audio
In the loudspeaker crossover circuit below, I believe the purpose of the resistor is to attenuate the signal to the second speaker (the tweeter).
However, in circuits I've seen that are supposed to perform attenuation only (l-pads), there are two resistors, one parallel as well as series (see second image).
Is the parallel resistor not required in the crossover, because the 0.4mH inductor is serving this purpose?
Put the capacitor in parallel with the LEDs and leave the resistor where it is.
When you power up, the voltage across the cap is 0 V. It will slowly charge up to match the voltage at the top of the LEDs.
A cross over needs to seperate bands of frequencies so that you are not wasting power feeding bass to a tweater and possibly damaging it. Firstly the bass crossover. I've chosen a cross over frequency of 500Hz but this needs to be considered in light of the speakers you wish to use. I've gone to this website and plugged some numbers in to the online calculator: -
The R in the circuit I've chosen to be the impedance of the speaker (8 ohms) although strictly speaking I should check to see that it is largely 8 ohms resistive at bass/middle. I've used 30uF and 3.3mH for the cap and inductor and this gives a 3dB cross over at 505Hz with a damping ratio of about 0.7.
See the graphs for predicted overshoot and passband - overshoot is about 1.07 (7%) and there will be an almost unnoticable peak in the spectrum. At 1kHz the signal level will be reduced by about 12dB. It is performing as a low pass filter.
The nice Mr. Okawa (the site I used) has got a similar page for a high pass filter using a series C and L//R down to ground - you should be able to follow the link and have a go yourself.
Best Answer
The second form is typically used to implement a "constant impedance" attenuator, replacing the 2R2 resistor in the sketch.
A first pass at designing the crossover network might assume the load is simply the tweeter, and thus uses the tweeter's impedance (typically 8 ohms) as the load resistance. The filter network is then designed and optimised to work into that load. (For example, the product of L and C determine the crossover frequency via the usual equation, while their ratio - with a load impedance of 8 ohms - determines the damping. The designer then chose 2u7 and 0.4mH as giving the response he wanted.
Then it turns out that the tweeter is a bit more efficient than the woofer, so the speaker sounds too shrill, so you need an attenuator to correct it.
The simplest attenuator - a series resistor - increases the load impedance to 10.2 ohms, thus reducing the damping factor of the filter. (You might hear an exaggerated shrill sound at the crossover frequency, for example).
The second form - a constant impedance attenuator, or L-pad, allows you to choose R1 and R2 such that the attenuation is the same, but the load impedance remains 8 ohms thus preserving the original properties of the filter.
In practice, while the second form is theoretically better, it is more complex and expensive, the simpler one may be adequate. Furthermore, loudspeaker design is not such an exact science, there are no perfect drive units, and cabinet design (shape of baffles etc) modifies the frequency response.
So it may even happen that the simpler filter compensates for an imperfection elsewhere in the system and both sounds and measures better than the theoretically better solution. But without extensive measurements and/or listening tests, you can't tell.