342  Bandpass and Notch Filters

Figure 12.8: Bainter filter with symmetrical notch at 1 kHz and a Q of 2.3.

An Elliptical Filter Using a Bainter Highpass Notch

The ability of the Bainter to give either a lowpass or highpass notch makes it a very useful building block for elliptical filters that have a zero or zeros in the stopband. I have made use of this in designing a comprehensive suite of elliptical highpass subsonic filters to assist with vinyl reproduction. [3] What I consider the most effective of these is shown in Figure 12.9, with 2xE24 pairs given for the awkward resistor values. It is a 4th-order elliptical filter with a single stopband notch centred on 10

Hz, where spurious vinyl signals are often at their maximum level due to arm/cartridge resonance.

The complete filter consists of a 2nd-order highpass stageA4, placed at the front to reduce internal clipping problems (I call this the New Order) and followed by a Bainter highpass notch. The response is shown in Figure 12.10. The noise output was −113 dBu (22Hz–22kHz, rms sensing) with all opamps 5532. The filter easily handled 10 Vrms in/out at low distortion from 50 Hz to 50 kHz. My recent book Electronics for Vinyl [3] contains much more on subsonic filtering.

I like the Bainter filter. It is a very useful and well-behaved filter configuration. It may not be the simplest of filters, but its inherently deep notch and its good noise and distortion behaviour are a joy to work with. Mr Bainter, I salute you.

There are relatively few references to the Bainter filter in the literature; Valkenburg [4] is one.

The Bridged-Differentiator Notch Filter

Anotch filter that can be tuned with one control can be useful in development work. Figure 12.5d shows a bridged-differentiator notch filter tuneable from 80 to 180 Hz by RV1. R3 must theoretically be six times the total resistance betweenAand B, which here is 138 kΩ, but 139 kΩ gives a deeper notch, about −27 dB across the tuning range. The downside is that Q varies with frequency from 3.9 at 80 Hz to 1.4 at 180 Hz; clearly it is no substitute for a state-variable filter where frequency and Q can be changed independently. It may be an economical circuit in terms of amplifiers, but it uses three capacitors instead of the two in the 1-BPand Bainter filters.

344  Bandpass and Notch Filters

Figure 12.11: Lowpassnotch (a) and highpass notch (b) Boctor filters. The design at

(b) has a notch at 150 Hz with a Q of 1.

Figure 12.12: Response of Boctor filter in Figure 12.7b, giving a highpass notch at 150 Hz with a Q of 1.

Figure 12.12 shows the highpass notch produced by the Boctor circuit of Figure 12.11b; the highfrequency passband gain is +12 dB, with a gain of +6 dB on the low-frequency side of the notch. The capacitor values may be scaled to change the notch frequency, but they must be the same. A lowpass notch is the mirror image of this sort of response, with the low-gain section on the high-frequency side.

Like Bainter filters, Boctor highpass or lowpass notch filters are frequently used as a component part of elliptical filters.

Bandpass and Notch Filters  345

Other Notch Filters

The field of active filters is rich in possibilities. Other notch filters that there is no space to examine here, but which can be found in the filter textbooks, can be derived from biquad filters such as the Fliege filter, [7] the Tow-Thomas filter, the KHN state-variable filter, the Berka-Herpy filter, the Akerberg-Mossberg filter, and the Natarajan filter; these give symmetrical notches. See Chapter 10 for more on them. Filters apart from the Bainter and the Boctor that can generate highpass or lowpass notches are Friend’s SAB circuit [8] and the Scultety filter. The only reference I can find for the latter is [9], which at least gives the schematic; the same reference also gives schematics of the other filter mentioned in this section.

The Wien-Robinson filter is not biquad-based but uses a Wien network with feedback around it. [10] Notch depth depends on component accuracy, unlike the Bainter, and it seems to have no compensating advantages.

Simulating Notch Filters

When simulating notch filters, assessing the notch depth can be tricky.You need a lot of frequency steps to ensure you really have hit bottom with one of them. For example, in one run, 50 steps/decade showed a −20 dB notch, but upping it to 500 steps/decade revealed it was really −31 dB deep. In most cases having a stupendously deep notch is pointless. If you are trying to remove an unwanted signal, then it only has to alter in frequency by a tiny amount and you are on the side of the notch rather than the bottom, and the attenuation is much reduced. The exception to this is the THD analyser, where a very deep notch (120 dB or more) is needed to reject the fundamental so very low levels of harmonics can be measured. This is achieved by continuously servo-tuning the notch, so it is kept exactly on the incoming frequency.

References

[1]Augustadt, H. Electric Filter US Patent 2,106,785, February 1938, assigned to Bell Telephone Labs

[2]Bainter, J. R. “Active Filter Has Stable Notch, and Response Can Be Regulated” Electronics, pp. 115–117, 2 October 1975

[3]Self, Douglas “Electronics for Vinyl” Taylor & Francis, 2017

[4]Valkenburg, Van “Analog Filter Design”, pp. 346–349

[5]Boctor, S.A. “SingleAmplifier Functionally Tuneable Low-Pass Notch Filter” IEEE Trans Circuits & Systems, CAS-22, 1975, pp. 875–881

[6]Valkenburg, Van “Analog Filter Design”, p. 349

[7]Carter and Mancini (ed.) “Opamps for Everyone” Third Edn, Newnes, 2009, Chapter 21, p. 447, ISBN: 978- 1-85617-505-0

[8]Valkenburg, Van “Analog Filter Design”, p. 356

[9]www.schematica.com/active_filter_resources/a_list_of_active_filter_circuit_topologies.html;Accessed July 2017

[10]Tietze and Shenk “Electronic Circuits” Second Edn, Springer, 2008, pp. 825–826