under what conditions do two single coils humbuck

[RedHouse]

I usually put it this way... you have two coils wired out of phase. Any common signal to both will be canceled out.

Then you have the opposite polarity magnets, which also put the two coils out of phase in regard to the strings.

Because the coils are wired out of phase, the signal from the strings is summed in phase, while the noise, which didn't rely on the magnets to be picked up, is still out of phase and is canceled out.

High frequencies are also canceled to a small extent, which is why it's common to offset the coils slightly.

That's exactly right. ...(in the voice of Maxwell Smart) Ahh yes, the old double secret reverse phase trick!

Besides it's already been described in the patents, no need to reiterate.

[Amplexus]

This has been an interesting discussion

As I understand it two coils wound in opposite directions will cancel hum even if no magnets are present.
What happens if you invert the phase of one of the coils with an inverting op amp? I would think they no longer cancel hum.
Is there any combination of 2 single coils that will be humbucking besides the combination of n magnet forward wound and S magnet reverse wound or its inverse?
I think there is not even allowing for op amp inverters.

[David Schwab]

As I understand it two coils wound in opposite directions will cancel hum even if no magnets are present.

That's correct. The cores do matter, but the magnets are for sensing the strings, and the hum doesn't need the magnets to get induced into the coil. A steel core would work well for a hum sensing coil.

What happens if you invert the phase of one of the coils with an inverting op amp? I would think they no longer cancel hum.

EMG uses the two inputs of an op amp to do the hum cancelation. One coil goes into each input.

Is there any combination of 2 single coils that will be humbucking besides the combination of n magnet forward wound and S magnet reverse wound or its inverse?
I think there is not even allowing for op amp inverters.

Any time you have two coils out of phase, you will get hum cancelation. The reverse magnetic polarity is so that the pickup senses the strings in phase.

[Mark Hammer]

Inverting one coil of a pair, and mixing it with the second coil would result in cancellations, assuming the noninverted coil was starting out "in-phase", and that there was nothing about the circuit that would introduce any phase shift or "group delay" that might make signal 'A' 175 or 185 degrees out of phase with signal 'B'.

As for EMG pickups, my understanding is that they use a differential op-amp configuration, with each end of a single coil going to a different input of the op-amp, exactly the way a balanced voice mic would.

[David Schwab]

Inverting one coil of a pair, and mixing it with the second coil would result in cancellations, assuming the noninverted coil was starting out "in-phase", and that there was nothing about the circuit that would introduce any phase shift or "group delay" that might make signal 'A' 175 or 185 degrees out of phase with signal 'B'.

If you think about it.. if you invert a coil in a humbcuker, it gets thin sounding, and it hums. That would interact with a second single coil pickup in different ways.

As for EMG pickups, my understanding is that they use a differential op-amp configuration, with each end of a single coil going to a different input of the op-amp, exactly the way a balanced voice mic would.

Exactly. There was a schematic posted here at one point by someone that took apart an 81 pickup.

[David King]

As for EMG pickups, my understanding is that they use a differential op-amp configuration, with each end of a single coil going to a different input of the op-amp, exactly the way a balanced voice mic would.

Wouldn't that coil need a center tap for CMRR?

[David Schwab]

Wouldn't that coil need a center tap for CMRR?

One end of each coil goes to ground, and the other ends to the (+) and (-) on the op amp.

[David King]

Doh! I forgot that the 81 was an HB not a strat pickup.

[David Schwab]

Doh! I forgot that the 81 was an HB not a strat pickup.

The Strat pickups are stacked.