Subject: [JN] the magic of fast bass
Hi all
I am not sure how many Joes are in the "its all magic" camp and how many are interested in how things really work but so far as how a woofer really works, this has been known for some time. Authors like Benson, Heyser have written very good books and papers on the subject. At least from being able to model / predict the performance of a real speaker from its electroacoustic equivalent circuit, there are no missing links or mysteries, just a few things mfr.'s chose not to explain and or things some choose not to look at.. Perhaps this explanation will help.
The number one misconception about woofers is that moving mass has something to do with "speed" of response or its high frequency limit. It does not, at least directly. What mass effects is efficiency and also the shape of the low frequency roll off.
A radiator that is small compared to the wavelength it is producing, experiences an increasing acoustic load with increasing frequency (one of the few places on sees a frequency dependent resistance with out a reactance). That radiator in an infinite baffle, driven at a constant velocity will produce a +6 dB oct rising response because its radiation efficiency increases with frequency. To make a driver like this have "flat response", we must roll off the voltage response 6 dB per octave, one pole. This is done by having a much larger amount of mass or weaker motor such that above some point velocity control is lost and then with increasing frequency, the velocity falls 6 dB oct. It is this range, where the velocity falls 6 dB /oct that one has flat response. Electrically, this speaker looks like and acts like an R/C filter, the R is the coil R+the amplifier source R and the C is the moving mass of the speaker reflected through the motor, which looks /acts like a capacitor.
Since the moving part is the C, it is the voltage across it (the voltage /velocity output) which falls 6 dB /oct, which is canceled out by the changing radiation resistance and now gives flat response. The -90 degree phase shift of the slope is not canceled out as the radiation resistance is pure resistance. Changing the size of the C (moving mass) has no effect on the slope angle, just its level and starting point.
99% of the people do not realize that when a point source has flat response, its mid band acoustic phase lags behind the input signal by about -90 degrees (once all fixed time delays are accounted for). This broad band lag is equal to a time delay who's amount increases with decreasing frequency. This -90 degree operation is how some of the simpler measuring systems "determine" acoustic phase, it is a Hilbert transform of the amplitude and at low frequencies for a simple piston, this is a safe assumption.
Consider how a normal "perfect" speaker spreads out a signal in time. Make an imaginary signal that has equal amplitude content from 100 Hz to 25 Hz, a specific waveshape which has this property. Take an imaginary perfect flat response speaker who's upper and lower cutoffs are way past our needed bandwidth. This mass controlled "flat" response speaker has a -90 degree lag or delay, at 100 Hz the phase shift is equal to a source 2.83 feet behind the speaker cone, at 50 Hz, the delay is equal to 5.66 feet, at 25 Hz is equal to 11.32 feet and so on. This test signal's wave shape defines the input "time" of each frequency component. When reproduced, the highest frequency component at 100 Hz emerges from the radiator 2.5 ms AFTER the signal arrived at the driver terminals. At 50 Hz, this component emerges 5 ms AFTER the signal hit the terminals and at 25 Hz, the signal emerges after 10 ms and so on. With the driver spreading the signals frequency components out in time, it is simply not possible to retain the same waveshape as the input signal, lower frequencies arrive progressively later in time than the original signal.. Any signal reproduced is done so with the spectrum rearranged in time by the drivers acoustic phase response.
If one had a driver which had a very strong motor or a normal motor but very low moving mass, one gets an "over damped" response. This term is from filter design meaning that it is not optimally flat, excessively damped, rolling off too soon and gradually Should the slope of the response reach 6 dB per octave, the driver is operating in the Velocity controlled mode, while the response is not flat, the acoustic phase DOES track the input signal (zero degrees) and the different frequency components are not spread out in time. The waveshape of the input signal is more closely replicated as the frequency components are in the original "time" although the amplitudes are off 6 dB/oct. Each 3 dB /oct change in the slope produces a 45 degree change in phase.
An over damped response more closely retains the time information where a flat amplitude response cannot.
A proper LF horn can have flat acoustic response AND roughly zero degree acoustic phase.
For a person more sensitive to "time errors", they will likely find an over damped system more realistic. For a person more sensitive to "amplitude errors" the traditional "flat response" system will be more satisfying. For the person lucky enough to have heard a proper lf horn system, you have heard that one can have "lightning fast" sounding bass and still make your pant legs flap.
A normal "flat" response point source speaker HAS this kind of delay built right in and it is unavoidable (currently). All conventionally driven point source speakers MUST have the phase shift / delay if they are to have flat frequency response (dictated by the falling velocity, acceleration controlled response needed to offset the changing radiation resistance with frequency).
Additional reactance's can alter this phase relationship. For example above midband at the point in the impedance called Rmin, the electrical series "L" is equal but opposite the reflected moving mass (capacitive reactance) of the driver thus canceling each out and being resistive (no phase shift). Above that frequency, the series Inductance dominates and produces a roll off with an inductive reactance.
At the bottom end ot the response, for a simple sealed box, there is a point where the parallel spring or "compliance" of the box and driver are equal but opposite the moving mass and this point is also resistive (at box resonance). Below that frequency, the spring constant dominates (an inductive reactance) and the acoustic phase leads
More complications from non perfect drivers and alignments..
In pro sound it is a common practice to evaluate subwoofers with a kick drum signal. Such a signal has a wide spectrum however it makes a bad test signal for a subwoofer alone.
Nearly always, the subwoofer with the best "snap" or attack is the one with the greatest distortion and or the highest low cutoff. Clearly, the ear hears the added hf content and judges it to be more lifelike.
In actual operation, the subwoofer is mated with midbass speakers who's job it is to produce the spectrum above the subwoofer. Now, with the actual drum signal being produced in the upper ranges, the subwoofers formerly desirable distortion spectrum interferes with the real drum signal. Now, the subwoofer with the least distortion will often have the best subjective sound.
A subwoofer can be made with a under damped low frequency corner, this puts a bump in the response right before roll off. Subjectively, this can make a woofer sound even slower and the "decay" of the too high Q takes more time.
Remember that it is acceleration which produces sound, it is the amplifier current which produces the force which produces the acceleration.
While few of you may have a TEF machine or are able to measure real acoustic phase, most of you can plot the current phase angle with respect to the voltage drive signal for a woofer. The phase shift curve of the current vs freq will have the same shape as the acoustic phase shift (although the degrees are different). If one had a speaker that was flat midband, one could look at the current phase in that range and assume the acoustic phase magnitude was about -90 deg . This acoustic phase IS time, it is essentially ignored in discussions about how speakers sound, yet it accounts for most of what you guys and others are talking about.
Tom Danley
