Maximum Power Transfer Ideal Transformer

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SUMMARY

The discussion focuses on calculating the load impedance (ZL) for maximum average power transfer in an ideal transformer circuit. The correct calculation yields ZL = 12 + 8j, derived from ZL = 4(3 + 2j). The maximum power transfer is confirmed to be 1.5W, calculated using the formula P = (12)^2 / [(8)(12)]. Participants emphasize the importance of using the equivalent circuit referred to the primary side for accurate power calculations.

PREREQUISITES
  • Understanding of transformer equations, specifically n = N2/N1
  • Familiarity with complex impedance calculations in AC circuits
  • Knowledge of power calculations in electrical circuits, including real and reactive power
  • Ability to analyze equivalent circuits in transformer applications
NEXT STEPS
  • Study the concept of maximum power transfer theorem in electrical engineering
  • Learn about calculating power in AC circuits using complex power (S = VI*)
  • Explore the implications of reactive power in transformer circuits
  • Investigate the use of equivalent circuits in analyzing transformer performance
USEFUL FOR

Electrical engineering students, circuit designers, and professionals working with transformers and AC power systems will benefit from this discussion.

OmniNewton
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Homework Statement


upload_2016-12-13_10-26-7.png

Given the following circuit find the value of ZL for maximum average power transfer and find the maximum power.

Homework Equations


n = N2/N1
V2/V1 = N2/N1
I2/I1= N1/N2

The Attempt at a Solution


move ZL from the secondary coil to the primary coil using Zs* = ZL/n^2
ZL = 4(3+2j) = 12 +8j
P = (12)^2/ [(8)(12)] = 1.5W

I want to verify if this is the right method
 
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OmniNewton said:
ZL = 4(3+2j) = 12 +8j
Right.
OmniNewton said:
P = (12)^2/ [(8)(12)] = 1.5W
This is incorrect. Looking at the equivalent circuit referred to primary, which formula will you use for calculating power dissipated in the load?
 
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cnh1995 said:
Right.

This is incorrect. Looking at the equivalent circuit referred to primary, which formula will you use for calculating power dissipated in the load?

I see thank you for the response. When dealing with this problem would you determine the current I by dividing the given voltage by the sum the 2 impedances. Then we can say that S= I^2Z so P = the real component of S
 
OmniNewton said:
I see thank you for the response. When dealing with this problem would you determine the current I by dividing the given voltage by the sum the 2 impedances. Then we can say that S= I^2Z so P = the real component of S
Right.
Note that the power you get will be the real power since there is no reactive power in the circuit. So, S=P.
 
And this would be the maximum power?
 
OmniNewton said:
And this would be the maximum power?
Yes.
 
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Thank you sir!
 

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