Q8Electromagnetics Waves
Question
8. Write the condition of (i) free space and (ii) lossy medium.
Answer
Two common impedance matching techniques for transmission lines are single-stub matching and quarter-wave transformer matching (double-stub matching and lumped L-network matching are also widely used).
Single-stub matching: a short-circuited (or open-circuited) length of transmission line (a 'stub') is connected in shunt (parallel) with the main line at a carefully chosen distance from the load; the stub's purely reactive input impedance is adjusted, via its length, to exactly cancel the reactive part of the line's admittance at the point of connection, leaving a purely resistive (matched) admittance equal to 1/Z0 looking toward the generator. Both the stub position and its length are determined graphically using a Smith chart.
Quarter-wave transformer matching: a section of transmission line exactly one-quarter wavelength long, with characteristic impedance Z1 = √(Z0ZL), is inserted between the main line (Z0) and a real load impedance ZL, exploiting the impedance-inverting property of a quarter-wave line to transform the load to exactly Z0 at the input, achieving a perfect match at the design frequency (though this technique works simply only for real ZL, or requires an additional line section to first present a real impedance for complex loads).