Example 10.6: Impedance matching

Question: An audio amplifier with an internal resistance of $2.0\,{\rm k}\Omega$ is used to drive a loudspeaker with a resistance of $R=5.0\,\Omega$. A transformer is used to connect the amplifier to the loudspeaker. What is the appropriate turns-ratio of the transformer for optimal power transfer between the amplifier and the loudspeaker?
 
Answer: We require the transformer to convert the actual resistance $R$ of the loudspeaker into an effective resistance $R'$ which matches the internal resistance $2.0\,{\rm k}\Omega$ of the amplifier. Thus, from Eq. (304),

$$\frac{N_1}{N_2} = \sqrt{\frac{R'}{R} } = \sqrt{\frac{2\times 10^3}{5}} = 20.$$