LT Spice odd Frequency Response after adding power Cap?

[teemuk]

I added a 47R and 10uF to ground between R8 and R12, but the peak in the power rail is still present.  De-emphasized, but present.

It will always be present with a "realistic" power supply.

When you plot the response of the supply rail wrt the input signal you see effects of low frequency roll-off due to hi-pass filtering of interstage coupling caps, and high-frequency roll-off due to decoupling caps of power supply. In many cases you will also see high frequency roll off due to such filters in signal path too, (but in this case this particular design we discuss about doesn't really have such before the final tone control stages).

You want power supply's filtering caps to shunt the entire audio bandwidth to ground so that the supply rail provides a low-impedance termination point for all AC that is audio. If it fails to do so there is a potential feedback path between the stages. Hence "crosstalk".

Look at the amplitudes. When the resonant peak is high it effectively means there is gain at audio frequencies present in power supply node (amplitude > 0 dB), when de-emphasized the peak has less gain. Ideally there will be a peak but still attenuation for the audio band (amplitude < 0dB).

In case of that 22nF vs. 1uF coupling cap the difference between resonant peak amplitudes is about 24 dB vs. 3 dB. That 3 dB boost will be present in the audio response but it's not nearly as drastic as 24 dB boost. With proper decoupling, however, the peak in power supply response drops below 0 dB and it won't effect the audio signal any longer.

Now, change that 220uF cap of the original circuit to, say, 440 uF. The doubling of capacitance shifts the roll off frequency even lower and you will again see de-emphasizing of the peak as result. By using an RC filter to decouple the gain stages instead you can both increase the effectiveness of these RC filters ...and have the resistance isolating AC currents, which find the path of least resistance through the shunt filter cap.

Now, plot the response of an "ideal" power supply, one without any series resistance in it. Note that this also means zero resistance for AC signals so they terminate to 0 ohm impedance of the power supply. The attenuation of an ideal supply is usually in the order of several hundreds of dB's. No audio signal can be present in such power rails because the rail is effectively similar to "ground" for them.

In practice you will never have such ideal supply in reality. Each power supply will always have some series resistance to it, be it winding resistance of transformers, resistance of rectifying diodes, or in case of batteries the internal resistance of the battery itself. You see why you need those capacitors there even with DC supplies. They have more functions than just the effect of filtering rectified AC. The more you have series resistance in your power supply line the more important these decoupling caps become in preventing feedback between stages through the supply rail.

47 ohms can be too excessive series resistance without proper decoupling between gain stages, or at least without ample filtering capacitance to begin with. Audio signals will develop current through such resistor and that means voltage variation in a reference that supposedly should be nothing but steady "DC".

This is really not much different from phenomenon that explains why "ground return" currents also need logical routing, one that doesn't generate audio signals to reference points where such shouldn't exist in the first place. Or ground loops. (Those wires have tiny, tiny amounts of resistance). The only difference is that power rails can be easily decoupled with shunting capacitors while ground rails can not.

[teemuk]

BTW, these same effects also explain some fundamentals of good "noding" practices:

Do not have stages with higher current draw draw their current through same power supply nodes that supply stages with lower current draw. Basically, in "schematical form", do not feed the power through first gain stage to last but through last gain stage to first. (Usually the current draw of stages decreases in such order). Might not mean a great deal with simple battery-powered circuits in which current draw is usually minimal to begin with, but if final stage happens to be a power amp that draws several amperes of current you can see how such current flow could cause major deviations in power supply voltage of those more sensitive stages.

Same applies to "ground current return" rails. Remember those tiny, tiny resistances developing voltage potentials? Do not have high return currents of stages return through the same nodes that are used by stages with lesser current draw.

Remember that current flows in loops.

If you ever wondered what it was all about with schemes like "star ground" etc. these things are all explained by noding practices that try to channel current flows to nodes where they interfere the least amount with each other.