Normalized input impedance of one quarter wavelength of transmission line terminated by load impedance ZL will be equal to Select one:a. (ZL / 4)b. YL = (1 / ZL) c. (YL / 4)d. (ZL / 2)
Question
Normalized input impedance of one quarter wavelength of transmission line terminated by load impedance ZL will be equal to Select one:a. (ZL / 4)b. YL = (1 / ZL) c. (YL / 4)d. (ZL / 2)
Solution
To find the normalized input impedance of a quarter wavelength transmission line terminated by load impedance ZL, we can follow these steps:
Step 1: Calculate the characteristic impedance (Z0) of the transmission line. This can be done using the formula Z0 = sqrt(Zin * ZL), where Zin is the input impedance of the transmission line and ZL is the load impedance.
Step 2: Determine the normalized load impedance (ZL') by dividing the load impedance (ZL) by the characteristic impedance (Z0). This can be expressed as ZL' = ZL / Z0.
Step 3: Calculate the normalized input impedance (Zin') by using the formula Zin' = (ZL' + jtan(beta * l)) / (1 + jZL'tan(beta * l)), where beta is the propagation constant and l is the length of the transmission line.
Step 4: Simplify the expression for Zin' by substituting the value of ZL' from step 2. This will give us the final expression for the normalized input impedance.
Therefore, the correct answer is not provided in the options given.
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