120V from both legs

Bottom l>> >> >It appears that, (and you were not clear on what you actually did)

You have now responded twice since I gave my above analysis, without any attempt to refute it, proving my phase angle, mechanical resistance, and input power is correct and yours is wrong. All your present handwaving is in vain, and your 30 pages plus of analysis is based on poor logic and is wortheless.

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

Bullshit- you really cant read. You are in your own little world trying to prove that I am wrong without trying to read and understand what i am saying. I see and understand your calculation but have simply point4ed out that calculation, on the basis of Berenak's models and the parameters that you have provided- there are seriousl inconsistencies.

Your solution leads to inconsistencies which have been pointed out and you havent addressed.

If your analysis is correct:

a)There are data errors in one or more parameters such as Rms, Rmr etc.(accepting the correctness of your results) as your results lead to inconsistencies with the results from the given parameters. b)There is a data error in Re even though your math is correct c) Failing either of the above, Berenak's model is wrong.

Simple math errors on either your part or mine has been eliminated.

Take your choice. There are 4 of them.

Bottom l>> >> >> >It appears that, (and you were not clear on what

models and the parameters that you have provided- there

No, you are the one not addressing my analysis. Nothing in it is inconsistent with Beranek. You just don't have the ability theory-wise to relate mechanical resistance to his eq. 7.1. Your understanding is weak in this area.

By the way... your desperation is showing in your typing above, and I can see why, since you are not only wrong on phase, resistance, and power, but on theory itself.

Desperation indeed...... I offered to have electrical resonance measured by a reputable independent lab (at my expense even) and you declined, saying (see above) " I will accept the resonant frequency as 203.4Hz and the input power as indicated."

We agreed on the parameter magnitudes used in my analysis above, which shows you wrong.

b)There is a data error in Re even though your math is correct

Bullshit.

You are the one having a problem with Beranek, not me.

Your choice is simpler, refute my analysis or be wrong.

Northstar

This motor you're so hot & heavily discussing seems to suck, big time }:)

For the little proton's sake: Follow your own advice & go back to school ~>

If you had really read what I had said before, I indicated that you had done your analysis correctly -based on the data provided and the existence of resonance at 203.4 Hz.

I also said that it doesn't agree with the model and other data provided.*******

I have gone over your analysis but you haven't bothered to check out the results from the model to see the conflict for yourself. You have all the information needed. Try using the circuit of Beranek's Fig.7.4 - the parts indicated as "mechanical" and "acoustic radiation" which together make Zmec (also see Fig.7.2) Plug in the values you provided for these elements (can you handle a series RLC circuit?) and evaluate Zmec -both magnitude and phase.

Do the results agree with your claimed Zmec- or with what I have said?. That is the problem If the model is incorrect - then why? And don't claim some mysterious unaccounted for resistance unless you are ready to write a paper to show that Berenak, Small, Kinsler etc all have it wrong.

I'm out of here- I may respond after a couple of weeks - then again I may not

In article , snipped-for-privacy@peeshaw.ca says...

This can be made simple: If electrical phase is zero at 203.4 Hz, we agree that power input at 203.4 Hz is Pin = E^2/Ze = 0.2425 watt, not "Pin=0.2162 watts" as you have previously claimed.

So I am sending the speaker to a reputable independent lab at my expense for measurement of Ze, electrical phase, and Re. If correct, then mechanical + acoustic power must be power in minus power lost as heat Pmec+Pa =(E^2/Ze)-(I^2 Re)=0.0328 watt or Pmec+Pa= v^2 (Rmec) = 0.0328 watt, then Rmec of 9.953 will be proven correct (along with power), though likely still mysterious to you. Northstar email snipped-for-privacy@hotmail.com remove high card to reply

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

Agreement of parameters and analysis:

Kelly: "It appears that, (and you were not clear on what you actually did) you started with the assumption that Ze was real - this gave Rmot=1.109 ohms which is fine if the assumption was correct."

Northstar: "Now since I measured the phase angle between voltage and current to be zero at 203.4 Hz, we agree that Ze *is* real and Rmot = 1.108 ohms. Then Ze = Re + Rmot = 7.09 + 1.108 = 8.198 ohms Power in is Pin = E^2 / Ze = 1.41^2 / 8.198 = 0.2425 watt Not " Pin=0.2162 watts " as you have consistently claimed.

THEREFORE YOU HAVE LOST THE ARGUMENT, since proof that E^2/Ze is the power in, is given by Kinsler on page 366, where he describes the electrical resonance fr where the positive (inductive) reactance of the voice coil cancels the negative motional reactance, resulting in a frequency at which the input reactance is zero. This occurs at 203.4 Hz, making Ze real and power in = E^2/Ze = 0.2425 watt or Pin = I^2 Ze = 0.2425 watt. "

Kelly: "If you are at resonance, I have no problem with that."

Northstar: "You have finally conceded that if 203.4 Hz is the frequency electrical resonance, then Ze is real at 203.4 Hz and power input is E^2/Ze = 0.2425 watt, and not your power magnitude of "Pin=0.2162 watts" as you have claimed, which would also make your phase angles and analysis in error as well. This leaves only the frequency of electrical resonance to be verified, so again, do you want me to send the speaker to an independent and reputable lab to have phase measured, or do you want to accept my measured frequency of 203.4 Hz?"

Kelly: "I will accept the resonant frequency as 203.4Hz and the input power as indicated."

Northstar: "Thank you."

Kelly: "the open circuit mechanical impedance Zmec= 2.4+j32.78 =32.87 @ 85.81 degrees. The magnitude compares with your value of 32.99 within reasonable error (data is good) but the phase angle differs from yours."

Northstar: "Yes, your phase angle is incorrect. Allow me to explain with a short analysis using that which we now agree on: With agreement that power input is E^2/Ze = 0.2425 watt, mechanical power then must be power in minus power into heat Pmec = Pin - Ph = E^2/Ze - I^2^Re = 0.2425 - 0.2097 = 0.0328 watt. Noting we agree that mechanical impedance Zmec = 32.99, mechanical power must also be velocity squared times the real part of impedance Pmec = v^2 (Zmec cos angle) = 0.0574^2 (32.99 * 0.3017) = 0.0328 watt We see that only cos angle = 0.3017 satisfies the equation, giving phase angle to be arc cos 0.3017 = 72.44 degrees. And the real part of mechanical impedance is Rmec = Zmec cos angle = 32.99 * 0.3017 = 9.953 Xmec is sqrt(Zmec^2 - Rmec^2) = 31.453 and mechanical impedance becomes Zmec = Rmec + jXmec = 9.953 + j31.453 = 32.99 @ angle 72.44 degrees The power in - power out equation can then be written then as E^2/Ze = (I^2 Re) + [v^2 (Zmec cos angle)] = (0.172^2 * 7.09) + [0.0574^2 (32.99 * 0.3017)] = 0.2425 watt Matching input E^2/Ze = 1.41^2 / 8.198 = 0.2425 exact Note that impedance was re-measured on Jan 19, 05, and is correct at 8.198 ohms, and can be proven by another lab if you wish. Noting that Zmec cos angle = Rmec, then in the form you use, power in = power out as E^2/Ze = (I^2 Re) + v^2 Rmec = (0.172^2 * 7.09) + (0.0574^2 * 9.953) = 0.2425 watt "

End of analysis

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

The independent lab results have arrived. How would you prefer to proceed? TIA

Northstar

Whatever way you want.

Did you calculate the Zmec as I asked- using the Berenak model and the parameters that you gave- that is Rms, Rmr, Xmd Cms?

Rather than go through the jumble of the past, please just state the equation for mechanical impedance as you see it, along with parameter values involved, and of course the value of Zmec itself.

Northstar

From Berenak Fig.7.3 or, if you prefer, the part of Fig.7.4a marked as Mechanical and acoustic.This is the open circuit impedance of fig 7.2a etc and corresponds to the (Zm+Zl) of Eq.3.60

Zmec=(Rms +2Rmr)+j(wMmd +2Xmr -1/wCms)

where Rms=1.57, 2Rmr=0.83, Mmd=0.0281 including the mass of the air load so that wMmd +2Xms=35.91, Cms= 0.000250 and w=1278 all data you provided.

Then Zmec =(1.57+0.83) +j(35.81-1/1278*0.00025) =2.4+j 32.78 Magnitude =root(2.4^2 +32.78^2) =32.87 (say 32.9 keeping to 3 significant figures) phase =arctan (32.78/2.4) =85.8 degrees

The magnitude is in good agreement with your value of 33.0 (32.99) but the phase angle is considerably different.

Do you have data on the coil inductance?

Mr. Kelly, Before proceeding, I believe the "dilemma" of (Bl)^2/Re in Berneks eq.7.1 and the relation to my mechanical resistance of 9.953 and my mechanical impedance of 32.99 to eq. 7.1 has been expressed as of prime concern. This leads to our differences regarding Pmec, phase, and Zmec (where if I am correct, the difference is small, but indeed is 32.99, not less). The point is that one of us is in error and until this relationship is understood, we will never reach agreement. This means that when the math is all in, one of us should acknowledge our error. Also there is no satisfaction in learning for either of us, if we cannot respect both the others ability and demeanor. If so, I am willing to continue and rationalize my magnitudes noted above, along with answering your last post. What do you think?

Northstar

The "dilemma" is not in (Bl^2)/Re which has nothing to do with either your value of 9.95 or my value of 2.4 for the actual mechanical resistance (not the virtual mech resistance) . It is very clear where the (Bl^2)/Re term comes from and we have beaten that to death.

As to the differences that we have. We agree that there is a discrepancy and both would like to find out why it exists. On the basis that 203.4 is the second resonance point- your calculations are correct. Using Berenak's models and the parameters that you gave me- I am correct. I have done my calculations several ways, with models and independently repeated these calculations. Mathematically they are correct. So now we have two sets of "correct" calculations which give different values. The conclusions that I previously made are:

a)Berenak's model is incorrect. ***The development of this model has been checked and verified, not only by me but by others. The only thing that has been ignored is the coil inductance.

b) The parameters Rms,Rmr, Xmd, etc are incorrect. ***I don't believe that they are as the magnitudes of I and U agree, well within possible error limits, with your measured values.

c)The assumption of resonance at 203.4 Hz is incorrect.*** For such resonance the inductance must be appreciable as the second resonance, if it exists, is dependent on L and Mmd. Calculation of Zin and its phase using a computer model with various values of inductance does not agree with your results. If L is set to get resonance at 203.4Hz, the Zin is real but near

Normally I would blame the errors on the model and the parameter values uses (i.e. a or b above) but it is interesting to note that, if L is negligable (no resonance in the valid range of the model) the reuslts using magnitudes Zin =8.198 , Zmec =32.99 and Re=7.09, and making no assumptions with regard to phase, leads to calculated results (checked by two different approaches) which agree, within reasonable error limits, to the results that I calculated from the model.

What value of L do you have for the coil? You have said, several times, that it was negligable- which would mean no second resonance point. Do you have a blocked coil input impedance measurement ?(impedance, not DC resistance alone). I am as anxious as you are to get to the root of the matter.

As to the magnitudes:

The difference in magnitude is small as you indicate. This difference is well within the possible accumulated errors in the data and the measurements. This is not a problem. The difference between 2.4 and 9.5 ohms is a problem and is related to our phase angle difference.

As to accuracy, values of 9.953 and 32.99 imply a meaningless precision as the base data used to calculate these values is not that precise. The current given is 0.172A, not 0.17200...A When using 3 significant figure data such as I=0.172, it is meaningless to get a result with 4 significant figures such as 32.99. In this case 33.0 is as good as it gets and this is normal practice (even taught grade 8 students) While it is useful to carry out calculations to a higher "accuracy", all this does is eliminate serious numerical roundoff errors but doesn't make the results any more precise. Thus when I write a magnitude of 32.9 it is implicit that it is between

I am as interested in finding the discrepancy as you are and that is why I cross check my results as much as possible.

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

Your calculations are wrong. See below.

Fretting this is of no avail regarding your power errors, as my measured Ze and Re have been verified. See below.

For a small fee I might tutor you up to this level on what really matters here.

Which is why I do such here and there.

I have four factory calibrated voltmeters. They read: Fluke 1.500 vac HP 1.499 vac Simpson 1.499 vac Triplett 1.501 vac

I use the Fluke for measurements. On current I get 0.2276 amps with

Now to address your errors:

Regarding electrical resonance, I stated: "This occurs at 203.4 Hz, making Ze real and power in = E^2/Ze = 0.2425 watt or Pin = I^2 Ze = 0.2425 watt. "

You replied: "If you are at resonance, I have no problem with that."

The following has been confirmed well within measurement tolerances by an independent and respected lab:

Electrical resonance = 203.4 Hz Electrical impedance at 203.4 Hz = 8.198 ohms Electrical resistance = 7.09 ohms So that: Real power in P = E^2 / Ze = 0.2425 watt Power creating heat Ph = I^2 Re = 0.2097 watt Mechanical power (here I include acoustic power) Pmec = (E^2/Ze)-(I^2*Re) = 0.0328 watt

Showing your power in of 0.2168 watt and your mechanical power of 0.0079 watt to be wrong, the latter off by over 400%.

Now we know mechanical resistance must be Rmec = Pmec / V^2 = 0.0328 / 0.0574^2 =9.955 and we know mechanical impedance must be Zmec = F/v = BLI/V = 11.01 * 0.172 / 0.0574 = 32.99 Phase angle between force and velocity is angle = arc cos Rmec/Zmec = 72.44 Xmec = sqrt Zmec^2-Rmec^2 = 31.452 as check on phase angle angle = arc tan Xmec/Rmec = 72.44 as check (Halliday 7.47, 6th.ed) *MECHANICAL* power is Pmec = Fv cos angle = BlI*v cos angle = 0.0328 watt. matching (E^2/Ze)-(I^2*Re) as above exactly.

Note you are in error with your power in of 0.2168 watt, your mechanical power of 0.0079 watt, your phase angle of 85.8 degrees, and power factor (cos angle) = 0.0732. This means your analysis is bunk, and you have strewn the internet with vast amounts of erroneous information in your long speils, which is indeed unfortunate for those doing Google searchs for information. Not a good legacy.

With your continuing snotty attitude (the grade 8 remark above), how about you now fret over Beraneks eq.7.1 as related to the mechanical impedance and resistance. Serves you right, and should keep you busy for a while as well.........

Northstar

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

--------- I stand by the results obtained- on the basis of the model used and the data you provided. You have not proven any calculation errors or errors in principle. What exists is a discrepancy which is not due to either your calculations or mine. >

------ What models and when calibrated? Do you have calibration curves for them? Do you go to the expense of getting them regularly recalibrated? Are they true rms?

Then when you say 0.172A, are you actually getting a reading of 0.1720A?

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

---------- Is this the blocked coil impedance or the impedance with the coil free to move?

I did want to know the blocked coil electrical impedance at 203.4Hz. I wan't to know the coil inductance as well as resistance. Is this too much to ask?

Another thing is that I would really like to know on which side of the ammeter (source or coil side) did you measure the voltage? Rather than go after you, I just want to clarify some things in the hope that it helps to resolve differences.

---------- If in fact, Rmec =9.95, then Berenak's model or your data is wrong? which?

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

-------- You are not carrying out independent cross checks of your results. Certainly you will get "exact" correlation. Should not Xmec =Xmd-1/wCms =32.78 using your prior data ? As for Halliday: please note that Fvcos angle =BlI*v cos angle =11.01*01.72*0.0574 cos 85.81=0.0079. so calling on Halliday doesn't prove anything. However, I am not quibbling with your results. On the basis of the data you are using - resonance and Ze, Zmec and Re as given. - they are correct and Berenak's model is wrong.

---------

----- My analysis is based on Berenak's models, which are accepted and well tested, along with data that you have provided which I have accepted as correct. The calculations that I have made are correct on this basis and repeated calculations by different approaches and versions of the models do agree.

You have apparently not gone over these calculations which were clearly laid out for you (and are simple circuit analysis) on a step by step basis and have not discovered any specific errors in what I have done.

Instead, you simply say that they are wrong- no reasoning, no pointing out of errors or questioning. You have made no attempt to show where I am wrong- sorry- you did question my use of (Bl^2)/Re +Zmec but this was shown to be correct.

I wrote: "From Berenak Fig.7.3 or, if you prefer, the part of Fig.7.4a marked as Mechanical and acoustic.This is the open circuit impedance of fig 7.2a etc and corresponds to the (Zm+Zl) of Eq.3.60

Zmec=(Rms +2Rmr)+j(wMmd +2Xmr -1/wCms)

where Rms=1.57, 2Rmr=0.83, Mmd=0.0281 including the mass of the air load so that wMmd +2Xms=35.91, Cms= 0.000250 and w=1278 all data you provided.

Then Zmec =(1.57+0.83) +j(35.81-1/1278*0.00025) =2.4+j 32.78 Magnitude =root(2.4^2 +32.78^2) =32.87 (say 32.9 keeping to 3 significant figures) phase =arctan (32.78/2.4) =85.8 degrees"

Did you even bother to read this or go over it for errors and or omissions? If there is an error in this- please let me know what you think it is. Simply saying it is wrong is useless. Look at this in terms of the model and the data that you provided- is this correct on this basis rather than the fact that it differs from your other results.

This is what your data and Berenak's model gives for the actual mechanical impedance. If you want to (incorrectly) include Bl^2/Re then you still won't have a resistive component of 9.95.

All that I have been trying to point out is that there is a discrepancy between your results and the model. If the model doesn't give the correct results, don't blame me as I am just the messenger- blame Berenak for errors or some of your measured parameters. You should have discovered these discrepancies yourself.

------ Hardly- more time spent typing than spent on the simple analysis.

. The models are straightforward, simple circuit analysis and I approached the solution by different methods, getting independent checks on values so there are no analysis errors. I also used Eq.3.59 and 3.60 to get a direct solution for I and U and the remaining values. If you had cared to actually try to follow my analysis- I laid it all out- hiding nothing, You apparently didn't try to do this.

All I have done is use the model and your data to calculate the theoretical results. The correctness or lack of correctness of the results is not due to my calculations which have been checked and rechecked but is due to the correctness of the Berenak's models (these have been checked-OK but unnecessarily cumbersome) or the correctness of the data that you provided. that's the way it is.

If the model or this data is wrong, then don't look at me as the source of any errors. Yes, there is a discrepancy between the model results and the results that you get. I gave possible reasons for this.

EITHER the theory is wrong OR the trivial circuit analysis is wrong, (both have been checked thoroughly) OR the data you provided for the model is incorrect - OR the input impedance data is wrong.

Which it is - I really don't now give a damn- but there is a discrepancy between your results and the model results. This can't be wished away nor blamed on me as you want to do. . As to fretting over 7.1- I am not fretting-I know just how it is obtained and what it means. It is falls out of a solution of Eq.3.59, 3.60 or of Fig

I am sorry for being repetitive but it appears to be necessary. If you have specific, point by point, problems with my analysis, that you want to raise- that's fine you should do that- but don't just say they are wrong because you cannot or will not follow my analysis which has been given in detail. I have looked at your analysis without dismissing it out of hand. and have asked for further information which might or might not help- some of which was pretty slow coming, and some which has not yet been offered. Do you want to resolve this discrepancy- it appears not.

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

You made an error in principle by not treating Ze as real, then real power in = E^2/Ze. Had you done so, Pin = Pout would have been evident, but the derivation of Rmec = 9.955 from 7.1 would likely have remained.

Villchur "Handbook Of Sound Reproduction", p. 11 " P=E^2/Ze "

The reference is a Fluke 189. It is true RMS and was factory calibrated less than a month ago. The other meters match as noted above.

Free to move.

I measured with the GenRad 1657 digibridge, however it uses a tone to do its reading, and I am not sure this gives an accurete reading with the coil moving. It reads a choke accurately of course, but I hesitate to block the coil completely lest the driver be damaged beyond repair. Best I can tell however L = ~ 0.0026 H. How does this fit in with your expectations?

Voltage was measured across the coil.

Rmec of 9.955 is derivable from Beraneks eq 7.1.

Checks provided below.

That's part of the "discrepency", but likely solvable with correct phasor diagrams.

Sorry, I disagree. Pmec must be F cos angle * v = 0.0328 watt. Basic and a good check on Pmec = v^2 Rmec = 0.0328 watt. Why would you not pick up on this?

Beranek has many models, and likely a few fine points do not correlate. Perhaps he was working them out as he wrote the book. Morse and Olson are more clear on a few of the basics.

Do you have Olsons book? If so take a look at Fig. 6.1.

As noted above, you made a fundamental error in principle by not treating Ze as real, thusly skewing some of your basic equations into error. There was no point in my "going over step by step" your calculations reflecting this error.

Not true. I repeatedly stated more mechanical power was dissipated than just in Rms + 2Rmr.

OK, look at fig 7.4a. This is the circuit for eq 7.1. E(Bl)/Re is the applied driving force, i.e. the numerator in 7.1. (Bl)^2/Re is an impeding resistance in series with Rms+2Rmr and the reactances, forming the denominator in 7.1 Velocity is v = Fapp / (Rmt + jXm) = 0.0574. Correct as measured. Now to eq. 3.60, note this is of pure mechanical nature, not containing (Bl)^2/Re. It just says v*Zmec = BlI = Bl E/Ze, but of opposing polarity such that the forces cancel to zero. You must add (Bl)^2/Re to Zm+Zl, i.e. use (Bl)^2/Re + Zm+Zl in the right-hand term of 3.60. Then the left hand term becomes BlI = Bl E/Re, not Bl E/Ze and forces are again equal and *then* you have correspondance to fig. 7.4a and eq 7.1. Does this help?

I refuse to accept blame - my analysis is correct. However since blame must be laid in all cases, perhaps you should discuss this with Mr. Beranek?

I gave up following in detail once I noted your phase was in error, and you were steadfast concerning it.

Rmec = 9.955 is there in eq. 7.1. Can you now find it?

I an sorry you feel repetitiveness appears necessary. Once you accept power must be dissipated to overcome back emf, i.e. the resistace due to back emf opposing the drive voltage of (Bl)^2/Re, the repetitiveness will be history. I came here to seek a little insight into this myself, and am now confident I have both the equations and logic that bears this out. BTW, some of this confidence was instilled by your prodding and my learning a facet or two about the math aspect. Thanks.

You mistake my intentions. They have been and remain to go beyond Beranek, Kinsler, Olson, et al. This was not made easy in my endeavers here by your condesendence at times.

In any event, you did not dispute my analysis but noted no cross checks, so I repeat it here with a few checks for you to now dispute any part of, otherwise I'll take it that you accept my analysis as correct:

Confirmed well within measurement tolerances by a prominent and independent lab:

Electrical resonance = 203.4 Hz Electrical impedance at 203.4 Hz = 8.198 ohms Electrical resistance = 7.09 ohms Giving::

Real power in P = E^2 / Ze = 0.2425 watt Power creating heat Ph = I^2 Re = 0.2097 watt Mechanical power (here I include acoustic power) Pmec = (E^2/Ze)-(I^2*Re) = 0.0328 watt Mechanical resistance must be Rmec = Pmec / V^2 = 0.0328 / 0.0574^2 =9.955 Mechanical impedance must be Zmec = F/v = BLI/V = 11.01 * 0.172 / 0.0574 = 32.99 Phase angle between force and velocity is angle = arc cos Rmec/Zmec = 72.44 Xmec = sqrt Zmec^2-Rmec^2 = 31.452 as check on phase angle angle = arc tan Xmec/Rmec = 72.44 as check Pmec = Fv cos angle = BlI*v cos angle = 0.0328 watt. matching Pmec (E^2/Ze)-(I^2*Re) = 0.0328 watt. as checks: Rmec = (Ze-Re) Zmec^2 / (Bl)^2 = 9.95 Pmec = v^2 Rmec = 0.0328 watt Pmec = I Blv cos angle = 0.0328 watt Zmec = F/v = BlI/v = 32.99 Zmec = Rmec/cos angle = 32.99 v = F/Zmec = 0.0574 Northstar

----- Original Message ----- From: "Northstar" Newsgroups: alt.engineering.electrical Sent: Wednesday, February 23, 2005 10:28 AM Subject: Re: Motor models

independently

------------ Not necessarily so. Given the data that you gave me- and solving Berenak's models- the results do not support Ze being real. That is why I worry about the discrepancy being more than due to accumulated errors.

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

---------- I have no problem with that- IF Z is real. Also the magnitude of the complex electrical power is given by E^2/Z - not a problem. The problem is that when Z is not real, the real power is not E^2/Z nor is it E^2/R The above references all refer to the Z=R+j0 situation. IF as you say, Ze is real, then it applies.

--------

-------- Thank you.

--------

----- Again thanks.

----------

---------- Coil moving is a problem as that will reflect the mass reactance into the measurement. Can you use a small voltage at 203.4 Hz to limit the current? - by the 3 voltmeter method? Put a known resistor in series with the coil (blocked) and measure voltage at the supply, across the coil and across the resistor. This will only work for blocked coil conditions so, if you cannot do so-so be it. -----------

------- Thanks -that helps.

-------

------------ Show me. Berenak's 7.1 uses Zm =(Rms+2Rmr +(Bl^2)/Re +j Xmd-1/wCms) [including air mass in Xmd] This gives Rm =19.5 and Xm =32.78 with a magnitude of Zm =38.14 If you have Rmech = 9.955 then you will get Berenek's Rm =27.06 and Xm =31.45 This will lead to a velocity of 0.0518 if inductance is ignored. If inductance is included, Eq.7.1 needs some adjustment- result is velocity is still not 0.0574 This is the kind of anomaly that I am concerned with.

---------

--------- This is not a problem in that there probably are a lot of accumulated measurement errors involved. I would say that , in an engineering sense, this is a good correlation.

---------

--------- Note that I used Halliday to "confirm" my result. Calling on Halliday doesn't prove anything except that we are using different pase angles.

--------.

-------- I don't but I recall Kinsler and, have developed Berenak's circuits from scratch ( his different circuits are all effectively the same. I also developed Eq.7.1 from scratch. The circuits are fine and quite clear. Kinsler is clearer and his notation is better.

------

------- Since my analysis was independent of the realness of Ze, that is not a valid criticism. My calculations were based only on Re, Xmd, Cms, Bl, E, f, Rms, Rmr as given. The value of Ze that I get is based on these. There is one more value- L which is important but I worked on your assumption that L was negligable. We are still down to the fact that the model, correctly applied, does not agree with your contention. Hence my list of possible problems.

----- If so, then there is a problem in that the additional dissipation is not taken into account anywhere. Berenak doesn't include it, Kinsler doesn't and circuits that I have seen, attributable to Small, do not account for it. So, where is the source of this added resistance as it is quite large and I should think that these sources should account for it.? In other words, saying that more power is dissipated should be accountable. In addition, assuming that this power dissipation exists, there should be an effect on velocity and there are discrepancies here.

--------

----------- No problem here: (assuming Rmt =(Bl^2)/Re +Rms +2Rmr)- Yes Eq.7.1 reflects the effect of Re and the circuit of Fig. 7.4 is fine. We have discussed this previously.

Correct as

------- No because it is wrong. We have been there before

Eq.3.59 and 3.60 are the fundamental equations of motion. Eq.7.1 is not and is derived from these.

Eq.3.59 E=ZcI +BlU where Zc is the coil impedance leads to I =(E-BlU)/Zc Ignoring coil inductance: I=(E-BlU)/Re

Eq.3.60 0=-BlI +ZmecU where Zmec =Rms+2Rmr +j(Xmd-1/wCms) is the open circuit mechanical impedance (I =0 or Re =infinite) Substitute for I in 3.60 to get BlI =Bl(E-BlU)/Re =ZmecU or BlE/Re-(Bl^2)U/Re =ZmU (NB BlI BlE/Re -(Bl^2)U/Re --definitely not BlE/Re) giving BlE/Re ={(Bl^2)/Zc +Zmec}U or U ={BlE/Re) /{(Bl^2)/Re+ Rms +2Rmr +j(Xmd-1/WCms) } which is Eq. 7.1

If coil inductance is not negligable, substitute Re+jwL for Re.

You are correct in saying Zmec =BlI/U but this Zmec does not include (Bl^2)/Re

-----------

------- Happily. I have no problem with him.

--------

------------ Too bad. I hoped for more.

-----------

If you use Zmec =9.955+j32.5 so the magnitude is 33.99 - no problem. If you then include the (Bl^2)/Re term you get 17.1 +9.955 +j32.5 =42.3 (angle is

so from Eq. 7.1 U=[11.01)(1.41)/7.09]/42.3 =0.0518 where it should be

The magnitude of 32.99 is fine but your phase appears wrong as if correct, it should return the correct U.

----------- Actually NO power is required to overcome back emf. A back emf exists only due to the motion of the coil. . If the source is to provide a current to cause this motion, then it must be such that E-Eb will provide the necessary current. The product of current and back emf is the power into the mech system, but this is not "power to overcome back emf" This is power dissipated in the mechanical elements. Eb/I is the same as U/F Please note also that back emf does not exist on the mechanical side so the resitance (Bl^2)/Re is not the resistance due to back emf. It is simply the electrical resistance as seen from the mechanical side.

----------- Going beyond would be looking at the acoustic parameters

------- Not a check - same data used

again not a check.

you are going around in circles with your checks.Based on Ze being real, the above is numerically correct, as I said before. It still leads to discrepancies which you have not addressed or attempted to address.

I was looking over a printout of a reply from you It included the following: "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 Berenak's denominator in E.q 7.1 times cos angle between voltage and current Zmec =38.142*Re/Ze =38.142*(7.09/8.128)=32.99 agreeing exactly with BlI/v

Youre method where Zm' =32.87 gives a *very* close approximation of Zmec"

I note that, at this time you are saying that Re/Ze =cos angle between voltage and current and this corresponds to 30 degrees. Obviously you were not thinking of 203.4 Hz being resonance at this time. As for the exact calculation- the little formula you used is based on the approximation that Xmec>>Rmec - that is Zmec is reactive. This neat little formula is incorrect if Rmec is appreciable (and note that the denominator of Eq.7.1 is (Bl^2)/Re +Rms +2Rmr +j(Xmd-1/wCms) =19.5 +j32.78 =38.14 magnitude which is 17.1 +(2.4+j32.78) and not related to 9.955+j31.5 Further, when asked about inductance, before and after this, you said it was negligable. On the basis of your values of Ze, Re and Zmec and making NO assumptions whatsoever as to phase I calculated (and gave you the calculations- doe in two different ways) the following results which satisfy these relationships. Rmot =0.2424 , Zmot =3.674 so the phase of Zmot is 86.22 degrees Zin =8.198 @ a phase angle of -26.57 degrees Zmec =32.99 @ 86.22 degrees =2.175 +j32.92 I=0.172 @26.57 degrees U=0.0574 Pin =0.2169 I^2Re =0.2098 so Pmec +Pa =0.0072 or Pmec+Pa =2.175*0.0574^2=0.0072

Now, I did not pre-assume that Ze was real as that would fall out of the calculations if it were so.

Compare these to the values calculated using Berenak's equations and circuits. There is some difference but generally there is a close correlation. However, I found Zin = 8.23 so I explored to find what L would make this

In other words, the theoretical results and the results from from the impedances, without making any assumptions about resonance are in good agreement.

If, on the other hand, I assume resonance by setting wL=-Xmot the input impedance calculated is about 7.32 ohms. which is definitely at odds with

So: assuming resonance at 203.4 Hz means that there are major discrepancies that occur. This has not been been clarified or resolved. If resonance is not assumed, there is a good correlation which indicates good data.

However, at what frequency was Rmr measured? I understand that it is proportional to the square of the frequency However, this still doesn't account for the discrepancies.

I gave my analysis and you noted 2 or 3 checks as using the same data. Fine, here is my analysis again, with those checks deleted.

Confirmed well within measurement tolerances by a reputable and independent lab:

Electrical resonance = 203.4 Hz Electrical impedance at 203.4 Hz = 8.198 ohms Electrical resistance = 7.09 ohms Giving: Real power in P = E^2 / Ze = 0.2425 watt Power creating heat Ph = I^2 Re = 0.2097 watt Mechanical power (here I include acoustic power) Pmec = (E^2/Ze)-(I^2*Re) = 0.0328 watt Mechanical resistance must be Rmec = Pmec / V^2 = 0.0328 / 0.0574^2 =9.955 Mechanical impedance must be Zmec = F/v = BLI/V = 11.01 * 0.172 / 0.0574 = 32.99 Phase angle between force and velocity is angle = arc cos Rmec/Zmec = 72.44 Xmec = sqrt Zmec^2-Rmec^2 = 31.452 Checks: Rmec = (Ze-Re) Zmec^2 / (Bl)^2 = 9.95 Pmec = v^2 Rmec = 0.0328 watt Pmec = I Blv cos angle = 0.0328 watt Zmec = F/v = BlI/v = 32.99 Zmec = Rmec/cos angle = 32.99 v = F/Zmec = 0.0574

Now I stated regarding electrical resonance: "This occurs at 203.4 Hz, making Ze real and power in = E^2/Ze = 0.2425 watt or Pin = I^2 Ze = 0.2425 watt."

You replied: "If you are at resonance, I have no problem with that."

An independent lab confirmed 203.4 Hz is at electrical resonance, so we have agreement that real power in is Pin = 0.2425 watt. Therefore your analysis is in error with real power in of 0.2168 watt, mechanical power of 0.0079 watt, phase angle of 85.8 degrees, and power factor (cos angle) = 0.0732.

You refer to discrepancies I have not accounted for. Well Pal, even though it is your responsibility to find your "discrepancies", attempts by me in the last post to help are met with a *very* weak understanding along with your continuing poor attitude. Certainly I made a few errors along the way, but I learned from them. Clearly with your limited understanding (of the subject at hand, at least) you cannot. Too bad.

Northstar

As follow up in explanation: You cannot show my analysis (re-stated below) in error, where Pin=0.2425 watt and Pmec=0.0328 watt. Yet when I explain how eq.3.60 relates to 7.1 and ask if that helps, you state flat-out "No because it is wrong" and then "explain" eq.3.6 using your erroneous data. IOW when I say 2+2=4 in effect you say, yes but with my data 2+2=3. There is no dealing with this attitude and logic. You could have said something like - with my data it is different, let's see why......

If that's not enough, your practical experience is so limited as to allow statements regarding L like "The value I got was 0.000051 henries". The value of L in 8 inch woofers typically runs between 0.0006 and 0.003 henries, average ~ 0.0018. You are off by a factor of over *** 35 ***. Since the electrical capacitance seen due to the mass on the electrical side is M/(Bl)^2=0.0281/121.22=0.000232, my value of L=~0.0026 H gives electrical resonance of fr=1/2 pi sqrt LC=1/[2*3.14 sqrt(0.0026*0.000232)]=205 Hz agreeing closely with the measured value of 203.4 Hz.

As you say "I expected more".

---------- Repeating: Confirmed well within measurement tolerances by a reputable and independent lab: Electrical resonance = 203.4 Hz Electrical impedance at 203.4 Hz = 8.198 ohms Electrical resistance = 7.09 ohms Giving: Real power in P = E^2 / Ze = 0.2425 watt Power creating heat Ph = I^2 Re = 0.2097 watt Mechanical power (here I include acoustic power) Pmec = (E^2/Ze)-(I^2*Re) = 0.0328 watt Mechanical resistance must be Rmec = Pmec / V^2 = 0.0328 / 0.0574^2 =9.955 Mechanical impedance must be Zmec = F/v = BLI/V = 11.01 * 0.172 / 0.0574 = 32.99 Phase angle between force and velocity is angle = arc cos Rmec/Zmec = 72.44 Xmec = sqrt Zmec^2-Rmec^2 = 31.452 Checks: Rmec = (Ze-Re) Zmec^2 / (Bl)^2 = 9.95 Pmec = v^2 Rmec = 0.0328 watt Pmec = I Blv cos angle = 0.0328 watt Zmec = F/v = BlI/v = 32.99 Zmec = Rmec/cos angle = 32.99 v = F/Zmec = 0.0574

Now I stated regarding electrical resonance: "This occurs at 203.4 Hz, making Ze real and power in = E^2/Ze = 0.2425 watt or Pin = I^2 Ze = 0.2425 watt." You replied: "If you are at resonance, I have no problem with that."

An independent lab confirmed 203.4 Hz is at electrical resonance, so we have agreement that real power in is Pin = 0.2425 watt. Therefore your analysis is in error with real power in of 0.2168 watt, mechanical power of 0.0079 watt, phase angle of 85.8 degrees, and power factor (cos angle) = 0.0732.

Northstar

Nasty , nasty , nasty. Note that all that I was trying to do was look at the various possibilities.

I read and understood the material below- the first time. I also note that your checks are simply checks on your arithmetic- and are circular. That is why I paid little attention to them.

You have two sets of data:

a)From set1- the results are as I originally said.

b)From set 2, making NO assumptions as to resonance, the results agree reasonably well with set 1 except for Ze, Adjusting the inductance makes the agreement excellent. When you first gave the data of set 2 your statements definitely did not indicate resonance (to the contrary) and questioning as to why you took Ze as real was like pulling teeth. Did you actually know at that time?

c)Rather than copying you and simply saying that you are wrong, without any attempt to understand and check, I took your word that resonance occurs and your value for Rmech =9.955 as you have calculated )(and i did checkyour calculations- a courtesy that you did not extend to me) and assuming that wL = -Xmot as required by resonance , the theory gives the results that you claim (Berenak's 7.1 is not applicable unless you replace Re by Re+jwL - this has been checked. As an aside, his circuit of Fig.7.5 is wrong- again checked-carefully).

The analysis that I used is EXACTLY the same as I carried out before except for the parameter values wL=3.505 (vs 0) and Rmech 9.955 (vs 2.4). The agreement with your results indicates that my calculation procedure is NOT the problem but that there is a data problem.

Now there is a choice- results which do not assume resonance- using Rms+2Rmr =2.4 as obtained from data set 1 but fit your data set 2. Consistent except that this does not imply resonance

OR,

Resonance exists and there is a mechanical- acoustic resistance of 9.955 for which there is no accounting, and which is in disagreement with your values of Rms=1.57 and 2Rmr =0.83 (sum =2.4).

Which is wrong, and why?. The values of 2.4 and 9.955 are both based on YOUR data

My method of calculation and the basic model I used is not at fault ( it results in results consistent with yours if I use your Rmec and the conditions for resonance at 203.4 Hz) - the difference (excepting the effect of inductance) is due to the apparent mechanical/acoustic resistance, whichever it may be. My concern is not in laying blame for errors (some of which you have learned from and others where you persist) but in finding out what is going on- hence I was trying to explore various "what ifs" - something you don't seem to be ready to do.

You have a problem- explaining this mysterious mechanical/acoustic resistance. If it exists, why? Why has it not been found before or discussed in the literature? You apparently do not have any explanation (and don't go on about "power to overcome back emf" as that is a crock). It comes down to three choices:

a) resonance doesn't exist -----You belatedly say that it does exist and claim support for this- fair enough . b) the values of Rms, Rmr( which is correct according to Berenak's 7.9),etc are incorrect. ---- Your measurements- which surely cannot be wrong or even have normal errors. c)there is some other term which has not been recognised as existing ---since this has not apparently been dealt with by Berenak, Kinsler and others you must have discovered something. You have the makings of a journal paper if you can come up with a plausible explanation (but expect a much rougher ride than I have given you). Is my understanding limited - yes it is - in terms of acoustics, per se.(but getting less so because I can read Berenak who is still highly regarded as an acoustic guru even though he does struggle with circuits) and the methods of obtaining speaker parameters or the practical details of designing enclosures, etc. This is your area of expertise. As I have said, I defer to you in these areas. However, it is quite apparent that your physical concepts, and circuit analysis skills are a lot weaker than you think they are. All that I would like to see you do is to look past the canned formulae (please, no more repetitions of Halliday's obvious power equation) to see what the hell is going on.

Do I expect that? Not really. Playing Devil's Advocate to induce critical thinking on your part, isn't working. Too bad.