Split RIAA Equalization

The RIAA curve can also be broken into two sub-curves, 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 low-pass 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 C₁ 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 R₁ and R₂, with the signal reduced to one tenth of its starting value. The time constants for this circuit are 3180µS for (R₁ + R₂)C₁ and 318µS for R₁C₁. The second coir defines a low-pass filter with a –3dB point of 2122Hz and its time constant is 75µS (R₁C₁). 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 sub-circuits 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 unity-gain 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 low-pass 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 low-pass 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 sub-networks 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 lower-mu 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 low-pass 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 low-pass filter will attenuate the power supply  and resistor noise along with the desired signal.

In the schematic above, we see both RIAA sub-networks added to the preamp. ( 12AX7 2-Stage Passive Eq Preamp.ckt ver 4.2) ( 12AX7 2-Stage 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 B² A/D Spice’s parameterized AC sweep test comes to the rescue again. This time we will varying resistor R₃’s value until we find a plot line that we like. Since the low-pass 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 low-pass 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 C₂’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 R₃’s value was incremented by 500 ohms per sweep, its value at the fifth sweep must be 55k.We now can change R₃’s value to 55k and move on to performing a similar parameterized AC sweep test to find R₁’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 R₁ 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 R₁ and R₃ were R₁=58k and R₃=56.5k. The final frequency plot is shown below and be sure to note the 0.05dB divisions.