Crossover Types  99

Fourth-Order Bessel Crossover

The 4th-order Bessel has its crossover point at −3 dB. It sums to give a −2.6 dB dip at the crossover frequency, as in Figure 4.48, while the summation with one phase reversed gives a +2 dB hump and two −1 dB dips as in Figure 4.49; the phase-reversed case does not look like a suitable case for

frequency-offset treatment, as pulling the cutoff frequencies apart will pull down the hump but deepen the dips, while pushing them together will pull up the dips but make the hump worse.

It looks more promising for the in-phase case, but pushing the cutoffs together for this crossover actually deepens the dip due to the phase-shifts involved. Pulling them apart by an increasing amount makes the dip more shallow to begin with, but before the response begins to straddle the 0 dB line, it undergoes a fairly complicated set of changes, with two new dips appearing either side of the central one, and they deepen as the offset ratio increases.

In this situation it is hard to say what constitutes the maximally flat solution, but a promising candidate is shown in Figure 4.50, where a frequency offset of ratio of 1.229 times gives only −0.18 dB at the crossover frequency, with dips either side that are −0.3 dB deep.

The summed group delay response has a moderate peak just below the crossover frequency.

Fourth-Order 1.0 dB-Chebyshev Crossover

Using the 1.0 dB-Chebyshev characteristic for each filter gives us Figure 4.51. The in-phase summed response has central peak at the crossover frequency of +2.22 dB, with the dips either side going down

Figure 4.48: The frequency response of a 4th-order Bessel crossover, resulting from in-phase summation. The dashed line is at −3 dB.

Figure 4.49: The frequency response of a 4th-order Bessel crossover, with reversed-phase summation. The dashed line is at −3 dB.

Figure 4.50: Zooming in on the frequency response of a 4th-order Bessel crossover, with an offset ratio of 1.229 times and in-phase summation. Vertical scale is ±1 dB.

Figure 4.52: The frequency response of a 4th-order Chebyshev crossover, resulting from reversed-phase summation. The dashed line is at −3 dB.

Figure 4.53: The frequency response of a 4th-order linear-phase crossover, resulting from in-phase summation. The dashed line is at −3 dB.