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In almost every component designed and built that I have seen, there exists an insidious form of feed back that is frequency dependent, and with varying degrees of phase shifting. This occurs with more than one stage and common power supply. RCA Radiotron Designers Handbook, 4th edition, saw this problem in the 40s, but I am sure it was apparent much earlier. With different signals and different phases, from the fundamental signal, one can see it being a serious problem unless the proper precautions are taken? This is just another form of distortion that must be dealt with.
How serious is the problem? Well, if a power cord makes a sonic difference even before the power transformer and well away from the direct signal path, and filter capacitors, resistors, chokes etc change the sonics closer to the direct signal path, imagine how the music is mucked up when frequency dependent feedback, with changing amplitude and phase are involved, is at the door step, right next to the "direct signal path".
Let's analyze some examples.
First, let's check out a simple circuit (fig. 5) and see what we can discern. (We will only address tube circuits although solid state designs are similar.)
Fig. 5 is a typical capactively coupled tube stage. From our previous article ,"Power Supplies and Capacitors"), C1 should theoritically be 0 ohms impedance at all frequencies. However, in practice this isn't true. As a general rule, the signal voltage present at capacitor C1 is dependent on:

Capacitance of C1 Frequency Voltage P-P at C1 Phase Shifts 10uf 20 4.5 volts Lagging nearly 90 degrees 20uf 20 2.3 " 40uf 20 1.15 " 100uf 20 .465 "
Even with C1 at 100uf and R1 of 15k, some .465 volts appears at C1 at 20hz, which is only approximately 46db down from the 90 volts present on the plate of V1. As mentioned above, the resistance of R1 also determines the signal voltage present at C1 as follows:
Resistance of R1 Voltage P-P at C1 1.5k 20 (gain of tube lowered by low value of R1, plate resistor) 15K 2.3 150k .24Typical 20hz signals at C1 (I have seen in some tube designs) range from only -21 to --45db range below the reference at the plate of tube V1, which is very poor. Increasing the frequency an octave accounts for only an approximate 6db reduction of this signal at C1. As we shall see in a moment, this will interact with the previous stages.
Let's look at some typical 2 stage designs in fig. 6 and fig. 7:

Fig. 6 adds another gain stage, and is typical in many designs I have seen. Feedback is occurring between V2 and V1, thru R1 and R3, with C1 the imperfect signal grounding component. In otherwards, low frequency signals (with large phase shifts) from both tubes are measurable at C1. From there, each tube's signal reaches the other's tube plate via the RL of that tube.
If we have 90 volt signal on the plate of V2, we know the signal of C1 (with 40uf capacitor) is 1.15 volts. Let's make the plate resistance (Rp) of both V1 and V2 a low 3k ohms. The voltage reaching the plate of V1 is approx 0.1916 volts. Let's say the gain of V2 is 10 times or 20db gain. That means we have 9 volts on the plate of V1. So the feedback voltage, 0.1916 volts, is approx 33db down from the fundamental, 9 volts. Visa Vera, the low frequency voltage from V1 to V2 is approx 73db down. So "feedback" occurs both ways.
On a side note, if we make C1 a typical electrolytic capacitor and continue to increase its uf size, the feedback will lessen as the frequency increases until the capacitor reaches resonance, which may be as low as 5khz. Above the resonant frequency, the capacitor becomes inductive and its reactance again rises, thus again increasing the feedback, but this time at high frequencies.

Fig. 7 adds an RC combination to the power supply circuit and adds, typically, another 10-30db of isolation, so maybe between 45-75db of isolation total. We also increase the phase shift of the feedback signal. Now it is possible at some low frequency to have up to 180 degrees of phase shift.
Replacing R4 with an inductor can actually worsen the feedback condition at low frequencies. This is because the reactance is low at low frequencies, often lower than using a resistor. It also changes the phase shift pattern and also creates a resonant circuit at some X frequency.

What if in Fig. 6 and/or Fig. 7, V2 is an output tube with R3 replaced by a typical audio output transformer. The interaction between V2 and V1 will be tremendous as the signal voltage of the output tube may be typically 250 to 500 hundred volts p-p, and already with phase shifting in the bass region. In multiple stage amps using these types of power supplies, we will see feedback to every previous stage of the amp, unless some extraordinary precautions are taken..
I hope you see how much of a problem the power supply can be. It not only supplies pure DC voltages to each stage, but also should eliminate incoming interference, and eliminate "hidden" frequency dependent feedback between stages.
This article was meant for the general audience, in simple language.