Final answer:
A low input resistance and high output resistance amplifier can function as a current buffer. For the given 500 Ω amplifier and 8 Ω speaker scenario, use a transformer with a turns ratio of about 7.9 to match the impedances for effective power transfer.
Step-by-step explanation:
An amplifier which needs a low input resistance and a high output resistance is typically a current buffer or current amplifier. In the scenario where an audio amplifier with an impedance of 500 Ω needs to drive a speaker with much lower impedance, a transformer must be used to match the impedances.
To calculate the appropriate turns ratio of this transformer, the square root of the impedance ratio is used:
- Zamp / Zspeaker = 500 Ω / 8 Ω = 62.5
- Turns Ratio (n) = √(Zamp / Zspeaker) = √62.5
The square root of 62.5 gives us a turns ratio of around 7.9. This means the transformer should have 7.9 times more turns on the primary side (connected to the amplifier) than on the secondary side (connected to the speaker) to effectively transfer power from the 500 Ω amplifier to the 8 Ω speaker.