Circuit Theories / Circuit Analysis

Circuit Analysis or Network Analysis

Definition of Circuit Analysis

Electrical Circuit Analysis is a process of finding out different unknown parameters of a circuit.

Description

The parameters are resistance, voltage, current, power, energy, impedance, admittance, inductance, reactance, capacitance, conductance, phase angle and many more. We often have to find out any of these parameters of a branch of a circuit in our practical engineering applications. The circuit analysis does the thing. There are many techniques in circuit analysis by means of which we can solve a circuit for finding out the desired parameters. We often refer to circuit analysis as network analysis, also.

Direct and Indirect Circuit Analysis

The techniques or methods used in circuit analysis may be either direct methods or indirect methods. In the direct method, we do not simplify the circuit, instead, we calculate the parameters by solving different circuit equations. Mesh analysis, nodal analysis, loop analysis are examples of direct methods of circuit analysis. On the other hand, in indirect methods, we first convert a complicated circuit into a simplified form. Then we calculate the circuit parameters by using required circuit analysis methods. Thevenin’s Theorem, Norton’s Theorem, Star Delta transformation are examples of indirect methods.

Relevant Terms used in Circuit Analysis or Network Analysis

We use different terms in network analysis such as.

Circuit

The circuit is a path through which electricity can pass or intended to pass. There are three types of circuits such as a closed circuit, open circuit and short circuit. A closed circuit provides a closed path to the current to flow through it. An open circuit does not allow any current to flow through it even after applying sufficient potential difference between its terminals. When a closed circuit does not offer any resistance or impedance to the current flowing through it we call the circuit as a short circuit.

Electrical Circuit Network
Electrical Circuit Network

Node

It is the junction point where more than one branches of a circuit meet. In other words, a node in a circuit is the connection point of two or more elements in a circuit.

Node
Node

Branch

It is the portion of the circuit between two adjacent nodes. A branch of a circuit must consist of a circuit element.
branch

Loop

A number of circuit branches may form a closed path. We call any such closed path in a circuit as a loop.

circuit loop
Loop

Mesh

A mesh is also a loop but it does not include any other loop inside it. Mesh is the smallest possible loop of a circuit.

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Circuit Elements

A circuit branch can consist of an element like resistance, inductance, capacitance, sources etc. Hence we call these elements as circuit elements. A circuit element can either be an active circuit element or a passive circuit element. Active circuit elements contribute energy to the circuit. Passive circuit elements consume energy from the circuit. Batteries, generators are the well-known examples of active circuits element. The resistor is one of the well-known examples of passive elements.

Circuit Elements
Circuit Elements

Bilateral Element

The circuit elements which have the same characteristics in either direction of current through it. Such as resistance, it develops the same value of voltage drop in either direction of current through it and it is the product of the current and resistance of the resistor.

Unilateral Element

The circuit elements which have a different characteristic in either direction of current are called a unilateral element. The diode is a well-known example of unilateral elements, the resistance is ideally zero in the forward flow of current and the same diode offers ideally infinite resistance in the backward flow of current.

The different methods used in circuit analysis are

Kirchhoff’s Laws

The laws are very basic laws of circuit analysis. Kirchhoff’s laws consist of two laws – Kirchhoff’s Current Law and Kirchhoff’s Voltage Law. Among these two laws, Kirchhoff’s current law says that the sum of the currents entering at a node is exactly equal to the sum of the currents leaving the node. On the other hand, Kirchhoff’s Voltage Law says that the sum of the voltage gains in a closed loop is equal to the sum of voltage drops in the loop.

Mesh Analysis

Mesh analysis is another basic technique of circuit analysis. Here we write equations for each mesh of a circuit. By solving these equations we can calculate the circuit parameters.

Nodal Analysis

We do nodal analysis by applying KCL at different nodes of the circuit.

Source Conversion

For simplifying complicated circuits we often need to convert current sources to voltage sources and voltage sources to current sources. An ideal voltage source in series with resistance is equivalent to an ideal current source in parallel with that resistance.

Thevenin’s Theorem

In Thevenin’s theorem, we can consider an active circuit as a voltage source with an international resistance equal to the equivalent resistance of the circuit.

Norton’s Theorem

In Norton’s theorem, we can consider an active circuit as an ideal current source in parallel with a resistance equal to the equivalent resistance of the circuit.

Compensation Theorem

Compensation theorem is based on the concept of Ohm’s law. When a current flows through a resistance, there is a voltage drop across the resistance. This voltage opposes the source voltage. Hence in an active network, we can replace resistance with a voltage source opposing the original voltage source.

Superposition Theorem

The superposition theorem says that simultaneous effect of all sources of a network on a particular branch is the sum of the effects (on that branch) of individual source acting alone on the network at its place.

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