Port Placement in DIY Bass Reflex Cabinet

[John Warren]

c

[Al Klappenberger]

John,

I think the again the answer is no! You are now dipping into another bag of

worms, that is "Phase delay". That would be to say that if the "insertion phase"

is 30 Degrees at 50 Hz, for example, then the "time" delay will be 30/360 * 1/50

or 1.666 mSec. I fell into that trap years ago when developing the analysis

program in my filter design package. In terms of filters, a direct scaled all-

pole bandpass filter goes from negative absolute "insertion" phase through zero

phase to positive phase as you move across geometric center frequency. Clearly

the delay (time or group) is not zero at center frequency! Also you can have

much higher phase numbers than 360 in a filter. In terms of woofers, I do not

believe you can make the leap of faith that it will work there either. Look at

the phase plot of the example you posted earlier using the same program. You

will see that the limits of insertion phase is 360 degrees. Doesn't that limit

the amount of total delay you can possibly have from any loudspeaker no matter

how big or how low it goes? I don't think so but I might be wrong. That's not my

area of expertise.

I am quite certain though that it is not equal to "group delay" either. That is

EXACTLY what I tried to do years ago. You are also still thinking in terms of

"time" delay. All that matters is if you sum up algebraically all of the many

elements of a complex waveform in phase and amplitude to determine what the true

waveform distortion will be. The instantaneous level of each element will be the

same, and sum up the same, if it is delayed 53 degrees, for example, or 53

degrees plus any multiple of 360 degrees! I also need to remind you that the

speaker is operating in a room where the phase of each "element" of the waveform

is being scrambled by the room. You will need to do it at some point in space.

Music is random to begin with. The bottom line here is that it does not matter

if the phase of the bass is shifted or not. You can't hear it when reproducing

music. Furthermore, a single driver having no filters at all has a group delay

curve that is not flat! Certainly the propagation "time" delay is however. To

worry about a triviality like the phase shift at a frequency you can't even hear

is silly. To worry about it a 50 Hz is also useless since simply taking a step

or two to one side changes all the phase relationships. Remember that every

element of the complex waveform is at a different frequency and has a different

wavelength. The distance you move will change the phase a different number of

degrees for each element. Again, you can hear group delay and phase distortion

only with special test signals and through headphones where the phase

relationships are fixed! In a speaker, it's a red herring!

Al K.

[John Warren]

c

[Al Klappenberger]

John,

"For any phase function, the Group Delay D(w) may be interpreted as the

time delay of the amplitude envelope of a sinusoid at frequency w."

Look at that quote carefully. it says "of the amplitude envelope".

That's why "group" delay is also called "envelope" delay. Use Fourier analysis

to construct the "envelope" and you have the time delay. You will be using the

phase and amplitude of each element at "frequency w". For the 1000 th time:

"envelope" delay utilizes absolute phase and amplitude of each "element", not

the change in phase with the frequency of each element or the derivative of the

phase of each element .

--------------

>"The phase of a speaker's frequency response has to change linearly with

frequency in order to preserve waveform fidelity. This is equivalent to saying,

the group delay has to be constant (f)."

"Waveform fidelity" is maintained only when "group" delay is flat over the

portion of the spectrum carrying all the elements to make that waveform. That is

the same thing as saying when the network is "linear phase". "Waveform fidelity"

is "envelope fidelity".

----------------

In the last quote, even this expert says that he is not certain! This is a very

sticky subject and I am not certain of what I say either! As my father used to

tell me "only fools are sure"!

-------------------

As to group delay flatness in a single driver. Yes, group delay errors are all

over the place! In the case of the single driver though, the group delay non-

flatness I am referring to is the driver itself with no help from anything else!

Al K.

[fini]

Geeze, you guys, get a room...

_________

I remember the good old days when John Warren would post pictures of unidentified pretty girls, and we'd all guess her name...

fini

[Al Klappenberger]

Fini,

Ahmen! I think both of us have presented his point of view to the best of his ability. It's time to take a step back and think it all over.

In truth, I have just written an article dealing with a subject similar to this (extreme slope crossover netwroks) for AudioXpress magazine and I'm expecting a lot of discussion about it from the same point of view as John is taking. I am doing all this sparing to get ready for the enevitable! Normally I would not have gotten into it!

Al K.

[John Warren]

c

[Al Klappenberger]

John,

I do have that issue of audioXpress. I suspect the fact that the thing goes up beyond 500 HZ has a lot to do with it's transient response too! Look at figure 18. Without that, a transient couldn't even get through!

I don't know when my paper will be published. Ed Dell is sending the paper to several experts (D'appolito included) to get some opinions first. He didn't say when it would appear.

Al K.

[John Warren]

c

[fini]

John,

You are more sensitive to the irony, given your metallurgy credentials.

fini

[Al Klappenberger]

John,

I think we should give this group delay thing a rest now! The fact is that I have not read the article. If you insist though, I do not believe group dealy as anything to do with "fast". It is an exremely and universally misunderstood concept. If you universally replace "group delay" with "phase linearity" and see if it fits wherever you see it, you will know if you are being "BSed" or not. Group dealy is ony important as to how wide an area it falt over, not it's absolute value as so many people try to tell you. Only it's flatness counts. That is, how "phase linear" it is. I have seen "group delay" misused so much it's silly! Like I said 50 times, you can't hear it in a room. Only with headphones. If you still don't believe it, reread the post of the letter to the editor I post earlier. It is Mr Lip****z saying the same thing in his reaponse! You can't hear phase distortion in a room through loudspeakers, especially a bass frequencies!

Al K.

[Clipped and Shorn]

fini, you silver tongued devil, glad to see you got the lead out and provided us with your golden tid bits of mercurial wit, which unlike this tinny and brassy statement, put the pedal to the metal.

-Si & Es

[Al Klappenberger]

John and anybody else who's interested,

Ok.. Here's comes the ultimate snow-job. Sorry, I just couldn't resist!

I have written a computer program that can be run using the old GWbasic BASIC

interpreter distributed with DOS for may years. Any BASIC language

interpreter or compiler will do though. The program will illustrate how a

complex waveform is "built up" from its elements (harmonics). The waveform is

a 1 KHz square wave. The fourier analysis of that waveform is a 1000 Hz sine

wave followed by a series of odd harmonics, also all sine waves (3 Khz, 5

Khz, 7 Khz on up), each in descending amplitude. That is, the 5th harmonic,

for example, is 1/5 the amplitude of the fundamental. If you calculate the

instantaneous level of each of these harmonics at enough points in time and

sum them all up and plot them you will draw a square wave. The number of

harmonics you include will determine the rise-time and the amount of ringing

on the top and bottom of the wave. The program does this and plots the

results into a file called SQUARE.TXT. You can look at this file with Windows

"Notepad" by double-clicking in it in Windows explorer. If you run the

program, keep in mind that the human can only hear to the 19th harmonic, at

best. That is, 19 KHz. This will illustrate that ringing CAN simply be the

number of harmonics you can hear, not only "stored energy" or other such

things in a filter.

In order to illustrate what "group delay" is and what effect it has, I have

added two lines in the program that can be activated to do the additional

calculations. The first is the line numbered 190. It shifts the phase of each

element (harmonic) by a fixed and constant rate, 50 Degrees per KHz in this

case. This illustrates a "flat" group delay equal to 139 MicroSeconds over

the entire frequency range. That is to say, it is "linear phase" or has

"flat" group delay. Simply remove the word "REM" and run the program again.

You will see that the waveform is simply moved in time but is not distorted

at all. Flat "group delay" does NOT cause distortion! Under these conditions

"group" delay equals "time" delay.

To illustrate group delay distortion, unREM line 240 and run the program

again. This adds phase changes that increase exponentially as frequency

increases. This generates a waveform with the distortion generated by group

delay that is NOT flat. The resulting waveform is so distorted that you can

not even begin to say what the "time" delay is even by looking at the plotted

waveform on a calibrated time scale by eye. I do not see how your hearing can

possibly decipher anything here as a time error. The waveform and elements

are simply scrambled. The big question is, can you hear this distortion or

not? It is so severe you would assume that you can. Clearly though, this is

phase distortion of each element with respect to all the rest. A loudspeaker

in a room bounces the sound off all the walls and the ceiling making the

phase totally random. This also happens when a sound is generated by a real

live source in your room, such as a person speaking. You have no problem

recognizing the person who is speaking from the sound of the voice to spite

what room he or she happens to be in. You learned how to do this from birth.

You know Momie's voice no mater if you are outside or in a cave! I suspect it

is because your brain ignores the phase scrambling and adjusts for it. It

maybe doing the same thing with a loudspeaker. You probably can't hear it

because your brain is programmed to unscramble this sort of thing naturally.

You hear with your BRAIN, NOT YOUR EARS! Maybe you can hear it through

headphones because your brain has no reference for that situation.

You may also conclude that, since with constant group delay, the waveform is

shifted in time by an amount equal to the group delay, you can assume each

harmonic can be considered to be delayed in time by the group delay at that

particular frequency. NOT! Look back at the scope plot of the outputs of the

extreme slope crossover I posted earlier. The group delay at 700 Hz is about

2 mSec. Nothing on the scope screen corresponds to 2 mSec to spite a burst of

700 Hz. It does not correspond to the insertion phase delay if 1 mSec either!

Also, consider a 2nd order crossover network. That is, Butterworth 12 dB /

octave slope. It has +90 degrees insertion phase out one port and -90 degrees

out of the other. This adds to 180 degrees total phase shift between the two

channels. This is true and measurable and the solution in practice is to

simply invert one of the drivers that is connected to it (invert the phase of

one driver only). Clearly the signal out of the channel with negative phase

is not arriving before it entered the input! That is what the negative phase

would suggest! Clearly then, insertion phase is not true "time" delay and

neither is the "group" delay at a single frequency.

To run the program simply cut and past it to Notepad and save it as file

"SQUARE.BAS".

I have also compiled the program and "ZIPed" it. You should be able to

download it and run it by double clicking on it and then on the square.txt

file that it will make after each run. The two optional program line are

activated by Yes/No queston prompts.

Al K.

Here's the program for old BASIC interpreters:

10 PRINT "1 KHz Fundimantal - 19th harmonic is 19KHz limit of hearing"

20 PRINT "Include harmonics up to 300 to observe group delay effects"

30 INPUT "Include up to what harmonic"; NUMBER

40 T2 = .001: ' time for 1 cycle

50 OPEN "square.txt" FOR OUTPUT AS #1

60 PRINT #1, TAB(38); "zero"

70 PRINT #1, "time (uSec)"; TAB(40); "/"

80 PRINT #1,

90 TIME = 0: GOTO 110

100 TIME = TIME + .00001: ' 10 uSec steps

110 SUM = 0

120 FOR I = 1 TO NUMBER STEP 2

130 HARMONIC = I * 1000

140 B = 360! * HARMONIC * TIME

150 '===================================================================

160 ' Add linear phase shift slope of 50 Degree per Khz

170 ' 50 Deg / Khz = 50 Deg / 360,000 Deg = 139 uSec flat "group" delay

180 ' Remove "REM" to activate:

190 REM b = b + 50 * i

200 '===================================================================

210 ' Add NON-linear phase shift with slope and "group" dealy increasing

220 ' exponentially with frequency.

230 ' Remove "REM" to activate:

240 REM B = B + (50 * I) ^ 1.1

250 '====================================================================

260 B = B / 57.29578: A = SIN(: ' Convert degrees to radians for sin()

270 SUM = SUM + A / I: ' Each harmonic deminishes in amplitude

280 NEXT I

290 PRINT #1, USING "#####.#"; TIME * 1000000!;

300 PRINT #1, TAB(SUM * 20 + 40); "*"

310 IF TIME < T2 THEN 100

320 PRINT "done - look at file square.txt with Windows Notepad"

330 END

Square.zip

[fini]

Al!! What planet are you from??

fini

[Al Klappenberger]

Fini,

Gee... I don't know! Where DO nerds come from?

Al K.

[jnorv]

All, It has been 20 years since I did a Fourier fit from scratch. Is the Fourier constant really as simple as 1/N for a square wave? I don't want to have to go back and find my text books and resolve the equations.

Thanks,

Jim N

[Al Klappenberger]

Jim,

I can't answer that! I did that program by the seat of my pants, and in fact, it was many years ago. I just pulled it out of my program "archives" and hacked it to verify to myself that I really understood group dealy. The fact that you asked that question tells me you know more about fourier analysis than I do!

Al K.