Active pickups have a battery powered preamp that gives them a thicker, hotter tone, while passive pickups do not.
"An active pickup is one that uses electronics to improve the sound and enhance its operation. There are a variety of ways to "Activate" a pickup. A simple "buffer" pre-amp will do the trick, but it will also amplify the hum and buzz the pickup produces. Just because a pickup is "active" doesn't guarantee you'll get great results. EMG pickups utilize an internal pre-amp (inside the pickup), which not only makes the pickup louder, it also reduces the noise. . ."

- EMG Website

Passive Pickup Systems
All basses and guitars generate an output signal by means of a pickup that translates some of the vibration energy of the strings in to voltage that gets sent to an amp. ?Passive? instruments send this raw signal to the amp, and passive volume and tone controls can only attenuate the signal and treble response, that is, make it quieter. In order for passive magnetic pickups to generate enough voltage to drive an amplifier, they must be wound with a large number of turns of wire. This causes high inductance in the coil, and a high impedance output signal. This has the effect of rolling off the extreme high and low frequency response and making the signal more susceptible to loss and degradation in the cable on the way to the amp. While this sounds bad, it?s one of the reasons passive pickups can sound ?punchier?, because the ear perceives more midrange when the high treble and low bass are rolled off. The powerful magnets and larger wire coils in passive pickups can also produce strange electromagnetic interactions with the strings and adjacent pickup coils, causing irregular response curves and dynamic effects usually not seen in active pickups. Both of these factors contribute to the unique voice and continued popularity of passive pickups.

Active Pickup Systems
Typical examples are EMG pickups and the Duncan/Basslines Active Pickups. These generally use low-impedance pickups with a smaller number of wire turns. This causes less loss in the high and low end, and generally allows a much broader, full-range, hi-fi sound. Unfortunately, it also means the voltage produced by the pickup is very low, not nearly enough to drive an amp through a long cable. So these pickups have miniature amplifiers, called preamps, built into the pickup housing itself. Thus the signal only has to travel a fraction of an inch before it gets amplified and buffered into a low-impedance output. These systems often, but not always, provide a higher output signal than passive systems, so you don?t need to turn up the gain as much on your amp, which can add noise.

To confuse matters, active systems can use passive volume and tone controls just like passive pickups. These controls are almost always have different values for potentiometers and capacitors, and you usually must use the parts supplied by the pickup manufacturer. In addition, because the connection from the pickup coils to the preamp is made inside the pickup housing, options like series/parallel switching and coil tapping are rare and generally not available unless the manufacturer has specifically designed the pickup for it.

Low-Impedance Pickups with Separate Pre-Amps
This kind of system is essentially an active pickup with the preamp taken out of the pickup housing and mounted separately in the instrument?s control cavity. This approach is typical of some Bartolini and Lace Sensor designs. You gain the ability to do things like coil-splitting and phase switching, because the pickup wires are accessible before they go into the preamp. However, adding a passive bypass switch is usually not a good idea, because the passive output of the pickup is so low. The preamps that go with these systems have a lot of gain to boost the output of the pickup?s signal to a useful level, and usually also offer some kind of active tone shaping E.Q.

High-Impedance Pickups with Separate Pre-Amps
This is essentially a passive instrument with high-output passive pickups that has an onboard preamp. All preamps will buffer the pickup?s output to a low-impedance signal and many add some gain to help drive your amp with less noise. This helps maintain signal integrity and retains much of the high and low end that would get lost in the cable run, resulting in a kind of ?ideal? passive sound. With this system you retain all the switching options you have with a passive instrument, and you can easily bypass the active circuit with a switch for a more ?vintage? sound, or as a fail-safe in case your battery runs out.

Onboard E.Q. Circuits
Most of these preamps also give you onboard active tone controls, where you can boost as well as cut frequencies, just like the E.Q. in your amp. There?s no sonic benefit to using these onboard controls rather than the ones on your amp, and they?re usually not as clean or quiet. The main advantage is being able to control your sound from the instrument, especially when going direct into a recording console or P.A. system.
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