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Please could someone explain how to compute the impedance with which to determine the frequency characteristics of the high-pass input filter in the following circuit?

My question is prompted by an example from Horowitz and Hill 2nd ed. 2.05. I think this question could be formulated with a simpler circuit, but I don't know how to simplify it while retaining the essential aspects. The sizing of the components is explained as follows:

  1. Choose the output voltage for a steady input voltage in order to maximize the range that won't be subject to clipping, i.e. 7.5v (half-way between the min/max of 0v/15v).
  2. Assuming a quiescent current of 1mA, we can calculate R3 to be 7.5k using Ohm's law.
  3. Now we choose R1 and R2 by deducing that the base voltage for Q1 will be 8.1v (since it is 7.5v + 0.6v drop from base to emitter). Also, we assume the gain of the transistor to be at least 100 meaning that its input impedance is at least 750k, and choose the parallel resistance of R1 and R2 to be at most a tenth of this, i.e. 75k. The two conditions give 130k and 150k for R1 and R2 respectively.
  4. Now we choose C1. This is supposed to be an audio device so we want to retain frequencies above 20Hz. The -3db point for the RC filter will be at 20Hz = 1/(2*piRC1), which we can use to find C1 given R.

My question is about the determination of R. We assume that the load driven by this emitter follower is high compared with the emitter resistor and therefore determine that the input impedance of the transistor will be gain*7.5k = 750k.

So R is the parallel resistance of R1, R2 and 750k, which works out at roughly 63k and C1 should be at least 0.15uF (a larger value is chosen in practice to reduce attenuation, and we get the final 0.5uF).

My question then, is why is R determined as the parallel combination of R1, R2, and the transistor input impedance? Or indeed, more simply, why is the input impedance of the voltage divider R1 and R2 equal to their resistance in parallel? -They are not in parallel, they are in series between +15v and 0v.

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My question then, is why is R determined as the parallel combination of R1, R2, and the transistor input impedance? Or indeed, more simply, why is the input impedance of the voltage divider R1 and R2 equal to their resistance in parallel? -They are not in parallel, they are in series between +15v and 0v.

You need to think like an AC signal - an AC signal doesn't recognize +15 volts as anything any more special than 0 volts. It regards them both as an infinite AC current sink and therefore, for the AC input signal, they can be regarded as both connected to 0 volts or, both in parallel to ground (or whatever terms you want to use). Ditto the resistive impedance offered by the base.

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