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One thing I've never managed to wrap my head around is why many analog designers insist on calling op-amp based analog circuit design "linear design". If there

One thing I've never managed to wrap my head around is why many analog designers insist on calling op-amp based analog circuit design "linear design". If there's one thing these circuits are absolutely not it's being linear. Every interesting circuit using op-amps basically is interesting because of the various non-linear behaviors you have to deal with when you optimize the circuit.

dreamcompiler 5y ago
Op-amps are (theoretically) just linear differential amplifiers with extremely high gain (like 10,000x or greater). They appear nonlinear in open-loop configuration because their gain is so high that any realistic input signal immediately pegs the output against the rails. But with negative feedback they start to appear linear again because you can set the gain to something more reasonable. They're marvelous devices.
tuatoru 5y ago
This is a somewhat contrarian statement--I'd like some explanation and examples of what you mean. I find a x10 amplifier with high Zin, low Zout, low noise, low error, and constant delay to be interesting enough. Every circuit is non-linear when used outside its design limits, but this hardly needs asserting. And of course real devices are not perfect. Resistors have inductance and capacitance and a thermal coefficient, capacitors likewise have flaws, wires have resistance and self-inductance, and circuit layout gives you stray capacitance, crosstalk, and instability. Op amps themselves produce noise, have input currents and offset voltages and limited slew rate and bandwidth. And so on, and on. But again, none of that needs asserting. While you certainly can design lot of deliberately non-linear circuits with op amps and non-linear devices in their feedback paths, it's difficult to design linear circuits without them, or instead with circuits, the core of which end up looking like simplified op-amps. So, what did you have in mind when you said "the various non-linear behaviours"?
mhh__ 5y ago
The one thing I wouldn't expect from electrical engineers is a focus on nomenclature - I do love electronics but I am perpetually annoyed by similar niggles as you are (it seems) + a tendency to teach the same equation 3 times in 3 different regimes even though I have spent years training myself to be able to identify these approximations myself.
- ur-whale 5y ago
  Oh man, you're so right. It's a rather general problem when hopping around scientific and technical domains, but I agree that it's particularly bad with EE
cushychicken 5y ago
"Linear", in circuit terms, means that you get the same output from a circuit every time you put the corresponding input into the circuit. It's not nearly as mystical as folks like to make it sound. A lot of the language around it dresses it up to appear more than it is in an effort to be rigorous.
- freemint 5y ago
  Capacitors are linear but stateful, so would be memristors. I am not sure you characterization is correct.
- pkaye 5y ago
  A linear circuit is one which obeys the superposition principle. Its easer to analyze under frequency domain for example. https://en.wikipedia.org/wiki/Linear_circuit https://en.wikipedia.org/wiki/Linear_circuit
- capn_duck 5y ago
  That's just not true. Its a very specific relation between the output and the input of a system.
- exmadscientist 5y ago
  As other comments note, this is not the definition of a linear system. However, it is the definition of a time-invariant system, which is probably why it's coming to mind here. Systems that are both linear and time-invariant, sometimes abbreviated to LTI systems, are the most common sort of thing (i.e., model) that one actually analyzes. When time-dependence is present, it is always modelled explicitly and usually modelled as a complication of a time-invariant system.
- ur-whale 5y ago
  >means that you get the same output from a circuit Not sure where you were taught that, but it does not strike me as the generally accepted meaning of the term "linear". Where I hail from, linear means: f(a*x + b*y) = a*f(x) + b*f(y) aka the superposition principle.
mikewarot 5y ago
The term Linear Design generally applies to things that have analog signals, as opposed to Digital Design (which is, of course never completely digital). RF design is the darkest of the arts.
capn_duck 5y ago
"Linear" means "Linear System" as in T(a+b)=T(a)+T(b). In practical terms this means sine wave in, sine wave out. If your system behaves as such then you have a much simpler time than if your sine wave gets distorted on the output because then that means you can no longer live in the world of Laplace transforms for understanding the PDE nature of your system. Op amps were hailed as a revelation because they behave much more ideally Linear than say a Common Emitter Amplifier, even when being constructed from non-linear components.
- ur-whale 5y ago
  > "Linear" means "Linear System" as in T(a+b)=T(a)+T(b). Fully aware. What I'm saying is: op-amp based-circuits just never do that in the real world, only in extremely limited circumstances (hence the whole small-signal model methodology). They are in general anything but linear.
- kragen 5y ago
  opamps predate common-emitter amplifiers by about 20 years. maybe you mean a common-cathode amplifier
analog31 5y ago
Historically, negative feedback in electronics was developed to stabilize and linearize the response of circuits. None of the characteristic curves of vacuum tubes and transistors would make you think that there was anything linear about them. However, passive components such as resistors and capacitors are quite linear and stable. So the trick with feedback is that the feedback network defines the response of the circuit despite using potentially nonlinear and unstable gain elements. This was of vital importance for making important circuits, like amplifiers for telephony, predictable, reliable, and reproducible. If you design something like a basic analog filter using op amps, and model its behavior under the assumption of linearity, the actual behavior of the circuit will resemble the model behavior to an uncanny degree. But naturally, terminology is not precise. For instance the term "linear" is used to describe things like power supplies and voltage regulators, in contrast to "switchmode" circuits. A "linear power supply" means a particular thing that has little to do with linearity.

dreamcompiler 5y ago

Op-amps are (theoretically) just linear differential amplifiers with extremely high gain (like 10,000x or greater). They appear nonlinear in open-loop configuration because their gain is so high that any realistic input signal immediately pegs the output against the rails. But with negative feedback they start to appear linear again because you can set the gain to something more reasonable. They're marvelous devices.

tuatoru 5y ago

This is a somewhat contrarian statement--I'd like some explanation and examples of what you mean. I find a x10 amplifier with high Zin, low Zout, low noise, low error, and constant delay to be interesting enough. Every circuit is non-linear when used outside its design limits, but this hardly needs asserting. And of course real devices are not perfect. Resistors have inductance and capacitance and a thermal coefficient, capacitors likewise have flaws, wires have resistance and self-inductance, and circuit layout gives you stray capacitance, crosstalk, and instability. Op amps themselves produce noise, have input currents and offset voltages and limited slew rate and bandwidth. And so on, and on. But again, none of that needs asserting. While you certainly can design lot of deliberately non-linear circuits with op amps and non-linear devices in their feedback paths, it's difficult to design linear circuits without them, or instead with circuits, the core of which end up looking like simplified op-amps. So, what did you have in mind when you said "the various non-linear behaviours"?

mhh__ 5y ago

The one thing I wouldn't expect from electrical engineers is a focus on nomenclature - I do love electronics but I am perpetually annoyed by similar niggles as you are (it seems) + a tendency to teach the same equation 3 times in 3 different regimes even though I have spent years training myself to be able to identify these approximations myself.

ur-whale 5y ago
Oh man, you're so right. It's a rather general problem when hopping around scientific and technical domains, but I agree that it's particularly bad with EE

cushychicken 5y ago

"Linear", in circuit terms, means that you get the same output from a circuit every time you put the corresponding input into the circuit. It's not nearly as mystical as folks like to make it sound. A lot of the language around it dresses it up to appear more than it is in an effort to be rigorous.

freemint 5y ago
Capacitors are linear but stateful, so would be memristors. I am not sure you characterization is correct.
pkaye 5y ago
A linear circuit is one which obeys the superposition principle. Its easer to analyze under frequency domain for example. https://en.wikipedia.org/wiki/Linear_circuit https://en.wikipedia.org/wiki/Linear_circuit
capn_duck 5y ago
That's just not true. Its a very specific relation between the output and the input of a system.
exmadscientist 5y ago
As other comments note, this is not the definition of a linear system. However, it is the definition of a time-invariant system, which is probably why it's coming to mind here. Systems that are both linear and time-invariant, sometimes abbreviated to LTI systems, are the most common sort of thing (i.e., model) that one actually analyzes. When time-dependence is present, it is always modelled explicitly and usually modelled as a complication of a time-invariant system.
ur-whale 5y ago
>means that you get the same output from a circuit Not sure where you were taught that, but it does not strike me as the generally accepted meaning of the term "linear". Where I hail from, linear means: f(a*x + b*y) = a*f(x) + b*f(y) aka the superposition principle.

mikewarot 5y ago

The term Linear Design generally applies to things that have analog signals, as opposed to Digital Design (which is, of course never completely digital). RF design is the darkest of the arts.

capn_duck 5y ago

"Linear" means "Linear System" as in T(a+b)=T(a)+T(b). In practical terms this means sine wave in, sine wave out. If your system behaves as such then you have a much simpler time than if your sine wave gets distorted on the output because then that means you can no longer live in the world of Laplace transforms for understanding the PDE nature of your system. Op amps were hailed as a revelation because they behave much more ideally Linear than say a Common Emitter Amplifier, even when being constructed from non-linear components.

ur-whale 5y ago
> "Linear" means "Linear System" as in T(a+b)=T(a)+T(b). Fully aware. What I'm saying is: op-amp based-circuits just never do that in the real world, only in extremely limited circumstances (hence the whole small-signal model methodology). They are in general anything but linear.
kragen 5y ago
opamps predate common-emitter amplifiers by about 20 years. maybe you mean a common-cathode amplifier

analog31 5y ago

Historically, negative feedback in electronics was developed to stabilize and linearize the response of circuits. None of the characteristic curves of vacuum tubes and transistors would make you think that there was anything linear about them. However, passive components such as resistors and capacitors are quite linear and stable. So the trick with feedback is that the feedback network defines the response of the circuit despite using potentially nonlinear and unstable gain elements. This was of vital importance for making important circuits, like amplifiers for telephony, predictable, reliable, and reproducible. If you design something like a basic analog filter using op amps, and model its behavior under the assumption of linearity, the actual behavior of the circuit will resemble the model behavior to an uncanny degree. But naturally, terminology is not precise. For instance the term "linear" is used to describe things like power supplies and voltage regulators, in contrast to "switchmode" circuits. A "linear power supply" means a particular thing that has little to do with linearity.