Intro And Disclaimer:
This article/any following articles are intended as guides, for people looking to learn more about effects/amplifiers/signal analysis with reference mostly to guitars. It is by no means intended as a complete guide to everything, but more of a starting point to initiate discussion/ get people going in designing their own guitar gadgets, most likely pedals/pickups/amplifiers. I will try not to drown you in equations and if I'm going too slow/too fast then let me know.
Given that in this field a certain amount of trust is required, my name is Andrew I'm in my mid 20's and I have a Masters degree in Electronics from Sheffield University. My main hobby is guitar but, alas, in reality I'm not particularly amazing at it. Until recently I never really combined my hobby with my livelihood but I figure it'd be an adventure to find out about it.
Where to start? Well, lets start on the guitar, if this one goes down well or at least is not laughed at, I'll move onto overdrive/distortion pedals, the good old true bypass, echo's, wah's and amplifiers, and for the real crazies out there we can always handle some DSP (digital signal processing).
The Guitar Signal:
So, where to begin in this adventure; well let's start with an overview. Just about all guitarists know that when you pluck a note/strum a chord, that you are essentially vibrating a bunch of metal wires.
These wires are placed close to your pick-ups (magnets wrapped in coils of wire) where an electrical current is induced in the coils because of the disruption caused in the flux around the magnet, this current being induced is the reason we don't need batteries on most guitars. (No this is NOT a source of free energy those that have thought about it, your arm is expending much more effort moving those strings then any energy that comes out of them).
Now For Some Electronics:
So I'm not going to bore you with why moving metal objects in a magnetic field induce current - that's just a description of the laws of physics, what I will bore you with is why Pickups all sound different;
Everything in electronics comes down to V=IR (voltage is current x resistance).
That equation gets me out of just about every single hole/problem I've ever been involved in (although shouting it at a gig when you're string breaks mid- solo is by no means an advisable course of action... though if you try it let me know).
A good and somewhat useless way of visualizing this equation is a motorway. If you look at V as the average Speed of traffic, I as the amount of cars getting through, and R as the amount of lanes you've got to play with you can get a vague impression of how Electrical current works
So right now you're asking yourselves how coils of wire around a magnet can sound different from each other when the equation is so simple? That or you're questioning whether this is one article too many and it's probably time to close you're browser and to return to the real world.
Well, actually R from our equation up above is a funny character, especially when dealing with coils of wire (this is where our motorway image completely falls apart), see if you have very small gaps in wire, or, if you coil wire up tightly it starts to exhibit capacitance and inductance respectively (I can deal with these more extensively at some point in the future). The thing with capacitors and inductors is that their resistance changes with frequency (impedance) so we end up with;
V = I * (R + (1/(2*pi*frequency*Capacitance)) + (2*pi*frequency*inductance))
The interesting thing we end up with here is that we have a non-linear relationship, so depending on how many coils each pickup has/ how they are spaced you have very specific tonal characteristics for every pickup just depending on how it's wired (regardless of the quality of magnet used).
Why Can't I Get A Humbucker Sounding Like A Single-Coil?:
Single-coil pick-ups act, annoyingly, as antenna's (antenna's are any long piece of non-shielded wire/metal), the humming you can hear most of the time in the background is probably the mains (50/60Hz). For reference the low E on your guitar is probably 82.4Hz.
Humbuckers are clever because as you can visually see it's for the most part 2 single-coils hacked together, HOWEVER, the second single coil has its windings reversed and its magnets are out of phase with each other which effects to make the random noise in each single-coil cancel it each other out but double the guitar signal (WOAH! Clever stuff), however having two wires coiled next to each other creates a lot more inductance, lowering the resonant frequency (the frequency at which you get the best response, ala V=IR... Above). This is why humbuckers have much less of a sharp attack then a single-coil, because it can't react as-well to sharp sounds (higher frequencies)
The Signal We End Up With:
Well take a look at you jack cable, What you have is a signal and a ground (the middle is the signal), the induced current (after going through your volume/tone resistors) looks like a sine-wave on the signal connector when looked at respective to ground (without a ground the signal is meaningless). Why does it look like a sine-wave? Well you're string is vibrating up AND down - opposite directions within the magnetic field.
So now for some discussion, a lot of people talk about sustain generated by the wood of their guitar, any ideas how this actually (if it ever?) makes it into an electronic signal? Answers below.