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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 at both 429 MHz and 1 GHz, the length of the transmission line can be approximately

1. 82.5 cm
2. 1.05 m
3. 1.58 m
4. 1.75 m

Correct answer: 1.58 m

Solution

A transmission line used as an impedance transformer must have an electrical length that produces the required transformation, and to work at two frequencies the length must satisfy the same condition modulo half-wavelength periodicity at both frequencies. The approximate length that satisfies the dual-frequency matching condition is 1.58 m.

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