Distortion Pedal Electronics (Explained for beginners!)

1. Short all capacitors and DC voltage sources, except for C4 which should be open-circuited for reasons that I’ll discuss later in the article. Also, for now, let’s deal with the preamp stage isolated from the clipping stage. 
   

    
2. Replace the transistor with an equivalent Ebers-Moll Model. The transistor as a whole can be broken down into simpler components called an equivalent model. One such transistor equivalent model is the- Ebers Moll model. 
   

   The Ebers Moll Model

    

r_e’ (part of the Ebers Moll equivalent) is ac resistance of the base-emitter diode. It can be easily calculated by using the formula-


r_e’= 25mV / I_E 
In our case, r_e’= 25mV/0.12mA = 208Ω


To get the value of the resistor, we multiply this value by β-
βr_e’=42kΩ


Finally, all you need to do is re-draw the circuit, in a way that the input and output circuits can be understood separately. Before you proceed, convince yourself that the circuit below is the same as the previous circuit, just that it’s better organized.

Finally, to calculate the AC amplification factor we, just need to compare the output of the circuit (tagged output), to the input guitar signal. The AC voltage source in all the diagrams is the guitar signal. 


AC Voltage Gain ( amplification factor ) = v_out/v_in


v_in =  i_{b *} 42k


For v_out, we need to find the voltage across the equivalent resistance for R3 and R5 connected in parallel. 

v_out = βi_b * 52k

v_out/v_in= 1.23 * β
with β= 200, 
we have –
AC Voltage Gain ( amplification factor ) = v_out/v_in  = 247
This means if you feed the amplifier with a 10mV (peak-to-peak) signal you obtain an amplified version of that signal at the output that’s almost 2.47 V (peak-to-peak).
Having said that, we have ‘analyzed’ the preamp’s amplification!


Now, if you clip the output voltage using two diodes connected to GND, the peak voltage would be limited to nearly -0.7v to 0.7 V (for typical diodes)  with the signal getting squarish and distorted. This is what happens in the very first circuit of the three examples we saw above (scroll up!). However, in this circuit, we don’t directly clip the output signal instead clipping happens through a feedback path that connects the output back to the input of the amplifier stage but through two diodes! 


Before we end our discussion, I want to talk about all the assumptions we’ve made to simplify the process and understand it better, that may be a bit far from reality.


1. The capacitors don’t act as perfect short circuits for AC signals.
The impedance of a capacitor is a function of its capacitance and frequency of the signal across it. 

If the product of its capacitance and frequency of the signal is a number big enough to make its impedance negligible, we directly replace the capacitor with a short. 
This is why we open-circuited C4, instead of shorting it. C4 is a filtering capacitor; whenever there’s high-frequency noise/squeak in coming in from the guitar’s input, its impedance decreases and allows the noise to be directed to the ground, hence preventing the noise from being amplified. This called also called passive low pass filter.

2.  The value of β varies from transistor to transistor and is not constant even for a given transistor.
There are a lot of factors on which the value of β depends on. But for most calculations, we can approximate its value to a number provided in that datasheet.

Putting it all together- 

 

 

Even such subtle squarish-ness can create significant audible distortion in the sound. 


That’s all for this article. I hope this article has equipped you with a better understanding of distortion circuits. If you enjoyed reading this article and would like to see more similar articles, do let me know by leaving a comment below!