Yet surely it's appropriate to question the accuracy or applicability of models?
To quote the great Flanders and Swann,
"So guard against gossip, and take every care,
Lest some blameless escutcheon you blot,
Such models of friendship are precious and rare,
Though the friendship of models is not."
Much thanks, as always,
Chris
To quote the great Flanders and Swann,
"So guard against gossip, and take every care,
Lest some blameless escutcheon you blot,
Such models of friendship are precious and rare,
Though the friendship of models is not."
Much thanks, as always,
Chris
Rest assured that I pointed multiple times, in a serious way, in both "feedback" threads, that these systems are not liniar, and thus the superposition principle, Fourier, Bode and Niquist do not apply. Yet the same people keep talking about "slewrate", "THD" and "liniar amp" in the same phrase, every few posts. If it's about creating hilarity through pretending not noticing the obvious, then let me join too. I can produce hilarious effects in Ltspice every so often.
As for the discussion on Linear Systems theory - it is limited to "small signal" analysis. Power amps are arguably "large signal", unless you limit yourself to a few mW.
that's exactly where your reasoning is "Sophomoric" - just because all practical systems have some nonlinearity doesn't mean Linear analysis, "...superposition principle, Fourier, Bode and Niquist do not apply"
the many decades of EE teaching and Industry practice, continued hiring of the "small signal, linear" trained EE are an existence proof that you are Practically wrong
Linear Systems Theory is a very useful approximation for the very nearly linear circuits used in Linear Audio Power amps
its a far cry from a "emperor's new clothes" situation - as any with the EE education and decades of professional design experience can testify
yes you need the nonlinear component to "explain" why any oscillator may have stable amplitude - but in fact the Linear Phase, Gain relations give very good approximation of the frequency of oscillation, Linear Feedback Theory margins give practical designs that don't oscillate
but you can read Self, Cordell, Duncan, Stone, Jones... Audio Amplifier Design books without finding a single Lyapunov equation
Bob, Doug do go into Practical Audio amplifier circuit Nonlinearities, show the limiting, local clamping that is the Practical attention/remedy given to Large Signal Nonlinear behavior in Linear Audio Power Amps
Cordell actually alludes to Describing Function Analysis which is the "Classical Frequency Domain" tool that can be useful
I personally have used Popov, Circle Criteria tests for sector nonlinearity gain design for Large Signal Nonlinear oscillation safety margin
you really should read B J Lurie's book, the appendix of commonly asked questions gives a look into what the book is about
B. Lurie's Discussions Page
Appendix 11, Classical Feedback Control
if you disagree with his points you should look at Lurie's C.V. - NASA let him design controls for $ Billion satellite systems
and consider reading the full arguments in the book
in Audio we also have Cherry's “Estimates of Nonlinear Distortion in Feedback Amplifiers” JAES V48#4 2000 which gives an interesting "quasi-linear" input referred distortion analysis method and shows good agreement with measured results from his EE student lab Hardware Audio Amplifier circuits
the many decades of EE teaching and Industry practice, continued hiring of the "small signal, linear" trained EE are an existence proof that you are Practically wrong
Linear Systems Theory is a very useful approximation for the very nearly linear circuits used in Linear Audio Power amps
its a far cry from a "emperor's new clothes" situation - as any with the EE education and decades of professional design experience can testify
yes you need the nonlinear component to "explain" why any oscillator may have stable amplitude - but in fact the Linear Phase, Gain relations give very good approximation of the frequency of oscillation, Linear Feedback Theory margins give practical designs that don't oscillate
but you can read Self, Cordell, Duncan, Stone, Jones... Audio Amplifier Design books without finding a single Lyapunov equation
Bob, Doug do go into Practical Audio amplifier circuit Nonlinearities, show the limiting, local clamping that is the Practical attention/remedy given to Large Signal Nonlinear behavior in Linear Audio Power Amps
Cordell actually alludes to Describing Function Analysis which is the "Classical Frequency Domain" tool that can be useful
I personally have used Popov, Circle Criteria tests for sector nonlinearity gain design for Large Signal Nonlinear oscillation safety margin
you really should read B J Lurie's book, the appendix of commonly asked questions gives a look into what the book is about
B. Lurie's Discussions Page
Appendix 11, Classical Feedback Control
if you disagree with his points you should look at Lurie's C.V. - NASA let him design controls for $ Billion satellite systems
and consider reading the full arguments in the book
in Audio we also have Cherry's “Estimates of Nonlinear Distortion in Feedback Amplifiers” JAES V48#4 2000 which gives an interesting "quasi-linear" input referred distortion analysis method and shows good agreement with measured results from his EE student lab Hardware Audio Amplifier circuits
You are right jcx, albeit in the sense that the "linear modeling" in audio and other fields has been beaten to death and there's little expectation to have any advancements by pursuing the path.
Post #102 should had been a wake up call, but if it didn't, let me augment it:
- from the observation that many musical instruments are non linear
- to the realization that propagation of sound is non linear too (see KZK equations)
- and the non linear character of human hearing
- and the use of highly non linear amplifiers to actually improve musical reproduction enjoyment (see compressors and vocal recording for sparse arrangement jazz)
- to the practical observation that many older, high THD amplifiers were more enjoyable than some of their 0.01% THD modern siblings
one may reach the conclusion that "linear audio" is an oxymoron, and if any advancements are to be made in musical reproduction, a look at the bigger picture is needed.
Post #102 should had been a wake up call, but if it didn't, let me augment it:
- from the observation that many musical instruments are non linear
- to the realization that propagation of sound is non linear too (see KZK equations)
- and the non linear character of human hearing
- and the use of highly non linear amplifiers to actually improve musical reproduction enjoyment (see compressors and vocal recording for sparse arrangement jazz)
- to the practical observation that many older, high THD amplifiers were more enjoyable than some of their 0.01% THD modern siblings
one may reach the conclusion that "linear audio" is an oxymoron, and if any advancements are to be made in musical reproduction, a look at the bigger picture is needed.
You are wasting time and space. Hypex will sell me, at reasonable cost, an amp that has practically unmeasurable distortion.😀
That other stuff you're bleating about is a matter for EQ and niceness knobs.🙄
That other stuff you're bleating about is a matter for EQ and niceness knobs.🙄
Class D is a differnt kettle of fish
Putzeys self oscillating Class D UCD and NCore amps do give plenty of scope for using Large Signal Nonlinear Oscillation Theory by their basic operating principle
of course the final result is good linearity over audio frequency - aided by global negative feedback, high loop gain at audio - but only when looking at the averaged/low passed rail-to-rail ~ 1/2 MHz switching output
http://www.hypex.nl/docs/papers/ncore wp.pdf
Putzeys self oscillating Class D UCD and NCore amps do give plenty of scope for using Large Signal Nonlinear Oscillation Theory by their basic operating principle
of course the final result is good linearity over audio frequency - aided by global negative feedback, high loop gain at audio - but only when looking at the averaged/low passed rail-to-rail ~ 1/2 MHz switching output
http://www.hypex.nl/docs/papers/ncore wp.pdf
Does the system really need to be linear in order to work with feedback... I mean if actions are close to realtime, then something that is not really describable in linear math can still be part of the corrective action.
When testing amplifier we usually use single tones like 1 Khz and also higer frequencies. when they are mixed we see IMD products, some of these are off course a result of the summed curve form, while others are generated by the circuit in itself. To understand this we have to look at the fact that the amplifiers OLG is not a constant, but is also a product of the signal driving it. Like if you bias the LTP with resistors, the you also modulate the driving currents with the input signal, you change the working conditions and thus also alter amplification. For me it is quite evident that if you look for a good performing amplifier circuit you have to try to make driving currents as high impedance as absolutely possible.
When testing amplifier we usually use single tones like 1 Khz and also higer frequencies. when they are mixed we see IMD products, some of these are off course a result of the summed curve form, while others are generated by the circuit in itself. To understand this we have to look at the fact that the amplifiers OLG is not a constant, but is also a product of the signal driving it. Like if you bias the LTP with resistors, the you also modulate the driving currents with the input signal, you change the working conditions and thus also alter amplification. For me it is quite evident that if you look for a good performing amplifier circuit you have to try to make driving currents as high impedance as absolutely possible.
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I think that is true, but the point with an amp not being time-invariant is that the equations do not accurately reflect what happens with the loop closed. Hysteresis being one example. I mean, feedback will still 'work' but the equations do not reflect reality good enough because they assume a time-invariant system.
It also is connected to a post above I think from DF96 that there's only so much you can understand intuitively. If you want to go deep enough you can't do it without math, and the math assumes some conditions to be valid, including the requirement that the amp is time-invariant. It can still be non-linear and cause distortion of course, otherwise there would be no need for feedback at all.
Edit: one example is the well known equation that Gain = Aol/(1+Aol*b). The usual reasoning is that if Aol*b is very large, we can neglect the '1' and we get Gain = Aol/Aol*b, and then divide numerator and denominator by Aol leads to G = 1/b. BUT you cannot do this reasoning when Aol = 0 (like at xover) because dividing by something that is zero is a forbidden operation in math so the equation is no longer valid!
Jan
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I think that negative FB works even if the system is time-variant as long as open loop gain Aol >> 1/b.
Aol(t) / (1+Aol(t) * b) goes to 1/b, even if Aol is a function of t.
Aol(t) / (1+Aol(t) * b) goes to 1/b, even if Aol is a function of t.
maybe i missed the point... but the math is correct as Aol/(1+Aol*b) does not assume a time-invariant Aol.
The math is correct even if the system is not time-invariant (but more complicated).
I think that feedback will work even if the input subtract action (the diff-amp) is nonlinear and the gain A is nonlinear as long as it is monotonic.
The trick is, that you can linearize any nonlinear function as long as the input is small.
This is the case for a big open loop gain Aol as the input error is very small.
In practice any amplifier has storage elements, hysteresis and nonlinearities and FB still works...
The math is correct even if the system is not time-invariant (but more complicated).
I think that feedback will work even if the input subtract action (the diff-amp) is nonlinear and the gain A is nonlinear as long as it is monotonic.
The trick is, that you can linearize any nonlinear function as long as the input is small.
This is the case for a big open loop gain Aol as the input error is very small.
In practice any amplifier has storage elements, hysteresis and nonlinearities and FB still works...
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Yes it still 'works', but as has been complained about many times here, you are not allowed to calculate the CL gain as we normally do and draw conclusions from the math about the system unless it is linear time invariant.
Jan
Jan
Real world 250W/4ohm amplifier with global negative feedback, please see output vs. input signal measured and plotted, sampled with 20ns per sample. One can see that the output "delay" is about 500ns (0.5 microseconds) and it is similar as if it was a pure passive RC circuit. Please let's stop fairy tales about slow feedback.
Attachments
Not quite. You can linearise any smooth (single-valued?) nonlinear function as long as the input is sufficiently small. Fortunately, most amplifiers have a smooth in->out function until you hit limiting.udok said:
...and as long as energy is finite and you have capacitance and inductance "Natua non facit saltus" is valid...
Well if you want to throw Google finds around rather than study the matter, try Catastrophe theory. I am not continuing this discussion with you.
Jan
The principle is very very simple. The circuit seeks the lowest possible differential difference, simply because that that is the closest thing to balance it can find, the lowest state of energy it can reach. So It will seek that state, regardless of linearity in transfer function or delay in time, as long as it meets stability criteria and that the resulting action from the feedback signal is subtraction.
The limits in excess gain (OLG-set gain) and deviation time simply sets the attainable amount of correction possible. When things are offset in time, and current is leaked through capacitance's you loose excess gain and thus you loose precision, you get a signal that is not true and fixed scale of the input, its distorted.
The limits in excess gain (OLG-set gain) and deviation time simply sets the attainable amount of correction possible. When things are offset in time, and current is leaked through capacitance's you loose excess gain and thus you loose precision, you get a signal that is not true and fixed scale of the input, its distorted.
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I did not say that the math is easy, but catastrophe theory does not apply here as it needs a lot of memory (different system states) and nonlinearities which a power amp simply does not have.
The worst case scenario are oscillations or an output stuck to V+ or V-.
A power amp can be nonlinear, but will always be time-invariant as long as the components are constant.
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No. I think it has already been explained to you that the circuit does not seek for anything other than matching input and output via the feedback loop. Nothing to do with "lowest state of energy" - this is circuit theory, not thermodynamics.MiiB said:
No the circuit matches the differential input to be as close to each other as possible. The output is a resistor based scale of this. when there is a differential difference at the input nodes the circuit has to do something. when not it's action is accomplished. With feedback action is done when output matches to the scale of the feedback. the way you get the subtraction is through V-I conversion over the input pair input signals are twisted 90 degrees, this is then fed back into the back side of the differential V-I and twisted additional 90 degrees, so the action is, the needed subtraction of the OLG to the desired gain, set by the resistor scale. The circuit can't 100% match the two inputs as there's not sufficient slew rate and not sufficient gain, and the two signals at the input nodes are shifted some nano-seconds in time. (time is a non issue for audio)
And yes it has something to do with lowest state of energy. because when there is a differential difference at the two input nodes the circuit has to do something. Of Course in real life the circuits is always doing something as nothing will ever be steady, The circuit produces signals (noise) for itself to correct all the time, so there will always be some differential voltage to process.
And yes it has something to do with lowest state of energy. because when there is a differential difference at the two input nodes the circuit has to do something. Of Course in real life the circuits is always doing something as nothing will ever be steady, The circuit produces signals (noise) for itself to correct all the time, so there will always be some differential voltage to process.
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