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The textbook I'm reading (Electronics for Guitarists by Denton J. Dailey) has this to say about the AC equivalent of the circuit:

The power supply voltage source VCC provides a low resistance path to ground for signals. This effectively places RC in parallel with RL. This gives us RC'=RC||RL. Also, an AC input signal “sees” two paths to ground via R1and R2, therefore the equivalent resistance from base to ground is RB'=R1||R2

Neither of these points make much sense to me. What properties of a power supply make it provide a low-resistance path for AC signals, and even then, how does that translate to an equivalent load resistance RC||RL when the resistors are not in fact parallel with each other?

Similarly, what is meant by the AC signal "seeing" R1 as a path to ground? I thought maybe this was something to do with the change in current direction, but the signal is biased to always be positive.

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    \$\begingroup\$ Ideal power supplies don't change voltage when current is taken out (or put in) so they have zero output impedance. Hence, for AC purposes, they are grounds. \$\endgroup\$ – Finbarr Jun 19 at 16:01
  • \$\begingroup\$ Oh! Somehow I went my entire EE undergrad without realizing that. Thanks! \$\endgroup\$ – Nick Nagy Jun 19 at 16:04
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What properties of a power supply make it provide a low-resistance path for AC signals

In AC analysis you treat the DC power supply as a short.

This is justified by the rule of superposition.

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