RIAA Preamps
By John Broskie
Contents:
 Phono Preamps
 RIAA Equalization Modeling in SPICE
 Active RIAA Equalization
 Simpler Active RIAA Equalization Preamp
 Passive RIAA Equalization
 12AX7 Phono Preamp Example
 Split RIAA Equalization
 Conclusion
Phono Preamps
Phono preamps haven't disappeared; well, at least not yet. In fact, interest in phono preamps seems to grow steadily, as many audiophiles (and quite a few music lovers) transfer their old record collections to CDRs or MP3 files. Like the groom who buys his first (and last) expensive haircut before his wedding, many are seeking a better phono preamp than the one that came in their old receiver, knowing that this playing of their old records will be the record's last playing. Thus, some adventurous home constructors are building discrete transistorbased preamps, hoping to avoid the "cheap IC sound," while others are building opampbased phono preamps that use premium ICs and run on batteries, while others still are building tubebased preamps to bridge the sound on their records to the ADC in their computer. (From vinyl to diamond to vacuum to silicon to paper: this quite an odd path to your ears, if you think about it.)
Regardless of the underling technology used, a phono preamp must undo the RIAA (Recording Institute Association of America) equalization curve or the CCIR (Comité Consultatif International des Radiocommunications, the European version of the RIAA) curve used in making the record. Why was this curve imposed on the records? Using it improved the signaltonoise ratio of the record by boosting the highs going to the cutting head, while greatly extending the playback time by cutting the lows. The end result was a fairly even grove cut, regardless of the frequency. The inverse of the RIAA curve returns the signal to flat by cutting the highs and boosting the bass. (Bare in mind that most records made before 1950 may not have followed the RIAA curve, but some other proprietarytotherecordlabel curve.)
Frequency 
Attenuation in dB 

Frequency 
Attenuation in dB 
10 
19.74 

1000 
0 
20 
19.27 

1200 
0.61 
30 
18.59 

1500 
1.4 
40 
17.79 

1800 
2.12 
50 
16.95 

2000 
2.59 
60 
16.1 

3000 
4.74 
80 
14.51 

4000 
6.61 
100 
13.09 

5000 
8.21 
120 
11.85 

6000 
9.6 
150 
10.27 

8000 
11.89 
180 
8.97 

10000 
13.73 
200 
8.22 

12000 
15.26 
300 
5.48 

15000 
17.16 
400 
3.78 

18000 
18.72 
500 
2.65 

20000 
19.62 
600 
1.84 

30000 
23.12 
800 
0.75 

40000 
25.6 
This reverseequalization (deemphasis equalization) can be performed in either an active or passive fashion. The active method works by selectively varying the amount of output signal given to the preamp's negative feedback input (in relation to frequency). The passive method places a complex filter network in series with the signal, which then shapes the desired equalization curve by shunting to ground (based on frequency) portions of the signal. Active equalization overcomes the problems of loose tolerances and part aging (assuming that the equalization parts are high quality, i.e. time stable and tight tolerance). On the other hand, passive equalization cannot not be voltage overloaded nor can it bring the preamp to oscillation. Both methods have their adherents and their distracters. Nonetheless, both methods are perfect candidates for analysis in SPICE, as the formulas are usually incomplete, assuming as they do, perfect conditions, conditions that seldom arise in actual practice.
RIAA Equalization Modeling in SPICE
With B^{2} A/D Spice we can model both active and pass RIAA preamps, as a phono preamp is a lownoise amplifier, but unlike most amplifiers, the output of a phono preamp is not flat, following instead the RIAA deemphasis curve. This makes evaluating a phono preamp's output problematic or, at least, labor intensive, with repeated visits to a equalization table (shown above) or to a hand calculator.
The realworld technique is to use an inverse RIAA equalization network in series with the phono preamp under test. These devices can be either passive or active in design. Unfortunately, they are seldom entirely useful, as they tend to add some noise and some frequency aberrations of their own to the test. (To be useful this device would have to be much better than the phono preamp under test, with wider frequency response and more accurate equalization, which is easily done when the preamp is a cheap affair, but much less easily done when the preamp is a cutting edge, highend preamp.)
In the SPICE world, this problem is easily overcome. In B^{2} A/D Spice, we can readily define the RIAA transfer function that was originally impose on the record as a standalone "black box" function, distilling just the mathematical transfer function of the RIAA equalization. Pause and considered just how useful this can be: with this mathematical "black box," the real world noise, parasitic and voltageswing limits do not exist. When placed in series with a of a phono preamp circuit that we wish to analyze in SPICE, the output should come out flat. If it doesn't, then the circuit is deviating from the correct frequency equalization contour.
How do we make this black box? We can use B^{2} A/D Spice's continuous time transfer function model. This "device" encapsulates the mathematical relationship of the output voltage vs. input voltage in the frequency domain and follows the form:
Vout(S) = Vout = a (SZ1)(SZ2)...(SZm)
Vin (SP1)(SP2)...(SPn)
where S is frequency, Vout is output voltage, Vin is the input voltage, a is a constant, Z1. Z2...Zm are the zeros of the system, and P1, P2,...Pn are the poles of the system.
The following are the available parameters
Name  Parameter  Units  Default Values 
HDeg  Highest degree of transfer function  2  
Coeff_Den  Coefficients of denominator  2 3  
Coeff_Num  Coefficients of numerator  1 2  
RIN  Input resistance  ohm  1 
ROUT  Output resistance  ohm  1 
Now, do not be frighten by the math, as it is not as bad as it looks. All we have to do is find a way to plug in the RIAA's inverse transfer function into our black box. The formula for the RIAA preemphasis (what's on the record) curve is the following:
Gain = (1 + 3.18^{3} · s)(1 + 7.5^{5} · s) / (1 + 3.18^{4} · s )
Where s equals 2pf (actually, j2pf). Converting this formula in the right form requires determining the highest degree (2) and multiplying out the numerator, which yields 0.0000002385 0.003255 1. The denominator becomes 0 0.000318 1, which will not work in SPICE because of the 0 that begins this string, so we use something close to zero: 0.000000000001 instead. The final transfer function is listed below:
Active RIAA Equalization
Let's now look at an active RIAA equalization network. Below is the classic active feedback equalization topology.
R_{2} X C_{2} = 3180uS
R_{1} X C_{1 }= 75uS
(R_{1}  R_{2}) X (C_{1} + C_{2}) = 318uS
GAIN_{DC} = (R + R_{1} + R_{2})/R
Gain_{AC} in dB= 20Log(GAIN_{DC})  20dB
The formulas look simple enough, until you actually take a hand calculator to them, as meeting the third line's condition (while using readily available part values) is tough. Below is a simple RIAA phono preamp based on Analog Device's excellent AD712 opamps, which are known for their low noise and smooth sound. ( Active RIAA Opamp Preamp.ckt Ver 4.2) ( Active RIAA Opamp Preamp.ckt Ver 2000)
Below we see the frequency response of the circuit above.
The circuit improves upon the classic topology in that the second (the RIAA equalizing) opamp runs in the inverting mode, which results in two benefits. The first is that the single coupling capacitor is enough to keep both the first amplifier's DC offset from coupling to the second amplifier and to keep the second amplifier from amplifying its own input DC offset, as resistor R_{5} does not terminate into a path that leads to ground, so it cannot define a voltage divider with resistors R_{1} and R_{2}. (In other words, the second amplifier function as a unitygain amplifier at DC, which prevents it from amplifying its own input DC offset.)
The second benefit deriving from inverting amplifier operation is that the inverse RIAA equalization curve is more closely followed, as the equalization network is effectively grounded at the opamp's negative input; whereas in a noninverting configuration, the equalization network will be thrown off by resistor R_{5}'s resistance. (Of course, the lower R_{5}'s resistance, the less the equalization's deviation.) An added benefit to running this amplifier in the inverting mode is that the 75µS (2122Hz) lowpass filter portion of the RIAA equalization is accurately followed beyond the audio band, instead of flattening out due to the noninverting amplifier's gain hitting the floor of unity gain, creating the famous fourth pole.
In other words, at extremely high frequencies, capacitors C_{1} and C_{2} become effectively dead shorts to the signal and resistor R becomes just a load resistor to be driven and the amplifier sees 100% of its output returned to its negative input, reducing its gain to unity, 1V in, 1V out. A simple RC lowpass filter is often added to an actively equalized noninverting preamp to compensate for the RIAA curve hitting the unity gain floor. How do we determine the value for the added resistor and capacitor? We start at the DC gain and deduce the frequency at which AC gain drops to unity:
T_{1}T_{2 }/ GAIN_{DC} = T_{3}T_{4}
T_{4} = T_{1}T_{2} / (T_{3}GAIN_{DC})
\T_{4} = 750µS/GAIN_{DC}
where T_{1} = 3180µS, T_{2} = 75µS, T_{3} = 318µS, and GAIN_{DC} = DC gain. Translating this time constant into a 3dB frequency is easy enough: just divide 159154.9 by T_{4 }(as µS, not seconds). For example a DC gain of 1,000 (+40dB @ 1kHz) will put the flattening at roughly 212kHz. On the other hand, some argue that record itself (and/or the cartridge) adds the missing time constant in that after a few playings, it is unlikely that the frequency response extends beyond 25kHz. Below is an example circuit that holds a compensating lowpass filter.
Is phase inverted signal a problem? If you think it is, then it
is. Fortunately, the solution is simple: just reverse the leads
that connect to the phono cartridge, which will send an inverted
signal to the preamp's input, which in turn will be inverted again,
resulting zero phase inversion (assuming the recording studio's
microphones and preamps and equalizers, mixing boards, maybe an
analogtodigital converter or two, and the cuttinghead amplifiers
all observed a consistent phasing).
A Simpler Active RIAA Equalization Preamp
By using two amplifiers we can greatly simplify the design of the preamp. Each amplifier can be made to handle one half of the equalization task. The circuit below imposes the 3180µS and the 318µS time constants on the signal leaving the first amplifier and the 75µS time constant on the second amplifier's output. In other words, the first amplifier handles the 50Hz to 500Hz shelving portion of the curve, while the following amplifier handles the 2122Hz lowpass filter portion, without any highfrequency curve flattening.
The first amplifier must have a DC gain of +20dB for the shelving to work correctly. The second amplifier gain can be set to any value (within reason). Notice that the two stages work independently of each other, which makes tuning the preamp's frequency response a much easier task. ( Active RIAA OPAmp preamp simple style.ckt Ver 4.2) ( Active RIAA OPAmp preamp simple style.ckt Ver 2001)
As can be seen in the graph above, this new phono preamp topology works quite well. Furthermore, the formulas for the setting the equalization curve are much simpler than the previous case:
R_{1}C_{1} = 3180µS
R_{2}C_{2} = 75µS
(The values in schematic above have been already adjusted to compensate for parasitic capacitances.)
Passive RIAA Equalization
Let's now look at some passive RIAA equalization networks. Passive RIAA equalization requires as little as two resistors and two capacitors. The classic configuration consists of a series resistor shunted by the combination of a capacitor and a capacitor and resistor in series. Below is the classic configuration and its values nicely represent the underlying equations for its design, as
R_{1}C_{1} = 2187µS
R_{1}C_{2} = 750µS
R_{2}C_{1} = 318µS
C_{1}/C_{2} = 2.916
Testing this equalization network is simple enough in B^{2} A/D Spice. First we add a voltage source to provide an AC signal source that can be made to sweep from 10Hz to 100kHz.
Second we add the network itself; and, finally, we add a voltage meter to the output to see the results. The following circuit was drawn in B^{2} A/D Spice and the file is downloadable here ( Passive RIAA Inversion Eq 1.ckt Ver 4.2) ( Passive RIAA Inversion Eq 1.ckt Ver 2001)
The graph follows the desired curve closely, as can be seen below.
Still as was mentioned earlier, comparing several tens of points to the table is tedious and error prone. One workaround is to have B^{2} A/D Spice create a table instead of the graph, which would allow comparing tables to tables, but there is still an easier way. We can place the RIAA inverse transfer function, which we have already covered earlier in this article, in series with the output and look for the deviations from a flat output.
Now, if we look at just the second voltage meter's output, we will see how close the network matches the desired equalization curve.
Not bad. If you think otherwise, be sure to check the units used on the two axes, 10Hz to 100kHz, not 2020kHz, and millidecibels (onethousandth of a decibel or onetenth of a mB), not dbs (decibels). If we change the Yaxis increments to dBs, then the overwhelming flatness is apparent. (Decibels differ from ohms and watts and coulombs and meters and kilos in that they do refer to any fix quantity, but rather they represent a relationship between two fixed units, such as volts and watts.)
Unfortunately, this equalization network seldom used with an infinite load impedance or a zeroohm source impedance. Well, two FETinput opamps do come close, but even in this case a coupling capacitor and ground resistor must be added to prevent the first opamplifier's DC offset from being amplified. For example, 1mV of input offset becomes 1V of DC offset at the output of a +40dB gain preamp, as the DC gain is 20dB higher than the gain at 1kHz.
How much influence will the added capacitor and resistor make to the equalization curve? The answer can be found by adding these two components to the B^{2} A/D Spice circuit.
Why didn't we add the actual opamp models to the circuit? One the things you quickly learn when using SPICE is that simple is better. If you examine the actual models provided by the opamps' manufacturers, you might be shocked to find that the models don't look anything like the opamps' actual schematics, with the models consisting of only a few transistors and a few resistors. What is going on here? Where are all the cascoded input stages and current mirrors? The answer is that the model only has to give the same results as the actual opamp, not define all of its hundreds of parts, which would only slow down or even possibly halt the SPICE engine's execution, particularly if the schematic held hundreds of opamps.
The preamp's results are not too bad, being only 1dB off at 10Hz. By the way, if you think the capacitor is the culprit here, your blaming the wrong part. The .1µF capacitor and the 1M resistor define a 3dB cutoff point of 1.59Hz, which is still far enough away from 10Hz to make no real difference. If you are still unconvinced, just remove the coupling capacitor or make its value 100µF. No, the real culprit is the 1M resistor, as it effectively reduces the 75k resistor's value to 69k, which throws the network's time constants off. Overcoming this problem requires using a source impedance of 6k or adding the 6k to the 75k to yield a 81k resistor. In the case of the opamps, the output impedance is usually well under 100 ohms, so the latter method works better, but with tube circuits, the source impedance might be even higher than 6k, which would require using a grid resistor even lower than 1M or reducing resistor R_{1}'s value. For example, a 12AX7 used in a groundedcathode configuration with a 150k plateload resistor results in an output impedance of roughly 44k (62k in parallel with 150k). When this value is added to equalization network's 75k, the error becomes more noticeable and moves in the opposite direction, giving a positive boost at 10Hz (+2.74dB).
If we reduce resistor R_{1}'s value to 37k, the output
returns to close to flat, but with a slight bump in low bass.
What would be the optimal value for resistor R_{1}? One
way to find out is to use B^{2}
A/D Spice's parameterized AC sweep test. Here we can enter
a beginning value for R_{1} and incrementally add 100
ohms to it until 39k is reached. After we run the test, we look
for the flattest graph plot.
In this case, the bold green line looks about as good as we can hope for. This line represents the 14^{th} sweep, so the value of R_{1} must be 14 times 100 ohms plus 36k (37.4k).
We can increase the accuracy of our circuit analyses by adding the gridstopper resistor and the Millereffect capacitance. Because the gridstopper resistor's value is so low compared to R_{1}'s value, this resistor's effect is minor at audio frequencies. And the Millereffect capacitance just adds to C_{2}'s value, so using a C_{2} value that accounts for the added capacitance is a good idea. Of course, some readers are going to want more than just the modeling of the equalization network; they will want the whole circuit. Well, here it is.
12AX7 Phono Preamp Example
Shown above is a complete 12AX7based phono preamp that uses passive equalization. ( 12AX7 Passive Equalization Preamp.ckt ver 4.2) ( 12AX7 Passive Equalization Preamp.ckt ver 2000)The gain at 1kHz is +49dB and the output is close to flat from 20 to 20kHz, as shown below.
The topmost graph above shows +20dB divisions; the bottom graph, 0.1dB divisions. The plotted "Gain" line is custom defined in the "Edit Signal" dialog box. Here we specify that Gain equals the signal leaving the preemphasis transfer function divided by the input signal's magnitude and then this result has 20dB subtracted from it to reference Gain to 1kHz.
Why not just plot and display the raw output signal instead? We could, of course, but then the output would not be flat, as it follows the RIAA equalization curve, which brings back to the problem of frequency/amplitude lookup tables. Furthermore, the graph displays the Yaxis in relation to a 1volt output signal, and as the input signal was only 0.001Vac, the graphing would fool many into believing that the preamp had no gain. For example, in the graph below (taken from the second voltage meter's output), the gain at 1kHz appears to be 11dB down, which it is relative to 1Vac, but not the actual 1mV input signal. (The old pros would quickly work out in their heads that 0.001 volts is 60dB relative to 1 volt and they would subtract 60dB from the displayed 11dBs of gain at 1kHz to get the final gain of +49dB; for the rest of us, the defined plot method is best.)
Split RIAA Equalization
The RIAA curve can also be broken into two subcurves, which when one cascades into the other will define the complete RIAA curve. The RIAA curve nicely breaks into a shelving network (50Hz and 500Hz) and a lowpass filter (2122Hz). The two circuits below embody the desired functions.
The first circuit defines the shelving function that starts flat at DC and begins to fall off at 50Hz until 500Hz is reached, where thereafter it returns to flat but attenuated by 20dB. This makes sense, as at DC, capacitor C_{1} represents an open circuit and there is no attenuation of the DC signal. And at infinitely high frequencies, the capacitor represents a dead short, which makes a voltage divider out of resistors R_{1} and R_{2}, with the signal reduced to one tenth of its starting value. The time constants for this circuit are 3180µS for (R_{1} + R_{2})C_{1} and 318µS for R_{1}C_{1}. The second coir defines a lowpass filter with a 3dB point of 2122Hz and its time constant is 75µS (R_{1}C_{1}). Notice how all these time constants match the ones we saw in the complete passive RIAA equalization circuit. How well do these two networks define the composite RIAA equalization curve? The following circuit sets out to test the accuracy of cascading the two subcircuits to create a complete RIAA equalization curve. ( Two Section Passive RIAA Equalization.ckt ) ( Two Section Passive RIAA Equalization.ckt ver 2001)
The buffer used is the Analog Device BUF04 and it serves to isolate the two networks. A custom SPICE modeled unitygain function could be defined to mimic a perfect buffer, but the BUF04 is more than good enough in this test, as can be seen below.
Now that we know that the two circuits will work, how do we go about implementing them? The order that they appear in the circuit does not matter to the curve realization, but it might matter to the preamp's overload and noise characteristics. For example, if the lowpass filter come first, the second gain stage would be less likely to clip with ultra high frequencies, but it might be more susceptible to do so with frequencies lower than 21kHz. If the shelving network come first, any RF signals entering this network from the first stage will be attenuated by only 20dB, not the 100dB that he lowpass filter would impose. (Most audio equipment designers do bother to consider such issues, because in the West we read from left to right, so the shelving network comes first, as it deals with lower frequencies and graph go from low to high frequencies. The same hold true in tube power amplifier design: the signal always goes from the physically smaller tube to the largest tube; thus you seldom see an 6SN7 driving 5687, although the 5687 is actually the stronger triode.) Returning to our tube circuit, we can easily plug these RIAA subnetworks in between three triodes. The only problem with configuration is that we pick up a great deal of gain with the third tube's addition. Using a lowermu triode would help, but maybe, if we think about it, we do not need to add an extra tube. The circuit's gain started out at +49dB, which was plenty for most moving magnet cartridges (although not enough for most moving coil cartridges). If we use the volume control's resistance as part of the lowpass filter, we will lose some gain because of the voltage divider we have created, but we will also lose much of the preamps noise, as the lowpass filter will attenuate the power supply and resistor noise along with the desired signal.
In the schematic above, we see both RIAA subnetworks added to the preamp. ( 12AX7 2Stage Passive Eq Preamp.ckt ver 4.2) ( 12AX7 2Stage Passive Eq Preamp.ckt ver 2001) The equalization network values are textbook correct, but they "off" in this circuit, as they do not reflect the influences from the triodes' output impedances and the grid resistor's and potentiometer's resistances. So what are the right values? Here B^{2} A/D Spice's parameterized AC sweep test comes to the rescue again. This time we will varying resistor R_{3}'s value until we find a plot line that we like. Since the lowpass filter's 3dB point is 2122Hz, we can limit the sweep to 1kHz to 20kHz. What should the starting value be? Well, we know that 12AX7's output impedance is about 44k and we know that the potentiometer's resistance is 100k, so 30k is a good starting value, as any lower value would make the lowpass filter too dependent on the triode and too high a value would result in too much attenuation of the signal at the potentiometer's input. (Here is an example of the art of analog electronics dictating what engineering to use.) All of which brings us to capacitor C_{2}'s value: its original value is unlikely to work in this circuit because of the potentiometer's shunting resistance, so let's increase its value to 0.015 before running our test, as this value is readily available off the shelf.
With the new capacitor value in place, we get the results shown below.
The fifth sweep looks darn close to flat. Since R_{3}'s value was incremented by 500 ohms per sweep, its value at the fifth sweep must be 55k.We now can change R_{3}'s value to 55k and move on to performing a similar parameterized AC sweep test to find R_{1}'s optimal value. This time we set the sweep to cover frequencies between 20Hz to 1kHz. And we arbitrarily pick 50k as a starting value for resistor R_{1} and 100k as the stopping value.
It looks like the right value lies somewhere between the top two plots (between 55k and 60k). the next step is to run a new parameterized AC sweep test with these two values as starting and ending values. After running a few more parameterized AC sweep tests, the best values I found for resistors R_{1} and R_{3} were R_{1}=58k and R_{3}=56.5k. The final frequency plot is shown below and be sure to note the 0.05dB divisions.
Conclusion
B^{2} A/D Spice has showed itself quite capable of unraveling many RIAA equalization problems for us. What appeals to me most is how quickly the parameterized AC sweep test gave a useable idea of what an optimal value might be (and this is an admission from someone who has rubbed the numbers off of several calculators from extensive use). Furthermore, B^{2} A/D Spice offers much more than just the parameterized AC sweep test; Monte Carlo analysis of the circuit would reveal which parts can make the biggest change to the equalization curve; and a distortion test would help reveal the overload voltages over frequency. The Single or Dual Parameterized DC Sweep test would help us quickly find the desired bias point for the triode by plotting plate voltage against cathode voltage increments.
Phono preamps are particularly nerve racking in the real world because of the difficulties that arise from the equalization curve and the miniscule input signals that are so easily contaminated by noise, but in the SPICE world, these issues disappear. Without melting any solder, we were able to design and refine several useable circuits. Of course, all the circuits we covered should be tested after being built, as the SPICE models are not perfect and actual parts differ from their ideal (and even from each other, the vacuum tubes being surprisingly consistent), but my guess is that the values found during this experiment will prove truly close.