I stumbled on this reasoning.
The impedance ( about a regulated PS ) increases with frequency, so it has an inductive behavior....Then they model this impedance as an inductor with a L and a R.
Well!
Sure an inductor has an impedance that increases with frequency, but can we say the converse is true ?
For this to be true, indeed the impedance amplitude must increase, but what about phase ?
May be actual circuits do have the right phase behavior when impedance increases with frequency.
What do you think ?
This might give me a way to identify where and what is inducing oscillations in an amplifier.
Here I am not taking about well understood oscillations of high loop gain linear systems.
Here, the scope is about unexpected oscillations.
My idea is to use Spice to see impedances at various places in an amplifier. This to dig out inductors hidden inside parts, that I can combine with layout estimated parasitics ( track inductors and capacitors ) . Hopefully to finally get at each node the possible resonances, high Qs, etc.
If this approach works, this would be a great tool to tackle mysterious instabilities where I only see fishing in the dark.
The impedance ( about a regulated PS ) increases with frequency, so it has an inductive behavior....Then they model this impedance as an inductor with a L and a R.
Well!
Sure an inductor has an impedance that increases with frequency, but can we say the converse is true ?
For this to be true, indeed the impedance amplitude must increase, but what about phase ?
May be actual circuits do have the right phase behavior when impedance increases with frequency.
What do you think ?
This might give me a way to identify where and what is inducing oscillations in an amplifier.
Here I am not taking about well understood oscillations of high loop gain linear systems.
Here, the scope is about unexpected oscillations.
My idea is to use Spice to see impedances at various places in an amplifier. This to dig out inductors hidden inside parts, that I can combine with layout estimated parasitics ( track inductors and capacitors ) . Hopefully to finally get at each node the possible resonances, high Qs, etc.
If this approach works, this would be a great tool to tackle mysterious instabilities where I only see fishing in the dark.
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Are they actual impedances with a module versus frequency like an inductor but a phase unlike this inductor ?
I do not think so.
May be actual circuits do so, in a way close enough to consider they are inductors.
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You might find this interesting-
Troubleshooting Analog Circuits - Robert A. Pease - Google Books
Troubleshooting Analog Circuits - Robert A. Pease - Google Books
This is precisely the text that started it all, in my mind.
Indeed a very interesting paper.
Sure they have, there are tons of calculators on internet to calculate them. I played with Spice inserting track inductance at critical places and found some interesting results about stability.
I am looking to go beyond that including inductors hidden inside parts.
There is no actual inductor hidden inside, of course. Thing is, as you noted, amplifiers (including regulators) have dropping loop gain with frequency. That causes an increase in output impedance with frequency. That acts inductive (including the expected phase shift). And if you want to look at oscillations because of this inductive character, what do you know, it is just as if there was a real inductance!
Maybe we should look at it in a different way. Anything that has a rising impedance and phase shift with frequency acts inductive. A coil is just one of those things.
Jan
Maybe we should look at it in a different way. Anything that has a rising impedance and phase shift with frequency acts inductive. A coil is just one of those things.
Jan
Do not misunderstand what I mean by there is an inductor inside the part. I do not imagine a coil inside. I see the component, a part, or a subsystem as a black box that I can model using inductors. There is no physical inductor inside, there is something that acts like it. Just like in a transistor model, there are things that act as resistors, capacitors, current source.There is no actual inductor hidden inside, of course. Thing is, as you noted, amplifiers (including regulators) have dropping loop gain with frequency. That causes an increase in output impedance with frequency. That acts inductive (including the expected phase shift). And if you want to look at oscillations because of this inductive character, what do you know, it is just as if there was a real inductance!
Maybe we should look at it in a different way. Anything that has a rising impedance and phase shift with frequency acts inductive. A coil is just one of those things.
Jan
I think we understand each other, as you say, it is as if there was a real inductor inside.
Only physics and math rules, wether inductances are real or virtual is irrelevant...I am afraid I hit a philosophical point.
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In the case of feedback amplifiers with shunt feedback at their outputs and one dominant pole in their loop gain, the magnitude and phase of the output impedance indeed behave similar to an inductor. The same holds for the input impedance of a feedback amplifier with shunt feedback at its input (a.k.a. virtual ground) and one dominant pole.
For amplifiers with higher-order compensation, the impedance can increase faster with frequency and the phase shift is then also larger. For example, with two-pole compensation you get impedances that increase with the square of the frequency and have a negative real part over a certain frequency range.
A simple emitter-follower stage acts like an inductor due to the decreasing current gain vs frequency. You can measure that inductance. And if you load the emitter output with a cap, this forms a resonant tank - making the circuit more or less unstable. This works theoretical and in reality as well.
You might be interested in reading about gyrators, where a circuit with impedance that rises with frequency is used deliberately in place of a real inductor.
Have a look at Intersil Application Note 1092 for an eye opening result.
If the output stage is (mis?)designed in a certain way, its output impedance behaves as a "superinductor", namely, the magnitude of its output impedance rises as frequency squared (!).
A normal inductor's magnitude of impedance is |jwL| and so it rises as frequency to the first power. A "superinductor's" impedance is quadratic in frequency. Ugh.
If the output stage is (mis?)designed in a certain way, its output impedance behaves as a "superinductor", namely, the magnitude of its output impedance rises as frequency squared (!).
A normal inductor's magnitude of impedance is |jwL| and so it rises as frequency to the first power. A "superinductor's" impedance is quadratic in frequency. Ugh.
R, L and C are theoretical properties used in circuit theory. A real world coil has all three properties. Just that L is the most significant.
So yes when looking at a complete active circuit you may also model it with R, L, C and even G (Gain). Maybe even E and I which also tie in with R. Add a bit more for AC circuit theory and even more.
The simple capacitance multiplier is a classic example of a circuit that is a gyrator. A simple circuit that allows a capacitor to behave as an inductor.
So modeling a power supply as an ideal battery in series with a resistor and inductor is quite valid. Even modeling it as an R C filter with a series inductor would still fit a simple model. More complex behavior can be modeled by even more circuit theory properties.
One common bit of confusion is that circuit theory is only a model and there are often issues it does not model correctly. (Diodes etc.)
So yes when looking at a complete active circuit you may also model it with R, L, C and even G (Gain). Maybe even E and I which also tie in with R. Add a bit more for AC circuit theory and even more.
The simple capacitance multiplier is a classic example of a circuit that is a gyrator. A simple circuit that allows a capacitor to behave as an inductor.
So modeling a power supply as an ideal battery in series with a resistor and inductor is quite valid. Even modeling it as an R C filter with a series inductor would still fit a simple model. More complex behavior can be modeled by even more circuit theory properties.
One common bit of confusion is that circuit theory is only a model and there are often issues it does not model correctly. (Diodes etc.)
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I would recommend downloading the free LTSPICE and have a play with that.
I have found it useful and sometimes not so useful.
I modelled a op amp circuit with it and it allowed me to get a circuit working before building it.
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