ECE 329 Tutorial 19 (2019/12/02)

Problem 1 (Warm-Up): Locate on a Smith Chart the following load impedances terminating a Transmission Line with characteristic impedance of 푍0 = 50 Ω:

(a) 푍퐿 = 200 Ω

(b) 푍퐿 = 25푗 Ω

(c) 푍퐿 = 50 + 50푗 Ω

(d) 푍퐿 = 25 − 200푗 Ω

Problem 2 (Smith Chart Reading):

A lossless Transmission line of length 0.690λ with characteristic impedance of 푍0 = 75 Ω is terminated by a load of 푍퐿 = 15 + 67푗 Ω. Use the Smith Chart to find:

(a) The reflection coefficient at load Γ퐿 (b) The Voltage Standing Wave Ratio (VSWR)

(c) Input impedance 푍푖푛

Problem 3 (One More Smith Chart Reading):

A lossless Transmission line of length 0.269λ with characteristic impedance of 푍0 = 100 Ω is terminated by a load of 푍퐿 = 60 + 40푗 Ω. Use the Smith Chart to find:

(a) The reflection coefficient at load Γ퐿 (b) The Voltage Standing Wave Ratio (VSWR)

(c) Input impedance 푍푖푛

ECE 329 Tutorial 20 (2019/12/05)

Input Impedance of Lossless Transmission Line:

푍퐿 + 푗푍0푡푎푛(훽퐿) 푍푖푛(퐿표푠푠푙푒푠푠) = 푍0 푍0 + 푗푍퐿푡푎푛(훽퐿) Where 퐿 is the length of Transmission Line, and 훽 the propagation wave number along the line.

Problem 1 (Warm-Up):

On a Transmission line of characteristic impedance 푍0 = 50 Ω, the VSWR is measured as 3.4. The voltage maximum is located 0.079λ away from the load. Determine the load, on the Smith Chart.

Problem 2 (Load Impedance Matching using Shorted Shunt-Stub):

We would like to match a load with impedance of 푍퐿 = 170 Ω to the Transmission line with characteristic impedance of 푍0 = 50 Ω: λ (a) If we use a quarter-wave transformer (replacing length of original Transmission line 4 segment connected with load terminal with another new segment of Transmission line with different characteristic impedance), determine the characteristic impedance of the new segment of Transmission line. (b) If we use shorted shunt-stub connected somewhere on the Transmission line to match the load impedance, what through-line length (the distance between the load terminal and the location where the shorted shunt-stub is connected) and stub length are required? (There are two solutions) ---> Use Smith Chart

Problem 3 (Find the Solution requiring Minimum Length):

A load with impedance 푍퐿 = 25 + 90푗 Ω is to be matched to a Transmission line with characteristic impedance of 푍0 = 50 Ω using a shorted shunt-stub network. Find the solution that minimizes the length of the shorted stub, and also find the corresponding through-line length. (Use Smith Chart).