Why Doesn't My Thevenin Equivalent Circuit Match the Book?

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Dhruv
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Homework Statement


Q. I have to write an equivalent circuit for the transformer coupled RLC load.My answer is not matching with that of book . I am uploading my work and the answer given in book.

Homework Equations


It is an N:1 ideal transformer.

The Attempt at a Solution

 
Attachments
  • Textbook figure 4-3-5 showing a cavity coupled to a generator: (a) coupling circuit with generator V_g, impedance Z_g, L_1 and an N:1 ideal transformer feeding a parallel RLC cavity; (b) equivalent circuit with N^2 Z_g, N^2 L_1, a voltage source N V_g, and parallel R, L, C.
    image.jpg
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  • Handwritten notes on lined paper deriving the Thevenin voltage of a transformer-coupled load: an N:1 ideal transformer with source Vg and Zg, and the open-circuit condition I2 = 0 giving V1 = Vg and V2 = Vg/N.
    image.jpg
    47.7 KB · Views: 478
  • Handwritten derivation on lined notebook paper: a transformer circuit diagram with Loop 1 containing Zg and jXL and Loop 2 with a current source I2, then equations I2 = -I N, I1 = -I2/N, I1(Zg + jXL) + V1 = 0, V1 = -I1(Zg + jXL), and V2 = V1/N.
    image.jpg
    44.1 KB · Views: 447
  • Handwritten derivation of the Thevenin equivalent for a transformer-coupled load: V2 = -I1(Zg+jXL)/N, RTh = V2/I2 leading to RTh = (Zg+jXL)/N^2, with a series circuit below showing source Vg/N, impedance (Zg+jXL)/N^2, resistor R, inductor L and capacitor C.
    image.jpg
    42.6 KB · Views: 429
Last edited:

Discussion

I didn't check your work through, but it's probably just due to an error in your book. You'd want a step-up (1:N) transformer to give a high-voltage source for the cavity.
 

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