Week Ten: "Thevenin & Norton's Theorem"

What is Thevenin & Norton's Theorem?

"Thevenin's Theorem"


         It often occurs in practice that a particular element in a circuit is variable (usually called the load) while other elements are fixed. As a typical example, a household outlet terminal may be connected to different appliances constituting a variable load. Each time the variable element is changed, the entire circuit has to be analyzed all over again. To avoid this problem, Thevenin’s theorem provides a technique by which the fixed part of the circuit is replaced by an equivalent circuit.


         Thevenin’s theorem states that a linear two-terminal circuit can be replaced by an equivalent circuit consisting of a voltage source VTh in series with a resistor RTh, where VTh is the open-circuit voltage at the terminals and RTh is the input or equivalent resistance at the terminals when the independent sources are turned off.

CASE 1:

         If the network has no dependent sources, we turn off all independent sources. RTh is the input resistance of the network looking between terminals a and b, as shown below:

Example:

"Norton's Theorem"

         In 1926, about 43 years after Thevenin published his theorem, E. L. Norton, an American engineer at Bell Telephone Laboratories, proposed a similar theorem.

         Norton’s theorem states that a linear two-terminal circuit can be replaced by an equivalent circuit consisting of a current source In in parallel with a resistor Rn, where In is the short-circuit current through the terminals and Rn is the input or equivalent resistance at the terminals when the independent sources are turned off.



         The proof of Norton’s theorem will be given in the next section. For now, we are mainly concerned with how to get Rn and In . We find Rn in the same way we find Rth. In fact, from what we know about source transformation, the Thevenin and Norton resistances are equal; that is,

Rn = Rth

Thus,

In = Isc

          Dependent and independent sources are treated the

same way as in Thevenin’s theorem. Finding Norton

current In . Observe the close relationship between Norton’s and Thevenin’s theorems: Rn = Rth, and:

Example:

Some Learnings:

1. If Rth takes a negative value. In this case, the negative resistance (v = −iR) implies that the circuit is supplying power.
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2. Thevenin’s theorem is very important in circuit analysis. It helps simplify a circuit.
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3. By Thevenin's theorem a large circuit may be replaced by a single independent voltage source and a single resistor. This replacement technique is very powerful in circuit design.
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4. If there is no independent sources in a circuit, we can conclude that Vth is equal to zero.
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5. Thevenin's Theorem & Norton's Theorem are related to each other.
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6. When getting for Rth or Rn, we turn off the voltage sources by replacing an open circuit and current sources by closed circuit. Then we replace an open circuit from terminal a to b.
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7. To find the Norton current In, we replace a short-circuit flowing from terminal a to b.

Videos:
For more information, you can watch the videos below:

(For Thevenin's Theorem)

(For Norton's Theorem)

That's all. Thank You for visiting my blog.

GOD Bless! :)

By:

AYALA, ARNY  S.   BSECE -3

ECE 311

Professor:

ENGR. JAY S. VILLAN, MEP - EE