Two lossless transmission lines having different characteristic impedances are to be joined end to end. The impedances are Z₀₁ = 100 and Z₀₃ = 25 Ω. The operating frequency is 1 GHz.

(a) Find the required characteristic impedance, Z₀₂, of a quarter-wave section to be inserted between the two, which will impedance-match the joint, thus allowing total power transmission through the three lines.

(b) The capacitance per unit length of the intermediate line is found to be 100 pF/m. Find the shortest length in meters of this line that is needed to satisfy the impedance-matching condition.

(c) With the three-segment setup as found in parts (a) and (b), the frequency is now doubled to 2 GHz. Find the input impedance at the line-1-to-line-2 junction, seen by waves incident from line 1.

(d) Under the conditions of part (c), and with power incident from line 1, evaluate the standing wave ratio that will be measured in line 1, and the fraction of the incident power from line 1 that is reflected and propagates back to the line 1 input.