RIAA Equalization Modeling in SPICE

With B² A/D Spice we can model both active and pass RIAA preamps, as a phono preamp is a low-noise amplifier, but unlike most amplifiers, the output of a phono preamp is not flat, following instead the RIAA de-emphasis 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 real-world 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, high-end preamp.)

In the SPICE world, this problem is easily overcome. In B² 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 voltage-swing 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 B² 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 (S-Z1)(S-Z2)...(S-Zm)

                          Vin             (S-P1)(S-P2)...(S-Pn)

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

            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: