Question about voltage dividers for input biasing

[garcho]

And why is bigger impedance good?

Think of the stomp box circuit as something that can be described as a "black box" with a certain amount of total resistance. That's everything included all together in a magical black box, don't worry about how it works. Your guitar's signal also has "built in" resistance. So think of your guitar as a black box with resistance and the pedal as a black box with resistance. What do we have? Two resistors. What do two resistors form in this configuration? A voltage divider. Voltage dividers are straight ahead with DC, do the simple math and you're done. But with AC you have to think about resistance at certain frequencies (look up reactance). If the pedal black box has say, low resistance for high frequencies, all those high frequencies rush to ground and "disappear" from the signal, leaving your signal with little high end, sounding muddy and muffled. If the pedal black box has high resistance for high frequencies then you get more of the "complete" or "original" signal and less high end rushing to ground. This is my crappy attempt at describing this as simply as possible. Look up voltage dividers for AC, with capacitors (this is how filtering is done, your tone stack is a voltage divider that changes based on frequency).

[antonis]

But how does the bias resistor increase impedance for the input? And why is bigger impedance good?

Not for the input but for incoming signal "splitting"..

Signal comes from a source of some impedance A(considered in series with the source) and goes into some circuit of some other impedance B(considered in shunt with signal path 'cause signal is taken from the upper edge of circuit's impedance).

On the meeting point of signal impedance and circuit impedance we have a (humble but nasty) voltage divider..

The greater the circuit's impedance (or/and the lower the signal's impedance) the greater the amount of signal passed (not lost into GND)

If we only had to deal with pure resistive items, impedance (mis)matching shouldn't be a big deal 'cause we could "recover" someway the amount of signal lost..
(but it's nonsense to loose power for nothing.. )

In reality, we usually deal with reactive items too, which form some kind of filters, so we better make signal/circuit impedance ratio the lowest the possible..

[GibsonGM]

Non technical....some of your input signal gets 'lost' by going thru the bias resistors, and does not make it to the input of your device, such as a transistor.   

Impedance is frequency-dependent resistance.   It is composed of actual resistance, and "reactance", or "frequency-dependent resistance".  You might need to go look that up, and that's ok for now      If you have a low input impedance, your signal will sound like the tone has been turned down (highs pass to ground faster than lows do....which is to say, a low input impedance favors high frequencies over low..it shunts them to ground and they get lost).      So, we want a low OUTPUT impedance on a device so it can 'source' current easily, and a high INPUT impedance, so that our signal is passed between the devices unchanged...so it is not DEMANDING current unnecessarily.  Perhaps 10x higher.

High value bias resistors help this...lower ones LOAD DOWN the signal, stealing some of it, where it goes to ground *through* them.  AC signals can go to "-"  OR "+", THEY DON'T CARE!  Ground is ground to them!!     BUT - the higher the resistor value, the more noise we create in the circuit.   So, it's a balancing act.   And sometimes, a bit of loading is GOOD, by taming some too-shrill high frequencies!     That is the 'art' of the DIY world.

A quick look at this phenomena:  https://electronicsclub.info/impedance.htm

[PRR]

> I know how voltage dividers work

The guitar and input resistor ARE a "voltage divider".

What is the division ratio?

What if we want "most" of the guitar signal?

We don't really know the guitar impedance. It runs 5K to 250K with frequency.

If we loaded with 5K, we would get from 1/2 to 1/50th of the precious guitar signal. Not good.

If we load with 1Meg we get 80% to 99% of the wonderful guitar signal. More to work with, and less variation with frequency.