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The humbucking pickup most people are familiar with is the PAF designed by Seth Lover in the 1950s. It is probably the most copied pickup, with more winding variations than any pickup design ever made. PAF design pickups are 2-3/4" x 1-1/2", which is the most common size for humbuckers.
Humbuckers reject electrical signals that oscillate at 60 cycles per second. They do this by having two coils that are electrically out of phase with each other. One coil creates a positive voltage at 60 cycles, and one creates a negative voltage at 60 cycles, so when you combine the two signals they cancel each other out. The level of cancellation will be dependant on how closely the coils match. In practice, the coils don’t match exactly, so hum cancellation is never completely efficient. You can still get 120-cycle hum; the level is determined by how well the pickup and guitar wiring is shielded. 120-cycle noise is minimized with shielding, and 60-cycle is minimized with hum-cancelling pickup designs.
How do you get any sound at all if it cancels itself out? The coils are electrically out of phase with each other but magnetically in phase with each other. Strings are made of ferrous material (iron, steel and any blend of metals that have iron as part of the content), so in the best circumstance (matched coils) the only thing the pickup will sense is the ferrous material vibrating in the magnetic field. When the string vibrates, it causes the magnetic field to move through the coil. This induces an alternating current to be generated that corresponds to the string frequency, which is then converted to sound by your amplifier.
Gibson made three other humbucking pickup designs most people will be at least vaguely aware of: the mini-humbucker, the Firebird and the Johnny Smith. Pickups in the mini family have a different tone than the larger PAF for various reasons—some apply to all the smaller buckers and some are specific to each design. All of these secondary pickups are smaller: 2-5/8" x 1-1/8". The narrower width of these pickups (1-1/8" compared to 1-1/2") sense a shorter length of string vibration, containing only the higher harmonics generated by the string and giving you a slightly brighter and more focused sound.
The tone of the minis is also different due to how much iron is in their core—the size of the core and content affects the inductance of the pickup. Inductance has an effect on the output and frequency response. More inductance usually gives more output and more bass. So a smaller pickup sensing a more focused area of strings with a smaller amount of iron content in their core will result in a little less output and an overall slightly brighter, clearer sound.
A mini-humbucker is made like a miniature PAF pickup: it has one bar magnet positioned under each coil, with adjustable pole pieces made out of a ferrous alloy; the other coil contains a ferrous metal bar that is not adjustable. This corresponds to a PAF with adjustable poles in one coil and a series of metal slugs in the other coil.
A Firebird on the other hand, has a bar magnet in each coil. Each coil is wound around a bar magnet, one coil is south up and the other is north up. The inductance properties of steel and alnico magnet grades are very different. Also the magnetic field shape and size are different between the mini-humbucker and the Firebird.
Steel cores tend to have a higher inductance; you get more bass and more output versus an alnico magnet core.
The mini-humbucker has a smoother attack with more sustain, and you’ll get more of a grind to the tone when you push your amp into distortion. Traditional Firebird pickups have a tighter, spankier tone that stays more defined when you really crank up your amp.
Johnny Smith pickups are a hybrid of both the mini-humbucker and Firebird; they combine the clarity of a Firebird with the smoother attack of the mini. It’s actually quite a clever invention— one coil has a bar magnet in it, like a Firebird, but it has a bottom plate made out of steel that is tapped and threaded to hold adjustable pole pieces for the second coil. The magnetism travels from the bottom of the bar magnet along the steel plate to the adjustable pole pieces. This makes the non-adjustable coil north up and the adjustable coil south up.
These small humbuckers were never very popular when they were first introduced. They tended to be overly microphonic and too bright. Recently, they have come back in to the spotlight. If they are made correctly they can be a very good pickup!
Jason makes extraordinary archtop, solid body and lap-steel guitars, and is a noted authority on nearly everything related to electric pickups; his book Basic Pickup Winding and Complete Guide to Making Your Own Pickup Winder sparked a new movement in boutique and aftermarket pickup manufacturing. lollarguitars.com