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