How to distinguish between linear and non-linear circuits?

In summary, linear circuits are those that obey linear functions, meaning that the output is directly proportional to the input. This is achieved by using components like resistors, capacitors, and inductors, which have linear relationships between voltage and current. Non-linear components, such as diodes and transistors, have non-linear relationships between voltage and current and therefore make a circuit non-linear. Non-linear circuits do not have the property of superposition, where the solutions can be added together, making them more challenging to analyze. However, it's important to note that all circuits have some degree of non-linearity, and it can be compensated for using techniques like negative feedback.
  • #1
Fascheue
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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?
 
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  • #2
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.
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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.
 
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  • #3
anorlunda said:
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.
 
  • #4
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.
 
  • #5
Fascheue said:
But what do V and I refer to?
V is for voltage.
I is for current.
 
  • #6
Fascheue said:
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. :smile:
 
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  • #7
berkeman said:
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. :smile:
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?
 
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  • #8
Fascheue said:
Would you say that a linear circuit is defined by its lack of non-linear components?
Yes. That is a good summary statement. :smile:
 
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  • #9
Fascheue said:
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.
 
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  • #10
Fascheue said:
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.
 
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  • #11
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.
 
  • #12
AVBs2Systems said:
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.
 
  • #13
Baluncore said:
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.
 
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  • #14
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.
 

Related to How to distinguish between linear and non-linear circuits?

1. What is the main difference between linear and non-linear circuits?

The main difference between linear and non-linear circuits is that linear circuits follow Ohm's Law, where the current through a component is directly proportional to the voltage across it. Non-linear circuits, on the other hand, do not follow this relationship and have a more complex behavior.

2. How can I identify if a circuit is linear or non-linear?

A circuit is considered linear if it follows the principle of superposition, meaning that the output is directly proportional to the input. This can be tested by applying different input signals and observing if the output also changes proportionally. If the output does not follow this pattern, the circuit is non-linear.

3. Can a circuit be both linear and non-linear?

No, a circuit cannot be both linear and non-linear at the same time. However, some circuits may have both linear and non-linear components. In this case, the overall behavior of the circuit will depend on the combination of these components.

4. What are some common examples of linear and non-linear circuits?

Examples of linear circuits include simple resistive circuits, where the output voltage is directly proportional to the input current. Non-linear circuits include diode rectifiers, transistors, and op-amps, which have more complex behavior due to their non-linear components.

5. How does the linearity of a circuit affect its performance?

Linear circuits are easier to analyze and design compared to non-linear circuits. They also tend to have a more predictable and stable output. Non-linear circuits, on the other hand, can exhibit more complex behaviors and may require more advanced techniques for analysis and design.

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