Question

Consider a step-down transformer with 15 turns in the primary and 6 turns in the secondary windings. Calculate the input impedance of this transformer loaded to an 8 Ω resistor, assuming that series resistances of the windings are negligible.

Answer 1

Input impedance of this transformer is 50 ohms.

Step-by-step explanation:

Given that,

Number of turns in the primary coil,
`N_p=15`

Number of turns in the secondary coil,
`N_s=6`

Output impedance of the transformer,
`V_o=8\ \Omega`

The number of turns and the impedance ratio in the step down transformer is given by :

`(15)/(6)=\sqrt{(Z_p)/(Z_s)}\\\\(15)/(6)=\sqrt{(Z_p)/(8)}\\\\Z_p=50\ \Omega`

So, the input impedance of this transformer is 50 ohms. Hence, this is the required solution.