Speaker/ Amp impdeance

"John Fields"

** Two errors:

1. The OPs question was about *equal value* impedance matching of sources and loads.

2. The source impedance at the plate of a tube output stage is not the same as the optimum load impedance.

In general - the *equal value matching theorem * has no application to sources using active devices.

..... Phil

Um, let me try it... You do know that power and energy are different quantities?

The maximum power will be delivered to a load with the same resistance as the battery's internal resistance but that only gives you 1/2 the energy to the load. The other half is dissipated by the battery. If the load is infinite the power delivered is zero but all of the energy gets dissipated by the load. ;-)

Now, do you want the maximum power or the maximum energy. ...or something else?

 impedance

The impedance changes with the *square* of the turns ratio. With a 2:1 ratio, the voltage doubles, but current halves. 2/.5 = 4.

Not for this calculation. See above.

Never touch them.

The problem with using the maximum power transfer theorem with your amplifier and speaker is that it might not (usually not) take into account all of the other factors that limit the output power of the amplifier. Amplifiers also have limits on their output current and voltage.

Try this example to illustrate the problems with using the maximum power transfer theorem for your stereo amplifier and speaker problem.

Assume that you have an amplifier that is designed to provide 8 watts into an 8 ohm speaker. Also assume that the output impedance of the amplifier is only 0.1 ohm.

Also we ail assume that our amplifier also is limited to a maximum RMS current of

1 amp and an RMS voltage of 8.1 volts. Please note that to get 8 watts delivered into an 8 ohm load we only need 1 amp RMS and 8 volts RMS so our example amplifier's current and voltage limits are reasonable.

The limits on the current and voltage exist due to things like the keeping the internal power dissipation of the amplifier components low enough to prevent over heating, etc. And finally, we will assume that the amplifier has internal protection circuitry to keep its output current and voltages within its design limits. (Most modern amplifiers have these protection circuits because the designers know that it is likely that some users will short the amplifier outputs or put too low of an impedance load on the amplifier.)

Now that we have stated all of our assumptions, lets look at the power delivered to four different speaker configurations: 8 ohms, 16 ohms, 4 ohms, and 0.1 ohms.

With 8 ohms, and driving the amplifier to its limits, we have 8 volts and 1 amp into the speaker. We also have 0.1 volts across the internal 0.1 output impedance of the amplifier. (Yes, that explains why I rated the amplifier at 8.1 volts instead of 8 volts.) This gives us 8 watts into the speaker. I.e. the amplifier meets its rated specification.

With 16 ohms, the current is 8.1/( 16 + 0.1) = 0.5031 amps. The power is I**2 * R and is equal to 4.05 watts. The output power is lower than the 8 ohm case because the output power is being limited by the maximum output voltage of the amplifier.

(Note: Did I mention that the limiter circuits have the magic ability to limit the RMS voltages and currents instead of the usual peak limiting. We could work with real peak limiter circuits and it would have some effect on the numbers but mostly it would complicate the math and muddy the concepts since peak limiters distort the output waveforms.)

With 4 ohms, the current is limited to 1 amp by the current limiter circuit. The power is I**2 * R = 4 watts.

And finally the 0.1 ohm speakers. This is the value that the maximum power transfer theorem says should give us maximum output power. Once again we are limited by the maximum current rating of the amplifier to 1 amp. The power is I**2 * R = 0.1 watts. I.e only 1.25 percent of what the amplifier can supply into an 8 ohm load.

If the amplifier could supply a much higher current (For example 8.1/(0.1 + 0.1) = 40.5 amps) then we could get much more power delivered into the 0.1 ohm speaker. Power is I**2 * R = 40.5 * 40.5 * 0.1 = 164.025 watts. However this current level would probably make the amplifier that we were discussing over heat and then die. (The limiter circuits were included in the amplifier design to protect it from this sort of abuse.)

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Yeah, I did a bit of this back in the 90's. I designed a 20 MHz Rf amp. Three stages with several watts at the output.. Driving coils to do NMR. The design approach was to calculate the power gain of each stage, and the input and output impedances and then insert the proper transformers to make it all work.... (And then f around to get it to turn on fast and not ring... )

George H.

George Herold a écrit :

Even EEs...

I just received a request for a 27MHz power amplifier design with >70% efficiency and an output SWR=1.1

--
Thanks,
Fred.

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How much power?

impedance

OK, now I'm confused. You asked if anyone had used the "maximum power transfer theorem". Sure, I've used it but it's silly in the context of a battery since the goal is rarely to transfer the maximum power from a battery to the load. Solar cell, sure. A battery? *Rarely*.

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The only tube I've used was in a ham rig back in high school[*]. They didn't even touch on the subject in college. The profs took them out of the syllabus in the '60s.

[*] The 750V plate supply literally hurt! Haven't touched them since. ;-)

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50W, but power has nothing to do in the non sense requirement.

--
Thanks,
Fred.

Yeah, when I was in school (late 60s) the EE department had already ditched tubes... but curiously they were still part of the ME curriculum. When I mentioned this to one of the EE profs he was pretty dismissive, equal parts "why would you want to know about that old stuff" and "it's easy enough to just figure out yourself". (Ha!) I was a bit miffed... not only were we missing out on a fundamental topic (and it was still pretty important then), but also those danged MEs were getting it and we weren't!

Best regards,

Bob Masta DAQARTA v6.01 Data AcQuisition And Real-Time Analysis

Scope, Spectrum, Spectrogram, Sound Level Meter Frequency Counter, FREE Signal Generator Pitch Track, Pitch-to-MIDI Science with your sound card!

In the 37 years since I graduated, I've run into the need to use a tube exactly zero times. I'd say they were justified in dropping them from the curriculum.

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Sorry for the confusion. So the "maximum power transfer theorem" is used in solar cell design? Obvioulsy we want the maximum power from a solar cell, is there a balancing of impedances? (I'll google and see what I find.)

George H.

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Got me, but the physics is there. The purpose, is to maximize power transfer, though the source isn't a simple linear Thevinin-ish source.

This is one case where maximum power transfer from a fixed source is the goal. It rarely is.

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Aren't all transducers involved with some sort of impedance matching? (For maximum power transfer)

George H.

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Everything real has some impedance. Superconductors have no resistance, but that's an irrelevant complication. ;-)

Do you want maximum power transferred or do you want maximum efficiency? Remember, the hard part of a problem is often defining it.

No. Why would you want to do that? If you're measuring voltage, you certainly don't (usually) want to burn half of it in the source. That'll just make your life difficult and reduce your S/N in half.