Understanding Thevenin's Theorem: Equivalent Circuits

June 28, 2019 Cadence PCB Solutions

Coiled and off light bulb versus straight, lit lightbulb on turquois background

 

During my initial studies of electronic theory, one of my instructors talked about the K.I.S.S. principle. My mind instantly jumped to, “Wow—this is really interesting!” As most of you already know, however, the K.I.S.S. method has nothing to do with romantic thoughts.

Instead, Keep It Simple Stupid (K.I.S.S) refers to our need as troubleshooters and designers to simplify highly complex concepts. At that time in my career, simplifying anything seemed unlikely. Yet, the idea continues to resonate with me. If we keep things simple, others will find the design or product useful.

Quoting Thevenin’s Theorem at Social Gatherings Helps Gain Instant Popularity

The principle of keeping things simple gains traction through circuit analysis theorems such as Kirchoff’s Circuit Laws, Mesh Analysis, and Thevenin’s Theorem. Let’s take a look at Thevenin’s Theorem as we contemplate “keeping things simple.”

“Any two-terminal network containing voltage or current sources can be replaced by an equivalent circuit consisting of a voltage equal to the open-circuit voltage of the original circuit in series with the resistance measured back into the original circuit.”

(M.L. Thevenin 1883)

Thevenin’s Theorem tells us that one single voltage in series with a resistance connected across a load can replace any linear circuit that consists of several voltages and resistances. In this context, we are speaking about an electrical equivalent. A single voltage source and a single resistance in series with the source serves as the electrical equivalent to networks of voltage sources, current sources, and resistors.

Thevenin’s equivalent considers everything in the circuit with the exception of the load. All the voltage sources seen in the linear circuit become one single equivalent voltage source. All the resistors become a single equivalent resistor.

Note that Thevenin’s Theorem applies to linear circuits. In this type of circuit, resistance, capacitance, inductance, and reactance remain constant. None of the circuit parameters change with respect to voltage or current. If we inject a sinusoidal waveform at the input of a linear circuit, the same waveform with either a smaller or larger amplitude at the output. A true linear circuit will have an output waveform that has the same frequency as the input waveform. As a result, a graph of the output amplitude versus the input amplitude of a linear circuit will appear as a straight line.

Applications and Examples of Thevenin’s Theorem

Complicated system’s analysis can be made simpler by utilizing properly Thevenin’s theorem for series resistances and voltage to replace networks with their Thevenin’s equivalent.

  • Thevenin’s Theorem in (DC) Power Systems: With load resistors that are frequently changing and incredibly frequent circuit re-calculation is necessary to determine the values of load resistances, voltage and current, Thevenin’s theorem can utilize the system by applying Thevenin’s equivalent circuits and temporarily compose the circuit of a singular voltage sources and series resistance.

Placing Thevenin's Theory into Practice

Let’s think about everything that Thevenin says with his theory. One branch of the work as the load while the remaining part serves as a two terminal network that supplies the load. When we apply Thevenin’s Theorem, we:

  • Remove or imagine that we remove the load

  • Identify the terminals for polarity identification

  • Calculate the open circuit voltage

  • Calculate the Thevenin resistance as it looks back into the network

  • Remove the independent sources but leave the internal resistances in place

  • Draw an equivalent circuit

  • Reconnect the load and determine the load current

When we examine the Thevenin equivalent circuit shown in figure one, we see a Thevenin-equivalent open circuit voltage (VTH). In addition, a Thevenin-equivalent source resistance (RTH) measures across A and B and looks in at the source. The phrase “looks in” tells us to view from the perspective of the current at the source. Applying a known voltage to the two nodes causes an amount of current to flow between the nodes through a slight impedance. As a result, we look in and see the amount of current that flows with the linear network independent sources deactivated.

 

original linear network and removed load and redraw circuits

 

When we remove the load and redraw the circuit, VOC equals 10 volts plus the rise across the 10 ohm resistor. We can use a loop equation to find that VOC equals 16.67 volts.

5ĺ + 10ĺ = 20 – 10 = 10

ĺ = 10/15 = 0.667 A

VOC = 10 + ĺ(10) = 10 + 6.67 = 16.67 V

Thevenin's equivalent voltage circuit

 

Now, we can solve for the RTH value.

 

RTH = (5)ǁ(10) = 3.33Ω

 

When we move to the final equivalent circuit, we can reinsert the load resistance and find that the load current equals 0.714 A or:

thevenin's equivalent circuit diagram and equation

Looking at the equivalent circuit, we calculate the output voltage (VOC) with an open circuit condition symbolized by the dotted lines. In the open circuit condition, the lack of a load resistor (RL) results in infinite resistance or the Thevenin-equivalent voltage (VTH). Short circuiting the output terminals gives us the output current (IAB). The short circuit condition gives us a value of zero for the load resistance.

We can use Thevenin’s Theorem to analyze power systems that varying values of load resistance. In addition, we use the Theorem to analyze single frequency AC circuits that have impedance values rather than resistance values.

Thevenin Parallel Termination in PCB Design

When you work with high speed PCB layouts, any mismatched impedance causes signals to reflect along the traces. In turn, the reflection causes ringing at the load receiver that reduces dynamic range and results in false triggering. You can eliminate reflections by matching the impedance of the source with the impedance of the trace and with the impedance of the load.

To accomplish impedance matching, you can use a Thevenin voltage divider. The Thevenin resistance (RTH) splits between R1 and R2 and equals the line impedance (ZO).

Circuit diagram of thevenin resistance and impedance

 

Although PSpice cannot directly calculate a Thevenin equivalent of a circuit, PSpice simulations capabilities assist with the rapid calculation by finding the open circuit voltage (VOC) and the short circuit current values (ISC). After building your circuit in PSpice, you can simulate a short circuit with a small resistance value and then replace the short circuit value with a larger value to obtain VOC.

Working through circuit analysis can be a bear to wrestle. When you’re thinking through what tools to utilize working through your circuit needs, though, you’ll find no better than those available within Cadence’s suite. OrCAD’s PSpice is capable of significant modeling and simulation while also boasting an over 34,000 model library.

If you’re looking to learn more about how Cadence has the solution for you, talk to us and our team of experts.

About the Author

Cadence PCB solutions is a complete front to back design tool to enable fast and efficient product creation. Cadence enables users accurately shorten design cycles to hand off to manufacturing through modern, IPC-2581 industry standard.

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