How do I design my own passive crossovers?

[Lee]

5.13 How do I design my own passive crossovers? [JSC, JR]

A first order high pass crossover is simply a capacitor placed inline with the driver. A first order low pass crossover is an inductor inline with the driver. These roles can be reversed under certain circumstances: a capacitor in parallel with a driver will act as a low pass filter, while an inductor in parallel with a driver will act as a high pass filter. However, a parallel device should not be the first element in a set; for example, using only a capacitor in parallel to a driver will cause the amplifier to see a short circuit above the cutoff frequency. Thus, a series device should always be the first element in a crossover.

When like combinations are used, the order increases: a capacitor in series followed by an inductor in parallel is a second order high pass crossover. An inductor in series followed by a capacitor in parallel is a second order low pass crossover.

To calculate the correct values of capacitors and inductors to use, you need to know the nominal impedance Z of the circuit in ohms and the desired crossover point f in hertz. The needed capacitance in farads is then 1/(2 * pi * f * Z). The needed inductance in henries is Z/(2 * pi * f). For example, if the desired crossover point is 200Hz for a 4 ohm driver, you need a 198.9 x 10^-6 F (or 199uF) capacitor for a high pass first order filter, or a 3.18 x 10^-3 H (or 3.18mH) inductor for a low pass first order filter.

To build a second order passive crossover, calculate the same initial values for the capacitance and inductance, and then decide whether you want a Linkwitz-Riley, Butterworth, or Bessel filter. An L-R filter matches the attenuation slopes so that both -3dB points are at the same frequency, so that the system response is flat at the crossover frequency. A Butterworth filter matches the slopes so that there is a peak at the crossover frequency, and a Bessel filter is in between the two. For an L-R filter, halve the capacitance and double the inductance. For a Butterworth filter, multiply the capacitance by 1/sqrt(2) and the inductance by sqrt(2). For a Bessel filter, multiply the capacitance by 1/sqrt(3) and the inductance by sqrt(3).

You should realize, too, that crossovers induce a phase shift in the signal of 90 degrees per order. In a second order filter, then, this can be corrected by simply reversing the polarity of one of the drivers, since they would otherwise be 180 degrees out of phase with respect to each other. In any case with any crossover, though, you should always experiment with the polarity of the drivers to achieve the best total system response.

One other thing to consider when designing passive crossovers is the fact that most passive crossovers are designed based on the speakers' nominal impedance. This value is NOT constant, as it varies with frequency. Therefore, the crossover will not work as it has been designed. To combat this problem, a Zobel circuit (also known as an Impedance Stabilization Network) should be used. This consists of a capacitor and resistor in series with one another, in parallel with the speaker, e.g.,

                  ________                __
         +  o----|        |----o-----o + |  | /
   INPUT         |  Xover |    R1        |  |/
                 |        |    C1        |  |\
         -  o----|________|----o-----o - |__| \

To calculate these values, R1 = Re (in ohms) x 1.25, and C1 = (Lces in henries / Re^2) * 10^6. See 4.1 for definitions of Re and Lces. R1 will be in ohms, and C1 will be in uF (micro- farads). As an example, an Orion XTR10 single voice coil woofer has Re = 3.67 ohms and Lces = 0.78 mH. So, R1 = 3.67 * 1.25 = 4.6 ohms. C1 = ( 7.8E-4 / 3.67^2 ) * 10^6 = 57.9 uF (be careful with units -- 0.78 mH = 7.8E-4 H)

As with the definition of crossover slopes, the above definition of the phase shift associated with a crossover is also an approximation. This will be addressed in future revisions of this document.