For matching a circuit of output impedance 200 ohms with a load of 8 ohms, the turns ratio of the two winding of transformer should be

Concept:

Transformers are used for impedance matching applications. This is explained with the help of the following figure:

\(n=\frac{N_2}{N_1}\)= transformation ratio

\(\frac{N_1}{N_2}=\) Turns ratio

The load impedance reflected on the primary side is redrawn as shown:

For the load to match with the source resistance:

\(R_S=\frac{R_L}{n^2}\)

\(n^2=\frac{R_L}{R_S}\)

Calculation:

With R_L = 8 Ω, and R_S = 200 Ω, the transformation ratio will be:

\(n^2=\frac{8}{200}=\frac{1}{5}\)

\(n=\frac{N_2}{N_1}=\frac{1}{5}\)

The turns ratio will be:

\(\frac{N_1}{N_2}=5\)