Calculating a complex circuit involves a complicated math. But there is a solution to simplify the circuit through **Theveninâ€™s theorem**. The theorem indicates that any **DC circuit **consisting of resistance and voltage can be replaced by Thevenin equivalent so the analysis can be simplified.

Even though the theorem originally states DC resistive circuit, it works for any linear electrical network. This theorem can help solve complex electrical circuits aside from using mesh analysis, Kirchhoffâ€™s law, or **nodal voltage method**. Keep scrolling to get to know more about the theorem.

**Get Closer to Theveninâ€™s Theorem**

First of all, **Theveninâ€™s theorem** can be defined as an analytical method that is used to alternate a complex circuit into a simple circuit. The simplified circuit is equivalent to the complex one, though it only consists of a source voltage and series resistance.

The theorem mentions that any linear circuit which contains voltage sources and resistances can be alternated by one voltage source in series with one resistance. In laymanâ€™s terms, any electrical circuit can be simplified no matter how complex it is.

The theorem is often used in circuit analysis of battery or power systems. Interconnected resistive circuits can also take advantages from this theorem.

As aforementioned, this theorem can be applied to any linear circuit. What is meant by linear circuit? There is a specific qualification to determine if a circuit is linear, which is quite identical to the qualification of Superposition theorem. The underlying equations of the circuit must be linear.

When you are using passive components such as capacitors, inductors, and resistors, the circuits are called linear because there are no exponents or roots. But, some components such as semiconductor components make a circuit nonlinear.

**Thevenin Equivalent Circuit**

The theorem helps simplify a circuit by removing the load resistance so that the equivalent circuit can be reduced. It leaves only series resistance and voltage source for the **Thevenin equivalent**. Once equivalent circuit is obtained, the load resistance can be reconnected.

This method offers easier and significantly simpler calculation, as if the network is only a circuit with a simple series. For instance, when a circuit consists of two voltage sources, three load resistors, it can be alternated into a simple circuit with the theorem.

The equivalent circuit is simple as it only consists of E Thevenin (combined voltage sources), R Thevenin (series resistance) as well as one assigned load resistor. The equivalent circuit will be exactly the same as the original one. And yet, the values of E Thevenin and R Thevenin must be calculated correctly.

*Everything has its own advantages.* So, what is the advantage of performing Theveninâ€™s theorem? Of course, this theorem helps make the analysis significantly easier to solve.

Compared to the original network that may be complex, using Thevenin conversion helps save time and effort to determine load voltage as well as load current. It also works well even for complex circuit, allowing you to calculate much easily.

Besides, calculating Thevenin source voltage as well as resistance is easy. Simply assign the load resistor you want to remove from the original circuit. After that, replace with an open circuit. Reconnect the load resistance after calculating.

**Theveninâ€™s Theorem Steps**

When it comes to following the theorem, there are some steps that should be taken into consideration. The following procedures have been simplified to help you understand each step.

- On any linear circuit, remove the load resistor to find Thevenin source voltage. Also calculate the voltage where load resistor was there.
- Remove all power sources to define Thevenin resistance of the original circuit. Calculate the total resistance.
- Draw the equivalent circuit with Thevenin voltage is in series with the resistance. Donâ€™t forget to reconnect the removed load resistor.
- Analyze the current and voltage of the load resistor.

**Defining Thevenin Voltage**

How to define the voltage of Thevenin equivalent? Any analysis method can be used such as Kirchhoffâ€™s law or Ohmâ€™s law. After removing the load resistor, the circuit becomes a simple series.

From the aforementioned example, the voltage between 2 loads can be configured from the voltages of one battery and the voltage drops of one resistor. This is how to define Thevenin voltage (E Thevenin) of the equivalent circuit.

**Defining Thevenin Series Resistance**

To define Thevenin series resistance is as easy as defining Thevenin voltage. With the load resistor is still removed from the original circuit, also remove the power sources. This may be similar to Superposition theorem. Wires are used to replace voltage sources while breaks are used to replace current sources.

According to the example above, once the two batteries are removed, the summed resistance is the same as of two load resistance in parallel. Now you have found the Thevenin resistance (R Thevenin) for the simplified circuit.

**Nortonâ€™s Theorem and Thevenin Equivalent Limitation**

As with **Theveninâ€™s theorem** which states that any linear circuit can be simplified, so does the **Nortonâ€™s theorem**. This theorem also mentions that simplifying any linear circuit is possible, even to the complex one. The Norton equivalent circuit has one current source and parallel resistor.

Much like Theveninâ€™s, this theorem also has linear qualification which is identical to Superposition theorem. The componentsâ€™ equations must be linear, which means no roots or exponents should present in the circuits.

However, both theorems have limitations in practices. Particularly to **Theveninâ€™s theorem**, the limitations include:

- Plenty of circuits are not always linear. As many of them are only linear over a specific range, Thevenin equivalent is only valid within this range of linearity.
- The characteristic of equivalent I-V is only from the loadâ€™s point of view.
- The Thevenin equivalentâ€™s power dissipation is not identical to the real system.

**Theorem Proof**

Proving **Theveninâ€™s theorem** can be conducted in two steps. Superposition theorem is used in the first step while uniqueness theorem is incorporated in the theorem proofing. Meanwhile, the second step usually involves literature. Superposition theorem is used to construct a solution. With the use of superposition configurations, you will find that the voltage of any linear circuit which contains resistors and voltage sources is always a linear function. It can be expressed as follows: V= V_{EQ} – Z_{EQ}I

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