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Imagine the electric guitar being invented today. What would the pick-up look like? For years I've been tinkering with guitars. Lately I noticed that my concept was simply ahead of it's time!

New school guitar pick-up
One wonders if rock music would have ever existed if the electric guitar had not been invented. Without this instrument the modern musical world would have been totally different. The great annual Air Guitar Contests had never been seen by anyone.
From an electronic point of view the electric guitar is a stranger with characteristics like a prima donna. You can connect the instrument to a line input but it will not sound great, even after digital processing, filters and overdrive. Only a real guitar amplifier with a high impedance input or a decent audio interface with an instrument input will give you a decent sound quality but even another connecting cable can influence the sound.
OK, there are some exceptions like EMG who build active pick-ups with a low output impedance, but in most cases guitars have a passive electromagnetic pick-up with - simply put - bad characteristics. You may wonder why the guitar pick-up is such a nuisance.

The origin
The design dates back more than 90 years by now and was developed by George Beauchamp, who wanted a louder guitar to be audible in the band. After some time experimenting he came up with a design that has changed little since then. Only tube amplifiers (or rather radio’s) existed at the time; pre-amps were not available in shops. So the best solution was to create a pick-up with a hefty output signal to drive the amplifier. He achieved this by wrapping a lot of copper wire around two horse shoe magnets.
The amount of copper wire was the solution then, but the problem now at the same time. The number of windings depends on the type of pick-up, but usually is between 5- and 10-thousand windings, combined with a iron core of some sort (and a magnet). The result is a coil with an induction of several Henry’s. But it does not stop there. The wire is thin, about 0.05mm (AWG 40) on average but 0.03mm (AWG 48) is pretty common too. And as we know, a thinner wire has higher resistance. If we take hundereds of meters of wire, or even more than a kilometre, it results in quite a significant dc-resistance. And it does not end there. The parasitic capacitance is in the region of 150 pF. That does not sound too bad, but has a significant influence and the cable to connect to the amplifier can add quite a relative portion to it.
A mismatched impedance is pretty rare to have a positive effect on the sound. Hank B. Marvin of The Shadows is an exception. His sound came into being when he plugged his guitar into an echo machine.

Resonant circuit
Most readers will have noticed by now that such a coil is a LRC-resonant circuit on its own. It is a non-ideal coil with a Q-factor that easily reaches 10 with a resonant frequency in a very audible range, mostly somewhere between 5 and 10 kHz. This explains mostly why this ancient design is still leading in the world of guitars: every pick-up design has its own characteristic  sound quality. But it means that you will need a decent cable with low capacitance and an amplifier with high input impedance to keep the characteristics.

Old school
The first guitar amps were simply repurposed radio amplifiers, or even simply unmodified radios. Often they had aged tubes or blown out parts, resulting in a distorted sound. This became a new sound. There is a story about an amp that broke because it had fallen out of a car, damaging the electronics - but sounding great. Another story is about a guitarist who slashed the speaker with a razor to get a distorted sound.
In later years guitar amps were purpose built to be able to sound distorted in some way or another, and it still is the norm. But there is a wind of change going in the music world.

New school
Guitar players often use several guitars during a gig to get different sounds, together with (lots of) effect pedals. To get the best sound every guitar should be paired with its own amp and speaker cabinet. Very few players will use this setup because of practical reasons and cost.
The solution is the increasing use of a neutral sounding amplification, combined with the right effect pedals to shape the sound. And since there are great options to simulate different amplifiers through digital processing means, this is the new way to go.
So why not build a guitar pick-up with better characteristics to get a neutral sound? That way you can shape the sound of your guitar the way you want. And since the electromagnetic principle is robust, cheap and easy to build without specialist tools, it remains an excellent choice. When using a low impedance, low inductance coil you don’t have the troubles of the traditional pick-up. So it’s a win-win situation.
I have established that a coil with about 1000 windings givest good results. Since the length of wire you need is limited - about 100 metres works fine, thicker wire can be used. I’ve built several pick-ups with 0.10mm enameled wire which can easily be wound by hand.

Pick-up modelling
The signal level will be less than we are used to, but with modern electronics it may not be a problem to build a low noise pre-amp to drive the pedals and amp with the correct level. And while we’re at it, why not make the output balanced, so we can directly connect to studio equipment? This way we can get the best of both worlds. With some modelled effect pedals and amps we can shape the sound the way we want to. All we have to do is wait for the first software that models guitar pickups to create the sound of a Telecaster. Les Paul or even the original Rickenbacker ‘Frying Pan’!
Right now I’m working on analog modelling electronics, the Virtual Analogue Modelled Pick-up, or VAMP.

Building a pick-up
I started using cheap commercial pick-ups, removing the wire and rewinding them - until I realised that there is no need to remove the wire first; just add an extra layer of copper wire. This way the original coil, output and sound still is available. The new coil needs its own output though, so I added a new connector to my guitar, through which I can connect to a balanced low impedance input. I used a TRS-connector, so I can use microphone cabling (+ and - signal, and ground).

No snake oil
There is no cure-for-all. No single pick-up will be the only solution to every sound you want. There are so many variables influencing the sound of the guitar. First of all the placement of the pick-up. Close to the bridge the sound is thinner with a strong attack; in the neck position the sound is smooth and big. Strings are an important factor too. The material of the magnet. The shape of the poles. Some people swear that even the paint makes a guitar sound different. 
There is no way to create a cure-for-all. But with a good neutral sounding pick-up we can take a leap in the right direction to shape the sound the way we want it to be.