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Figure 5.5 shows that the two Bainter notch filters for lowpass and highpass are very similar, with only three components differing in value. This sort of convenient behaviour is what makes the Bainter filter so popular. The relationship between R3 and R4 in the lowpass filter, and between R13 and R14 in the highpass filter, determine the kind of notch produced. If R4 is greater than R3, you get a lowpass notch. If R3 = R4, you get the standard symmetrical notch. If R3 is greater than R4, you get a highpass notch. The value of R6 (or R16) sets the notch Q.

There are however some aspects of this circuit that are less convenient. The lowpass notch response does not actually start out at 0 dB at low frequencies; instead it has a gain of +10.6 there. The response then drops into the crevasse and comes back up to 0 dB. There is then the gain of +1.3 dB from

the lowpass filter, giving a total of 11.9 dB of passband gain, which may not fit well into the gain/ headroom scheme planned for the crossover.

The highpass notch response has a passband gain of 0 dB at high frequencies, and at frequencies below the notch comes back up to −10.8 dB.With the final highpass filter added the passband gain is +1.2 dB. Therefore we have a level difference of 11.9 − 1.2 = 10.7 dB between the two outputs, and this will have to be accommodated somewhere in the crossover system design. There is more information on the Bainter filter and other notch filters in Chapter 12.

Amost interesting paper on the use of Chebyshev filters (ripples in the passband), inverse-Chebyshev (notches in the stopband), and elliptical filters (ripples in the passband and notches in the stopband), with the added feature of a variable crossover frequency, was published in the JAES by Regalia, Fujii, Mitra, Sanjit, and Neuvo in 1987. [3] It is well worth studying.

Neville Thiele MethodTM (NTM) Crossovers

One of the better-known notch crossovers is that known as the Neville Thiele MethodTM crossover, introduced by Neville Thiele in an AES paper in 2000. [1] This does not appear to consist of elliptical filters as such (as far as my knowledge of elliptical filters goes, anyway) but a rather more subtle arrangement that sums to unity much more accurately than the Hardman crossover we have just looked at. One of the few examinations of this technique that has been published is that by Rod Elliot. [4]

I should say at once that the Neville Thiele MethodTM or NTM is a proprietary technology addressed by US Patent 6,854,005 and assigned to Techstream Pty Ltd, Victoria,AU, and that if you plan to use it for anything other than a private project you might want to talk to them about licensing issues.

The information given here is published by permission and is derived solely from the public-domain

References [1] and [5], which I have to say are not an easy read. I have never seen a schematic of a manufactured crossover using this technology, nor have I ever deconstructed any related hardware.

Using References [1] and [4], it appears that the lowpass path of a 6th-order NTM crossover filter (8th-order versions are also possible) consists of a bridged-T lowpass notch filter, followed by a 2nd-order lowpass filter with a Q of about 1.6; this is followed in turn by two 1st-order filters. This structure, together with the matching highpass path, is shown in Figure 5.6.

The result of this rather complicated-looking block diagram is shown in Figure 5.7. Each filter output has a fast roll-off after the crossover point, terminating in a shallow notch; the response then comes

126  Notch Crossovers

Figure 5.6: Block diagram of a 6th-order NTM crossover.

Figure 5.7: The 6th-order NTM crossover. The dashed line is at −6 dB.

back up a bit but then settles down to an ultimate 24 dB/octave roll-off. The filter responses may not look very promising for summation, but in fact they do add up to an almost perfectly flat response when the phase of one output is reversed. If summed in-phase there is a central crevasse about 12 dB deep, of no use to anyone.

Figure 5.8 shows a much closer view of the summed response. The bump below the crossover frequency peaks at +0.056 dB, while the flat error in the level above the crossover frequency is at −0.031 dB. Since these very small errors are asymmetrical about the crossover point, it seems more likely that they are due to opamp limitations or similar causes, rather than anything inherent in the crossover. They are negligible compared with transducer tolerances, or with the summation errors of crossovers that approximate flatness by using frequency offsetting; the performance is much better than that of the Hardman elliptical crossover, which has flatness errors of 0.9 dB.

Figure 5.9 attempts to show how the NTM crossover works; the response of each filter stage in the lowpass path is shown separately. (The responses of the two 1st-order filters have been combined

Notch Crossovers  127

Figure 5.8: Zooming in on the summation of the 6th-order NTM crossover, showing very small errors. The vertical scale is ±1 dB.

into a single response for the two when cascaded.) The bridged-T filter creates a lowpass response that comes back up to −5 dB after it has been down in the notch.You will note that the notch is much shallower than that of the more complex Bainter filter used for the Hardman crossover, but this has only a very small effect on the summed response, and the simplicity of the bridged-T circuit is welcome.

The next stage in the crossover is a 2nd-order lowpass filter with a cutoff frequency of 1.0 kHz and a Q of approximately 1.6. This is quite a high Q for a 2nd-order filter and gives a +4.5 dB peaking of the response before the ultimate 12 dB/octave roll-off. This will need to be taken into account when planning the gain structure; rearranging the order so the 1st-order filters come before the 2nd-order should ease the situation considerably.

The two 1st-order filters both have a cutoff frequency of 1.0 kHz, and so their combined response is down −6 dB at 1.0 kHz, with an ultimate slope of 12 dB/octave. The action of these two stages together is the same as that of a 2nd-order synchronous filter, as described in Chapter 7. If

implemented as simple RC networks, they must be separated by a suitable unity-gain buffer to give the correct response.

Figure 5.10 shows the schematic of my version of an NTM crossover based wholly on the information given in [1] and [4].

An interesting point is that in each path the two 1st-order filters can be combined into a single Sallen & Key 2nd-order stage with a Q of 0.5, thus saving an opamp in each path.As Figure 5.11 shows, the component values used are exactly the same. This is my modest contribution to the NTM.

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Figure 5.11: Replacing the two 1st-order filters with an equivalent 2nd-order Sallen & Key stage. This saves two opamps, as no output buffers are required.

References

[1]Thiele, Neville “Loudspeaker Crossovers with Notched Responses” JAES, 48(9), September 2000, p. 784

[2]Hardman, Bill “PreciseActive Crossover” Electronics World,August 1999, p. 652

[3]Regalia, PhilipA., Nobuo Fujii, Sanjit K. Mitra andYrjo Neuvo “Active RC Crossover Networks With Adjustable Characteristics” JAES 35 (1/2), January/February 1987, pp. 24–30

[4]Elliot, Rod http://sound.westhost.com/articles/ntm-xover.htm

[5]Thiele, Neville “Crossover Filter System and Method” US Patent 6,854,005 Feb 2005 (Assigned to Techstream Pty Ltd, Victoria,AU)