Linear circuit

A linear circuit is an electronic circuit that follows a special rule called the superposition principle. This means that if you combine two signals and send them through the circuit, the output will be the same as if you had sent each signal alone and then added the results together. This special behavior makes linear circuits very useful in electronics.

In a linear circuit, the output—whether it is voltage or current—changes in a straightforward way as you change the input. This is different from the straight lines you might see on a graph, even though the word “linear” is used in both cases.

When the parts inside a circuit, like resistance, capacitance, and inductance, stay the same no matter how much voltage or current is flowing, the circuit is called linear time-invariant (LTI). This means that if you send a smooth, repeating signal, like a sine wave, into the circuit, the output will also be a sine wave of the same frequency.

Linear circuits are very important because they can make signals bigger or change them in useful ways without adding unwanted changes or “distortion.” One common device that uses linear circuits is an amplifier, which makes audio or radio signals stronger so they can be heard or used properly.

Alternate definition

The superposition principle for linear circuits can also be described using two properties: additivity and homogeneity. Additivity means that if you combine two signals and put them into the circuit, the output will be the same as if you put each signal in separately and then added those outputs together. Homogeneity means that if you change the size of an input signal by a certain amount, the output will also change by the same amount. These two properties help define what makes a circuit linear.

The links additivity and homogeneity provide more information on these concepts.

Linear and nonlinear components

A linear circuit is a type of electronic circuit that does not contain any nonlinear parts. Examples of linear circuits include amplifiers, differentiators, integrators, and linear electronic filters. These circuits are made up of ideal parts such as resistors, capacitors, inductors, and op-amps.

Nonlinear components, like diodes, transistors, and saturated iron core inductors or transformers, behave in more complex ways. Circuits that use these parts in a nonlinear way include mixers, modulators, rectifiers, radio receiver detectors, and digital logic circuits.

Significance

Linear time-invariant circuits are important because they can process analog signals without mixing different frequencies together. This helps keep the original sounds or signals clear and separate.

These circuits are also easier to study and understand. Because they follow certain math rules, scientists can use special tools to analyze how they work. This makes it simpler to describe their behavior using words like volume control, timing changes, and frequency ranges.

Small signal approximation

Main article: small-signal model

Some parts of electronic circuits, like transistors, act in a straight-line way when only small signals are used. This makes it easier to study circuits, such as those in TVs and radios, by using simple math rules.

But even parts that seem straight-line can stop working that way when the signals get too big. For example, the power supply of a circuit can only handle so much voltage, and beyond that point, the output won't grow in a straight way with the input.