Thevenin’s Theorem
There are times when it is advantageous to isolate a part of the circuit to simplify the analysis of the isolated part of the circuit. Rather than write loop or node equations for the complete circuit, and solving them simultaneously, Thevenin’s theorem enables us to isolate the part of the circuit we are interested in. We then replace the remaining circuit with a simple series equivalent circuit, thus Thevenin’s theorem simplifies the analysis.
There are two theorems that do similar functions. The Thevenin theorem just described
is the first, and the second is called Norton’s theorem. Thevenin’s theorem is used when
the input source is a voltage source, and Norton’s theorem is used when the input source
is a current source. Norton’s theorem is rarely used, so its explanation is left for the reader to dig out of a textbook if it is ever required.The rules for Thevenin’s theorem start with the component or part of the circuit being replaced.Referring to Figure 2–7, look back into the terminals (left from C and R3 toward
point XX in the figure) of the circuit being replaced. Calculate the no load voltage (VTH)as seen from these terminals (use the voltage divider rule).
Look into the terminals of the circuit being replaced, short independent voltage sources,and calculate the impedance between these terminals. The final step is to substitute theThevenin equivalent circuit for the part you wanted to replace as shown in Figure 2–8.
The Thevenin equivalent circuit is a simple series circuit, thus further calculations are simplified.
The simplification of circuit calculations is often sufficient reason to use Thevenin’s theorem because it eliminates the need for solving several simultaneous equations. The detailed information about what happens in the circuit that was replaced is not available when using Thevenin’s theorem, but that is no consequence because you had no interest in it.
As an example of Thevenin’s theorem, let’s calculate the output voltage (VOUT) shown in Figure 2–9A. The first step is to stand on the terminals X–Y with your back to the output circuit, and calculate the open circuit voltage seen (VTH). This is a perfect opportunity to use the voltage divider rule to obtain Equation 2–13.
Still standing on the terminals X-Y, step two is to calculate the impedance seen looking into these terminals (short the voltage sources). The Thevenin impedance is the parallel impedance of R1 and R2 as calculated in Equation 2–14. Now get off the terminals X-Y before you damage them with your big feet. Step three replaces the circuit to the left of X-Y with the Thevenin equivalent circuit VTH and RTH.
The final step is to calculate the output voltage. Notice the voltage divider rule is used again. Equation 2–15 describes the output voltage, and it comes out naturally in the form of a series of voltage dividers, which makes sense. That’s another advantage of the voltage divider rule; the answers normally come out in a recognizable form rather than a jumble of coefficients and parameters.
There are times when it is advantageous to isolate a part of the circuit to simplify the analysis of the isolated part of the circuit. Rather than write loop or node equations for the complete circuit, and solving them simultaneously, Thevenin’s theorem enables us to isolate the part of the circuit we are interested in. We then replace the remaining circuit with a simple series equivalent circuit, thus Thevenin’s theorem simplifies the analysis.
There are two theorems that do similar functions. The Thevenin theorem just described
is the first, and the second is called Norton’s theorem. Thevenin’s theorem is used when
the input source is a voltage source, and Norton’s theorem is used when the input source
is a current source. Norton’s theorem is rarely used, so its explanation is left for the reader to dig out of a textbook if it is ever required.The rules for Thevenin’s theorem start with the component or part of the circuit being replaced.Referring to Figure 2–7, look back into the terminals (left from C and R3 toward
point XX in the figure) of the circuit being replaced. Calculate the no load voltage (VTH)as seen from these terminals (use the voltage divider rule).
Look into the terminals of the circuit being replaced, short independent voltage sources,and calculate the impedance between these terminals. The final step is to substitute theThevenin equivalent circuit for the part you wanted to replace as shown in Figure 2–8.
The Thevenin equivalent circuit is a simple series circuit, thus further calculations are simplified.
The simplification of circuit calculations is often sufficient reason to use Thevenin’s theorem because it eliminates the need for solving several simultaneous equations. The detailed information about what happens in the circuit that was replaced is not available when using Thevenin’s theorem, but that is no consequence because you had no interest in it.
As an example of Thevenin’s theorem, let’s calculate the output voltage (VOUT) shown in Figure 2–9A. The first step is to stand on the terminals X–Y with your back to the output circuit, and calculate the open circuit voltage seen (VTH). This is a perfect opportunity to use the voltage divider rule to obtain Equation 2–13.
Still standing on the terminals X-Y, step two is to calculate the impedance seen looking into these terminals (short the voltage sources). The Thevenin impedance is the parallel impedance of R1 and R2 as calculated in Equation 2–14. Now get off the terminals X-Y before you damage them with your big feet. Step three replaces the circuit to the left of X-Y with the Thevenin equivalent circuit VTH and RTH.
The final step is to calculate the output voltage. Notice the voltage divider rule is used again. Equation 2–15 describes the output voltage, and it comes out naturally in the form of a series of voltage dividers, which makes sense. That’s another advantage of the voltage divider rule; the answers normally come out in a recognizable form rather than a jumble of coefficients and parameters.
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