That is when you have the zero to begin with. Once you introduce a non-zero value at a given time point, you'll introduce a defined inifity factor into the FB system (output). You will overshoot to either + or - infinite in zero time and never reach an output of zero any more. Since +infinity / (Rfb/Rin) is still +infinity, closed loop gain stops having a meaning. Try to imagine an oscilation between + and - infinity in zero time. Now that sounds wonky, like a singularity. Does your static formula take this into account?
Or is my reasoning off 😉
Edit: yes it was, with infinite gain an error can never occur and will always be zero.
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Well we are dealing with idealised theory here. In idealised theory, I can have no "to begin with", i.e. error signal was always zero and will always be zero.
I think we all understand that the error residual in a conventional feedback system is asymptotic to zero and can in theory be made arbitrarily small with application of feedback.
No need to complicate things, the above limit definition covers the complex case as well, since the |...| operator is in general the "norm" (or "metric") in any vector space, in particular for RxR or C (x^2+y^2, since the complex vector space and the vector space of ordered pairs of real numbers are isomorphic).
i^2 = -1 is different from ordered pairs of reals...
and noise at the input amplified by infinite gain is a largish problem too
and noise at the input amplified by infinite gain is a largish problem too
I disagree. That is the trouble with playing with rudimentary algebraic expressions: an amplifier with infinite gain and zero error voltage would nevertheless saturate on its own internal noise.
Even assuming this isn't the case and the amplifier is miraculously noise free, with zero error the amplifier simply wouldn't work, viz. there is no feedback.
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But that is Mr Lee all over.Have you trouble understanding that the ratio of two quantities
that approach both infinity as close as one wants will converge
to a finite number assuming both quantities are approaching
infinity at the same rate.?.
Hence an amp with infinite gain will work , mathematicaly.
Which two quantities are approaching infinity at the same rate in an amplifier with infinite gain?
But enough of this: there is no such thing as an amplifier with infinite gain, so why are we debating this? 🙂
But enough of this: there is no such thing as an amplifier with infinite gain, so why are we debating this? 🙂
yes the internal saturation with physically limited supplies, devices makes considering noise helpful in avoiding having to argue over "infinite gain" theory
considering noise can for instance show the futility of pursuing say 200 dB excess loop gain
people have shown Bode Integrals can be interpreted as Information Theoretic relations
interpreting complex numbers, relations can involve vigorous wrigglers all over the place
I have a problem with an oversimplified identification of complex numbers with real valued 2-D vectors - a process that requires adding conjugation rules – usually poorly motivated on 1st encounters
I like Hestenes “Geometric Algebra” - real valued Clifford algebra with geometric and operational interpretation of the elements
then a view of complex numbers is that they are isomorphic with the even sub-algebra of 2-D “Geometric Algebra” - they are the “Rotors/Spinors” of 2-D
and complex numbers “operate” on (real valued) vectors to reflect/rotate, scale them by multiplication
complex numbers are the result of multiplying/dividing vectors
complex numbers may be mapped to real 2-D vectors by multiplying by a vector basis element
but they are algebraically distinct
considering noise can for instance show the futility of pursuing say 200 dB excess loop gain
people have shown Bode Integrals can be interpreted as Information Theoretic relations
interpreting complex numbers, relations can involve vigorous wrigglers all over the place
I have a problem with an oversimplified identification of complex numbers with real valued 2-D vectors - a process that requires adding conjugation rules – usually poorly motivated on 1st encounters
I like Hestenes “Geometric Algebra” - real valued Clifford algebra with geometric and operational interpretation of the elements
then a view of complex numbers is that they are isomorphic with the even sub-algebra of 2-D “Geometric Algebra” - they are the “Rotors/Spinors” of 2-D
and complex numbers “operate” on (real valued) vectors to reflect/rotate, scale them by multiplication
complex numbers are the result of multiplying/dividing vectors
complex numbers may be mapped to real 2-D vectors by multiplying by a vector basis element
but they are algebraically distinct
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Yes, I think we can move on.
Talking of which, Monte-Carlo was mentioned earlier.
There is indeed an example in the examples folder of LTspice, but this uses the built-in "mc" function. For some reason, this uses a uniform distribution for producing its random numbers. At least the schematic file notes that users may wish to use Gaussian instead.
A really good guide to Monte-Carlo in LTspice is provided on a blog here:
K6JCA: Monte Carlo and Worst-Case Circuit Analysis using LTSpice
Be sure to read the comments, in particular the one starting "Thanks for this blog post, I found it very useful. However, there are a couple of things that concern me:" (contributed by yours truly) and those that follow.
I have not had time to enhance my Monte-Carlo implementation to account for manufacturers who "make" e.g. their 0.1% parts by removing them from the production line, leaving 1% parts with a 0.1% "hole" in the middle. (Not all manufacturers do this but good luck getting any manufacturer to tell you if they do or not.) Should be a fairly simple alteration to make.
For those that are interested, my example .asc files for Monte-Carlo and worst-case simulation are attached. Strictly speaking, a Monte-Carlo simulation should produce a histogram of a particular circuit measure/parameter. In the example attached, a .measure command is used. When the simulation is finished, the results of the .measure can be found in the "error" log and these can then be plotted with a tool such as Excel.
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Harrydymond,
Understanding that most high precision devices like a resistor are selected, automatically I would think most often, from a wider variance production process I am trying to understand your dislike of the process? Since the larger groups will have a wider variance and therefor normally would be used where that wider variance is allowed why would it matter that the closest center precision devices have been removed? If the wider selection matches requirements is your dislike because you can no longer purchase the wider tolerance parts and find the close tolerance parts?
Understanding that most high precision devices like a resistor are selected, automatically I would think most often, from a wider variance production process I am trying to understand your dislike of the process? Since the larger groups will have a wider variance and therefor normally would be used where that wider variance is allowed why would it matter that the closest center precision devices have been removed? If the wider selection matches requirements is your dislike because you can no longer purchase the wider tolerance parts and find the close tolerance parts?