# What are Linear and Non-Linear Circuits and It's Differences

An electrical circuit or network is made up of several elements, input and output signals. An electrical element or components are the basic building block of an electrical circuit. Several electrical elements are interconnected to form an electrical circuit.

Electrical circuits are categorized into different ways, they are linear and non-linear circuits, bilateral and unilateral circuits, and lumped and distributed circuits. In this article let us learn about what is a linear and non-linear circuit, examples, and their differences.

## What is a Linear Circuit?

An electrical circuit in which the value of parameters or elements remains constant is said to be known as a linear circuit. In other words, the parameters of a linear circuit don't change with respect to the voltage and current in the circuit.

The term 'linear' refers to a straight line which will be a diagonal that describes a linear characteristic in between current and voltage in the circuit. The current in the circuit is directly proportional to the voltage i.e., when the current increases the voltage increases, and vice-versa.

In linear circuits, the output response is directly proportional to the input. If the input voltage applied is of a sinusoidal type having an 'f' frequency, the output of the circuit will be also a sinusoidal type with the same frequency 'f'.

A linear circuit is both additive and homogeneous, it follows the principle of superposition due to which they can be analyzed with frequency domain mathematical techniques, Fourier analysis, and Laplace transform.

### Examples of Linear Circuits :

A linear circuit contains only elements with linear characteristics i.e., the elements in which current changes linearly with applied voltage. Some examples of linear elements are resistors, inductors, capacitors, etc.

Thus a circuit made of a resistor, inductor, capacitor, and other linear elements is regarded as a linear circuit. The below shows the output characteristics curve of the linear circuit between current and voltage. It can be seen that the curve will be a straight diagonal line.

Most of the resistors are linear whose resistance doesn't change with changes in factors like temperature, voltage across its leads, etc. The current flowing through the resistor will be directly proportional to the voltage applied across it. However, in practice, there will be small changes in the resistance that can be ignored thus making them linear.

The linearity of an inductor depends on the core material used. Inductors with ferromagnetic cores have hysteresis, saturation, frequency, and core eddy current effects due to which the linearity remains between two points. Inductors with ceramic/ferrite cores have very less hysteresis effect due to which linearity remains over a wide range of frequencies. Air core inductors have more linearity since air doesn't saturate quickly.

A capacitor is considered a linear element because the voltage is proportional to the charge.

## What is a Non-Linear Circuit?

An electrical circuit in which the value of parameters or elements does not remain constant and varies with the applied voltage and current is called a non-linear circuit. In non-linear circuits, the curve between the current through it and the voltage across it do not result in a straight line (non-linear).

In non-linear circuits, the output response is not directly proportional to the input. Since there is a non-linear relationship between current and voltage, the superposition theorem is not applicable to non-linear circuits.

### Examples of Non-Linear Circuits :

A circuit that contains at least one non-linear element is regarded as a non-linear circuit. Examples of electrical elements with non-linear behavior are diodes, transformers, transistors, iron core inductors, etc. Below shows a non-linear circuit and its V-I curve.

A diode is a two-terminal semiconductor device that allows current only in one direction. If you notice the V-I curve of a diode it has two main non-linearities. Firstly, a diode conducts in forward bias condition, and in reverse bias condition, current flow is negligible thus changing its properties. The other is V-I curve in forward conduction mode is not linear (not a straight line).

An ideal transformer has linear characteristics where the output is directly proportional to the input. But in practice, it can be a non-linear device due to saturation, hysteresis, and eddy-current effect.

A transistor can be linear or non-linear depending on how it is biased. A transistor works as the linear element in active where it works as the amplifier, but in cutoff and saturation region it works as the non-linear device.

## Difference Between Linear and Non-Linear Circuits :

Linear CircuitNon-Linear Circuit
A linear circuit is an electric circuit in which the value of elements connected doesn't vary with current and voltage.A non-linear circuit is an electric circuit in which the value of elements connected varies with current and voltage.
A linear circuit is made up of only elements which exhibit a linear relationship between current through and voltage across it.A non-linear circuit is made of elements that exhibit a non-linear relationship between current through and voltage across it.
The superposition theorem is applicable to linear circuits.The superposition theorem is not applicable to non-linear circuits.
Ohm's law is applicable for linear circuits.Generally, ohm's law is not applicable for non-linear circuits.
The output characteristics curve between current and voltage for a linear circuit looks like a straight line.The output characteristics curve between current and voltage for a non-linear circuit looks like a curved line.
A linear circuit satisfies both the properties of additivity and homogeneityA non-linear network does not satisfy both additivity and homogeneity properties.
It is easy to solve linear circuits with simple techniques.It is difficult to solve non-linear circuits compared to linear circuits.
Examples of linear elements are resistors, inductors, capacitors, etc.Examples of non-linear elements are diodes, transformers, transistors, etc.

## Key Differences Between Linear and Non-Linear Circuits :

#### In a linear circuit, the parameters (resistance, inductance, capacitance, etc) are always constant irrespective of variations in current or voltage. Whereas in a non-linear circuit, the parameters change with voltage or current. The current is directly proportional to voltage in a linear circuit, but in a non-linear circuit, the characteristics between current and voltage are non-linear. A linear circuit consists of only linear elements, whereas a non-linear circuit consists of at least one nonlinear element. A linear circuit obeys the properties of superposition (additive) and homogeneity (scaling). Whereas a non-linear circuit doesn't obey any of these properties. Examples of linear circuits are amplifiers, circuits with resistors, inductors, capacitors, and other linear circuit elements. Examples of non-linear circuits are rectifiers, modulators, etc.

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