120V from both legs

First.. Since you replied by email, the sole contents consisting of a web site reference re math, and you have not yet answered my last post, I assume you feel you have dodged a bullet here. Impressive. So, I'll go with your last response.

Sorry for the oversight, but frequency is simply f=1278/2 pi = 203.4 Hz. Hope you were not overworked in reconstructing.. :)

Yes. Mechanical reactance Xm per Beranek 7.3 is Xm = (wMmd+2Xms)-(1/wCms) = 38.70

No. Zm' = (Rms+2Rmr)+j[(wMmd+2Xms)-(1/wCms)] = 38.78. Xm = (wMmd+2Xms)-(1/wCms) = 38.70. Note that Rms and 2Rmr are so small as to make little difference, but they are *not* the same. Not like mice traps and bear traps.. :)

No. Beraneks Zm, is: Zm = [(Bl)^2/Re+Rms+2Rmr] + j[(wMmd+2Xms)-(1/wCms)] = 43.34

Yes, the magnitude of Zm' is 38.78.

Wrong. Adding (Bl)^2/Re to Zm' gives Zm per Kelly = [(Bl)^2/Re] + jZm' = sqrt (17.097^2 + 38.78^2) = 42.38. where (Bl)^2/Re is resistive per Small (AES preprint #1251) and others.

No. We see that Beraneks Zm is 43.34, and your Zm is 42.38. You are wrong.

No, you are caught with both hands in the trap and your pants down :(

A sermon from the devil? :)

Anyway, as proven at the top of the post, you try to change history rather than admit an error. Also, you have mentioned I am deceptive, thusly you project. Finally, you appear to be that which you accused me of, i.e. at sopomoric level.

Future calculations (other than pertaining to the above) will be as referenced in my last post.

Northstar

----- Original Message ----- From: "Northstar" Newsgroups: alt.engineering.electrical Sent: Tuesday, December 07, 2004 12:38 PM Subject: Re: motor models

---------snip----------

---------- Apologies and TIA accepted but two questions arise:

1) Why did you give E as, so far it doesn't enter into the mix. Is it rms? (in which case any velocity, current etc calculated will be rms)

2) Why do you expect a different answer than that given by Beranek's expression? Putting different numbers in doesn't change the relationship.

.

Using Beranek, I get Zm =38.14 @ angle 59.26 degrees This agrees with the magnitude that you gave (you didn't give phase)

Now Zm' =2.4 +j 32.78 =32.87 @ angle 85.81 degrees.

Using Bl^2)/Re +Zm' gives 17.1 + {2.4 +j 32.78)] = 19.5 +j 32.78 =38.14 @ angle 59.26 degrees

EXACTLY THE SAME AS BERANEK' S Zm

This is obvious without having to plug in numbers. The "corrected" data doesn't change the above fact nor does it change the fact that you have completely missed the points below.

a)Adding magnitudes is incorrect as the (Bl^2)/Re is not in phase with Z'

b) What you erroneously call "Vector addition" {i.e. using root(17.1^2 +

32.87^2) =37.05 } is also incorrect as the two terms are not 90 degrees apart in phase. (Zm' is 85.8 degrees out of phase from (Bl)^2/Re - close but no cigar.)

Both conclusions can be determined with a simple sketch.

Your second message adds nothing useful such as a valid point. Note that your "one parameter" is actually made up of several individual circuit elements in series. I could write Berenak's Zm as [(Bl)^2/Re +j0] + [(Rms+j(wMms-1/wCms)]+[2Rmr +j0] that is: separated into electrical, mechanical, and acoustic element groups.

I sent you information for a couple of sites which show how to add vectors. There are also sites where you can interactively set two vectors and get their sum shown graphically. Here is a site:

Is it too much to ask you to look at the information available (not take my word) rather than simply repeating the same problem with modified numbers and invalid "addition"? Since it apparent that all that will happen is repeated full agreement with Beranek, there is no point in replying to this approach.

Don Kelly snipped-for-privacy@peeshaw.ca remove the urine to answer

It applies to Beraneks eq. 7.1, which is at the heart of what we are discussing, and I thought you might find it helpful. Yes, the 1.41 volt input is RMS and is sinusoidal.

I expected different magnitudes, since mass reactance was too high by

5.92. I explained that. I did *not* expect any relationship to change. I explained that as well, saying "I shall solve each equation exactly as before, but with correct total mass reactance, and my comments (as left unclipped above) are unchanged. All your criticism should be unaffected, but the magnitudes will be accurate and valid as a true representation of the driver."

Northstar

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

Thank you. That is fair enough.

I do apologise for some typos that I had > >This agrees with the magnitude of 38.78 that you give for Zm'

.

Ah, I see. The po> No. Beraneks Zm, is:

--------- You are right- I had a typo. If you had checked, 19.5+j38.71 =43.34 @63.27 degrees. This agrees with Beranek. I > Wrong. Adding (Bl)^2/Re to Zm' gives

I have apologised for my typos above. Note that I do not calculate Zm by root(....) but as shown above. If you want to do it by your approach, it is correct using root (19.5^2

+38.71^2) =43.34 but not as you have done it.

(Bl)^2/Re is resistive ( and I have said that before- it is obvious) but Zm' is NOT purely reactive. This means that the "addition" that you have done is not valid. Look at the sites I gave you which explain how to do the addition.. These were sent as courtesy- not as a method of dodging bullets (besides which your gun still has a string attached to its cork) :). What you claim above is not mere typos but a fundamental conceptual error. You are trying to apply Pythagorus theorem ( that's what it is) to something that is not a right triangle. It doesn't work. If you ignore Rms +2Rmr then you could use Pythagorus to get an< approximate > value for the magnitude of Zm which would be root (17.1^2 +38.71^2) =42.3 which is not a bad approximation-in this case. However, if the R/X ratio was higher, the Pythagorus approximation would be useless.

---------- I see no comments on the material below. -- Don Kelly snipped-for-privacy@peeshaw.ca remove the urine to answer

I agree, Zm' is not purely reactive, and shall trust that your math is correct, such that your equation gives the same result as Beranek. Please accept my apology, as well as the same for any possible previous contention re your math ability per se.

Now.. It appears your objective is to flaunt your ability with calculus or math, and even though the correct answer is available with a method different than yours, you arse off about sopomoric level re math, and get a kick out of pointing out need for someones improvement. Well.. I am tired of your shitte game. I am not here for your enjoyment with such practices. In short, if you want to continue I am willing, but note I am through with you sorry-arsed personal insults.

Now if you want to continue, the specs as ammended are:

Bl = 11.01 Re = 7.09 Rms = 1.57 2Rmr = 0.83 w = 1,278 f = 203.4 Mmd = 0.0281 (includes mass of the air load, such that *total* mass reactance wMmd+2Xms = wMmd = 35.91 Cms = 0.000250 E = 1.41 Rg = 0

To which you replied:

Again, if you want to continue, you now have the values to calculate velocity by Beraneks equation 7.1, and I suggest you do this, and we shall see if it matches my measured magnitude.

Northstar

to

---------- Who is insulting now? What my main point was that you contended that my approach was incorrect and refused to try to understand the difference between it and Beranek's which was simply that I kept the (Bl^2)?Re term separate from the actual mechanical/acoustic impedance while he incorporated them. Numerically they are the same. Nor have I used calculus- no need to do so. I do use phasor arithmetic as a)notation is easier, b) calculation with a scientific calculator allows me to do number work with a lot less effort. I could calculate a magnitude per se and also calculate a phase angle separately and then convert to a real and reactive form when I want to add. However, why take the root of sum of squares and also find the angle when I can simply enter two numbers and get the result by pressing one key?. In other words, why do it the hard way?. As for the insults- You have made some conceptual and mathematical errors which were not just typos. It is not an insult to question these and other statements that I disagree with. You have quite rightly jumped on things that I have said and I reserve the right to question those points where you have made fundamental errors.

Using Beranek:

Rm =(11.01^2)/7.09 +1.57 +0.83 =19.5 Xm =35.91 -1/1278*0.00025 =32.78 U=[(11.01)1.41/(7.09)]/(19.5 +j 32.78)] =2.19/(38.14 @59.26) = 0.0574 @ -59.26 m/s Magnitude 0.0574 m/s rms and phase -59.26 degrees Both are important.

Now I could calculate root(19.5^2 +32.78^2) = 38.14 which is apparently what you have done. I could also calculate arctan (32.78/19.5)=59.26 degrees This requires two squarings, a sum, one square root , a division and calculation of the arctan. 6 operations compared to doing a single one. Let the calculator do the bull work. Note that the actual computation is the same by the two approaches. I use complex numbers because it is easier to keep things straight and not make the mistake of dropping the phase where it must be kept.

From past experience, I'm not at all sure that I want to continue, as so far, I have learned nothing that I didn't know or find for myself.

Snip - leaving the basics:

Bl = 11.01 Re = 7.09 Rms = 1.57 2Rmr = 0.83 w = 1,278 f = 203.4 Mmd = 0.0281 (includes mass of the air load, such that *total* mass reactance wMmd+2Xms = wMmd = 35.91 Cms = 0.000250 E = 1.41 Rg = 0 I = 0.172 during steady state motion

I have a problem with your Zmec = 38.14 @ angle 59.26 degrees Your velocity is correct as measured at 0.0574, then Zmec must be force/velocity, such that with your magnitude of 38.14

Zmec = BLI / v = 38.14

Current must be 0.1989 to obtain your magnitude of 38.14, and this is blocked coil current of E/Re = 1.41/7.09= 0.1989. Now with blocked coil, velocity is zero and it is my impression that a number divided by zero is undefined or meaningless.

If you save the magnitudes at the top I shall list more with them as needed. Note I added dynamic current = 0.172.

Northstar

---------------- Note that the Zm=32.87 is exactly that used by Berenak in 7.1

or Zm=19.5+j32.78 =38.14 @ 59.26 degrees and the solution that I gave uses 7.1. If I am wrong, then Beranek is also wrong.

We are back to the misconception that you had before.

Zm (=38.14) as per Beranek is clearly NOT the actual mechanical impedance, nor does he claim that it is. It includes the effect of the electrical resistance as seen from the mechanical side.

Fig 7.3 indicates a step in determining the final circuit model. It is a Norton Source and will give the correct information to its terminals but not "inside " . The (Bl^2)/Re term is interior to the source. The actual mechanical force is given by BlI = BlE/Re -[(Bl^2)/Re]U =[(Rms+2RmR)+j (WMmd -1/wCms)]U The force that you calculated comes down to BlE/Re which is not the actual applied force. but does correspond to E/Re We have been through this before.

The actual mechanical/acoustic impedance, as I have been saying all along, is what we are now calling Zm' =2.4 +j32.78 =32.87 @ angle 85.81 degrees. Note that (0.0574*32.87)/11.01 = I= 0.1714 in this case.

Here is a complete solution starting from (refer to Beranek Ch.3) E=ReI +BlU

0=-BLI +Zm'U or 1.41 =7.09I +11.01U 0=-11.01I +(2.4+j32.78)U

From these two equations: U=0.0574 @ -59.26 degrees I=0.1714 @ 26.56 degrees

Check: Eb=BlU =0.6320 @ -59.26 degrees=0.323-j0.543 v E=IRe +Eb = (0.1714 @26.55)(7.09) + 0.323 -j0.406= (1.087+0.323)+j(0.543-0.543) =1.41 +j0 OK

Pin=0.2162 watts I^2R =0.2082 watts Pin-I^2R =0.00791 watts =Pmech loss + Pacoustic

Check:

2.4U^2 =0.00791 watts OK

Qin =0.0108 va = Qmech Check: 32.78U^2 =0.0108 OK

Zin=E/I =8.23 @-26.56 degrees Check: Zin =Re +(Bl^2)/Zm' =8.23 @-26.56 degrees. OK

PAE = 0.98% Actual efficiency =1.4%

No, Beranek is right, and your Zm' is a *very* close approximation, within 0.36%. So close that without applying practical experience to Beraneks eq. 7.1, most people would likely draw the same conclusion as you.

No misconception if one accepts that (Bl)^2/Re is a mechanical resistance (or virtual at minimum) per the following:

Beranek. Eq. 7.1 where he adds (Bl)^2/Re arithmetically to Rms and 2Rmr Small. Preprint 1251. " (Bl)^2/Re = mechanical resistance of driver motor " Keele. JAES 11-82. "damping factor of driver" Kloss. Audio Mar. 71 "an impedance (real), which we are calling damping force" Lahnakoski.

" Virtually equivilant mechanical resistance" Note he gives a derivation and detailed explanation. You might want to look at this.

I defer to these experts that (Bl)^2/Re may be termed as mechanical resistance.

I noted Zmec on the data sheet for driver #19 years ago as

Zmec = BlI/v=11.01*0.172/0.0574=32.99

Note Bl, I, and v were measured.

Otherwise Zmec is derivable simply as Beraneks denominator in eq.7.1 times cos angle between voltage and current Zmec = 38.142 * Re/Ze = 38.142*(7.09/8.198)=32.99

Agreeing exactly with BlI/v.

Your method where Zm'=32.87 gives a *very* close approximation of Zmec. Perhaps an inexpensive cigar :)

Sorry, but there appears to be a rather large error in your analysis. Electrical to acoustic efficiency n is

Thiel/Small reference efficiency (Smalls eq. 31)

n = (po/2 pc c) (Bl)^2/Re) (Sd^2/M^2) = 0.000544 * 17.097 * 0.5909 = 0.00550 = 0.55 %

Beranek 7.5 and 3.53 as acoustic power out/real power in

n = (v^2 Rmr)/[(E^2/Ze)]=(0.0574^2*0.415)/[(1.41^2/8.198)]=0.00564= 0.56 %

Northstar

A question please: Is your " 2.4U^2 =0.00791 watts " mechanical power? TIA

Northstar

It is the total power in watts delivered to the mechanical and acoustic system. That is mech loss =1.57U^2=0.0052 watts Acoustic power =0.83U^2=0027 watts sum is 0.0079 watts

I will respond to your other message later. By the way, is it acceptable to you to send you a message directly so that I can include graphics which might clear up misconceptions.?

Thank you for the clarification.

Lets handle it this way please. Give me a day or two and I'll get back to you with my last response to your analysis (the response preceding the above, and the one you say above you will respond to later) with contents unchanged, but with an added comment or two. Perhaps we can sort it out in an accurate and amicable manner.

Northstar

Fair enough

I have gone ahead and taken time to respond today, as I believe it is time to settle our arguments. The reason is that the number of fundamental errors you have made does not bode well for future discussion, unless the issues are resolved. Now re the above:

No, Beranek is right, and your Zm' is a *very* close approximation, within 0.36%. So close that without applying practical experience to Beraneks eq. 7.1, most people would likely draw the same conclusion as you.

No misconception if one accepts that (Bl)^2/Re is a mechanical resistance (or virtual at minimum) per the following:

Beranek. Eq. 7.1 where he adds (Bl)^2/Re arithmetically to Rms and 2Rmr Small. Preprint 1251. " (Bl)^2/Re = mechanical resistance of driver motor " Keele. JAES 11-82. "damping factor of driver" Kloss. Audio Mar. 71 "an impedance (real), which we are calling damping force" Lahnakoski.

" Virtually equivilant mechanical resistance" Note he gives a derivation and detailed explanation. You might want to look at this.

I defer to these experts that (Bl)^2/Re may be termed as mechanical resistance.

I noted Zmec on the data sheet for driver #19 years ago as

Zmec = BlI/v=11.01*0.172/0.0574=32.99

Note Bl, I, and v were measured.

Otherwise Zmec is derivable simply as Beraneks denominator in eq.7.1 times cos angle between voltage and current Zmec = 38.142 * Re/Ze = 38.142*(7.09/8.198)=32.99

Agreeing exactly with BlI/v.

Your method where Zm'=32.87 gives a *very* close approximation of Zmec. Perhaps an inexpensive cigar :)

Your angle is wrong. The correct angle is 72.44 Back emf Eb *must* be E-(IRe)=1.41-(0.172*7.09)=0.1905 Then cos angle = cos 72.44 = 0.3017 Eb = Blv cos angle = 11.01 * 0.0574 * 0.3017 = 0.1907 Checks.

Incorrect. Power input during steady state is Pin = E^2/Ze = 1.41^2/8.198 = 0.243

As check, Pin must be Pa/n where acoustic power on one side of the cone is Pa=V^2 Rmr = 0.0574^2*0.415=0.001367 Efficiency n per Small and Beranek below = 0.0056 Giving power input as Pin = Pa/n = 0.001367/0.0056 = 0.244 Checks

I ask "Is your " 2.4U^2 =0.00791 watts " mechanical power? and you clarified "It is the total power in watts delivered to the mechanical and acoustic system. That is mech loss =1.57U^2=0.0052 watts Acoustic power =0.83U^2=0027 watts sum is 0.0079 watts"

Incorrect.

Mechanical power + acoustic power is electrical power input minus power lost as heat. With other losses considered nil, this is conventional wisdom. Mechanical power + acoustic power then is Pmec+Pa=Pin-copper loss =(E^2/Ze)-(I^2 Re) =(1.41^2/8.198)-(0.172^2*7.09) = 0.0328 watt Pmec = 0.0328 - 0.001367 = 0.0314 watt (lost if you prefer) Pa = V^2 Rmr = 0.0574^2*0.415=0.001367 Sum is 0.0328, Your magnitude is way too low.

Note my magnitude of 0.0328 agrees with conventional wisdom for mechanical power applied to the load (where here the load is the sum of the mechanical and acoustic load) Pmec = I Eb = 0.172*0.1905 = 0.0328 watt

Sorry, but there appears to be a rather large error in your analysis. Electrical to acoustic efficiency n is

Thiel/Small reference efficiency (Smalls eq. 31)

n = (po/2 pc c) (Bl)^2/Re) (Sd^2/M^2) = 0.000544 * 17.097 * 0.5909 = 0.00550 = 0.55 %

Beranek 7.5 and 3.53 as acoustic power out/real power in

n = (v^2 Rmr)/[(E^2/Ze)]=(0.0574^2*0.415)/[(1.41^2/8.198)]=0.00564= 0.56 %

Northstar email snipped-for-privacy@hotmail.com remove the high card to reply

------------- I have not deal with the above list directly. I have dealt with some of the things below and the only phase angle that you have given appears to have come out of the air without any justification or reasoning. > >>

***Correction**** ****Should be 38.14 as below**********

------------ Using your data, with the modified mechanical reactance:. In fact, my (Bl^2)/Re +Zm' ={(Bl^2)/Re +Rms +2Rmr}+j{wMmd -1/wCms)} Berenak's Zm ={(Bl^2)/Re +Rms +2Rmr}+j{wMmd -1/wCms)} This is exactly the same so that any error in my (Bl^2)/Re +Zm' will also be there using Beranek's Zm, which, in fact, is what I used to calculate U. Since I used double precision arithmetic, any errors that have been produced are due to errors in the data that you have provided. As with any results based on measured data, there will be errors. Note that the data really only justifies use of 3 significant figures so all that should actually be claimed would be Zm =32.9 and it would be foolish to claim any greater accuracy. I will discuss this below. In addition if you assume that Zm (Beranek) is the actual mechanical impedance, then you get the following condition At any frequency U=[BlE/Re][1/Zm] so that ZmU =BlE/Re always. Since Bl is constant this implies that I =E/Re always. [At 100Hz for example, Zm=22.53 @

30.1degrees leading to U=0.0972 @ -30.1 so that ZmU/Bl =0.1989 A. ] Similarly E/I then becomes Re at all frequencies Do you consider these conclusions reasonable? Of course not, but that is what is a result of your contention which will lead to blocked coil current at all frequencies. .

--------------------- I have seen Beranek and have given you reasons, based on his development, that Zm is not the "actual" mechanical resistance. Certainly one can call it the equivalent mechanical resistance of the driver. It certainly must be taken into account as per Eq.7.1 to find U as the coupling of the electrical and mechanical parts of the speaker must be taken into account. The two equations E=RI +BlU and )=-BlI +Zm'U must be solved simultaneously as I have done. My interpretation agrees with Beranek and Kinsler. I expect that it also agrees with Small etc but I don't have their statements in context but I assume that they know their business and their math/physics. I looked at your reference, Lahnakowski and find that it says, exactly, what I have said before and also have indicated below. He says: F=BlI =Blv/Re -[(Bl^2)/Re]dx/dt substituting E for v and U for dx/dt F=BlI =BlE/Re - [(Bl^2)/Re]U as I have indicated below and in the past. No conflict exists except in your mind.

---------------- Noting that Bl, I and v were measured, this value as well as my value of Zm'=32.87 (@ 85.8 degrees) are approximations due to the measurement errors. Neither is "exact" I don't know what meters you are using but, for example, a typical Fluke 3

1/2 digit multimeter, on AC amps may have an error of 1.5 to 2% of reading +2 to 3 counts. Assuming autoranging to the 600ma scale, this means that the current of 0.172 A may actually be somewhere between 0.175 and 0.169 A The fact that your 32.99 figure and my 32.87 figure are so close is a tribute to both the meter manufacturer and to your skill in measurement. The difference, in fact, in engineering terms is negligable. In addition, you have effectively admitted that Zmech is essentially the same as I have been saying- that it is my Zm'. and not Beranek's Zm. What you have provided, is not an inditement of my "approximation" but is a damned good check on both the calculations that I have made and the measurements that you have taken. You get a cigar, but don't take the wrapper off yet as you have not provided any error estimation on any of your data and measurements. There will be errors. Also, in fact, I can say, within the given 3 sig figure accuracy of my measurement and that which you made, that we are comparing, at best 32.9+/- 0.05 and 33.0 +/-0.05 and are more likely comparing values +/- 0.1 to 0.2

------------- You have given absolutely no information from which one can determine the pf. Re/Ze will give a power factor ONLY if Ze =Re +jX . This would require that the mechanical and acoustic impedance be neglected. Do you want to do this? However, the magnitude that you have obtained, based on your Ze is correct. With my values based on data you have provided: (38.14 @59.257)(7.09)/{8.227 @-26.555) = 32.87 @ 85.81 degrees which agrees with what I had for Zm'. This calculation does not provide any independent check as it is a circular argument where a value is found in terms of itself.. Your current of 0.172 A vs mine of 0.1714 does provide a check and this is a damn good check by any reasonable standards (particularly in that, in use, considering varying room parameters, a much larger error might well be considered quite reasonable).

-------- Because it is a circular argument.

---------- You have given no basis for this assertion.

--------- Why? You are assuming E and I are in phase. Do you have any basis for that assumption?. You have also given no basis for the angle of 72.4 degrees that you have presented. How did you get this? If you got it by taking arccos (0.1905/(11.01*0.0574) then you are wrong. . Please note that I have made no such assumptions and have laid out all the values so thatr you can follow my calculations. I found U =0.0574 at a phase angle determined by 1/Zm (59.26 degrees) You seem to have no problem with this. I then found a Zm' =2.4 +j32.78 =32.87 @ angle arctan 32.78/2.4 =85.81 You have a Zm' =32.99 at some unspecified angle. -magnitude is fine -but no angle means half the information is lost.

Eb is in phase with U so Eb =0.632 @ -59.26 degrees I =Zm'U/Bl =0.1714 @ (85.81-59.26) =0.171 @ 26.6 degrees

Could it be that the problem is that I solved the simultaneous equations

1.41 =7.09I +11.01U 0= -11.01I +(2.4 +j 32.78)U by using matrix methods. We can solve thes by Beranek's Eq 7.1 to find U = 0.0574 @ 59.26 degrees This you have had no problem with. Then I =Zm'U/Bl which, with the data you gave me and double precision calculation, gives I as i have given it.

Sorry, your assumption of 72.44 is incorrect. You have given absolutely no information to indicate how you got this value. That is unacceptable.

--------- . Eb is in phase with U, Bl doesn't have any phase. Magnitude of Eb =(11.01)*

0.0574 =0.632 Phase of Eb is the phase of U>

Eb=BlU is true. However, Eb =(BlU) * (De Bougerre's factor) as you want to apply it is not true.

By the way De Bougerre's factor is the number that you multiply the actual value by to get the value you want. This appears to be what you have done. This is about as kind as I can be about this sort of thing.

Your problem is you do not understand eq. 7.1.

Untrue. The conflict is in *your* mind and leads you to wrong conclusions.

I use Fluke, agreeing with HP, Simpson, and Triplet. No such variation was or is possible.

Round and round you go...

No. It is different parameters giving the same result, such that one substantiates the other. You have a problem with basic logic.

Basis? The data itself that I gave proves the angle of 72.44 is correct. Redo your vector math and get it correct. It is not my duty to teach you vectors. I provided accurate data, use it.

Sorry, but *****************NO************************* , as in

*****************NO************************* Again you do not understand Eq. 7.1. ***Think*** on it. What happens to the numerator, when the denominator is changed to Zmec? E and I are *****NOT***** in phase. There is absolutely no point in arguring further until you understand the equation.

Arrrgggggghhhhhhhhhhhhhhhhhhhhhhh...

As I said, do your friggin' vectors correct and you will get 72.44 deg.

What is unacceptable is that you don't accept that which is proven.

K " Your angle is wrong. The correct angle is 72.44 Back emf Eb *must* be E-(IRe)=1.41-(0.172*7.09)=0.1905 Then cos angle = cos 72.44 = 0.3017 Eb = Blv cos angle = 11.01 * 0.0574 * 0.3017 = 0.1907 Checks. "

I'll rearrange the order of the lines, and explain as I go:

The correct angle is 72.44 Then cos angle = cos 72.44 = 0.3017

We have derived cos angle, ***assuming 72.44 degrees is correct***.

Back emf Eb *must* be E-(IRe)=1.41-(0.172*7.09)=0.1905

We have derived back emf, assuming Eb=E-(IRe) is correct, and it is per 1. Convention 2. Fitzgerald eq. 7.11 3. Morse P.35

Note E,I, and RE were all measured.

Then checking if Blv cos angle equals 0.1905, as it should, if the angle 72.44 is correct

Eb = Blv cos angle = 11.01 * 0.0574 * 0.3017 = 0.1907

It does, meaning the angle is correct, since Bl and v were also measured. If you need references on Eb = Blv cos angle, there is no hope here. Also if you do not agree that 72.44 is correct, there is no point in further argument until you learn eq. 7.1. Also, phase is taken care of in the Eb = Blv cos angle, so it will behove you not to start hooting about vectors.

An error on my part is not possible based on your gross and false assumption that I consider or calculate Ze as resistive.

More lack of understanding on your part. You are simply out of your field.

See what I mean about your understanding.

No it doesn't, as the discrepancy is yours.

And you are off by ~ 12.5%. Unacceptable.

Again, you are lost until you learn 7.1. Believe me, I've been there.

Ahaaaa...... Now we see your true color. Having never gained sight of reality, you think you are right to the point of this. Too bad.

Bullshit indeed. You live in your own egotistical little world, with a drape over the window into reality into the view of the worlds greatest experts, and when that drape is drawn for you, you look the other way, deep into the corner of an area that you are not familiar with, and learn nothing. Well.... you do learn how to sidestep...

As Ronnald used to say... There you go again...

No, as the discrepancy is in your mind.

Yes, but way out in left field. Unacceptable.

Now here we see the futility of trying to help you. Do you see the reference to Small's eq. 31 DIRECTLY ABOVE THE EQUATION??? It is the reference standard for efficiency, has been for over

30 years, yet you ignore it, or are not familiar with it and make no effort to become familiar with it, and further hoot about looking in Beranek for it. I'll refrain from commenting further here.

Over and over and over you go re your gross and false assumption that I term Ze as real. Talk about arrogant ignorance... or is it desperation?

I had originally thought you were projecting, but am now leaning toward believing you actually think you are right. Further you have been too closed-minded to consider the relationships as given by the worlds experts, and are in no position to suggest such.

Northstar

-------- Bullshit- no meter will ever give you an exact measurement of an analog quantity. Put enough money and care into instrumentation and you will get better approximations. Your digital meters can be in error by +/- one or more counts plus a % of reading. Read your manuals and check the Fluke site re measurement accuracy. Chances are that all are well under the error bounds. Agreement between meters is not a guarantee of a correct reading.. Note that the current could be 0.1714 with the meter reading 0.172. Since the calculations that I made are based on your data, presumably gathered with the same instrumentation, and I used double precision arithmetic, then the values I calculate are just as likely to be correct as those that you calculate.

---------- Does that mean that you can't give an answer?

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

@59.257)(7.09)/{8.227

-------- No, Since, in the part you snipped, I could get the same agreement with my numbers. If mine were wrong, a proper check should show this.. Since this check works in both cases, it is useless. >

----------- You gave accurate data. which I used. I would like to know just how you got the 72.44 degrees as there is nothing in the data which leads to this. Are you afraid that I would find out that you have done something that is obviously incorrect? Your response indicates that.

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

----------- I agree, they are not in phase. That is absolutely true and, in my calculations, I have kept trakc of the phase so that I get I =0.1714 @26.6 degrees. YET in doing your calculations for power and for Eb you treat them as if they are in phase. You can't have it both ways. If you knew the phase angle, why didn't you use it? (it isn't 72 degrees)

I gather that from the change you are saying that A/Zm' =(BlE/Re)/Zm =U (taking Zmech=Zm') So A=(11.01*1.41/7.09)(32.86 @85.82)/(38.14 @ 59.26) =1.885 @ 26.56 and 1.885/11.01 =0.1714 This seems to be an awkward way to calculate the current but it works. why not use I =Zm'U ?

Still no angle of 72.4 degrees.

From what? Certainly not from the above. How did you get it?

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

If you could prove it, Your saying so is not proof- show how you got it. I laid out all calculations for you to see. based on 7.1 I got U. From U , find I =Zm'U/Bl values as given.

------------->

Because you said so?

Incorrect- see below

Incorrect

This is based on E and I being in phase. They are not, so Eb is not 0.1905

----------- Oh, dear, This is AC, You cannot do it that way unless E and I are in phase, E and I are phasors but you have treated them as scalars. This is an elementary error. Please go back to those sources and see how they handle the situation for AC where consideration of the phase angle is important as you have done it incorrectly. See below. You have a simple series circuit E=RI +Eb Eb =1.41 -7.09* 0.172 @ angle ? Assume that the angle between E and I is 26.6 degrees Eb =1.41 -1.22 @26.6 degrees =1.41 -(1.09+j0.545) =(0.32-j0.545) =0.632 @-59.6 degrees Note that Eb/BlU =0.0574 @-59.6 Ring a bell?

---------- Eb =BlU is valid This is true for DC, AC using phasors or AC of any waveform using instantaneous values of E and U------It comes from Faraday's Law----- what you have said is incorrect- wrong, kaput.>

---------- See below- E^2/Ze =real power only if Ze is resistive. I sttand by what I said. You have made a gross error.

------- In acoustics- yes, In analysis of AC circuits, I seem to be miles ahead of you.

-----------

----------- Possibly the error is what you have used as input power which is wrong.

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

-------- The equation by itself is meaningless- I want the background on it.

discrepancies

--------- I have read your response. Rather than take on each point at a time, I will go over some of the things that you said. Firstly, you have an angle of 72.44 degrees stated.as fact. but don't care to show how you got it. You imply that this is the angle between Force and velocity then you apply it to Eb=BlU This is a fundamental relationship which all experts back to Faraday deal with either as above or as e(t)=Bl u(t) for general purposes. In the phasor form, Bl=11.01 is a scalar constant. Multiplying a vector by a scalar changes only its magnitude and doesn't affect phase. Eb and U are in phase. They are directly related. In addition, the magnitude of Eb is simply 11.01 *(magnitude of U) There is no power factor "correction" To make such a correction is fundamentally flawed.

Now lets go to your calculations: Taking I=0.172 A, E= 1.41V, and U= 0.00574 all magnitudes as you have given no phase information. You have calculated: Ze=1.41/0.172 =8.198 ohms. Magnitude only given. The angle of Ze and that of I are unknown. In fact there is an infinite number of points for which Re/Ze is constant - these lie between +30 degrees and - 30 degrees ( I can show you but you should be able to figure this out)

You have also calculated Pin =E^2/Ze =0.2425 watts (you give 0.244 but I assume that this is a typo) This is true only if Ze is resistive. (Berenak's 3.53 is general in that his (|e|^2)/Z =W +jQ or the complex power) It follows also that Qin=0. More importantly, this means that I is in phase with E.

You didn't assume this but you do your calculations as if this is true. If they are not in phase,then your calculations must properly reflect that fact. They don't.

Going ahead with this you get Pmech +Pa =0.2425-(0.172^2)7.09 =0.0328 watts. This is correct if your input power E^2/Ze =Pin +j0 ( resistive circuit) Now you determine that Eb =1.41-(0.172)(7.09) =0.1905 Volts This calculation uses scalar arithmetic which can only be used if E and I are in phase. Again, you are treating E and I as being in phase and the resultant Eb is in phase with I.

Now let us go the other way as a check.- using U as the base value and not using I at all or using of any assumed power factor. Pmech +Pa =(Rms +2Rmr)U^2 =2.4(0.0574) =0.00791 watts. Compare with 0.0328 watts - this doesn't check.

We can calculate the mechanical reactive by (Xm) U^2 =32.78(0.0574^2)=0.108 Compare this to Qin = Qmech =0 It doesn't check.

To the voltage: Eb/U =Bl =11.01 which is a constant. Ignoring the fact that Eb and U MUST be in phase (Bl is a scalar multiplier), the magnitude of E =11.01(0.0574) = 0.632 volts. This is based on the well established physics of the relationship. Compare this with 0.1905 - it doesn't check. Multiplying this by some power factor which happens to be exactly

0.1905/0.632 is, at best, simply invalid and meaningless. The relationship is Eb=BlU is valid The relationship Eb =BlU *some power factor ) is WRONG for any power factor except 1.0000... Check your references.

Now to some forensic analysis.

Your values of I and Ze are fine as far as magnitudes are concerned.

What is wrong is that although you say that E and I are not in phase, you do yyour calcualtions as if they are.

Just suppose that Ze=Re +R' +jX' where R'+jX' is the mechanical impedance as seen from the electrical side You have a value of Zm' = 32.99 - suppose that its real part is 2.4 Estimate Xm =root(32.99^2 -2.4^2) =32.90 (where its actual value based on the information you give me for Mmd and Cms etc, is 32.87 ) and Zmech =2.4

+j 32.9 =32.99 @85.83 Using this gives Ze =8.22 @ -26.48degrees (N.B. working from the mechanical side and U, I got 8.23 @ -26.6)

This is a bit high implying that there are some small errors in either I or U or the mechanical resistance. However, using this estimate, Pf in =cos 26.48 =0.895 Pin =1.41*0.172* 0.895 =0.217 and Pmech +Pa =0.217- 7.09(0.172^2)=0.0073 which is a bit low. Obviously the effects of small errors have crept in and I would guess that the angle of Zmech= Zm' is a bit off. Eb= 1.41 -(7.09)(0.172 @26.5 ) =0.631 @ angle 59.6 degrees. Compare this to a value of 11.01*0.0574 =0.632 (@ 59.3 degrees)

In other words, taking into account the phase angle of I, even by making an approximation, leads to more consistent and reasonable values than you have obtained for power and Eb. They also are more consistent with the values that I calculated on the basis of the actual equations of the speaker.

You are not handling your phase angles correctly, and in one case, at least, you have applied a phase angle of 72.4 degrees where it should not be applied and in fact have given no indication of how you got this value in the first place. You must have got in from somewhere. Blustering that I don't know my phasor calculations is not a sufficient or satisfactory answer. It is strange that when I point out discrepancies or want to know where you got a particular value, I get bluster and references to authorities ( of which, the ones that I have seen, are in agreement with my viewpoint) but no explanation of just what you did to get your values. That's not good enough.

Yes I did use 2Rmr in calculating efficiency and when you questioned my results - I checked them out and then realised that you were using the one sided output. (note that the acoustic energy on the other side is still there but is lost). The difference between my corrected numbers and yours are due to my use of the correct input power. Since the Pa is small, a very small difference makes a large change in n. As for Small's equation, Since I do not have Small I have to determine what the terms are and relate them to what is in Beranek. That is all- I simply have not done this exercise. By the way, both Small's and Beranek's expression are of the form n=Pa/Pin and n is calculated in terms of Pa and Pin. Now, to use this calculated n to find Pa given Pin doesn't prove a damned thing - a circular argument.

Now, as far as the experts are concerned, It appears that any to which I have been exposed, are expressing models which I agree with. I have as much circuit analysis capability as they have and do understand what they say. What I disagree with is your interpretation of what they say and dependence on quoting some equation rather than knowing what it is all about. I do not claim expertise in the acoustics but do claim as much experience as they have as far as analysis of circuit models and of the simple electromagnetic conversions that exist in a speaker. Certainly, it is quite apparent that you do not have a fundamental understanding of AC circuit analysis and you understanding of error sources and analysis is not there. There is no such thing as a perfect measurement in an analog world. -even with digital meters.

Sheesh, what is the use.

Your argument about meter accuracy appears to be a red herring. The difference between 0.172 and 0.1714 for current is moot anyway.

You say above "I would like to know just how you got the 72.44 degrees" How I got 72.44 is defined at the very top here, did you not see it? It is the angle between force and velocity. If you cannot figure out the arc cos R/Z bit, that is not my fault.

You data will be in error until you accept Bl E/Re as applied force in Beranek's equation, *however* you must understand that Small's electrical input power of E^2/Re is accurate, and how it relates to Beranek's eq.7.1. This you have not done. I have tried to give you a hint or two, but your condescending attitude of the past does not invite a lot of help. Anyway... you say above "Possibly the error is what you have used as input power which is wrong". This is one of *your* errors. Small and Thiele both define input power as E^2/Re = 0.280. I have clarified the power magnitude at the top of 0.244 as dynamic Pin = 0.244, to show the distinction. I have given you reference on Small and Thieles power input before. Some of your errors hinge on you not accepting this. I know what you need to know in order to do so, and to use your words above "your understanding of error sources and analysis is not there". Too bad (for you, that is).

Your approach to back emf is arse backwards, and in fact you have the answer to your dilemma above, but scoff at such a possibility. Eb = Blv. The E-(I Re) is just straight arithmitec and is given by dozens of textbooks. It is *not* wrong. Phase is taken care of on the mechanical side here, not the electrical side. Blv concerns the phase between force F and velocity v. Blv... velocity v, see? And here PF = cos angle = cos 72.44 = 0.3017. Then Blv PF = 11.01*0.0574*0.3017 = 0.1907. This is the real part of *generated* back emf. As I said above "Eb = Blv cos angle = 11.01 * 0.0574 * 0.3017 = 0.1907" and you replied "Incorrect". You are incorrect, not me.

With due respect to your math ability (which is unquestioned by me), you are not as familiar with the dynamics of how parameters relate in what we have discussed. You say "Sheesh, what is the use", and I agree.

BTW, you say above "No, Since, in the part you snipped". This implies at least mild dishonesty, and since I snipped nothing, then any dishonesty is coming from you. Surely you can do better, it is not my responsibility to keep you honest.

Northstar

--------------much repetive stuff removed------------

----------- Agreed but you were insisting on the accuracy of your data. I agree it is very accurate but not perfect.

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

------ You have claimed it is the angle between force and velocity but have not shown any calculation of it. Arccos which R/Z? It is not the angle between E and U. that is arctan

32.78/19.5 =59.3 degrees It is not the angle between BlE/Re and U as that is 59.3 and BlE/Re is not the actual force. It is not the angle of the actual mechanical impedance which is 85+ degrees It is not the angle between the actual force (BlI) and U as that is 26.6 degrees. It is not the angle determined from Re/Ze as this can be in the range from 0 to 30 degrees and, in fact, is 26.6 degrees So what is it and how did you get it.? All that I can see is that it is the bugger factor between Eb=BlU =0.632 and your incorrect calculation of E-RI =0.190 ---------->

--------------- A) Berenek does NOT claim that BlE/Re is the applied force. Neither do other references. It simply does not make sense and is an artifact of the model. This is clear in Beranek, Kinsler and the reference from Lahnakoski, as well as from the basic equations 1 to 4 as given below. If you assume BlE/Re as the applied force and Berenak's Zm as the impedance then the phase angle between them is 59.3 degrees., not 72.4 degrees. Even if it was so, the only place you have used it was in calculating an unrelated term Eb. The actual force will be BlE/Re only under blocked coil conditions. Of course, under those conditions, U will be 0 , the mechanical power will be 0 and all the input wil be I^Re loss. B) electrical input power of E^2/Re implies that the input impedance Ze =Re and this situation only occurs for blocked coil conditions. It is not the input power under any condition. It is used for calculation of PAE which is not the actual efficiency. There is no relation to Eq.7.1

Your statements fly in the face of both the physics and the math of the situation and do NOT reflect what your references actually say.

----------- This you have not done. I have tried to give

------------- You are labelling E^2/Re as input power and the actual input power as "dynamic input power" OK but there is no need to do so and the value of

0.280 is an upper limit under blocked rotor conditions. Are you thinking that this power actually exists except under blocked rotor conditions? It appears that Small, Theile are using this as a reference- fair enough - simpler calculations and close enough over the frequency range of interest. Beranek does it differently -using the maximum power theorem as he includes Rg while the others ignore it. Note, as I said before, and you agreed, Input power is always less than this.

Oh, yes, with regard to Small's Eq.31 - I have reconstructed this using Beranek's 7.1 and 7.9 and using a reference power E^2/Re. It wasn't difficult to do so. The interesting thing is that Small's equation contains an approximation for simplicity. Can you find it? One consequence is that it is frequency independent and another is that it is about 10-12% high at the frequency of concern (better at higher frequencies- did he mention that?). The "non-approximate" value is 0.49% which agrees with U^2Rmr/(E^2/Re) and my corrected value. In your use of Beranek the efficiency calculation is based on input power =E^2/Ze which is wrong by about 12 % You are uptight about an unacceptable error of this level, while It appears that it is acceptable to Small. Of course he is an engineer.

Cute- but all wrong. Eb is not force. In addition, the basic relationships are given , not by Eq. 7.1 but by the following>

E-RI =Eb (Eq1) F=Zmech*U (Eq2) where Zmec = my Zm' These, for AC are both vector equations- . In general, for AC, E, I and Eb are not in phase. Hence scalar arithmetic is not valid. Go back to your references and see how they handle it for AC.

There are two scalar arithmetic relationships applicable for the geometry of a speaker. They are Eb=BlU (Eq3) F=BlI (Eq4) Note that Bl is a scalar so there is no phase shift between Eb and U. There is also no phase shift between I and F

Eq. 7.1 and the whole basis of the circuit model is based on these relationships. Also - from these relationships Eb/U =Bl =11.01 and F/I =Bl =11.01 No power factor term, real or ficticious is involved.

--------------- > And here PF = cos angle = cos 72.44 = 0.3017. Then

--------------- Let us assume that your "out of the air" angle is correct. and is the angle between Force and velocity -(which it isn't.) Eb is not force so the angle of 72.44 degrees is NOT the angle between Eb and U. If your angle is between E and U then this angle is also between E and Eb . This would mean that there would be some other angle between E and I , and hence between F and U. Go over my calculations and try to understand them. At least they are consistent. If you are attempting to calculate Eb=E-RI using only the real parts of E,I and Eb, then you will get wrong answers. (oh, yes the real part of Eb is 0.323 Volts ).

------------ Since your errors are mainly in how you do your math, are you admitting that my math is correct. The fact that it fits the physics is also correct. The math must fit the physics and mine does. As for the dynamics of the system- we have only looked at the steady state situation and the models based on the basic equations (1 to 4 above)above). I would suggest that my understanding of the dynamics involved in these very simple relationships is well ahead of yours because of what appears to be a fundamental understanding, on your part of the physics (i.e dynamics) involved coupled by a great ability to quote sources without thinking of what they are really saying.

An example is that you calculate (incorrectly) that the power transferred to the mechanical side is Pin -I2Re =0.0328 = Pmec +Pa But Pmec +Pa =(U^2)(Rms +2Rmr) =(0.0574^2) (1.57+0.83)=0.0079 watts so you are saying 0.0328 =0.0079 Do you hear alarm bells? You have just thrown out the most fundamental principle of physics - "conservation of energy".

Another example is reading a lot more into Beranek's Eq.7.1 than really exists. Instead of replacing Zm by Zm' - try using (BS) instead. Eq.7.1 will then, after manipulation reduce to U(BS)=U(BS) which is true as U=U and BS=BS are both true.

Another is real power Pin=E^2/Ze which is also not true unless Ze is purely resistive.

There are more.

My understanding of acoustics, per se, may be less (but I am beginning to wonder) but so far we have been dealing with a very simple dynamic system model in terms of an electrical equivalent and you have a failing grade in that. It probably doesn't matter as you can simply plug in data into Small's work and turn the crank and large errors won't make much practical difference.

You have made statements that are mathematically incorrect, and others that are physically incorrect and some of the math errors are attempts to patch up the physical inconsistencies. You quote references without understanding them. You may be very good a building speaker systems and may have made it an art. Good for you. Otherwise????