I sometimes get the question “Does a pulldown resistor affect input impedance?”. The short answer is “Yes”.
As we see here, the guitar pickup is modeled as a signal source in series with an output impedance (Z1).
When you add the pulldown resistor at the input of a pedal circuit, that new resistor becomes the maximum impedance (Z2) into which the pickup is looking. It can never be higher than the value of the pulldown, even if the circuit input impedance is infinite.
Once you add the circuit input impedance, the combination of the pulldown Z2 and the input Z of the circuit will be the parallel value of the impedances. In this illustration, the circuit has a 10M impedance and it is in parallel with the 1M pulldown, so the pickup is loaded by 909k.
The only way to raise the circuit’s imput impedance is to increase the value of the pulldown. If you substitute a 10M resistor for the pulldown, the circuit input impedance is now 5M, which is the parallel value of the 10M (Z2) and the 10M circuit impedance.
Let us look at a real world example. This is a model of the AMZ Mini-Booster with the input impedances of the circuit shown. Z2 will be the pulldown that is to be added, C1 is the input capacitor, R1 is the gate bias resistor, C5 is the RF protection capacitor and Q2 is the jfet’s gate impedance.
It can be seen that the impedance will vary because the capacitor’s reactance will change according to the frequency through it, so the input impedance is actually a slightly different value all across the audio band.
In a simplified analysis, the input capacitor is considered to be a dead-short and ignored, while the C5 capacitor is too small to have an impact and it is considered to be open. The gate impedance of Q2 is so high as to be essentially infinite and can be ignored as well. This leaves the simplified impedance as the parallel value of Z2 and R1, or about 500k.
In the more complex analysis, at 82 Hz., C1 is 39k, R1 is 1M, C5 is 194M and Q2 is still infinite. I’ll leave it as an exercise for you to work out the final impedance with the Z2 pulldown at 1M.
In the more complex analysis at 10k Hz., C1 is 318 ohms, R1 is 1M, C5 is 1.6M and Q2 is still essentially infinite. You can see that at the higher frequency, the input coupling capacitor has little impact but the RF capacitor C5 is beginning to roll off some of the highs.
At the higher frequencies, the gate is still extremely high impedance but the gate-to-source capacitance is actually beginning to have an audible impact on the sound of the circuit. This inherent capacitance in the jfet is only a few pF but it will begin to leak some of the signal to the source (and thereby to ground).
What about the Miller effect? The stacked configuration of Q1 and Q2 virtually eliminates the Miller Effect from the mu-follower, which is one of the reasons that the Mini-Booster will sound different from a typically common source amplifier of the same gain. The Miller Effect is causing a rolloff of the highs with the common source circuit and this does not happen with the Mini-Booster so it has a slightly brighter top end.
This is a nice to the point piece on input impedance. What target input impedance do you like to use for pedals?
Many tube amps have 1M input Z so that’s a good place to start. However, I will use less (or more) as the circuit requires. The Mini-Booster is 1M but the Mosfet Booster is 10M, which makes it good with high impedance signal sources (such as piezo pickups), but I used 100k in the Fat Gnat distortion pedal.
What pedal input impedance do you think is optimal? Do you vary the pedal input impedance with the type of pickups on the guitar and/or with the desired output impedance or …