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Re: Just wanted to check as......

Posted by Kurt Strain on March 25, 2002 at 13:22:28:
>>as Mr. Lipshitz says, if I read properly, multiplying R2C1 will give incorrect value for time constant, others the same way. Other time constants interact and according to him, some 18% off on this one, if I understand correctly. <<
It's a very good point and one I worried myself over in the past to the point I didn't think I could actually calculate these ratios properly.
Well, I derived the whole transfer function of the network Rs, R2, C1, C2, and from there I had to iterate a lot to get the ratios correct because there is so much interaction. But the solution for these ratios does indeed converge beautifully.
The zero that forms time constant 318 usec (500.5 Hz) stands alone at the numerator in the transfer function vo/vi, with the equation R2*C1*s + 1 there. This single zero is at s = jw = -1/(R2*C1). This zero has to be placed at 318 usec, there is no choice, by RIAA definition. So there's a precisely calculated relationship between R2 and C1, where R2 = 318 usec / C1. This is the only breakpoint in this network that has no interaction. Simulations will show differences everywhere when you move away from this, but the zero is still well defined where it should be.
The denominator was the hard part because all the parts in there form the coefficients a and b in the quadratic a*s^2 + b*s + 1 = 0. This requires iteration to solve for the perfect ratios where the solution for s = -1/(3.18 msec) and s = -1/(75 usec) are precise. But it does converge to those exact numbers, neglecting the other "side components" in the circuit when using the right RIAA component ratios. I thought that it was cool that it wasn't that difficult to get them. Obviously, as Paul was showing that J. L. Hood's book 'The Art of Linear Electronics' gives equations for these relative values as well, and they agreed to mine precisely.
The upshot is that it's very interactive, but as a whole, there's a known ratio for all these values that provides a final solution that fits all the time constants at once.
Kurt