Fullscreen HTML5Med Res (??MB)HTML4

AUDIO OUT AUDIO OUT L R By Jake Rothman All-pass filters, part two – time delays from audio filters Along with the all-pass filters described last month, ordinary low-pass and high-pass filters also generate a group delay, as shown in Fig.20. This can either be a useful or an undesirable feature. A very rough approximation for filter delay can be achieved by taking the reciprocal of half the maximum phase shift (180°) at the cut-off frequency. So for a 1kHz fourth-order filter, the group delay would be 1 ÷ 2f = 500µs. Lower-order filters will have less delay. Bessel filters have a flat group delay, whereas the more Group delay (µs) 350 common Butterworth type (which has a flat passband response) has a small hump in delay at the rolloff point. If the outputs of a high-pass filter and a low-pass filter are combined, the delay remains, resulting in an all-pass filter, as shown in Fig.21. In loudspeaker crossover networks, the same effect occurs, although the summation is acoustic. In another example, the second-­ order state-variable filter is a common building block of many audio systems, providing low-pass, highpass and band-pass outputs. By Tweeter 300 250 Input Woofer 200 High-pass filter 150 All-pass filter output + Low-pass filter 100 All-pass filters in equalisers The state-variable filter, although incredibly useful, uses integrators. These can suffer instability at DC and high frequencies with some op amps. I’ve had this a few times with my favourite, the NE5532, in parametric equalisers. Mixer 50 0 1kHz Frequency 2kHz 3kHz Fig.21: mixing the outputs of a highpass and low-pass filter gives an all-pass filter. Fig.20: the group delay for the 1.8kHz fourth-order Linkwitz Riley high-pass and low-pass filters used in the TI active loudspeaker. R1 22kΩ + VR3 1kΩ R5 620Ω – C4 100nF VR2a 100kΩ Antilog State variable filter CW – C3 100µF R14 330kΩ IC1a TL072 R4 5532 4.7kΩ Low C10 6.8nF C6 100nF VR2b 100kΩ Antilog High f ÷ 10 SW1a CW + Input R2 22kΩ + + C1 1µF adding the low-pass and high-pass outputs together, a notch filter is formed because the outputs cancel where the frequencies overlap. If these outputs are subtracted using a differential amplifier, an all-pass output results. The whole system is shown in Fig.22 and Photo 11. A cheap way of obtaining a variable all-pass filter in the studio is to combine the outputs of an off-the-shelf active crossover. These units are normally based on fourth-order state-variable filters with Linkwitz-Riley curves (-6dB at the crossover frequency); some typical rack-mountable adjustable crossover units are shown in Photo 12. R8 620Ω + IC1b TL072 R7 5532 470Ω – C5 100µF R15 330kΩ 0V C11 6.8nF SW1b R10 100Ω LP + 0V IC2a TL072 5532 R9 470Ω R11 100Ω BP Trim for peak resonance HP + C2 220µF 0V CW Pin 8 C9 470nF Pin 4 + C7 10µF C8 10µF From HP 10µF 0V From LP 10µF + 0V + +V 10kΩ –V 10kΩ R14 22kΩ 12kΩ 10kΩ – TL071 5534 + 47pF R16 22kΩ R12 100Ω From HP 100Ω + VR1 10kΩ Antilog + Switch out for min Q 47pF 10µF All-pass From LP R15 22kΩ R17 470Ω R13 470Ω – + IC2b TL072 5532 For mix notch Inverting summing stage 0V 0V Fig.22: the second-order state-variable 0V filter can give high-pass, band-pass & low-pass outputs simultaneously with only two frequency determining capacitors. Notch and all-pass outputs can be obtained by summation/subtraction of the high-pass and low-pass outputs. 54 Practical Electronics | May | 2026 Photo 11: a lecture lab demonstration set-up of the state variable filter shown in Fig.22. Fig.23: a musical parametric equaliser using all-pass filters designed by Steve Dove. It is more stable than the more common SVF type using dual integrators. 39pF 10kΩ 10kΩ 10kΩ – IC2a TL072 10nF Input 39pF + 470Ω Output + 470Ω Frequency CW VR2a 47kΩ Antilog – IC2b TL072 10nF CW VR2a 47kΩ Antilog 0V 10µF Input 0V 10kΩ 100kΩ Boost 0V Cut CW 10kΩ – IC1a TL072 + 10kΩ 47µF 47Ω + Loudspeaker phase problems Multi-way loudspeakers are the greatest embodiment of phase and polarity problems in audio. 10kΩ + Steve Dove, one of the most influential mixing console designers, replaced the state-variable filter in his EQ with a pair of all-pass filters, using the arrangement shown in Fig.23. This allowed each op amp to be individually stabilised, rather than via an overall loop; 10kΩ feedback resistors and the 39pF phase-lead capacitors do the job. AC-coupling capacitors (with DC biasing resistors) can then be put in series with the pots to prevent scratching without the risk of latch-up. This circuit configuration never really took off because of the dual-­ gang anti-log Bourns 91A potentiometers specified, which were very expensive. I think it is worth revisiting now that equivalent cheap pots are readily available, making a few tweaks and creating a PCB. Of course, such a circuit with lots of positive feedback becomes an oscillator. A similar all-pass system was used in Marconi audio analysers. Variable all-pass filter Output 100kΩ 0V 39pF 4.7kΩ 68pF 3.9kΩ – IC1b TL072 + CW Input Variable Output all-pass filter 33kΩ VR3b 22kΩ Antilog CW 220kΩ 0V VR3a 22kΩ Antilog 4.7kΩ Photo 12: a selection of low-cost Chinese active crossover units. At the top is a third-order unit from Pulse; the lower black units are fourth-order LR crossovers from Behringer. Practical Electronics | May | 2026 55 Fig.24 shows the seven phase variables in a typical two-way speaker. A three-way system is even worse. The anti-phase nulls around the crossover region can be clearly heard with white/pink noise if one bobs one’s head up and down in front of the speaker. If a square wave is put through a multi-way loudspeaker, it invariably emerges as a scrambled mess due to its complex overall phase response. In the 1970s, there was a craze of attempting to make “linear phase” loudspeakers. While never achieved, this did provide a significant impetus to crossover development. These speakers had a strange appearance, having stepped fronts in an attempt to provide phase alignment on the listening axis. The B&W 801 and KEF 105 were denigrated as looking like the Daleks from Dr Who, but their crossovers were superbly smooth. Later on, these physical manifestations of phase correction disappeared as crossover designers added all-pass filters. The loudspeaker system I described in part one (Fig.16 last month) is shown in Photo 13 and looks completely conventional. Note Photo 13: this little LS3/5a derivative, using a Morel MDT29 tweeter instead of a KEF T27, has an all-pass filter to allow a conventional baffle with flush front-mounted drivers to be used. Fig.24: a two-way loudspeaker system has seven phase variables. Only by defining each in stages can a good crossover network be designed by calculation. Anti-phase null Tweeter polarity flip ‘phase shift’ #2 Filter delay phase shift #1 High-pass filter + – Tweeter Tweeter lower roll-off: phase shift #6 Tweeter fundamental resonance: phase shift #7 Input Ideal on-axis response crossover sums in phase In-phase lobe Low-pass filter Filter delay phase shift #3 Upper roll-off: phase shift #5 Woofer Null Time delay due to distance: phase shift #4 the crossover with the hard-wired all-pass filter (with yellow capacitors and white inductors) on top. However, all-pass filters are still rare in passive crossover systems. One I am familiar with was the Tannoy Broadcast Monitor 8, made in the 1980s. This was the monitoring system we had at the university studio when I was an undergraduate. Of course, I had to take it to bits to trace the crossover circuit, with the result shown in Fig.25. The larger delay needed for matching High-pass filter + Drive unit polarity It’s essential to connect the woofer correctly, with its positive terminal being driven from the positive connector (on the back of the box) to ensure consistent absolute polarity. The mid-range and tweeters are often All-pass delay network Impedance correction for tweeter makes a resistive 8Ω load for all-pass filter 3.3µF 0.19mH 8µF 0.2mH a 25mm dome tweeter to a 200mm bass/mid unit was achieved with a second-order all-pass network with four inductors. I’ve noticed that time-aligned systems such as this have superior stereo imaging. 0.19mH 3.3µF 12Ω 2.5W + Input 2.26mH 3Ω – 3.3Ω 2.5W 0.19mH 3.3µF 6.8µF 3.3µF 25mm soft dome 0.19mH 3.3µF 2mH laminated core Fig.25: this crossover from the Tannoy Broadcast 8 studio monitor loudspeaker was one of the first to use a passive all-pass filter. 56 4.7µF + 8-inch polypropylene bass/mid driver 4.7Ω 10W Practical Electronics | May | 2026 + + Fig.26: the 12kΩ 12kΩ 12kΩ Brooke Siren 12kΩ f C Systems – – 100 – 200 68nF IC1a IC1b FDS 360 was Input 100µF 220 – 400 47nF 2.2µF 220nF 470Ω LF353 LF353 500 – 800 22nF + + one of the Output 47µF 1kHz – 1.3kHz 15nF 16V 1.5kHz – 2kHz 10nF Polarity first active Phase 2.5kHz – 4kHz 4.7nF 470kΩ 220kΩ trim 4.5kHz – 7kHz 3.3nF 220kΩ crossovers to 100kΩ C* 12kΩ use all-pass 0V *Select C according to 0V crossover frequency f filters. wired in reverse polarity to ‘correct’ 1993. Unfortunately, I put one back All-pass filter time correction filter phase shift and physical offset together with the tweeter wires Several stages of all-pass filtering, problems. flipped and she noticed. I was secret- typically two or three, are needed to This is a naughty bodge, since ly miffed that her hearing was better get the required delay for most tweetwe are using a polarity inversion to than mine; I now get her to listen to ers. This is because there is often a compensate for a phase shift, which is everything I make. droop in group delay with all-pass not mathematically correct. You can’t filters at the higher frequency end. theoretically correct a time delay Speaker phase response The number of stages can often be problem with a polarity inversion. When the acoustic outputs of reduced if a tweeter polarity flip is However, it can eliminate a notch rea- speaker crossovers filters are com- introduced and the group delay of sonably well over a small frequency bined with the drive units’ re- the filters is added in. band, such as the crossover overlap. sponses, the all-pass response is The general approach in the indusThe tweeter is often inverted with almost chaotic, usually with a large try for all-pass filter stages seems to 2nd-order crossovers, where the additional increase in group delay be to make the turnover frequency of low-pass and high-pass outputs are around the crossover point. the all-pass filters (1 ÷ 2πRC) around theoretically 180° apart in phase. At higher frequencies, around three to four times the crossover With fourth order, they are 360° the typical mid tweeter crossover frequency. This means more stages apart, which gives the illusion they range of 1.8kHz to 4kHz, the sonic are needed because of the higher are of the correct ‘polarity’ again. effect of all-pass filtering has been frequency. One has to be careful though, with shown to be practically inaudiIf you actually knew the group the off-axis dips that may occur just ble by Jim Wilkinson (Bookshelf delay of the filters, the group delay outside the crossover area. Loudspeaker Mk II, Wireless World, of the drivers (due to their roll-offs) A similar scenario exists where June 1979) and Siegfried Linkwitz as well as the physical displacement, all-pass filters are used to compen- (www.linkwitzlab.com). the calculations could be performed. sate for driver displacement and However, at low frequencies KEF managed all this data crunchfilter phase shift, since they also (<700Hz), it becomes noticeable due ing with a Hewlett-Packard mainoperate over a finite frequency range. to the longer time delay for the same frame computer in the late 1970s. Going back to my bad habit of number of cycles shift. They included all the parameters taking everybody’s stuff apart. I did necessary to generate an electrical it with my then-girlfriend’s, now Stepping back filter that would give the desired wife’s, KEF Coda speakers back in The old way to obtain time align- electroacoustic target function, such ment with the bass/mid unit is to as a Butterworth curve. This was the Photo 14: a stepped baffle can be position the tweeter behind the combination of the electrical and used to align the acoustic radiation woofer to line up the drivers’ acous- acoustic response, giving a predictplanes of the woofer and tweeter, but tic centres, as shown in Photo 14, by able crossover result. it’s a bit of a faff to build and ugly. using a stepped baffle. This was first The process is described in an ardone for the UK home constructor in ticle titled Crossover Networks in the Jim Wilkinson’s High Quality Book- December 1981 issue of Electronics shelf Loudspeaker (Wireless World, Today International (ETI). It’s still October 1977). very apparent from most speaker I remember struggling with the designs today that this lesson has woodwork for this design aged 15 “still not been learned”, as a UK civil at school in Suva, Fiji, in 1978. The servant would say, after 45 years. teacher thought I was insane, saying Many designers still think the in his Indian accent, “Why you build crossover electrical slope defines silly box?” I didn’t bother to explain. the speaker slope, hence all the Such steps are generally not a good low-cost crossover units just seem idea because the reflections and to have Linkwitz-Riley Butterworth diffraction anomalies wipe out the slopes. They only work if all your gains. Applying thick felt helps, but drivers have a DC-to-light frequency it looks bad. 48 years later, the WW response. speakers still live on in a studio in One exception was the Brooke Bath (I’m 63 now). Siren Systems FDS 360 crossover, It’s better engineering to use an where you could have any slope or all-pass filter to delay the signal to frequency selected by a plug-in card. the tweeter. A more recent design It was also the only one at the time also worth reading is the Analog Ac- with variable all-pass filters on every tive Crossover Circuit for Two-Way output, as shown in Fig.26. It could Loudspeakers by John Caldwell for minimise nulls that the polarity Texas Instruments (TI). switch could not deal with. Later + Practical Electronics | May | 2026 57 10pF 1kΩ 1kΩ – IC1a Input Fig.27: this third-order all-pass filter used in the TI loudspeaker provides a 155µs delay at 1.8kHz. 100nF 220Ω 100nF + 10pF 422Ω – 475Ω 330Ω + 1kΩ 0V 0V 100nF Op amps are three sections of NE5532 or OPA1604 IC1b Inverting multiple feedback band-pass filter 1kΩ – IC1c + 0V Output Summer 58 Photo 15: this speaker, based on Wavecor drivers (PE Feb-Mar 2020) has the tweeter next to the woofer to ensure good integration up-close. No all-pass filter was necessary due to an asymmetric crossover. I have given up determining this mathematically, since I can get it right much quicker by twiddling a knob on the all-pass filter tweeter compensation jig I made, shown in Fig.29 and Photo 16. This will compensate for the variables, including the unknowns. When I get the perfect summation and reverse polarity cancellation dip, I simply measure the resistance value of the pot. Of course, if you later alter the crossover filters or driver equalisation, it will need readjusting again. This is how loudspeaker design is for the home constructor, unless you have accurate drive unit models and love playing with complex software. There are some excellent books on the computer-based design V+ 100nF 100nF V– +12V + 10µF 25V + 0V 10µF 25V Standard decoupling network 0V –12V 22kΩ 10µF Input 25V + Time delay compensation To calculate the distance to be compensated for, the familiar time equals distance divided by velocity equation is used, or T = D ÷ c, where c is the speed of sound, which is about 343m/s at sea level with standard temperature and pressure. This allows a rough estimate to be made. It’s best to take the measurements from the drivers’ actual acoustic centres, or by sliding the tweeter back and forth relative to the bass/mid unit for best summaFig.28: tion at the crossover frequency. Tweeter moving the A more sensitive test here is to tweeter reverse the tweeter polarity, tune up is an for the deepest notch, then put it old trick to back to the correct polarity. minimise... The tweeter delay circuit used in the TI design comSlight lobe tilt (exaggerated) bined second-order and first-order Wide spacing all-pass stages to give the required delay of 155µs at 1.8kHz, as shown ...the in Fig.27. downward tilt in the Integration and design main An essential part of good driver radiation Woofer integration is to get the drivers lobe physically as close as possible, caused such as the Wavecor design in by the Photo 15. woofer’s On some passive speakers, the acoustic tweeter may be placed a couple of centre Tweeter inches (~50mm) higher because it being reduces the tilt angle of the main further radiating point. A quick applicaback than tion of trigonometry, the tweeter. shown in Fig.28, Close as Greater lobe tilt demonstrates this possible spacing effect. I don’t approve of increased spacing, since the tweeter sounds disembodied It also Woofer when the system is gives a used for near-field flatter baffle monitoring. In active speakers, it for the gives the best results to put the tweeter to drivers’ flanges virtually touching radiate from. and then dial in the correct time Displacement of acoustic centres alignment. they made a digital unit that could provide any delay required. One all-pass stage wasn’t quite enough for some systems, but it was a useful trim after the driver boxes had been sensibly positioned. The FDS 360 crossovers were used for the Turbosound PA system. They had a higher frequency and shallower slope on the mid-range horn low-pass filter compared to the tweeter high-pass. When I worked there in the late 1980s, I enjoyed setting up the 360s. 22kΩ 22kΩ 100kΩ 100Ω – + IC1 NE5534 Polarity flip 0V Practical Electronics | May | 2026 of loudspeakers, such as Vance Dickason’s Loudspeaker Design Cookbook, and the software is getting cheaper. You don’t have to spend £5k on proprietary software to run on a £500 computer anymore, but £375 software, such as Crosslite+, may be needed. (I’ve not tried it, only watched a video showing how to use it, and it looked ‘too easy’). Watch out for subscriptions as well; they are becoming an unpleasant certainty in life, along with death and taxation. Just to be contentious, I would say that with the most popular computer-­designed speaker format, the LR fourth-order reflex, makes the speakers all have a similar sound, tailored for the studio showroom and possibly no better than good empirical designs such as the Spendor BC1 and BBC LS3/5a. Conversely, most of the inaccurate speakers around seem to have been designed by people with defective hearing. Photo 16: the tweeter time alignment jig. Now I have the PCB, I can replace this and make a wellfinished unit. ness, so this topic will continue next month, including some more all-pass filter theory. That will include some hybrid crossovers used by KEF that provided group delay for phase alignment as well as crossing over the drivers in the speaker. After that, we’ll look at combining regular and all-pass filters to make new kinds of filters, including those that use signal subtraction to form new filters. We’ll also discuss the purpose of Linkwitz-Riley crossovers in a bit more detail. After that, we’ll get to the practical side of this topic and build a universal all-pass filter board, with up to eight cascaded all-pass sections or poles available, built around four PE dual op amp chips. Bass-to-mid crossover phase The effect of a physical displacement in the drivers is usually insignificant at the lower bass/mid crossover points due to the long wavelengths involved. Using the equation λ = c ÷ f, the “Ohm’s Law” of acoustics, for say f = 300Hz, (a common crossover point for 3-way designs with 100mm mid units), the wavelength λ = 343m/s ÷ 300Hz = 1.14m. A typical driver displacement distance is around 60mm, which is virtually insignificant compared to a wavelength of over one metre. Next month We are running out of space but still have some unfinished busi- Maximum delay sections 10µF + 10kΩ 10kΩ 0V 10kΩ Test points to measure pot value 47kΩ Lin – CW IC2a NE5532 10kΩ 47kΩ Lin 100Ω 2018-2022 £49.95 2017-2021 £49.95 2016-2020 £44.95 Purchase and download at: www.electronpublishing.com 2 3 22kΩ + 10µF £49.95 4 22kΩ 0V 22kΩ 2019-2023 Output 0 1 5-year collections – CW IC2b NE5532 10µF + + 0V 10kΩ 10kΩ 47kΩ Lin 100Ω 22kΩ 22kΩ – CW IC3a NE5532 0V 10µF 10kΩ – CW IC3b NE5532 + + + + 4.7nF 4.7nF 4.7nF 4.7nF 0V 0V 0V 0V 1MΩ 10µF 10kΩ 47kΩ Lin 100Ω + 0V 100Ω Quad-gang 47kΩ linear potentiometer Fig.29: an adjustable all-pass filter for tweeter – a useful bit of kit for any active speaker designer. It enables you to find out the number of all-pass stages required and the optimum RC frequency by twiddling a knob. Practical Electronics | May | 2026 59