The correct question at this point is why do you care if the equalizer has complementary phase shift? Damned, if I know. I can tell you why they say it is important, and I can tell you why they are misleading you.
The popular demonstration involves setting up one channel with an arbitrary curve and then adjusting the other channel for the opposite response.
Passing a signal through both channels in series produces a flat frequency response. No phase shift. No time delay.
Now this result seems to have overwhelmed them. They describe the results as bizarre, remarkable and baffling. I can find no one else that is the least bit surprised. This is one of the few places where your intuition is correct.
If you take two equalizers set for complementary curves and put them in series you get a response of unity. You do not get an all-pass response, as they claim. There is no amplitude variation, no phase shift, and no time delay.
Basic sophomore electrical engineering tells us why. Something called a transfer function represents each channel. This mathematical equation completely describes the amplitude, phase and time response of a signal passing through that channel.
The complementary channel’s transfer function is the reciprocal of the first. Putting them in series causes the two transfer functions to multiply. Anything times the reciprocal of itself produces the answer of unity, i.e., (1/X)(X)=1. Nothing too difficult here. One is not the transfer function of an all-pass filter. One is the transfer function of a piece of wire.
So what does all this have to do with what kind of equalizer you may want to buy? Not much, really. The implication is that you must have a complementary phase equalizer to correct for a room’s frequency anomalies—not true. Any equalizer that produces the opposite room response works—and works just as well.
MYTH #4: Constant-Q means non-symmetrical boost/cut curves.
Until 1986, I wouldn’t have considered this an official myth. At that time, F. Alton Everest published a book entitled Successful Sound System Operation. It is a well-done introduction to the business of sound reinforcement, and I recommend it to anyone just starting out. His treatment of constant-Q equalizers (p. 252), however, needs some revising.
Mr. Everest states erroneously and unequivocally that constant-Q equalizers characterized themselves by having asymmetrical boost/cut curves. (This occurred from a misreading of a popular parametric equalizer’s data sheet; something easy to do.) This myth involves a mixing of two separate issues.
Reciprocity of boost/cut curves and constant-Q have nothing to do with each other. You can find constant-Q symmetrical and non-symmetrical equalizers and you can find non-constant-Q symmetrical and non-symmetrical equalizers. The terms characterize two different aspects of an equalizer.
Constant-Q refers to the bandwidth behavior for different amounts of boost or cut. If the bandwidth stays constant as a function of boost/cut amounts, then it is constant-Q. If it does not, then it is not a constant-Q design.
If the cut curves are mirror images of the boost curves, then the equalizer has symmetrical (or reciprocal) response. If the curves are not mirror images of each other, then the equalizer is of the non-symmetrical school. Two separate issues, both available in any combination from several manufacturers. Your choice.
MYTH #5: Given identical equalizers, one passive and one active, the passive unit will sound different.
The key to whether this is a myth involves the crucial word, identical. If two equalizers do not produce the exact transfer function, then they will definitely sound different. That is not the issue here. At issue is whether there exists some sound quality attributable to active or passive circuits per se. There does not.
A transfer function exists characterizing every equalizer’s output behavior to a given input change. Any two equalizers with the same transfer function, when operating within the constraints necessary to behave according to that function, will give the same results no matter what physical form makes up the equalizer. In general, any equalizer response can be implemented by many different types of circuits, both active and passive.
The perceived differences between equalizers designed for the same response function must be explained by factors other than whether the equalizer is active or passive. Some characteristics that can contribute to the misbehavior of the circuit are nonlinearities that occur because the components are being used improperly or stressed beyond their linear operating region. Sometimes the perceived differences are nothing more than one circuit is quieter than another.
Any two equalizers with the same frequency domain transfer function will behave the same in the time domain. The transfer function determines responses such as overshoot, ringing, and phase shift regardless of implementation.
Nothing mysterious exists within the realm of active and passive equalizers. Simple electronic theory explains all differences between these two, if differences exist. If not, they will perform and sound the same to the objective observer.
Never assume that because an equalizer is active or passive it is automatically better or worse for your application. Study your needs and consult with knowledgeable people to make the correct equalizer selection.
MYTH #6: An ideal equalizer would add no phase shift when boosting or cutting.
Phase shift is not a bad word. It is the glue at the heart of what we do, holding everything together. That it has become a maligned term is most unfortunate. This belief stands in the way of people really understanding the requirements for room equalization.
The frequency response of most performing rooms looks like a heart attack victim’s EKG results. Associated with each change in amplitude is a corresponding change in phase response. Describing them as unbelievably jagged is being conservative.
Every time the amplitude changes so does the phase shift. In fact, it can be argued that phase shift is the stuff that causes amplitude changes. Amplitude, phase and time are all inextricably mixed by the physics of sound. One does not exist without the others.
An equalizer is a tool. A tool that allows you to correct for a room’s anomalies. It must be capable of reproducing the exact opposite response of the one being connected. This requires precise correction at many neighboring points with the associated phase shift to correct for the room’s opposing phase shift. It takes phase shift to fix phase shift. Simple as that.
One way people get into trouble when equalizing rooms is using the wrong type of equalizer. If an equalizer is not capable of adding the correct amount of phase shift, it will make equalizing much more difficult than it has to be. The popularity of the many constant-Q designs has come about because of this phenomenon.
Equalizers that produce broad smooth curves for modest amounts of boost/cut make poor room equalizers, and good tone modifiers. They lack the ability to make amplitude and phase corrections close together.
Lacking the ability to make many independent corrections with minimal interference to neighboring bands restricts their usage primarily to giving a shape to an overall response rather than correcting it. Serious correcting requires sharp constant-Q performance, among many other things.
Only by adding many precise, narrow phase shift and amplitude corrections do you truly start equalizing a system’s blurred phase response. You do not do it with gentle smooth curves that lack the muscle to tame the peakedness of most rooms. Broad smooth curves do not allow you to correct for the existing phase shift.
It’s just that simple, you must pre-shape the signal in both amplitude and phase. And that requires narrow filters that preserve their bandwidths at all filter positions.
Read and download a PDF of the original article here.
Dennis Bohn is a principal partner and vice president of research & development at Rane Corporation. He holds BSEE and MSEE degrees from the University of California at Berkeley. Prior to Rane, he worked as engineering manager for Phase Linear Corporation and as audio application engineer at National Semiconductor Corporation. Bohn is a Fellow of the AES, holds two U.S. patents, is listed in Who’s Who In America and authored the entry on “Equalizers” for the McGraw-Hill Encyclopedia of Science & Technology, 7th edition.