Any filter, whether electrical, mechanical or acoustical, has both reactivity and resistivity. Acoustic filters are formed with things like chambers and ducts, and stuffing can be used to damp them. Mechanical filters are things like masses and springs, and resistance to motion like viscous fluids (shock absorbers) can be used to damp their motion. Electrical filters have inductors, capacitors and resistors.
Inductors tend to resist change of current flow through them. Current flowing through them generates a magnetic field around them, storing the energy in the field. When current flow is reduced, the magnetic field collapses into the coil, putting energy back into the circuit. This has a current stabilizing effect.
Capacitors tend to resist the change of voltage across them. When voltage is applied across the plates, energy is stored in the dieletric between them. If the voltage across the plates is reduced, the dielectric discharges, releasing energy into the circuit. This has a voltage stabilizing effect.
Resistors resist the flow of current and the change of voltage across them equally. They simply impede current flow through them.
When an inductor and capacitor are placed in a circuit, they resonate at a certain frequency. If there is no resistance in the circuit, the resonant peak will be very high and the bandwidth of the peak will be narrow. Adding resistance to the circuit reduces the amplitude of the peak, but widens the frequency range of the peak. This is called damping.
You can see how these things interact in the documents below:
When I came up with the Pi Crossover, my goal was three-fold:
1. Provide SPL level matching
2. Provide top-octave augmentation
3. Provide a flat shelf up to mass rolloff
The way I did this was to first use a resistive voltage divider network (fixed L-Pad) to attenuate the passband, and bypass the series resistor with a capacitor to provide 6dB/octave augmentation. You could do this with textbook L-Pad values, except that would not satsfy goal #3.
The compression driver is flat up to mass rolloff, around 4kHz. Only above that point do you want the diagonal line of rising response. That's the problem with most CD equalization schemes in active crossovers - if you jumper in CD EQ, you get a diagonal line of rising response. That may work with some horns, if there is enough of a quarter-wave mode around the crossover frequency to boost the bottom end enough to make the whole tweeter passband have falling response. But I'm not sure I'd want to crossover to a tweeter horn in an area where it had quarter-wave modes, because that's probably too low for it to sound good.
So there's the rub. If you have the top-octave compensation filter providing 6dB/octave augmentation, then you need something to flatten out the bottom end, up to 3kHz.
The way I do it is to slightly underdamp the splitter filter. This lifts the region right around the crossover frequency, just enough to get the first octave or so flat, up to mass rolloff. The amount of damping should be chosen specifically for the horn/driver used, as this is where they are the most different. Some horns have more peaking down low, others have less. The goal is to use a horn that is not peaking at all, and then to use a filter with this transfer curve:
Wayne,
Please explain what "damping" means in this context, I've been struggling with this concept a while and I know it's an elementary part of circuit design, but it's not clicking.
I understand initial attenuation of the hi-pass is required to allow the compensation filter latitude to "remove" attenuation in the conjugate of the rolloff above 3 or 4 kHz.
When you say the "core" crossover in your designs is allowed to be underdamped, I visualize less attenuation at the crossover point, but now I think it refers to the slope of the filter. To make the shelf flatter, the slope has to be sharper, or steeper -- this gives a flatter initial response to mass rolloff because the filter has less-gradual rise from the core filter.
So does an underdamped higher impedance load provide this?
Sorry to be basic.