The image Orig.png is the schematic of the originally published network.

The image T4_3_18.PNG shows the values when T4 is changed to 3.18 uS.

InvRIAA.png shows the formulas in pretty print.

OK, and here's what the error on your network looks like when it is
simulated -- plugging the time constants into a "transfer function" -- you
should be able to do better than 0.1dB -- my Audio Research SP8 is acurate
to this level.

The Phantom wrote:

The image Orig.png is the schematic of the originally published network.

The image T4_3_18.PNG shows the values when T4 is changed to 3.18 uS.

InvRIAA.png shows the formulas in pretty print.

I have a recollection that such a network cannot ever produce a true RIAA curve.

Lipschitz discussed this in depth in the AES journal about 30 years ago.

Graham

On Fri, 18 May 2007 08:28:06 -0400, "jack" wrote:

OK, and here's what the error on your network looks like when it is
simulated -- plugging the time constants into a "transfer function" -- you
should be able to do better than 0.1dB -- my Audio Research SP8 is acurate
to this level.

If you'll look carefully at Orig.png, attached to my original post,
you'll see that the resistor you've labelled R3 should be 47 ohms.

If you make this change, you should get an error curve like the one I've
attached to this post, showing that even with component values not equal to
the theoretical, the error is +- .01 dB.

If you use the theoretical values (good to only 12 digits), the error is
substantially better than +- 1 nano dB, limited only by the number of
digits used in the arithmetic. Your simulator will have to do its
computations with at least 12 digit arithmetic to see this result. The
RIAA curve you compare to must include a 4th time constant of .07492 uS
because that is what the theoretical values were calculated with.

The theoretical values are for these time constants:

T1 = 3180 uS
T2 = 318 uS
T3 = 75 uS
T4 = .07492 uS

R1 = 47.0000000000 ohms
R2 = 470454.868661 ohms
R3 = 68368.6219769 ohms
C1 = 4648.06079550 pF
C2 = 1595.29788607 pF

And, of course, these reference designators are the ones I used in my
original post, not the ones you chose.

On Fri, 18 May 2007 12:45:28 GMT, Eeyore
wrote:



The Phantom wrote:

The image Orig.png is the schematic of the originally published network.

The image T4_3_18.PNG shows the values when T4 is changed to 3.18 uS.

InvRIAA.png shows the formulas in pretty print.

I have a recollection that such a network cannot ever produce a true RIAA curve.

Lipschitz discussed this in depth in the AES journal about 30 years ago.

Graham

If by "true RIAA curve", you mean that the curve has only the 3 time
constants:

T1 = 3180 uS
T2 = 318 uS
T3 = 75 uS

then I suppose it would be technically correct to say that the network
cannot ever produce the curve "exactly", since this network does in fact
have a 4th time constant, which must be placed at some frequency.

If the theoretical component values are used, and the network performance
is compared to the "official" 3 time constant RIAA curve, the error
smoothly increases as we approach 20 kHz, reaching a maximum of .0004 dB at
20 kHz. A physical network made of real components will never be this good
anyway. It seems to me that this is good enough for practical work.

And, as I said in my response to Jack, if you add the 4th time constant
(which for this network with the originally published values, is at about 2
MHz) to the "official" RIAA curve, this network with the theoretical
component values has an error of substantially less than 1 nano dB. Even
this error is an artifact of the limited precision arithmetic. The network
can match the 4 time constant RIAA curve exactly.

On Fri, 18 May 2007 12:45:28 GMT, Eeyore
wrote:



The Phantom wrote:

The image Orig.png is the schematic of the originally published network.

The image T4_3_18.PNG shows the values when T4 is changed to 3.18 uS.

InvRIAA.png shows the formulas in pretty print.

I have a recollection that such a network cannot ever produce a true RIAA curve.

I dug out the Lipschitz paper from a box in the basement. The only place
he says *cannot* is in footnote 9 of the section where he discusses the
effect of inadequate open-loop gain in active equalizers. To quote:

"Of course, we assume that the shifts involved are not so large that the
roots of the equations (6), (18) and (20) become complex, for then the
configurations under consideration CANNOT be made to follow the RIAA curve,
and the amplifier's open-loop gain must be considered to be totally
inadequate."

Passive networks such as the ones under discussion lately can always
follow the RIAA curve if their topology gives the right pole-zero
configuration.


Lipschitz discussed this in depth in the AES journal about 30 years ago.

Lipschitz's paper, "On RIAA Equalization Networks", appeared in the JAES
in 1979.

I also found with Lipschitz's paper a copy of a 6 page reply by Peter
Baxandall which was published in the JAES in the Jan/Feb 1981 issue. He
showed an inverse RIAA network identical in topology to the one I've
analyzed in this thread. He used 27 ohms for R1 and also added another 27
ohm resistor in shunt at the input, solving the problem of ensuring
sufficiently low impedance at the input. He accounted for the effect of
the two 27 ohm resistors.


Graham

My apologies -- in my haste to get out the door I put in the wrong load --
here it is with the values you specified out to 100kHz -- using the number
significant digits that are allowed in Multisim -- and using 74.92
nano-seconds as T4 --