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The superposition theorem is a derivational result of the superposition principle suited to the network analysis of electrical circuits. The superposition theorem cases that for a linear system (notably combining the subcategory of time-invariant linear arrangements) the response (voltage or current) in any branch of a reciprocal linear circuit having more than one independent source corresponds to the algebraic sum of the responses generated by each independent source beginning alone, where all the other independent sources are replaced by their intramural impedances.
To determine the addition of each individual source, all of the other origins first must be “turned off” (set to zero) by:
- Changing all other independent voltage sources with a short circuit (thereby get rid of difference of potential i.e. V=0; internal impedance of ideal voltage source is zero (short circuit)).
- Restoring all other independent current sources with an open circuit (thereby excluding current i.e. I=0; internal impedance of the ideal current source is infinite (open circuit)).
This procedure is followed for each origin in turn, then the resultant responses are added to determine the true action of the circuit. The resultant circuit action is the superposition of the different voltage and current sources.
The superposition theorem is very essential in circuit analysis. It is used in modifying any circuit into its Norton correspondent or Thevenin equivalent.
The theorem is germane to linear networks (time-varying or time-invariant) subsisting of independent sources, linear dependent sources, linear passive elements (resistors, inductors, capacitors), and linear transformers.
Superposition pursues voltage and current but not power. In other words, the sum of the powers of each source with the other sources turned off is not the real absorbed power. To calculate power we first use superposition to find both the current and voltage of each linear element and then calculate the sum of the aggregated voltages and currents.
However, if the linear network is achieving in steady-state and each extraneous independent source has a distinctive frequency, then superposition can be applied to compute the average power or active power. If at least two independent sources have the clone frequency (for example in power systems, where many generators conduct at 50 Hz or 60 Hz), then superposition can’t be used to regulate average power.
What Is Superposition Theorem?
“If more than one source acts together in an electric circuit, then the current through any one of the arms of the circuit is the addition of currents which would flow through the branch for each source, keeping all the other sources dead.”
To calculate the personal contribution of each source in a circuit, the other source must be replaced or abolished without altering the final result. While abolishing a voltage source, its value is set to zero. This is done by changing the voltage source with a short circuit. When abolishing a current source, its value is set to zero. This is done by replacing the current source with an open circuit.
The superposition theorem is very critical in circuit analysis because it converts a complex circuit into a Norton or Thevenin equivalent circuit.
Guidelines to keep in mind while using the superposition theorem
When you sum the particular contributions of each source, you should be careful while accrediting signs to the quantities. It is suggested to assign an allusion direction to each unknown quantity. If a contribution from a source has the clone direction as the reference direction, it has a positive sign in the sum; if it has the differing direction, then a negative sign.
To use the superposition theorem with circuit currents and voltages, all the segments must be linear.
It should be noted that the superposition theorem does not apply to power, as power is not a linear abundance.
How to apply Superposition Theorem?
- The first step is to select one source among the multiple sources being in the bilateral network. Among the various sources in the circuit, any one of the sources can be contemplated first.
- Except for the selected source, all the sources must be replaced by their intramural impedance.
- Using a network simplification approach, appraise the current flowing through or the voltage drop across a particular aspect in the network.
- The same considering a single source is reiterated for all the other sources in the circuit.
- Upon accessing the respective responsibilities for the individual source, perform the summation of all responses to get the overall voltage drop or current through the circuit element.
Steps for Solving network by Superposition Theorem
Considering circuit diagram A, let us see the various steps to solve the superposition theorem:
- Step 1: Take only one self-sufficient source of voltage or current and deactivate the other sources.
- Step 2: In-circuit diagram B shown above, consider the source E1 and replace the other source E2 by its internal resistance. If its internal resistance is not given, then it is taken as zero and the source is short-circuited.
- Step 3: If there is a voltage source then short circuit it and if there is a current source then just open-circuit it.
- Step 4: Thus, by mobilizing one source and deactivating the other source find the current in each branch of the network. Taking the above example find the current I1’, I2’and I3’.
- Step 5: Now acknowledge the other source E2 and replace the source E1 with its internal resistance r1 as shown in circuit diagram C.
- Step 6: Determine the current in various sections, I1’’, I2’’, and I3’’.
- Step 7: Now to determine the net branch current utilizing the superposition theorem, add the currents accessed from each individual source for each branch.
- Step 8: If the current obtained by each branch is in the same direction then add them and if it is in the opposite direction, deduct them to obtain the net current in each branch.
The actual flow of current in the circuit C will be given by the equations shown below:
Prerequisites for the Superposition Theorem
Quite simple and delicate, don’t you think? It must be noted, though, that the Superposition Theorem works only for circuits that are reducible to series/parallel combinations for each of the power sources at a time (thus, this theorem is useless for acknowledging an unbalanced bridge circuit), and it only works where the elemental equations are linear (no mathematical powers or roots).
The precondition of linearity means that Superposition Theorem is only relevant for determining voltage and current, not power!!! Power dissipations, being nonlinear functions, do not algebraically add to an accurate total when only one source is considered at a time. The need for linearity also means this Theorem cannot be conducted in circuits where the resistance of a component changes with voltage or current. Hence, networks accommodating components like lamps (incandescent or gas-discharge) or varistors could not be analyzed.
Another essential for the Superposition Theorem is that all components must be “bilateral,” meaning that they behave the same with electrons flowing in either direction through them. Resistors have no polarity-specific behavior, and so the circuits we’ve been examining so far all meet this principle.
The Superposition Theorem encounters to use in the study of alternating current (AC) circuits, and semiconductor (amplifier) circuits, where sometimes AC is often blended (superimposed) with DC. Because AC voltage and current equations (Ohm’s Law) are linear just like DC, we can use Superposition to analyze the circuit with just the DC power source, then just the AC power source, associating the results to tell what will appear with both AC and DC sources in effect. For now, though, Superposition will suffice as a break from having to do concurrent equations to analyze a circuit.
Superposition Theorem Circuits:
The Superposition Theorem is a fundamental concept in electrical circuit analysis. It states that in a linear circuit containing multiple independent sources, the response (current or voltage) at any given point can be determined by considering the effects of each source separately, with all other sources turned off. This allows for a simplified analysis of complex circuits.
For example, consider a circuit with multiple voltage sources and resistors connected in various configurations. By using the Superposition Theorem, we can analyze the individual contributions of each voltage source by considering one source at a time and treating the rest as if they were turned off. Then, we can find the total response by summing up the individual responses.
Superposition Theorem Examples:
To better understand the application of the Superposition Theorem, let’s consider an example. Suppose we have a circuit with two voltage sources, V1 and V2, connected in series with a resistor, R.
V1
|——–R——–|
V2
To find the voltage across the resistor, we can apply the Superposition Theorem. First, we consider V1 and turn off V2 by replacing it with a short circuit or 0V. Then, we calculate the voltage across the resistor using Ohm’s Law. Next, we consider V2 and turn off V1 by replacing it with a short circuit or 0V. Again, we calculate the voltage across the resistor. Finally, we add the individual voltages to obtain the total response across the resistor.
Superposition Theorem Calculator:
A Superposition Theorem calculator is a tool that helps in analyzing circuits using the Superposition Theorem. It simplifies the process of manually calculating the individual responses and summing them up. By providing the circuit parameters, such as resistor values and independent sources, the calculator can automatically apply the Superposition Theorem and provide the desired output.
These calculators are available online and can save time and effort when dealing with complex circuits. They are particularly useful when analyzing circuits with numerous independent sources and components.
Superposition Theorem Animation:
An animation or visual representation of the Superposition Theorem can enhance the understanding of its application. It can demonstrate the concept by showing how the individual responses from each source are combined to determine the total response.
For instance, an animation can illustrate the process of sequentially turning off each source, calculating the response, and then combining the results to obtain the final solution. This visual aid helps learners grasp the concept more effectively.
Superposition Theorem Formula:
The Superposition Theorem can be expressed mathematically using the following formula:
V_total = V1 + V2 + V3 + … + Vn
where V_total is the total response (voltage or current) at a given point in the circuit, and V1, V2, V3, …, Vn are the individual responses caused by each independent source in the circuit.
This formula highlights that the total response is the sum of the individual responses from each independent source, considering the effects of all other sources turned off.
Superposition Theorem Proof:
The Superposition Theorem can be proven mathematically using the linearity property of linear circuits. The proof involves expressing the circuit equations in terms of voltage or current sources and resistors and then applying basic circuit analysis techniques, such as Kirchhoff’s laws and Ohm’s Law.
The proof demonstrates that when each independent source is turned off, only one source remains active at a time, resulting in a simplified circuit. By solving these simplified circuits individually and summing the responses, we obtain the total response of the original circuit.
Superposition Theorem Statement:
The Superposition Theorem statement can be summarized as follows:
“In a linear circuit containing multiple independent sources, the response (voltage or current) at any given point can be determined by algebraically summing the responses caused by each source, considering the effects of all other sources turned off.”
This statement emphasizes that the Superposition Theorem is applicable to linear circuits and allows for the simplification of circuit analysis by breaking it down into individual source contributions.
Superposition Theorem Questions:
When studying the Superposition Theorem, it is common to encounter questions that test understanding and application. These questions may involve analyzing circuits to find voltages, currents, or power dissipation.
For example, a question might ask to find the current flowing through a specific resistor in a circuit with multiple voltage sources and resistors. To solve such a question, one would apply the Superposition Theorem, considering the effects of each source separately and then summing up the individual currents to obtain the total current.
Superposition Theorem Theory:
The theory behind the Superposition Theorem lies in the linearity of circuit elements and the concept of superposition. Linear circuit elements, such as resistors, capacitors, and inductors, exhibit proportional responses to applied voltages or currents. Superposition states that the total response in a linear circuit is the sum of the responses caused by individual sources.
The Superposition Theorem theory allows circuit analysis to be simplified by breaking down complex circuits into smaller, more manageable parts. By considering the individual contributions of each source, the theorem enables a step-by-step analysis of the circuit.
Superposition Theorem Application:
The Superposition Theorem finds applications in various fields related to electrical engineering and circuit design. Some common applications include:
– Power system analysis: The Superposition Theorem can be used to analyze complex power systems with multiple sources and loads. It allows engineers to calculate voltages and currents at different points in the system, aiding in power flow studies and fault analysis.
– Amplifier design: The Superposition Theorem helps in designing amplifiers with multiple input sources. By considering each source individually, engineers can analyze and optimize the amplifier circuit for different input scenarios.
– Signal processing: In signal processing applications, the Superposition Theorem can be used to analyze circuits involving multiple signals and filters. It helps in understanding the combined effect of different input signals on the circuit’s output.
Conclusion
This post examines the superposition theorem, another approach for circuit analysis. The superposition theorem states that a circuit with various voltage and current sources is equal to the sum of simplified circuits using just one of the sources. A circuit belonged to two voltage sources, for example, will be equal to the amount of two circuits, each one using one of the sources and having the other eliminated.
To facilitate a circuit using the superposition theorem, the following steps to be followed: identify all current and voltage sources in the circuit; create various versions of the circuit and the other sources must be removed using the following rule: voltage sources must be replaced with a short circuit and current sources just removed from the circuit, every version including just one of the sources; find the currents and voltages required, and sum the results obtained in all circuits.
Frequently Asked Questions About Superposition Theorem
Is The Superposition Theorem Valid For Ac Circuits?
The Superposition Theorem Is Valid For Ac Circuits.
Is The Superposition Theorem Applicable To Power?
The Requisite Of Linearity Indicates That The Superposition Theorem Is Only Applicable To Determine Voltage And Current, But Not Power. Power Dissipation Is A Nonlinear Function That Does Not Algebraically Add To An Accurate Total When Only One Source Is Considered At A Time.
Can The Superposition Theorem Be Applied To Non-linear Circuits?
No, The Superposition Theorem Can Only Be Applied To Non-linear Circuits.
Why Do We Use The Superposition Theorem?
The Superposition Theorem Is Very Important In Circuit Analysis Because It Converts A Complex Circuit Into A Norton Or Thevenin Equivalent Circuit.
What Is The Theorem Of Superposition?
The Superposition Theorem is a principle in electrical circuit analysis that states that in a linear circuit containing multiple independent sources, the response (voltage or current) at any given point can be determined by considering the effects of each source separately, with all other sources turned off. In other words, the theorem allows us to analyze the circuit by considering one source at a time and summing up the individual responses to obtain the total response. The Superposition Theorem simplifies the analysis of complex circuits by breaking them down into smaller, more manageable parts.
What Is The Formula For Superposition Of Power?
The Superposition Theorem applies to both voltage and current, but power is not directly additive. Power is a nonlinear quantity and does not follow the principles of superposition. Therefore, there is no specific formula for superposition of power. In order to calculate power, it is necessary to consider the complete circuit and analyze it using methods such as Kirchhoff’s laws, Ohm’s Law, or other power formulas specific to the circuit elements involved.
What Is The Superposition Theorem With Two Voltage Sources?
When applying the Superposition Theorem to a circuit with two voltage sources, the theorem states that the response at any given point can be determined by considering the effect of each voltage source separately, while treating the other voltage source as if it were turned off (replaced by a short circuit or 0V). The individual responses caused by each voltage source are then combined to obtain the total response.
For example, if we have two voltage sources V1 and V2 connected in series with a resistor, we can determine the voltage across the resistor by turning off V2 and calculating the voltage using Ohm’s Law. Similarly, we can turn off V1 and calculate the voltage across the resistor caused by V2. Finally, we add the individual voltages to obtain the total voltage across the resistor.
What Are The Conditions In Application Of Superposition Theorem?
The Superposition Theorem is applicable to linear circuits under the following conditions:
– The circuit must be linear: The theorem relies on the linearity of circuit elements such as resistors, capacitors, and inductors. Nonlinear elements, such as diodes or transistors operating in active regions, cannot be analyzed using the Superposition Theorem.
– Independent sources: The circuit must contain multiple independent sources, such as voltage sources or current sources, acting simultaneously. The theorem does not apply to dependent sources, which are influenced by other circuit variables.
– Linear circuit elements: The circuit should consist of linear elements that exhibit a proportional relationship between applied voltage or current and the resulting response (voltage or current). Nonlinear elements, such as diodes or transistors, require different analysis techniques.
Why Superposition Theorem Is More Useful For Analysis Of Multiple-source Linear Circuits?
The Superposition Theorem is particularly useful for analyzing circuits with multiple independent sources for several reasons:
– Simplification: It allows complex circuits to be simplified by breaking them down into smaller, more manageable parts. By considering one source at a time, the analysis becomes less complicated compared to analyzing the circuit as a whole.
– Individual contributions: The theorem enables the calculation of individual responses caused by each source separately. This allows engineers to understand the contribution of each source to the overall circuit behavior.
– Linear circuit analysis: The Superposition Theorem is specifically applicable to linear circuits. Since many practical circuits are linear or can be approximated as linear under certain operating conditions, the theorem finds wide application in circuit analysis.
When Is The Superposition Theorem Used?
The Superposition Theorem is used when analyzing circuits that contain multiple independent sources. It is particularly helpful in situations where a comprehensive analysis of the entire circuit would be difficult or time-consuming.
The theorem is commonly employed in fields such as electrical engineering, electronics, power systems, and telecommunications. It aids in the analysis and design of circuits with multiple sources, allowing engineers to determine voltages, currents, and power distributions in complex systems.
When Is The Superposition Theorem Applied to a Circuit?
The Superposition Theorem is applied to a circuit that meets the following conditions:
– The circuit contains multiple independent sources, such as voltage sources or current sources.
– The circuit is linear, meaning the behavior of circuit elements follows linear relationships, such as Ohm’s Law for resistors.
– The desired response in the circuit, such as voltage or current at a specific point, needs to be determined.
By applying the Superposition Theorem, engineers can simplify the analysis of the circuit by considering the individual effects of each source and summing up the responses to obtain the total response.