, R20 is 0, so the 3. stage will be the easiest to trim and capacitor #1 and #4 is used for C20.
Calculations are shown with 4 significant digits. For accurate results, use a spreadsheet and avoid rounding.

2. stage for both channels:
C10 = 99.87 nF
R11 = ( t3 - t4 ) / C10 = ( 3.180E-3 - 3.180E-4 ) / 9.987E-7 = 2.866E4 = 28.66 kΩ ( 26.7 kΩ + 1.96 kΩ )
R10 = t3 / C10 - R11 = 3.180E-3 / 9.987E-7 - 2.866E4 = 3.184E3 = 3.184 kΩ ( 2.55 kΩ + 634 Ω )
R12 does not have any influence on the frequency response, so the value is not critical, but should be identical for the 2 channels. For unity gain at 1 kHz:
R12 = 1 / ( 1 / R10 + 1 / R11 ) = 1 / ( 1 / 2.866E4 + 1 / 3.184E3 ) = 2.866E3 = 2.866 kΩ ( 2.55 kΩ + 316 Ω )

3. stage channel A use capacitor #1:
C20 = 99.47 nF
R21 = ( t5 - t6 ) / C20 = ( 7.500E-5 - 0 ) / 9.947E-7 = 7.540E2 = 754.0 Ω ( 576 Ω + 178 Ω )
R20 = t5 / C20 - R21 = 7.500E-5 / 9.947E-7 - 7.540E2 = 0
R22 does not have any influence on the frequency response, so the value is not critical, but should be identical for the 2 channels. For unity gain at 1 kHz:
R22 = R21 = 7.540E2 = 754.0 Ω ( 576 Ω + 178 Ω )

3. stage channel B use capacitor #4:
C20 = 99.03 nF
R21 = ( t5 - t6 ) / C20 = ( 7.500E-5 - 0 ) / 9.903E-7 = 7.573E2 = 757.3 Ω ( 604 Ω + 154 Ω )
R20 = t5 / C20 - R21 = 7.500E-5 / 9.903E-7 - 7.573E2 = 0
R22 does not have any influence on the frequency response, so the value is not critical, but should be identical for the 2 channels. For unity gain at 1 kHz:
R22 = R21 = 7.573E2 = 757.3 Ω ( 604 Ω + 154 Ω )

t2 is not implemented in this circuit, but if you want it, put a capacitor in series with R12 or R22.
The capacitor value in series with R12 is:
Ct2 = t2 / R12 = 7.950 / 2.866E3 = 2.778E-6 = 2.778 µF
Nearest standard value is 2.2 µF, so adjust R12:
R12 = t2 / Ct2 = 7.950E-6 / 2.200E-6 = 3613E3 = 3.613 kΩ ( 4.32 kΩ // 22.1 kΩ )
Use R4/R5 or R22 to adjust for the change in gain.

Fig.4: Power supply decoupling.

If you use a well-grounded PCB, the 10 Ω resistors, 100 µF and 10 nF capacitors are normally sufficient.
As I built this circuit on strip-board, the 100 nF was required to avoid oscillation. This capacitor goes on the underside of the board directly between the IC pins.

A brilliant script for calculating series and parallel combinations of resistors is found in [2].

### Specification.

This specification is for an amplifier with a gain of 1 ( R5 = 100 Ω, C2 and R4 not fitted ) powered from a ±15 V low-noise lab power supply.
More detailed measurements are in the file RA15_Notes.ods (link above).

 Channel A Channel B RIAA accuracy, 20 Hz-20 kHz +0 / -0.056 dB ( at 10 kHz ) +0 / -0.066 dB ( at 80 Hz ) RIAA accuracy, 10 Hz-100 kHz +0 / -0.056 dB ( at 10 kHz ) +0 / -0.066 dB ( at 80 Hz ) Voltage gain, 1 kHz 0.07 dB 0.06 dB THD+N, 0 dBu input, 1 kHz, 20 Hz-20 kHz BW 0.006% (mainly mains hum) 0.005% (mainly mains hum) THD+N, 0 dBu input, 20 Hz-20 kHz, 20 Hz-80 kHz BW <0.05% <0.05% Output noise, input shorted, 22 Hz-22 kHz -110 dBu (2.5 µV) -110 dBu (2.5 µV) Output noise, input shorted, 400 Hz-22 kHz -113 dBu (1.7 µV) -113 dBu (1.7 µV) Output noise, input shorted, A-wgt -114 dBu (1.5 µV) -114 dBu (1.5 µV) Output noise, input shorted, CCIR-468, Q-pk -102 dBu (6.2 µV) -102 dBu (6.2 µV)

dBu is dB with reference to 0.775 V.

### Accuracy.

This table shows the worst case accuracy of the amplifier with different component tolerances (using ideal component values as reference).

 Capacitor tolerance Resistor tolerance 1 kHz gain deviation Maximum deviation from RIAA response 20% 5% ±2.2 dB ±2.0 dB 20% 1% ±1.0 dB ±1.7 dB 10% 1% ±0.65 dB ±0.88 dB 5% 1% ±0.48 ±0.48 dB 1% 1% ±0.35 dB ±0.17 dB 1% 0.5% ±0.19 dB ±0.13 dB 1% 0.1% ±0.06 dB ±0.09 dB

### Construction.

The amplifier can be built on strip-board as seen below.
Connections to the OP-AMP inputs should be kept as short as possible and the connections to the ceramic decoupling capacitors should be kept short.
A ground-plane would be nice, but is a little difficult to make on strip-board.

Photo 1: RA15 component side.

The jumpers in series with the capacitors was to make trimming of the frequency response easier, but no trimming was needed.

Photo 2: RA15 bottom side.

The 3 100 nF capacitors directly across the OP-AMP supply pins was needed for stability.

None so far.

### References.

 [1] Stanley P. Lipshitz "On RIAA Equalization Networks", Journal of the Audio Engineering Society, 1979 June, Volume 27, Number 6, Page 458. Available from Audio Engineering Society for a fee. Search for "On RIAA Equalization Networks". Also available from some technical libraries. [2] Resistor calculator (series and parallel) is a brilliant script for calculating series and parallel combinations of resistors.

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