On Reference RIAA Networks
by Jim Hagerman
You’d think there would be nothing left to say. Everything you need to know about RIAA networks has
already been published. However, a few years back I came across an interesting chapter in a vacuum tube
book[1] which spoke of a mythical 3.18µs corner in the RIAA response. Huh? That’s 50kHz. The
seminal works[2][3] never mentioned this, equalization was to appear as Figure 1.
Figure 1. Desired inverse RIAA response from Lipshitz.
Hmmm. The mythical corner frequency is shown as f4 but ideally should be missing. Or should it? To
quote from Allen Wright’s book[1]:
“... look back at the graph of the recording EQ, they cut the LF and boost the HF. But do
you really think they continue boosting to way out past whatever? Of course not, they’d
burn out their cutter heads or something even more expensive ... This new 3dB point,
according to a Neumann cutting amp manual, is set at 3.18µs – which equates to
50,048Hz ...”[1]
Not only does the cutting head response have a pole at f4, but it must also have one at f5! No amplifier has
gain out to infinity. Hopefully, all cutting head manufacturers chose the same 3.18µs corner for limiting
gain. Where is all this leading? It means that the RIAA equalization networks in our phono preamplifiers
should have a zero at 3.18µs, putting back some gain before finally rolling off at higher frequencies. The
legacy reference network[2] shown in Figure 2 has an f4 pole at 337kHz – too high of frequency.
Figure 2. Legacy reference inverse RIAA network from Lipshitz.
Reference Inverse RIAA
What we need is a new modified RIAA reference curve to help us properly design phono equipment. I like
using SPICE to simulate filter circuits and decided this would be a good way to generate a new standard.
The generic filter section shown in Figure 3 is a simple lag-lead type with a zero and pole in the right
places.
Figure 3. Lag-lead filter section.
Its voltage transfer function is given by
1
s+
R1C1
H ( s) =
R + R2
s+ 1
R1 R2 C1
with zero and pole time constants determined by
τ z = R1C1
RR
τ p = 1 2 C1
R1 + R2
The lower RIAA zero-pole pair is at 3180µs and 318µs. Using an arbitrary capacitance value of 1µF, the
resistances are calculated as
τ z 3180µs
R1 = = = 3.18k
C1 1µF
R2 =
R1τ p
=
(3.18k )(318µs ) = 353.3
R1C1 − τ p (3.18k )(1µF ) − 318µs
The values for a second section (zero at 75µs and pole at 3.18µs) are 7.5k and 353.3 ohms respectively
using a 10nF capacitor. The final circuit is shown in Figure 4. Note, I used a voltage controlled voltage
source (E1) to decouple the responses of the two sections, otherwise the input impedance of the second
section would load the first section and alter response.
Figure 4. SPICE schematic for generating reference inverse RIAA curve.
Listing 1 is the input text file to my SPICE simulator. Figure 5 shows the resulting frequency response of
the circuit, which is also given in tabular form in Listing 2. I offset the data so that gain at 1kHz would be
0dB. I find it helpful to sweep a wide frequency range of 1Hz to 1MHz as it gives a better view of the total
response and what occurs outside of the 20 to 20,000Hz “audio band”.
PSPICE Input
Inverse RIAA Curve
Vin 1 0 ac 1
R1 1 2 3.18k
R2 2 0 353.33
C1 1 2 1u
E1 3 0 2 0 1.0
R3 3 4 7.5k
R4 4 0 353.33
C2 3 4 10n
.ac dec 20 1 1000k
.print vm(4)
.probe
.end
Listing 1. SPICE input file for generating modified reference curve.
Figure 5. SPICE output of reference inverse RIAA curve with 1kHz set to 0dB.
Modified Inverse RIAA
frequency dB frequency dB frequency dB
10.00 -19.74 223.9 -7.43 5012 8.18
11.22 -19.70 251.2 -6.64 5623 9.04
12.59 -19.64 281.8 -5.88 6310 9.92
14.13 -19.58 316.2 -5.15 7079 10.81
15.85 -19.50 354.8 -4.46 7943 11.72
17.78 -19.40 398.1 -3.81 8913 12.63
19.95 -19.27 446.7 -3.20 10000 13.55
22.39 -19.12 501.2 -2.63 11220 14.46
25.12 -18.94 562.3 -2.11 12590 15.37
28.18 -18.72 631.0 -1.63 14130 16.27
31.62 -18.46 707.9 -1.19 15850 17.17
35.48 -18.16 794.3 -0.77 17780 18.04
39.81 -17.80 891.3 -0.38 19950 18.89
44.67 -17.40 1000 0.00 22390 19.71
50.12 -16.93 1122 0.38 25120 20.50
56.23 -16.41 1259 0.77 28180 21.25
63.10 -15.84 1413 1.17 31620 21.96
70.79 -15.22 1585 1.60 35480 22.62
79.43 -14.55 1778 2.07 39810 23.23
89.13 -13.83 1995 2.57 44670 23.79
100.0 -13.09 2239 3.12 50120 24.28
112.2 -12.31 2512 3.72 56230 24.72
125.9 -11.51 2818 4.36 63100 25.11
141.3 -10.70 3162 5.05 70790 25.44
158.5 -9.88 3548 5.78 79430 25.72
177.8 -9.05 3981 6.55 89130 25.96
199.5 -8.23 4467 7.35 100000 26.16
Listing 2. Results from SPICE simulation.
New Network Design
Figure 2 can be modified to achieve the desired results. In order to shift the high frequency pole the value
of R3 must change. Unfortunately, this also changes the gain of the network. However, by moving part of
R3 to the input side, we can control both gain and pole frequency independently.
A reference network should interface nicely between test equipment and phono preamplifiers. Therefore, I
selected the following design parameters:
• 50 ohm source impedance (many generators do not use the 600 ohm audio standard)
• 600 ohm output impedance
• Dual output gains of –40dB and –60dB @1kHz
• Standard capacitance values.
Figure 6 shows my new modified RIAA network.
Figure 6. Modified inverse RIAA circuit.
Optimizing component values is easily done by iterative SPICE simulations, but a good starting point is
needed. Approximate values can be calculated by utilizing known boundary conditions. Since output
impedance should be 600 ohms, and the two outputs are 20dB apart, we can write
R3 + R4 = 600
R4
= −20dB = 0.1
R3 + R4
Solving we get
R4 = (0.1)(600) = 60
R3 = 600 − 60 = 540
At high frequency the capacitors appear as short circuits and the network simplifies to a resistor divider
comprised of R5, R3, and R4. From Figure 5 we see that high frequency gain is about 27dB higher than at
1kHz. Since desired 1kHz gain is –40dB, our high frequency gain will be about –13dB. The gain equation
dB = 20 log AHF
is rewritten and solved as
dB −13
AHF = 10 20 = 10 20
= 0.22
High frequency divider gain is then given by
R3 + R4
AHF = = 0.22
R3 + R4 + R5
and we can solve for R5
R3 + R4 600
R5 = − R3 − R4 = − 600 = 2.1k
AHF 0.22
At low frequency we have the opposite effect and the capacitors appear as open circuits. The divider again
is resistive and has a gain of –60dB. This is written as
R3 + R4
ALF = = 0.001
R1 + R2 + R3 + R4 + R5
and the equivalent series resistance of R1 and R2 is solved as
R1 + R 2 = 999(R3 + R4 ) − R5 = 597k = Req
Our high frequency pole at 3.18µs is equal to the series resistance of R3, R4, and R5 times the equivalent
series capacitance of C1 and C2. This capacitance is given by
CC
Ceq = 1 2 =
3.18µs
=
(3.18µs ) = 1.2nF
C1 + C 2 R3 + R4 + R5 600 + 2.1k
Finally, we have four equations and four unknowns
R1C1 = 75µs
R2 C 2 = 3180µs
C eq = 1.2nF
Req = 597k
I’ll spare you the math, R1 is solved as
(R1C1 )(R2 C 2 ) − (R C )R
1 1 eq
C eq
R1 = = 50k
(R2 C 2 ) − ( R1C1 )
and R2 as
R2 = Req − R1 = 597k − 50k = 547k
and the capacitors as
75µs
C1 = = 1.5nF
R1
3180µs
C2 = = 5.8nF
R2
These are only starting values. For a best fit real world design I optimized for the nearest 1% resistor and
standard capacitor values (as shown in Figure 6).
Comparison: Old vs. New
As a reference network the performance must be pretty good. Figure 7 shows the frequency response
errors relative to Listing 2. My new network is accurate to within +/-0.1dB over the full frequency range.
For comparison I ran an error simulation of the Lipshitz network in Figure 2. It is extremely good up to
about 10kHz where it drops off as expected due to the missing 3.18µs corner. The Lipshitz circuit can,
however, be modified by adding a 3.83k resistor as R5 at the input to reposition the high frequency pole.
Figure 7. SPICE generated error responses for Lipshitz and Hagerman networks.
To check the sensitivity of component values I ran a few more simulations varying capacitances by 5%.
Errors remained within +/-0.3dB.
I hope this information is helpful to designers of high end audio equipment.
References
[1] A. Wright, “The Tube Preamp Cookbook”, Vacuum State Electronics, 1995.
[2] S. Lipshitz, and W. Jung, “A High Accuracy Inverse RIAA Network”, Audio Amateur, 1980.
[3] S. Lipshitz, “On RIAA Equalization Networks”, JAES 1979.
[4] “AN-124: Three High Accuracy RIAA/IEC MC and MM Phono Preamplifiers”, Analog Devices, 1992
[5] M. Giles, “Audio/Radio Handbook”, National Semiconductor, 1980
[6] A. Wright, “Secrets of the Phono Stage”, Sound Practices #15, 1998
Sources
The network of Figure 6 is available as a kit (order #KF-1) from Old Colony Sound Lab for $25. The two
channel kit comes complete with PCB, 1% metal film resistors, 2% polypropylene capacitors, connectors,
and instructions.
Old Colony Sound Lab
PO Box 876
Peterborough, NH 03458-0876
603-924-6371
http://www.audioxpress.com
