There's a few things going on in a passive blend, so I'll share what I've learned when building the LBCA-02 active blend control. I'd always wondered why the center blend position either had a dip in volume, or a sort of scoop tone on a regular blend pot but not when using the EMG active blend.
With passive pickups, anything that loads the pickup changes the frequency response. This is why they work better with very high resistance volume and blend pots in the 250K or 500K range: the coil of the pickup and a resistor becomes a tuned circuit. Changing the resistance will change the tuning of the circuit. This is why backing off the volume on a Strat or Les Paul not only reduces the volume, but mellows the tone.
With the typical blend we add another variable to this tuned circuit: the other pickup. We like to think of the blend as being two totally separate audio inputs with a pot in the middle that lets us select the amount of bridge and neck to mix. But you need to think in reverse: what does the pickup see when connected to a blend pot?
It sees the pot, of course. The blend pot resistance will add to the whole tuned circuit problem. But... it'll also see a WHOLE NEW INDUCTOR in the circuit! Yep, the other pickup.
That coil of the other pickup also changes the resonant frequency of that tuned circuit.
When blended at 50%, the bridge pickup will it's own side of the blend pot (let's call that Gang 1) as well as:
1. The entire inductance of the neck pickup (if you are using an M/N taper blend)
2. A large percentage of the neck pickup inductance (if you are using an A/C taper blend), or
3. 50% of the neck pickup inductance (if you are using a Linear taper blend)
This is because the OUTPUT of the blend pots (which are two pot operating in reverse) are tied together. So the output of Gang 1 of blend pot is not only fed forward to the amp, but ALSO fed back into the other side (Gang 2 of the blend pot) where the other pickup lives. The bridge pickup is now driving the blend pot Gang 1, Gang 2, the other pickup, and whatever else you've got in the circuit (volume pot, tone control) after it.
So how does EMG solve this with their active blends?
Instead of typing the output of each gang of the blend pot together, each gang goes through a fairly large capacitor (EMG uses 2.2uf, we use 4.7uf) and a 2k resistor before the gangs are connected. They also use a Linear taper pot for blending.
The cap and resistor trick goes way back to how old passive mixers are wired: the input was a cap and resistor, which prevented one input from loading down other inputs. In the ABCX blend, this output is then fed into a buffer, which effectively stops anything downstream (volume pots, tone controls, and the impedance of whatever you're plugging the bass into) from impacting that tuned circuit.
The cool thing, is that this trick will work on a passive blend without a buffer on the back end. There is a slight loss of volume in total, but that's the thing sacrificed to have a smoother blend with less interaction between pickups.
Sorry for all the words... ask a geek a question and you'll get a book!