Measuring Qtc

[MCPete]

In experimenting with a woofer in a closed-box, I've got an odd-ball network around the woofer. As best I could, I calculated what I thought Qts of the driver and network should be and multiplied that by the square root of alpha plus one. That calculation gave me Qtc = 1.2.

However when I measured f3 nearfield, f3 is above the box resonance frequency Fc.

So my question is, which is correct, what I calculated or Qtc less than 0.707 based on f3 greater than Fc? If f3 is higher than Fc, does that mean without fail that Qtc must be less than 0.707?

All of you seriously loudspeaker system-devotees should really like this question, at least I hope so.

-Pete

[bjorno]

Originally Posted by MCPete

In experimenting with a woofer in a closed-box, I've got an odd-ball network around the woofer. As best I could, I calculated what I thought Qts of the driver and network should be and multiplied that by the square root of alpha plus one. That calculation gave me Qtc = 1.2.

However when I measured f3 nearfield, f3 is above the box resonance frequency Fc.

So my question is, which is correct, what I calculated or Qtc less than 0.707 based on f3 greater than Fc? If f3 is higher than Fc, does that mean without fail that Qtc must be less than 0.707?

All of you seriously loudspeaker system-devotees should really like this question, at least I hope so.

-Pete

Hi Pete,

Will this picture be of any help:

b

[speaker dave]

Originally Posted by MCPete

In experimenting with a woofer in a closed-box, I've got an odd-ball network around the woofer.
-Pete

Your problem is the added network. I'm not really sure what that network is, but be aware that Thiele/Small definitions and math will only be really accurate for ideal cases where external networks aren't influencing either the impedance curve you need to measure or the voltage getting to the woofer teminals. Even high woofer inductance will impact the accuracy of measured and calculated parameters and predicted response.

Is it possible to remove the network, get some better parameters and then model the woofer plus network combination?

David

[MCPete]

Thanks Bjorno and David.

My first concern is whether or not f3/ fc and a particular value Qtc are in a "if and only if" relationship. That is, for a given ratio of f3 to fc, then a particular Qtc follows and vice versa.

For example, let's say I have a closed-box system with Qtc = 0.6. With Qtc = 0.6, then f3 = 1.3 times Fc. Next I connect this system to an amplifier fed with a line level signal that has been operated on by an equalizer such as the Linkwitz Transform Circuit. With the line level equalization, now f3' = 0.79 times Fc. So the question now is, does the closed speaker system still have a Qtc of 0.6 or has it changed to 1.0? In other words, with this arrangement am I getting my cake and eating it too, or not? If Qtc of the speaker system remains 0.6, then what I've done is kept the superior transient response associated with Qtc equal to 0.6 while getting a lower f3 than ordinarily "travels" with Qtc= 0.6.

In trying to figure out how to calculate the way my network is changing Qtc of the speaker system, I want to know if I can rely on the ratio of f3 to Fc as an indicator of the "true" Qtc of the combination. In my mind at this point, I think that f3/ fc related to Qtc works both ways so long as room effects are eliminated by measuring frequency response near-field.

Hope that this clarifies what I'm driving at,
Pete

[speaker dave]

Hi Pete,

The way I understand it the f3, fc, Qtc relationship is fixed, "if and only if", but only when we are talking about a pure 2nd order highpass filter. Any filters you add, or non-ideal characteristics of the woofer (high self inductance) distort it away from a pure 2nd order system and disturb the exact f3/fc vs. Qt relationship.

Room effects definitely remove us from the simple world of f3/fc vs. Qt relationships. Even moving the system from 2pi to 4 pi breaks the simple relationship.

Not fully following the Linkwitz Transform numbers you are giving but if you are using the circuit to cancel out a given fc and Qt and then replace it with a new second order corner, then the new corner determines the impulse or step response based on the new f and Q. this, of course, assumes the original corner is perfectly cancelled out. Other wise we aren't talking a second order system, but a 6th order system.

In the end the transient response is always tied to the total frequency response and it doesn't matter if you got to that response via mechanical parameters or electrical means.

Hope that makes sense.

David

[MCPete]

Dave,

Yes, what you are saying makes a great deal of sense. After all, with an equalizer it is possible to obtain f3/ fc = 0.5 and that can't be modeled with any 2nd order high-pass filter.

The example I posed was meant to be a general case using any sort of line level compensating circuit, not necessarily the Linkwitz Transform. All that I was saying was that it is entirely possible to to make f3 of a sealed system with Qtc equal to 0.6 initially greater than fc to less than fc by means of an active compensating circuit. Then the question is whether or not the speaker system retains the good transient response corresponding to Qtc= 0.6.

I wouldn't know how to go about doing it, but I think that probably there would be some way to assign a Q to a line level compensating circuit and a speaker system functioning in combination. I mean Q or resonance magnification is a general characteristic that applies to active filters as well as speaker systems. Being able to do that I think would be interesting as there is some debate about equalizers adding distortion. I have an old Speaker Builder article by Dennis Colin in which he seems to be claiming that his compensating circuit reduces distortion.

-Pete