Topic: Electromagnetics
What is the turns ratio of the transformer needed to match 1 k$\Omega$ source resistance to a 50 $\Omega$ load?
- A. 4.47:1
- B. 400:1
- C. 20:1
- D. 0.05:1
Answer: A. 4.47:1
Explanation: For a transformer matching a load, the impedance relationship is $Z_L' = n² Z_L$.
Given $Z_L = 50~\Omega$ and required $Z_L' = 1~\text{k}\Omega = 1000~\Omega$.
$n² = \frac{Z_L'}{Z_L} = \frac{1000}{50} = 20$.
$n = \sqrt{20} \approx 4.47$.
Thus, the required turns ratio is 4.47:1.