How to analyse this distortion circuit (for a guitar pedal) ?

[rgehan]

Hello,

This is my first post on the forum, I've read a lot of materials about electronics, and I think I understand the basics of this circuit.

Here is the schematic:


This is what the oscilloscope is showing (yellow signal is Vin, blue signal is Vout, and the purple one represents the GND):


Q1 acts here as an amplifier: it amplifies the current flowing from the input. We have C1 and C2 in series to remove the DC component of the signal. And R1 allows us to "re-inject" a little current into the base of Q1 to amplify a little bit more (is it called feedback ?).

I'm quite familiar with Ohm's Law, Kirchoff, and know approximately the behavior of a transistor, but I can't figure out how to "solve" this circuit. I mean, how to get all the interesting relations between the input voltage, and the output voltage.

I don't want to start building something without fully understanding it, and that's why I'm asking for your help.

Here are the "relations" I came up with :

- Currents (Kirchoff's):
I(R2) = I(Amp) + I(c) + I(out)
I(b) = I(In) + I(Amp)
I(c) = hFe x I(b) = 40 x I(b)
I(e) = I(c) + I(b) = 40 x I(b) + I(b) = 41 * I(b)

- Voltage (Ohm's)
I(R2) = V(R2)/68k
I(Amp) = V(R1)/2.2M
I(e) = V(R3)/470

At that point, is there any mistake I could have made ?

- 1) Usually, when I'm done with the intensity, I try to determine voltages across know resistors, but here, I can't figure out how to make loops in order to use the "equivalent resistor" to determine current/voltage.
How should I proceed to determine voltages, or at least relation between them, since the input is variable ?
For example, I've tried to determine what was the expression of V(out), I thought V(out) was going to be equal to V(R3) but according to my simulation, that's wrong.

- 2) How can I determine the current flowing from my input ? It all depends on the mic ? But is there an average value I could use to analyse the circuit ?

- 3) On the 2N3904 Datasheet, there are multiples values for hFe. I ran a simulation (with an sin wave on the input: 1v amplitude, 10kHz since the audible frequencies range is [20Hz;20kHz]) and probed the I(c) current, it was about 0.1mA, so I took the value of the datasheet corresponding to .1mA. Is this the right value ? Is there a better way to proceed ?

- 4) Finally, do you know a great book/textbook on circuit analysis, but that would be understandable by a beginner ? I've taken some electronics class, but they were only high-school level. I'm really trying to complete my understanding of electronics, and I'm not afraid of maths, even if I highly prefer a "practical" book.

Thanks in advance.

Oh and I apologize for all the grammatical mistakes I probably made, this is not my mother tongue