In Fig. 32-39 let the rectangular box on the left represent...

In Fig. 32-39 let the rectangular box on the left represent the (high-impedance) output of an audio amplifier, with $r=$ $1000 \Omega$. Let $R=10 \Omega$ represent the (low-impedance) coil of a loudspeaker. For maximum transfer of energy to the load $R$ we must have $R=r$, and that is not true in this FIGURE $32-39=$ case. However, a transformer can be $\quad$ Problem 37 . used to "transform" resistances, making them behave electrically as if they were larger or smaller than they actually are. Sketch the primary and secondary coils of a transformer that can be introduced between the amplifier and the speaker in Fig. $32-39$ to match the impedances. What must he the turns ratio?

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Key Concepts

Impedance Matching

Impedance matching is a concept in electronics where the impedance of the power source is made equal to the impedance of the load in order to maximize the transfer of power. This is particularly important in audio systems to ensure efficient energy transfer and to minimize signal reflection or loss.

Transformer Impedance Transformation

A transformer can be used to modify the impedance seen by the source by taking advantage of the square relationship between the turns ratio and impedance transformation. Specifically, the impedance seen on the primary side of the transformer is equal to the square of the turns ratio (primary to secondary) multiplied by the load impedance on the secondary side. This property allows a transformer to effectively transform impedances to achieve proper matching between components.

Turns Ratio Calculation

The turns ratio required to achieve impedance matching can be determined using the relation Z_primary = (N_primary/N_secondary)^2 * Z_secondary. To find the appropriate turns ratio, one can take the square root of the ratio of the source impedance to the load impedance. This ensures that the source 'sees' an impedance equal to its own, thereby maximizing power transfer.

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