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Active Filters
Here is a itemize of line-level circuits that I have found useful for building active loudspeakers. Many other topologies are possible, but 1 should e'er analyze a circuit'south signal handling capability and its contribution to overall system racket before choosing it. A CAD software package such equally CircuitMaker is well-nigh convenient for analyzing and designing active filters. LspCAD software allows you lot to run into how an active filter changes the measured frequency response of a driver and lets you optimize information technology to a target response. All the line level filters below are included in LspCAD standard and professional versions. Component values for all the filters below and for a dual power supply tin be adamant from a circuit pattern spreadsheet contributed by Bernhard Faulhaber. It covers more cases than the before spreadsheet by Alister Sibbald.
1 - Buffer phase
2 - 12 dB/october Linkwitz-Riley crossover
iii - 24 dB/oct Linkwitz-Riley crossover
4 - Delay correction
5 - Shelving lowpass & passive circuit
6 - Shelving highpass & passive excursion
7 - Notch filter
8 - 6 dB/october dipole equalization
ix - 12 dB/oct highpass equalization ("Linkwitz Transform", Biquad)
ten - Variable gain & fixed attenuation
11 - Line driver
12 - Power supply
13 - Printed circuit boards
14 - Literature
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1 - Buffer stage
A buffer as the outset stage of an active crossover/blaster provides the necessary low source impedance to the post-obit filter networks. The buffer too provides a loftier impedance load to the preamplifier output excursion and the option of a highpass filter for dc blocking. (westward-xo-lp2.gif, pmtm-eq1.gif, 38xo_eq.gif) Meridian
2 - 12 dB/oct Linkwitz-Riley crossover
The ii outputs from the LR2 crossover filter are 180 degrees out of phase at all frequencies, which requires to utilise ane of the drivers with reversed polarity, so that the two audio-visual outputs add in phase. At the crossover frequency the filter outputs are 6 dB downwardly.
The acoustic frequency and polar response is controlled by the electrical filters and the response of the mounted drivers. The electric filter will non give the desired results, if at that place is insufficient overlap and flatness of the driver frequency response and when they are offset from each other. This can exist corrected in many cases with the addition of a phase shift correcting network. I consider the crossover marginally useful, considering the 12 dB/october coil-off of the highpass filter beneath the crossover frequency does not reduce the excursions of a commuter's cone when apartment frequency response is obtained. My before assumption that the group filibuster of a quaternary society LR4 crossover at low frequencies would innovate audible baloney was not right. Therefore I recommend non to use the LR2 crossover. (38xo_eq1.gif, FAQ19, xo12-24b.gif)
The LR2 excursion uses the Sallen-Key active filter topology to implement the 2nd order transfer office. The response is defined by due west 0 and Q0 which sets the location of a pole pair in the complex frequency s-plane and past an additional two zeros at s = 0 for the highpass filter. In the case of the LR2 filters Q0 = 0.v, and Q0 = 0.71 for each of the two cascaded 2nd order filters that form the LR4 filter. The frequency response is obtained by setting s = j westward and solving the transfer function for magnitude and stage. The formulas below can exist used to design filters with different values for w 0 or Q0, or to analyze a given circuit for its due west 0 and Q0 values.
Any order Linkwitz-Riley filters can be implemented by a cascade of second order Sallen-Key filters. The Q0 values for each phase are listed in the table below. The component values of each stage for a given crossover frequency f0 can be calculated by using Q0 and selecting a convenient value for C2 or R2 in the formulas to a higher place.
LR2 | LR4 | LR6 | LR8 | LR10 | |
Q0 of phase 1 | 0.5 | 0.71 | 0.5 | 0.54 | 0.5 |
Q0 of phase 2 | 0.71 | one.0 | one.34 | 0.62 | |
Q0 of stage 3 | i.0 | 0.54 | one.62 | ||
Q0 of stage four | ane.34 | 0.62 | |||
Q0 of stage 5 | one.62 | ||||
dB/octave slope | 12 | 24 | 36 | 48 | 60 |
Crossover filters of college order than LR4 are probably not useful, because of an increasing peak in grouping delay around f0.
Pinnacle
3 - 24 dB/oct Linkwitz-Riley crossover
The 24 dB/oct LR4 crossover filter provides outputs which are 360 degrees beginning in phase at all frequencies. At the transition frequency Fp the response is 6 dB downward. The electric network will only give the targeted exact acoustic filter response, if the drivers are flat and accept wide overlap. This is seldom the case. The steep filter slopes make the combined acoustic response less sensitive to magnitude errors in the commuter responses, but phase shift errors usually have to be corrected with an boosted allpass network. (xo12-24b.gif, 38xo_eq1.gif, models.htm#E) Height
Russ Riley and Siegfried Linkwitz, September 2006, Douglas City, CA |
In the sixties, early seventies, I worked with Russ Riley at Hewlett-Packard's Palo Alto R&D laboratory for the development of RF and Microwave test equipment. Like many other engineers we had "G-Jobs", building such things as electronic ignitions for our VW bugs and vans, FM receivers, phase-locked pulse width FM demodulators, short-wave receivers, sound pre- and power amplifiers, third octave audio analyzers, headphone equalizers, and of grade, loudspeakers. After measuring the audio-visual and electrical responses of commercial speakers we equalized them and tried to empathize why they were designed with strange looking commuter layouts, used large baffles, were blimp with a variety of internal damping materials and used various box stiffening and damping techniques. Eventually we completely redesigned them and built our own speakers. Russ and his wife, Vicky, an accomplished organist, always had the nigh critical and reliable ears. He was an ingenious design engineer, a stiff correspondent, who inspired and challenged many of the states on our HP and unofficial design projects. Russ retired later on over 40 years in R&D for HP/Agilent and now lives with his wife in a remote mountain valley, in a 18-carat log cabin, amongst pear, plum and walnut trees, berry bushes, craven and deer, the sounds of a large creek, and the pino and fir copse that climb up the slopes. He died peacefully in his log cabin on December six, 2010. |
4 - Delay correction
A first society allpass filter section with flat aamplitude response but stage shift that changes from 0 degrees to -180 degrees, or -180 degrees to -360 degrees, is often used to correct stage response differences between drivers. Multiple sections may delay the tweeter output and compensate for the driver being mounted forward of the midrange. Active crossover circuits that practise not include phase correction circuitry are only marginally useable. (allpass.gif, allpass2.gif, models.htm#E, 38xo_eq1.gif) Elevation
5 - Shelving lowpass
This type of circuit is useful to bring upwardly the low frequency response in gild to compensate for the high frequency boost from front panel edge diffraction. It can as well serve to equalize the depression frequency roll-off from an open up baffle speaker. (shlv-lpf.gif, 38xo_eq1.gif) Pinnacle
A passive RC version of the shelving lowpass is shown beneath.
half-dozen - Shelving highpass
A circuit used to boost high frequencies or to smooth the transition betwixt a flooring mounted woofer and a free standing midrange. (shlv-hpf.gif, 38xo_eq1.gif, models.htm#F) Top
A passive RC version of the shelving highpass is shown below.
7 - Notch filter
Notch filters are used to innovate dips in the frequency response in guild to cancel commuter or room resonances. The 3 circuits above have the same response. A) is difficult to realize because of the large inductor. B) is used to remove the peak in the 6 dB/october dipole response. C) gives convenient component values for room EQ below 100 Hz. (room EQ, inductr1.gif, inductr2.gif, 38xo_eq1.gif ) Elevation
8 - 6 dB/oct dipole equalization
Equalization of the dipole frequency response roll-off usually requires not just a half dozen dB/oct heave towards low frequencies, but also removal of a height in the response. (Models A2) The iii circuits differ in their ability to remove such pinnacle.
A) The shelving lowpass filter cannot correct for a tiptop.
B) The bridged-T based circuit is limited in the shape of curves that can be realized. It has also higher gain for opamp noise than signal at high frequencies.
C) The shelving lowpass with added notch filter is the most flexible circuit. (models.htm#D) Top
ix - 12 dB/oct highpass equalization ("Linkwitz Transform", Biquad)
A majority of drivers exhibit second order highpass behavior considering they consist of mechanical mass-compliance-damping systems. They are described past a pair of zeroes at the s-plane origin and a pair of complex poles with a location defined by Fs and Qt. The circuit above allows to identify a pair of complex zeroes (Fz, Qz) on meridian of the pole pair to exactly recoup their effect. A new pair of poles (Fp, Qp) tin can then exist placed at a lower or a higher frequency to obtain a different, more desirable frequency response.
This allows to extend the response of a closed box woofer to lower frequencies, in the above excursion case from 55 Hz to 19 Hz, provided the driver has adequate book displacement adequacy and power handling. The equalizer frequency response is shown below, correcting for a woofer with peaked response (Qp = 1.21) and early coil-off (Fp = 55 Hz), to obtain a response that is 6 dB down at 19 Hz and with Q = 0.five .
The associated stage and group delay responses are shown below.
Not but is the frequency response extended, but the time response is also improved, as indicated past the reduced overshoot and ringing of the lower cutting-off highpass filter step response.
Information technology can be seen from the s-airplane description of the transfer functions that the complex poles of the driver in the box are canceled past a prepare of complex zeros in the equalizer. The specified real centrality poles of the equalizer, together with the commuter zeros at the s-aeroplane origin, determine the overall loudspeaker response in frequency and time.
The equalizer activeness is difficult to visualize in the fourth dimension domain, because the driver output waveform is the convolution of the input signal s(t) with the impulse response of the equalizer hone(t), which in turn must exist convolved with the impulse response h2(t) of the driver. Convolution is a process whereby the electric current value of the time response is adamant by the fourth dimension weighted integral over by behavior. Below are the responses of driver, blaster and driver-equalizer combination, if the input signal due south(t) is an impulse.
More illustrative are the responses to a four-cycle, rectangular envelope 70 Hz toneburst s(t). For example, the driver output is the convolution of the burst s(t) with the driver's impulse response htwo(t). Annotation that the driver phase leads the input signal, as would be expected for a highpass response. Upon turn-off of the input burst at 57.14 ms the commuter response rings towards zero, governed by Fp = 55 Hz and Qp = 1.21.
The equalizer output response lags its flare-up input. This point will force upon the driver a response correction then that information technology is no longer dominated by Fp = 55 Hz and Qp = i.21. The equalizer output point is convolved with the impulse response h2(t) of the driver to obtain the desired equalized driver output. Now, the decay of the driver output follows the 2d club highpass filter response determined by Qp = 0.5 and Fp = 19 Hz of the equalizer, after the excitation has stopped.
Of form, none of the driver mechanical parameters like mass, compliance and damping accept been changed in the procedure of equalization, merely the input bespeak to the driver has been modified.
The above excursion can as well be used to right the low frequency roll-off of a tweeter and then that the equalized tweeter becomes a filter section in an exact LR4 acoustic highpass. (f0Q0fpQp.gif, pz-eql.xls, f0Q0.gif, FAQ15, sb80-3wy.htm, sb186-48.gif , sb186-50.gif)
The 'CFL Linkwitz Transform Designer with Monte Carlo Sensitivity Ananlysis' past Charlie Laub makes component value selection like shooting fish in a barrel and shows the effect of component tolerances upon the frequency response. Keep in mind that the LT is based on a measurement of commuter parameters Fs and Qt. Just the modest signal parameters are easy to ascertain. Fs and Qt change with increasing signal level and to varying degree for unlike drivers. This makes the equalization imprecise, but it remains effective in practise.
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x - Variable proceeds & fixed attenuation
A major reward of line-level active crossovers is the efficiency with which drivers of different sensitivity can be combined in a speaker system. The three circuits utilise linear taper potentiometers but obtain a gain variation that is approximately linear in dB. Circuits B and C assume a 10k ohm load such equally the input impedance of the ability amplifier. Excursion A is optimal between filter stages considering of its depression output impedance. The placement of the variable gain stage in the filter chain must be carefully considered, because it affects noise performance and signal handling. (gain-adj.gif, attnrout.gif, 38xo_eq1.gif) Tiptop
Occasionally a fixed attenuation of A dB or a is needed for the input voltage V2 of a excursion stage with input impedance R3 when driven from an operational amplifier with output voltage V1. In the example below a iii dB (a=1.41) attenuation is desired. The load Rin that is seen by the opamp should be about 2000 ohm. The post-obit amplifier stage has an input impedance of 10k ohm.
For designing an attenuator with specified output impedance Rout see: attnrout.gif
11 - Line driver
The output phase of the filter must be capable of driving cables, which typically have a capacitances in the order of 150 pF per meter length, without going into oscillation. A 196 ohm resistor maintains a resistive load component and tying output to negative input for out-of-band frequencies (>100 kHz) reduces loop gain. All of the in a higher place circuits can drive cables if operational amplifiers such as the OPA2134 or OPA2604 are used. In about cases it is non necessary to have a carve up line driver.
Performance of active circuits should always be checked for inter-stage clipping, and for oscillation with a wideband (>10 MHz) oscilloscope. Top
12 - Power supply
I recommend to get out the endeavour of building a regulated ability supply to 1 of the many vendors that offer wallplug and tabletop models. An output specification of +/-12 V to +/-15 5 DC at >250 mA and with <1% ripple and dissonance volition suffice. Often such supplies can exist found at electronic surplus stores. Top
thirteen - Printed circuit boards WM1 and MT1
To simplify the construction of agile line-level equalizers and crossovers I offer three printed circuit boards, ORION/ASP, WM1 and MT1. The circuit traces are laid out to allow for a variety of filter designs. It is upwardly to the user to determine the actual circuit configuration and component values. Then the necessary components and jumpers are loaded at the appropriate locations on the board to obtain the desired filter response. I will provide specific information for assembling the PHOENIX crossover/equalizer on the ORION/ASP pcb and a Linkwitz Transform on the WM1 pcb.
WM1 is designed to implement the functionality of circuits 1, five, 6, 7, 8, 9 or 10 and diverse combinations of these. The circuit lath provides ii of the topologies beneath for two channels of equalization or for a more elaborate single channel response correction.
The WM1 lath can exist used for:
- Equalization of an existing speaker with passive crossovers, baffle step correction and extension of the low frequency response.
- Pole-zip equalization of a closed box woofer and a LR2 crossover lowpass filter. Variable proceeds.
- Pole-zero equalization of a midrange and a LR2 crossover highpass filter.
- Dipole woofer equalization with notch and variable gain. LR2 crossover lowpass.
- Dipole woofer equalization for low Qts drivers.
- Depression frequency, individual channel and overall response equalization of multi-mode speakers, so long every bit elements of this topology let you to generate the response you need.
- Equalization of improver woofer , FAQ10, FAQ15
MT1 is designed to implement the functionality of circuits i, two, iii, four, 5, 10 or 11 and diverse combinations of these. On the circuit lath are two of the topologies below.
The MT1 lath tin be used to construct:
- A two-way speaker with crossovers of order 1, 2, 3, or four. The tweeter aqueduct has variable proceeds and delay circuitry to marshal the tweeter's acoustic center with the woofer. The input buffer phase can provide 4 p to 2 p polar response (baffle step) correction.
- The tweeter and midrange channels of a iii-style system. The midrange highpass filter of the woofer to mid crossover would accept to be provided by the WM1 board.
- The tweeter and upper midrange or upper midrange and lower midrange channels of a 4-way system.
- A bully diverseness of active multi-channel line level filters in combination with the WM1 board.
- Crossover for add-on woofer, FAQ10, FAQ15
The excursion boards are practical tools to experiment with and to learn about active electronics. You will find that active loudspeaker systems requite you the freedom to friction match drivers of greatly different sensitivities, are easier to design, and can give greater accuracy of audio reproduction, than is possible with passive, loftier-level crossovers and filters.
Run into the Excursion Board page for ordering information. Meridian
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fourteen - Literature
Much useful information can exist obtained from application notes of the various opamp manufacturers. If you lot need a refresher or an introduction to circuits, then read:
[i] Martin Hartley Jones, A applied introduction to electronic circuits, Cambridge University Press, 1995. It is a well illustrated, like shooting fish in a barrel to read, yet technically solid text. It covers a broad range of devices - from tubes to ICs - and many basic circuit functions.
The following books cover a range of concepts and go into depth on specific, relevant topics to strengthen agreement of electronic circuits and electro-acoustic models.
[two] Herman J. Blinchikoff & Anatol I. Zverev, Filtering in the Time and Frequency Domains, John Wiley, 1976. A broad and fundamental wait at filters.
[3] Arthur B. Williams & Fred J. Taylor, Electronic Filter Blueprint Handbook, McGraw-Loma, 1995. Design and assay formulas for all types of filters.
[4] Jasper J. Goedbloed, Electromagnetic Compatibility, Prentice Hall,1990. Cardinal concepts and practices for dealing with radio frequency interference.
[v] Henry W. Ott, Noise Reduction Techniques in Electronic Systems, John Wiley, 1976. Practical steps to combat RFI.
[6] Manfred Zollner & Eberhard Zwicker, Elektroakustik, Springer, 1998. The near comprehensive and solid applied science level presentation of electro-acoustic transducers and related subjects.
In German, no comparable English language text available, to my knowledge.
[7] Walter K. Jung, editor, Op Amp Applications, Analog Devices, 2002. Everything yous e'er wanted to know almost using operational amplifiers, and non simply at audio frequencies.
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Source: https://www.linkwitzlab.com/filters.htm
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