3.4. Thevenin Equivalent Circuit

Now, let us move to another important theory in electrical technology what is called Thevenin equivalent circuit. And, we will be frequently using and interestingly we can see that how it can be used for not only DC, but also for AC and mixed kind of situation.

Thevenin's Theorem is a fundamental concept in electrical engineering that simplifies the analysis of complex circuits. It allows us to replace any linear circuit with an equivalent circuit that has just a single voltage source (Thevenin equivalent voltage) and a single resistor (Thevenin equivalent resistance). This simplification makes it much easier to analyze the circuit and understand how it functions, especially when load components are connected to it.

Think of Thevenin's Theorem like a recipe for a complex dish. Instead of explaining every ingredient and step in detail, the recipe gives you a summary of how to create a simplified version of the dish. By focusing on just the essential flavors (the Thevenin voltage and resistance), you can replicate the experience without needing to know all the details of the complex cooking process.

So, suppose we do have a DC source, we do have a DC source and it is connected across 2 elements say R and R . So, we do have R and then R and suppose this is our output node, this may be say common node ground and then suppose this is the supply voltage V .

To find the Thevenin equivalent voltage, you first identify the open-circuit voltage at the output terminals where you want to connect the load. This is done by calculating the voltage drop across the resistors when no load is present. In the case of a simple circuit with a DC source, the Thevenin voltage (Vth) can be calculated using the voltage divider formula: Vth = V_CC * (R2 / (R1 + R2)). This voltage represents the maximum voltage available at the output terminals when the circuit is open.

Imagine you have a water tank (the voltage source) that supplies water to two different pipes (the resistors). The height of the water in the tank represents the supply voltage. When you only consider the pipe heights (the resistors), the Thevenin equivalent voltage is like finding out how much water pressure (voltage) can push through to the output when no other connections are made – essentially, how high up the water can go when it’s flowing freely.

Now, the moment you connect one load here of course the voltage it will not remain same as the Thevenin equivalent voltage. Depending on the strength of these two resistors who are trying to maintain this voltage close to V you may you will be getting a voltage which will be in between threshold voltage and of course, this ground.

When a load resistor (RL) is connected across the output terminals, it changes the voltage measured at those terminals because it draws current from the source. This loaded voltage (Vout) can be calculated using the Thevenin equivalent circuit. The voltage at the terminals will be less than the Thevenin equivalent voltage because of the voltage drop across the Thevenin equivalent resistance. The new voltage can be calculated using the formula: Vout = Vth * (RL / (Rth + RL)).

Think about this as connecting a new appliance to an electrical outlet. The outlet represents your Thevenin equivalent voltage source. Without any appliances plugged in, you get the maximum voltage available (like the Thevenin voltage). However, once you plug your appliance in (the load), the voltage might drop because the appliance uses some power (current), thus affecting the amount of voltage available at the outlet.

In fact, it can be extended for a signal also. Namely, instead of having a DC voltage here suppose you do have a signal source and say this signal source it is applied across say R and R. .

The concept of Thevenin's equivalent circuit is not limited to DC circuits; it can also be applied to AC circuits. The Thevenin equivalent voltage for AC signals is similar: you still identify the open-circuit voltage at the output, but you have to account for the impedance of circuit elements at different frequencies. The results from AC analysis can also be treated the same way. The AC Thevenin voltage and equivalent resistance help in analyzing circuits with alternating signals more straightforwardly.

Imagine tuning a radio to pick up a certain frequency. The radio represents the circuit components, and the selected frequency is the AC signal. The Thevenin equivalent would be like finding the best settings (voltage and resistance) that allow the radio to operate efficiently at that frequency, so you can enjoy clear audio without interference from other frequencies.

So, let us see what other possible situation you may have. Suppose you do have a voltage source and then you do have R and R and then you are feeding a signal at this node through different circuit.

Mixed situations occur when both DC and AC sources are present in the same circuit. In this case, the Thevenin equivalent circuit considers both sources for analysis. The DC voltage defines a baseline level, and the AC signal rides on top of this baseline. The two can interact, and this interaction must be managed carefully to ensure the circuit operates correctly. The key is to use capacitive or resistive components strategically to decouple the AC and DC effects.

This can be compared to a busy highway (your DC component) where cars (the AC signal) are constantly changing lanes. The highway has a steady flow of traffic, while individual cars may speed up or slow down as they change lanes. The overall traffic pattern (the mixed situation) needs to be managed so that cars can move smoothly without too much interference, demonstrating how AC and DC signals can coexist in circuit operation.

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