Technical Discussion about Frequency Dependent Terminal Impedance - diyAudio
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Old 10th August 2005, 11:27 PM   #1
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Lightbulb Technical Discussion about Frequency Dependent Terminal Impedance

Hi all,

I'm starting this thread to be a serious discussion on speaker terminal impedance and what it means to frequency response, phase response (or time/group delay), and gain characteristics (or more correctly the transfer function) of a the speaker.

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1. Be familiar with the thread. (Understand what's being discussed)

2. Identify Known facts (Physics, Engineering etc.) as such.

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3. Identify Opinions as such. (Please keep these to a minimum)

4. Be respectful of other posters, and discuss disagreements off forum (via private messages, email etc.) before posting. In this case, post a brief description of the disagreement, With both sides following (This can be harder than it seems)

5. When posting personal observations, back them up with physics or engineering, and an explanation of what was noted, and your theory as to why this happened.


I will start the first post, in just a moment...
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Old 10th August 2005, 11:38 PM   #2
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Default Measured Impedance

At this point, I will start off by posting an actual graph of measured terminal impedance vs. frequency of a speaker. This graph was created by measuring voltage (Via a TDS3032B O-scope) and Current (Via a TDS3032B and TCP202 Current probe) and the phase relationship between the two, of a swept sine wave (Generated by an Agilent 33220A Signal Generator) into a production speaker (3 drivers, Bass, Mid, and High, including a passive crossover) from 10Hz to 100KHz. (The signal generator, and scope are part of an automated test setup).

This graph was created by taking the voltage and current (including phase relationship) of each frequency point measured and through ohms law (V/I = R) calculating the resultant complex impedance (Magnitude and phase). This impedance was then plotted vs. frequency.

What I first noted in this graph was the impedance bump, at ~68Hz. From my limited understanding of speakers, this is probably the resonant frequency of one of the drivers. (It is possible that it is also an artifact of the crossover).

Please start by posting any observations from the graph, or aspects of the graph worth noting.
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Old 10th August 2005, 11:46 PM   #3
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Default Re: Measured Impedance

Quote:
Originally posted by dkemppai
What I first noted in this graph was the impedance bump, at ~68Hz. From my limited understanding of speakers, this is probably the resonant frequency of one of the drivers.
It is actually the system resonance of the bass driver in the box. Given the single peak (and its magnitude) it is likely a sealed box.

As a generalization we can say that the f3 of the box is in the neighborhood of this peak.

dave
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Old 11th August 2005, 12:00 AM   #4
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The 2nd hump is probably at the mid-woofer crossover.

The phase angle doesn't get too nasty until way high in frequency where there is not a lot of energy so it shouldn't drive the amo too crazy.

(keep in mind that due to the sign term in the power equation, if the phase gets to 90 degrees tha amplifier can no longer deliver any power into the load (since sin 90 = 0, P = 0))

dave
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Old 11th August 2005, 12:45 AM   #5
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Default Re: Re: Measured Impedance

Quote:
Originally posted by planet10


It is actually the system resonance of the bass driver in the box. Given the single peak (and its magnitude) it is likely a sealed box.

As a generalization we can say that the f3 of the box is in the neighborhood of this peak.

dave
Dave,

You are quite right. The speaker is in a sealed box, and it is the resonance of the driver in the system, not free air. (I'm warming up my test system, to run the free air sweep now... ...looks like the Resontant point is 33.9Hz)

At this time, I'm trying to wrap my mind around how mechanical resonance acts in such a way as to reflect reactive impedances back through the speaker terminals. I cannot seem to correlate the mechanical and electrical equivalents. I still have to do some reading on the subject, but am trying to correlate the electrical equivalent to a spring mass system in my own mind.

What I also noted was the leading phase from 10Hz up to the resonant point indicated a capacitive impedance up to the resonant point (If my phases are correct). This seems to make sense, as I remember from RF theory, a short antenna is also appears capacitive, and thus the reason an inductor in series is required to bring the antenna into resonance. Im starting to understand speakers are more of a transmitting antenna than I originally envisioned.

In any case, I'm suspecting that the reactive component of the impedance will affect the ultimate speaker system gain (if you will). In the case of the speaker being driven by a purely voltage feedback amplifier (as most are) the output power vs. frequency (or amplitude, SPL, however you measure it) should be affected by this system impedance. The resultant phase shifts would reduce power delivered to the speaker, and ultimately to the air. This is of course, not taking into account other losses within the speaker system. (This is a truly a ‘system' as you correctly pointed out)

-Dan

By the way. It's nice to see you're still on the boards. It's been awhile since I've been here!
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Old 11th August 2005, 02:17 AM   #6
MJK is offline MJK  United States
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OK, I'll toss this out for thought and comment. First the equations that couple the electrical side to the mechanical side of the driver.

ed = BL ud

fd = BL i

ed = back emf voltage at driver terminals
ud = cone velocity
fd = force on mechanical parts like the cone mass, stiffness, and mechanical damping
i = current in coil due to applied eg
eg = voltage source which will be assumed constant

Below say 100 Hz, the voice coil inductance is small and the resistance is constant. The large peak in the impedance curve is really a reflection of the driver velocity, at resonance the velocity increases. But when the velocity increases so does ud which lowers i for a constant eg. Lower i means less force f so ud decreases. Kind of a control loop which attenuates the driver mechanical resonance so it does not flap back and forth violently and destroy or bottom the suspension.

Bottom line, at low frequencies the impedance curve is really a good measure of driver velocity. Now if you can convert cone velocity into pressure, and thus SPL, you have a complete transformation from electrical input to SPL response. You can use the impedance curve to grapically construct the SPL curve. I have done the math and the graphical exercise but that was years ago and without looking back in my notes I cannot reproduce it off the top of my head.

Hope that helps,
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Old 11th August 2005, 03:43 AM   #7
JohnG is offline JohnG  United States
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One comment.

The sharp peak near 50-60Hz looks to me like there is a measurement error, where it really takes off. You can see the slope of the magnitude change abruptly, which should not happen. My guess is that one of your traces (voltage) on the scope went out of range. JMHO.

John G
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Old 11th August 2005, 08:27 AM   #8
gpapag is offline gpapag  Greece
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Ref. Post #7
There is no reason to suspect a measurement error. Abrupt magnitude change at this point (50-60 Hz) indicates a reasonably high Q at system resonance, consistent with closed box (of not very large volume Vb) construction.
Reversal of direction on amplitude curve coinciding (to a few 0.00 of a Herz) with a zero crossing on phase curve, indicates a resonance point and not a measurement error.
In general, let (n) the number of completed peaks (high points) on amplitude curve, then, the number of zero crossings on phase curve is 2(n), coinciding with the highest and (following) lowest points of the amplitude curve.

Regards
George
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Old 11th August 2005, 12:12 PM   #9
MJK is offline MJK  United States
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I agree with John G, the spike in the first plot's magnitude curve looks like a measurement error, or maybe a data entry error. Looking closely the right side appears to be rolling over when it spikes to a much larger value off the scale, it appears to only be one data point. The phase curve looks OK but the magnitude is suspect in my opinion.
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Old 15th August 2005, 03:23 AM   #10
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Electrical model of a woofer in a sealed box, courtesy of Siegfried Linkwitz.

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