Topic: Electromagnetics
A transmission line with a characteristic impedance of 100 $\Omega$ is used to match a 50 $\Omega$ section to a 200 $\Omega$ section. If the matching is to be done both at 500 MHz and 1.2 GHz, the length of the transmission line can be approximately,
- A. 1.75 m
- B. 1.0 m
- C. 1.35 m
- D. 1.5 m
Answer: C. 1.35 m
Explanation: $Z_{1}=50~\Omega$, $Z_{2}=200~\Omega$. $Z_{0}=\sqrt{Z_{1}Z_{2}} = \sqrt{50 \times 200} = 100~\Omega$. Hence, quarter wave matching is suitable, and length will be odd multiples of $\lambda/4$.
At $f=500\text{ MHz}$, $\lambda = \frac{3\times 10^{8}}{5\times 10^{8}} = 0.6\text{ m}$. $\lambda/4 = 0.15\text{ m}$.
At $f=1.2\text{ GHz}$, $\lambda = \frac{3\times 10^{8}}{12\times 10^{8}} = 0.25\text{ m}$. $\lambda/4 = 0.0625\text{ m}$.
Checking multiples: $0.15 \times 9 = 1.35\text{ m}$ and $0.0625 \times 21 = 1.35\text{ m}$. Both match at 1.35 m.