I just noticed that the mentioned 210R termination in #2868 was 50R instead.
It should have been 210R, here is the correct attachment.
1) The original filter has a very nice almost flat impedance within a small band, see Red trace below.
2) The filter proposed in your recent posting in Blue, has a rather large peak at 80Khz, when the design was understood correctly
3) The 5th order passive filter in Green has an even higher peak and rather disqualifies for the purpose when opting for a flat impedance versus frequency.
4) The 4th order passive filter in Teal, terminated with 210R, has a nice flat 590R impedance up to almost 80Khz and goes to 380R upwards from 100Khz.
This version has a 3dB lower output as a version with 380R termination, but even then, the noise from the amp (OPA1632 ?) behind the filter will still be quite a bit lower
Hans
Hi Hans,
On one hand, I would like to keep the signal voltages at the FIRDAC summing nodes as small as possible because they make the current drawn from the reference data-dependent. On the other hand, I don't see how you could keep the impedance there really low while still having substantial passive filtering before you reach the first active device of the analogue output filter.
As you can see in your own simulations by subtracting the source impedance, the red and blue traces have the lowest impedance at the summing node over the frequency range traditionally considered audible for humans (*), but I don't know if that is the right criterion. It helps to keep the summing node signal swings (and hence any artefacts those may cause) small when it is mostly audio causing those swings, like when you listen to loud passages. During near silence, it is mostly the shaped quantization noise causing swings. The blue trace indeed has a rather nasty peak around its cut-off frequency.
By definition, a lossless LC filter passes all power the signal source delivers to its input on to its load (it has to, as it's lossless). It can therefore only suppress signals in the stopband by changing its input impedance such that the signal source can't deliver much power to it anymore. For a filter working between two equal resistive terminations, you have the maximum power transfer when the filter input impedance equals its load resistance, and a change of the filter input impedance in any direction (up, down, or added positive or negative reactance) reduces the transfer.
In its passband, a lossless LC ladder filter normally has an input impedance essentially equal to its terminating resistance. For example, in a low-pass filter with inductors as series and capacitors as shunt branches, the whole filter becomes one big short between source and load when the frequency goes to zero.
I suspect that lossless LC filters designed to work between a current source and a resistive load will tend to have an input impedance that drops to zero in their stopband. The real part of the input impedance will definitely have to drop, as that is the only way the filter can reduce the power
I2Re(
Zin) delivered by the current source.
So maybe the best approach would be an LC ladder filter designed for an infinite source and low load resistance (or one designed for a high source resistance and low load resistance having component values close to those of a filter designed for an infinite source and low load resistance). I don't agree with your remark about 3 dB less signal, as the current through the load resistance only goes up, and both in your and my proposal, the stage after the LC filter essentially looks at the current rather than the voltage. The values of the filter capacitors will increase as the load resistance is reduced, this will eventually cause an excessive noise gain for the stage after the LC filter. The required values of the inductors go down, leading to higher self-resonance frequencies and possibly less inductor distortion at a given current and core size. I don't know yet whether there is some way to intertwine this with an MFB stage without getting nasty impedance peaks.
Thanks Hans, I think I have a better idea about what I'm trying to do now.
Regards,
Marcel
(*): Cats can hear some two octaves more, but despite their superior hearing, they are usually less fussy about sound quality.