Work backwards from (a) the sensitivity of your AC millivoltmeter (could be an Oscope); and (b) the maximum undistorted power output of the test amplifier.
To get a feeling for the numbers involved, how many millivolts will be registered on the AC millivoltmeter, when you use a test amplifier that pumps {let's just suppose} 15 Watts RMS into the test circuit. Assume the amplifier-under-test has an output impedance of 0.1 ohms, when you perform your calculations.
To get a feeling for the numbers involved, how many millivolts will be registered on the AC millivoltmeter, when you use a test amplifier that pumps {let's just suppose} 15 Watts RMS into the test circuit. Assume the amplifier-under-test has an output impedance of 0.1 ohms, when you perform your calculations.
It depends mainly at what current level you want to do the measurement: a good amplifier should have little difference between high/low currents, but if the OP stage has crossover issues for example, it could manifest itself by a larger impedance at low level.
I= V1/R1, and you can determine V1 from the input voltage, based on the gain, just as Mark said.
If Zout is too large compared to R1, and you don't want to make a differential measurement, an obvious fix is to make R1 larger.
If you stick to the differential measurement, but you only have a scope available, you can use its subtract function to measure the differential voltage between V1 and V2: it will be vectorially correct too (provided the channels and probes are reasonably well matched)
Elvee, it seems to me that this is a problem where solving the general case (don't know whether Zout < Rtest or Zout > Rtest) turns out to be the simplest approach.
Just program up the general two-resistor voltage divider equation into Excel: Vout = Vin * Zout / (Rtest + Zout).
Use ordinary algebra to rearrange the equation so that Zout is isolated on the left hand side.
Done! Plug in Vin, Vout, and Rtest ---> you get the amplifier-under-test's Zout .
Presto, you get the correct value of Zout without ever estimating (or measuring) the current. Why is this important? Because Current =approx= (Vout / Rtest) is only an approximation, valid only when Zout <<< Rtest. The voltage divider approach doesn't need or use such an approximation.
Now, to SELECT the values of Rtest and Vin when building the test fixture, I think assumptions may be appropriate. I think it's probably okay to assume the amplifier-under-test's damping factor is less than 100, i.e., that its Zout is greater than 0.08 ohms. I also think it's probably okay to run the test at (80% of Rtest's max power dissipation) and (80% of the fixture amp's max power output), whichever is less. This sets an upper limit upon Vin.
Just program up the general two-resistor voltage divider equation into Excel: Vout = Vin * Zout / (Rtest + Zout).
Use ordinary algebra to rearrange the equation so that Zout is isolated on the left hand side.
Done! Plug in Vin, Vout, and Rtest ---> you get the amplifier-under-test's Zout .
Presto, you get the correct value of Zout without ever estimating (or measuring) the current. Why is this important? Because Current =approx= (Vout / Rtest) is only an approximation, valid only when Zout <<< Rtest. The voltage divider approach doesn't need or use such an approximation.
Now, to SELECT the values of Rtest and Vin when building the test fixture, I think assumptions may be appropriate. I think it's probably okay to assume the amplifier-under-test's damping factor is less than 100, i.e., that its Zout is greater than 0.08 ohms. I also think it's probably okay to run the test at (80% of Rtest's max power dissipation) and (80% of the fixture amp's max power output), whichever is less. This sets an upper limit upon Vin.
The voltage divider doesn't need the approximation, but to be general, the equation needs to be solved for a complex value of Zout, because a simple scalar extraction is equivalent to the loading method, which gives such poor results when Zout has a reactive or non-linear component.
Solving the equation with Zout= R +jX is not going to be simple, especially if you do not know firsthand what type of reactance is going to be present.
The method based on the magnitudes only, for the current the voltages and the impedance might look more complicated, but it always works, and does not require vector calculations, just a differential voltage measurement (or an approximation)
Elvee,
It is a quick and easy merit of excellence, and of course reactance is not included.
The vector might only change the value by a few percent any way........
I put it to you that most Zout figures are really taken at one frequency, like THD.
It is an extremely useful tool, as is Mark's technique taken directly from the simulation.
You can make it as accurate if you wish by using 8R and 6R, for example, and at any desired frequency and measured with a rms DMM. You can even include your 31.6uH inductor if you wish.
It is a rule of thumb which is very helpful during bench testing........ and that is what it was intended. X mentions 2.83Vrms, 8Vpp, that is a useful output to benchmark.
HD
It is a quick and easy merit of excellence, and of course reactance is not included.
The vector might only change the value by a few percent any way........
I put it to you that most Zout figures are really taken at one frequency, like THD.
It is an extremely useful tool, as is Mark's technique taken directly from the simulation.
You can make it as accurate if you wish by using 8R and 6R, for example, and at any desired frequency and measured with a rms DMM. You can even include your 31.6uH inductor if you wish.
It is a rule of thumb which is very helpful during bench testing........ and that is what it was intended. X mentions 2.83Vrms, 8Vpp, that is a useful output to benchmark.
HD
Elvee,
I appreciate you pointing out the math and pathological cases where a simplistic method fails. However, what I presented is a simple way to get a figure of merit at one frequency. It is quick and easy and more likely that someone will try to do it and to report the figure at the measured frequency.
I just want to point this out because the way you criticize it, makes people think it is of no use. And that’s not the case. It’s a figure of merit and allows quick comparisons between various designs.
Where else do we use single frequency figures of merit?
THD at 1kHz and 1w 8ohms figure of merit. We all know it doesn’t mean anything without the profile, but nonetheless it is often used.
ESR of caps at 120Hz, 1kHz and 10kHz.
Ripple current of a cap at 120Hz.
inductance of voice coil winding at 10kHz.
Inductor value at frequency X. We know it’s not flat to infinity!
Impedance of speaker at 1kHz or DCR of speaker voice coil at 0Hz
Etc, ....
Similarly output impedance could be normalized to where it matters: at mid bass frequencies like 100Hz to 300Hz. That’s where speaker cone control matters. That’s where I am concerned about it. Perhaps tests should be done at 100Hz then and reported as such.
Without a simple figure of merit approach, I fear about 10ppm of people who wonder what the DF of their amp is are going to take out a secondary amp, function generator, two DVM’s and set up the test you describe above. I admit your method is mathematically correct and accounts for vector magnitude. But how many people will actually do that test?
Regards,
X
I appreciate you pointing out the math and pathological cases where a simplistic method fails. However, what I presented is a simple way to get a figure of merit at one frequency. It is quick and easy and more likely that someone will try to do it and to report the figure at the measured frequency.
I just want to point this out because the way you criticize it, makes people think it is of no use. And that’s not the case. It’s a figure of merit and allows quick comparisons between various designs.
Where else do we use single frequency figures of merit?
THD at 1kHz and 1w 8ohms figure of merit. We all know it doesn’t mean anything without the profile, but nonetheless it is often used.
ESR of caps at 120Hz, 1kHz and 10kHz.
Ripple current of a cap at 120Hz.
inductance of voice coil winding at 10kHz.
Inductor value at frequency X. We know it’s not flat to infinity!
Impedance of speaker at 1kHz or DCR of speaker voice coil at 0Hz
Etc, ....
Similarly output impedance could be normalized to where it matters: at mid bass frequencies like 100Hz to 300Hz. That’s where speaker cone control matters. That’s where I am concerned about it. Perhaps tests should be done at 100Hz then and reported as such.
Without a simple figure of merit approach, I fear about 10ppm of people who wonder what the DF of their amp is are going to take out a secondary amp, function generator, two DVM’s and set up the test you describe above. I admit your method is mathematically correct and accounts for vector magnitude. But how many people will actually do that test?
Regards,
X
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I am afraid it is not the case: as I said, all amplifier subjected to GNFB have a significantly reactive output impedance (and others might also have one, for other reasons).
Here is a simple example, based on an LM101 opamp for ease and simplicity, but the behavior is common to all amplifiers, discrete or integrated.
This sim shows the |output impedance| vs frequency.
You can notice that the output impedance rises at the rate of 6dB/octave between a few Hz and and few tens of kHz, which is already a strong hint.
Another hint is the phase: it remains in the vicinity of +90° for that range.
Thus, it looks like an inductor, it smells like an inductor, but is it dominant?
We can plot together the real (red) and imaginary (green) parts of the impedance:
We see that the reactive part is indeed heavily dominant for all of this frequency range.
So, the phenomenon is not anecdotal at all.
We can convert this imaginary part into an inductance:
It is 38.5µ for most of the frequency range.
Some people might think that this synthetic inductor is completely virtual and has no effect in the real world.
Not so: any amplifier that shows some measure of ringing during a squarewave test on a pure capacitive load (without Zobel) demonstrates that the effect is real.
You can compute the equivalent inductance of this amplifier based on the ringing frequency and capacitor value.
There is another mechanism resulting in a reactive impedance, for cap-coupled amplifiers: the output capacitor.
For a 1000µF @1kHz, it is 0.16Ω.
Considering the damping factor of SS amplifiers, this is certainly not marginal.
I never said anything else, and I do not say you have to make a frequency sweep, I just pointed out that depending on the frequency, different effects might kick in, resulting in a reactive impedance.
Even if the reactive effects are negligible, the loading method has another weakness: the accuracy.
For a 8Ω amp having a damping factor of 100, the output impedance will be 0.08Ω, meaning that for 10V open-circuit, you will measure 9.99V loaded.
What is going to be the reliability and accuracy of the value obtained that way?
It will generally yield extremely optimistic results, which could explain its popularity....
RMS measurements are not required, and the value of the inductor can only be accounted for if you have some means of determining it, meaning using the proper method.
As I said, making a correct measurement is not difficult at all, and does not require special equipment, except a test amplifier, which will generally be available for free since most of the amplifiers are stereo (at least)
Attachments
The first example I gave was pathological: the estimated Zout was 4mΩ, against 200mΩ for the actual value; that is a 1:50 ratio.
However, in the real world, you could very easily end up with 1:5 ratio, which is hugely optimistic (and worthless)
For lots of SS designs, it is of no use.
An exception would be a direct-coupled, zero FB, common source or emitter SE amplifier
You can use both the correct method and the other at a single frequency...
Once again, the method is not more complicated (perhaps a bit less intuitive), and most DIYers already have the gear necessary: one generator, one DVM, one power load and one test amplifier.
Even if you don't test a stereo amplifier, you will probably have some functioning amplifier lying around, and if you don't, it is a good opportunity to build a general purpose test amplifier: it is an invaluable piece of kit
One more thing: I showed the A.U.T. + test amplifier setup in the context of |Zout| measurement, but it would be a pity to use it for just that miserable purpose: it can do a lot more.
The first interesting thing to do is to examine the residue present on the A.U.T.'s output: ideally, it should be sinusoidal (if the stimulus also is, obviously) but in fact it will generally not be perfect, because it concentrates all the current-related errors and distortions of the AUT, to the exclusion of others (typically voltage-related ones).
It is easy to test the voltage-linearity aspect of an amplifier: just remove the load.
However, using conventional testing, voltage and current cannot easily be disentangled.
With this type of test, you can see the effect of current practically in isolation, which is very useful, not only in reality but also in sim.
When an amplifier has a sub-ppm THD level, simply measuring it is already a challenge; attributing it is even more difficult.
The setup acts not only as a discriminator, but also as a concentrator: the amplitude is perhaps 100x smaller than in regular conditions, but the absolute level of current-induced distortions remains the same, which considerably eases measurements.
Applications do not stop there: you can also look at the way the amplifier reacts to maintain its output node at ~0V when subjected to a high perturbation current.
You can examine each critical node, VAS output, VAS input, etc and extract useful information based on the amplitude, phase and shape of the signal.
In short, it is a goldmine of information for a keen designer.
It can be compared to the short-circuit testing of transformers, where only RI losses and leakage effects appear.
The first interesting thing to do is to examine the residue present on the A.U.T.'s output: ideally, it should be sinusoidal (if the stimulus also is, obviously) but in fact it will generally not be perfect, because it concentrates all the current-related errors and distortions of the AUT, to the exclusion of others (typically voltage-related ones).
It is easy to test the voltage-linearity aspect of an amplifier: just remove the load.
However, using conventional testing, voltage and current cannot easily be disentangled.
With this type of test, you can see the effect of current practically in isolation, which is very useful, not only in reality but also in sim.
When an amplifier has a sub-ppm THD level, simply measuring it is already a challenge; attributing it is even more difficult.
The setup acts not only as a discriminator, but also as a concentrator: the amplitude is perhaps 100x smaller than in regular conditions, but the absolute level of current-induced distortions remains the same, which considerably eases measurements.
Applications do not stop there: you can also look at the way the amplifier reacts to maintain its output node at ~0V when subjected to a high perturbation current.
You can examine each critical node, VAS output, VAS input, etc and extract useful information based on the amplitude, phase and shape of the signal.
In short, it is a goldmine of information for a keen designer.
It can be compared to the short-circuit testing of transformers, where only RI losses and leakage effects appear.
Elvee,
I use this simple technique to assess Vout and have done so for thirty years with little reason to move to a more accurate method. This is audio, not instrumentation, and the usual tests of actual power into a load are quick and easy.
I will not pursue this thread; my technique is what it is and no more. It gives a rough estimate, particularly given that most power tests are used with pure resistive loads.
The more complex you make the technique, the less it will be used. It has to be simple and quick. Your approach is correct but one does not always have an identical amp when developing a bench amp. I agree with your last thread as details at each node during the amp are a goldmine!
HD
I use this simple technique to assess Vout and have done so for thirty years with little reason to move to a more accurate method. This is audio, not instrumentation, and the usual tests of actual power into a load are quick and easy.
I will not pursue this thread; my technique is what it is and no more. It gives a rough estimate, particularly given that most power tests are used with pure resistive loads.
The more complex you make the technique, the less it will be used. It has to be simple and quick. Your approach is correct but one does not always have an identical amp when developing a bench amp. I agree with your last thread as details at each node during the amp are a goldmine!
HD
That's fine by me: this is DIY after all, and everyone can do as he pleases, as long as he/she is the only person impacted by his/her choices, and doesn't spread falsehoods: after all, even I have designed DC filament DHT supplies for members, even if I personally think that in this day and age, such technologies have their place in a museum rather than in a listening room, but I have no problem with that, and I am quite happy to be of some help to other people, even if I don't share their views: that's their hobby, that's their own personal trip, and if they are happy with it, that's fine by me.
What I object to is the dissemination of beliefs, methods and principles that clearly contravene the current state of the art but try to camouflage as such, and mislead "naive" members: when such bold statements are made, they should come with a health warning.
Loading methods originate from the 19th century, when you had (mostly) linear, DC generators and receptors.
They are still relevant to test the load regulation of DC supplies, but other than that, they are essentially outdated, but traditions die hard
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