How to distinguish between linear and non-linear circuits?

[Fascheue]

TL;DR Summary

What makes a circuit linear?

Many circuit analysis techniques only apply to linear circuits. I don’t quite understand how to distinguish between linear and non-linear circuits.

I understand the mathematical concept of linearity. I understand why components like resistors, capacitors and inductors are linear. I don’t quite understand how linearity applies to entire circuits. Circuits don’t necessarily have singular inputs and outputs.

What exactly makes a circuit linear?

 

[anorlunda]

The simplest thing, if you have twice the stimulus, you get twice the response.

For example, V=IR. Double V, holding R constant, and you double I.

An example of nonlinear.

Edit: An important property of linear circuits is that you can superimpose solutions.

With V=IR, suppose we solve for a step function in V, then solve for V=sin(wt). Add both kinds of V together, and you just add the separate solutions for I together. That's a huge advantage in analysis.

 

[Fascheue]

The simplest thing, if you have twice the stimulus, you get twice the response.

For example, V=IR. Double V, holding R constant, and you double I.

An example of nonlinear.
View attachment 280463

But what do V and I refer to? I understand in the context of a component like a resistor that has a singular voltage and current.

Most circuits don’t have a voltage/current, they have multiple nodes or segments with varying voltages and currents. I don’t understand how the concept of linearity applies in this context.

 

[Averagesupernova]

Take a simple example of a voltage amplifier. Assume it has a voltage gain of 10. We can input .15 volts and expect 1.5 volts out. Within the limits of the design frequency-wise we can amplify AC signals as well. A non-linear amplifier would not amplify linearly in that you may put in .15 volts and expect 1.5 volts on the output but put in .5 volts into the same amplifier and only get out 2 volts. The gain is not linear in this case.

 

[anorlunda]

But what do V and I refer to?

V is for voltage.
I is for current.

 

[berkeman]

What exactly makes a circuit linear?

It's probably easier to ask "What makes a circuit non-linear?". The short answer is that there is some sort of semiconductor device in the circuit, like a diode, transistor, etc. Semiconductor devices generally have non-linear relationships between V (voltage) and I (current) in most situations and configurations. There are things you can to do try to make their behavior more linear (like using negative feedback around amplifier stages), but they will always have some amount of non-linearity.

Do Google searches on the bold phrases above for more detailed information, and ask questions about that reading if there are still things that are confusing for you.

 

[Fascheue]

It's probably easier to ask "What makes a circuit non-linear?". The short answer is generally that there is some sort of semiconductor device in the circuit, like a diode, transistor, etc. Semiconductor devices generally have non-linear relationships between V (voltage) and I (current) in most situations and configurations. There are things you can to do try to make their behavior more linear (like using negative feedback around amplifier stages), but they will always have some amount of non-linearity.

Do Google searches on the bold phrases above for more detailed information, and ask questions about that reading if there are still things that are confusing for you.

I think I understand why devices like diodes and transistors are non-linear. The voltage/current functions that those devices obey are non-linear functions.

Resistors, capacitors and inductors obey linear functions.

I’m struggling to understand what it means for a complex circuit to be linear or non-linear. This - as I understand it - is the condition that needs to be met for circuit analysis techniques like the superposition theorem or thevinin’s theorem to be valid.

Would you say that a linear circuit is defined by its lack of non-linear components?

 

[berkeman]

Would you say that a linear circuit is defined by its lack of non-linear components?

Yes. That is a good summary statement.

 

[Baluncore]

What exactly makes a circuit linear?

If the circuit multiplies signals together, it is non-linear.
If signals are simply added together, or subtracted, it is linear.

If a circuit does NOT distort a pure sinewave, it is linear.
If a circuit distorts a pure sinewave, it is non-linear and will generate new signal components at higher harmonic frequencies.

 

[sophiecentaur]

Would you say that a linear circuit is defined by its lack of non-linear components?

A practical note here. Linearity is a matter of degree. All electrical components will cease to be linear under 'hard enough' conditions. If you try to operate a transistor or valve such that you are demanding a voltage swing that's nearly equal to the power supply volts then it will 'limit' and the linear transfer function hits end stops. Valves are all inherently non-linear but non linearity can be compensated for by using Negative Feedback. All linear circuits use negative feedback to 'tame' high performance devices which (and they all do) have nonlinear behaviour.

And then there are deliberately non-linear circuits and components which handle logic signals. They are purposely designed to be on or off and designed not to have a 'straight line in/out function.

I often advise people not to get too involved with classifying things too tightly. It's so easy to be confused when something doesn't quite fit your particular classification system. Aim at getting the sort of understanding that works irrespective of just names.

 

[AVBs2Systems]

IIRC, 2 things for certain can classify circuits as non-linear:
1. Non linear elements such as diodes.
2. Changing frequency of sources or input waveforms.

Mathematically, a linear circuit will obey the superposition principle with regards to signals across the output.

 

[Baluncore]

1. Non linear elements such as diodes.

It will depend on how the diode is used.
Diodes, and PN junctions in bipolar transistors, are used in many linear amplifiers.

 

[Averagesupernova]

It will depend on how the diode is used.
Diodes, and PN junctions in bipolar transistors, are used in many linear amplifiers.

Absolutely. I had thought of this early on in this thread, but wasn't sure it was worth posting. Now is as good of a time as any to say that just because a circuit contains non-linear components it does not mean that the transfer function is non-linear.

 

[sophiecentaur]

Take an analogue to digital decoder. It takes in signals with discrete, digital values (highly non-linear) but, if you pay enough for your system, the linearity of the analogue signal that emerges can be a good as you like. So where does classification take you with that sort of circuit?

Beware classification without knowledge.