Thevenin’s Theorem | Electronics

Thevenin’s Theorem

According to Thevenin's theorem any two terminal linear network containing linear impedances and one or more generators can be replaced with an equivalent circuit consisting of an equivalent impedance (Z_eq) in series with an equivalent source of e.m.f. (E_eq).
E_eq = e.m.f. between two terminals, when the external load is removed or when the circuit is open.
Z_eq = impedance at the output terminals, when all the sources of the e.m.f. are short circuited or replaced by their internal impedances.

Proof

Applying KVL in loop (1), E = I₁ (Z₁ + Z₃) - IZ₃
Applying KVL in loop (2), 0 = I (Z₃ + Z₂ + Z_L) - I₁Z₃⇒ I = [Z₃ / (Z₂ + Z₃ + Z_L)] I₁

Determination of E_eq

Applying KVL in loop (1)
E = I' (Z₁ + Z₃) ⇒ I' = E / (Z₁ + Z₃)
Open circuit voltage, E_eq = I'Z₃ ⇒ E_eq = E Z₃/(Z₁ + Z₃)

Determination of Z_eq

Z_eq = Z₂ + {Z₁Z₃ / (Z₁ + Z₃)}
Since E_eq = EZ₃/(Z₁ + Z₃) and I = [E {Z₃ / (Z₁ + Z₃)} / [Z_L + {Z₂ + Z₁Z₃ / (Z₁ + Z₃)}]
Therefore I = E_eq / (Z_L + Z_eq)

This is Thevenin's equivalent circuit.
By applying KVL in this loop we get
E_eq = I (Z_eq + Z_L) ⇒ I = E_eq / (Z_eq + Z_L)
Since the equations shown in red colour are same, hence Thevenin's theorem is varied.

To know more about Thevenin's theorem please click on the link https://youtu.be/zJQXHWm1Ifk

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