The superposition theorem is a fundamental principle in electrical engineering that states that the response of a linear system to any input can be represented as the sum of the responses to individual inputs. In other words, the output of a linear system to a combination of inputs is equal to the sum of the outputs that would be produced by each input individually.
The superposition theorem states that:
“In any linear bilateral network with multiple sources, the response (voltage and current) in each element is equal to the sum of all responses induced by each source functioning independently. While eliminating other sources from the circuit.”
Why is it referred to as “superposition?
Superposition comes from the Latin words
Super – Above
Position – Place
Superposition Theorem Expression:
Mathematically, the superposition theorem can be expressed as:
y(t) = ∑[y_i(t)]
where:
y(t) is the output of the system
y_i(t) is the output of the system to the ith input
∑ denotes the sum of all the y_i(t) values
The superposition theorem applies to any linear system, which is a system that satisfies the principle of superposition. A linear system is one in which the output is directly proportional to the input and the system’s response to a combination of inputs is equal to the sum of the responses to each input individually.
The superposition theorem is a powerful tool for analyzing and designing linear systems. It allows engineers to simplify complex systems by breaking them down into simpler components that can be analyzed individually and then combined using the theorem. The theorem is widely used in the analysis of electrical circuits, mechanical systems, and other types of systems that exhibit linear behavior.
Procedures for Superposition Theorem:
Step-1: Identify a number of network-accessible independent sources.
Step-2: Select a single source and delete all others. If a source is dependent on the network, it cannot be eliminated. It remains unchanged for the duration of the calculation.
If you have determined that all potential energy sources are optimal, you do not need to consider internal resistance. And directly short-circuit the source of voltage and the source of current. However, if internal resistance of sources is specified, internal resistance must be replaced.
Step-3: Now, just one independent energy source is present in a circuit. It is necessary to discover a solution using a single energy source in the circuit.
Step-4: Repeat steps 2 and 3 for all available energy sources on the network. If there are three independent sources, these steps must be performed three times. And each time users receive a valuable response.
Step-5: Now, combine all responses acquired from individual sources using algebraic addition. And will receive the final response value for a specific network element. If it is need to find a response for other elements, users must repeat these procedures for each element.
How is the superposition theorem utilized?
It is utilized in the conversion of any circuit to its Norton or Thevenin equivalent. The theorem applies to
- Linear [time-varying (or) time-invariant] networks composed of independent sources,
- Linear dependent sources,
- Linear passive elements (resistors, inductors, & capacitors), and
- Linear transformers.
When to Apply the superposition theorem?
To implement the superposition theorem, the network must meet the following conditions.
- Linear components must be employed in the circuit. It indicates that the current flow in resistors is proportional to the voltage, whereas the flux linkage in inductors is proportional to the current flow. Resistor, inductor, and capacitor are hence linear elements. However, diodes and transistors are not linear elements.
- The components of the circuit must be bilateral elements. This indicates that the size of the current is independent of the polarity of the energy source.
- The superposition theorem allows us to determine the current passing through an element, the voltage drop of the resistance, and the node voltage. However, we cannot locate the power lost by the element.
