Maximum Power Transfer By An Ideal Transformer Through Impedance Relection
TECTechnics Classroom   TECTechnics Overview

Maximum Power Transfer By An Ideal Transformer Through Impedance Relection

Given the ideal transformer of Figure 7.14, determine the turns ratio N =1/n that will provide maximum power transfer to the load.

The strings: S7P3A32 (force-push).

The math:
Pj Problem of Interest is of type force (push).

Equations: N = n2/n1
V2 = NV1
I2 = I1/N

Where N = turns ratio; n1 turns in primary coil; n2 turns in secondary coil
V2 = output voltage; V1 = input voltage
I2 = output current; I1 = input current

Impedance matching equation: ZL = conjugate of Zs
Impedance reflection equation: ZL/N2 = conjugate of Zs
.
Maximum power transfer occurs when impedance matching or impedance reflection equation holds.

There is no complex parts of the load and internal resistance of the ideal transformer of figure 7.14
So, ZL = RL
And conjugate of Zs = Rs.
So, by the impedance reflection equation,
Maximum power transfer occurs when RL = N2Rs
S0, 8 = 1800(1/n)2
So, n2 = 1800/8 = 225
So, n = (225)1/2 = 15
So, the turns ratio that will provide maximum power to the load = 1/15.

Blessed are they that have not seen, and yet have believed. John 20:29