Normalized input impedance of one quarter wavelength of transmission line terminated by load impedance ZL will be equal to Select one:a. (ZL / 2)b. YL = (1 / ZL) c. (ZL / 4)d. (YL / 4)
Question
Normalized input impedance of one quarter wavelength of transmission line terminated by load impedance ZL will be equal to Select one:a. (ZL / 2)b. YL = (1 / ZL) c. (ZL / 4)d. (YL / 4)
Solution
To find the normalized input impedance of a quarter wavelength transmission line terminated by a load impedance ZL, we can use the formula:
Zin = ZL * (Z0 + jZL * tan(beta * l)) / (ZL + jZ0 * tan(beta * l))
where Zin is the input impedance, Z0 is the characteristic impedance of the transmission line, beta is the propagation constant, and l is the length of the transmission line.
In this case, since we are dealing with a quarter wavelength transmission line, the length l will be equal to lambda/4, where lambda is the wavelength.
Substituting this value into the formula, we get:
Zin = ZL * (Z0 + jZL * tan(beta * lambda/4)) / (ZL + jZ0 * tan(beta * lambda/4))
Simplifying further, we can rewrite the formula as:
Zin = ZL * (1 + j * tan(beta * lambda/4)) / (1 + j * ZL/Z0 * tan(beta * lambda/4))
Now, to find the normalized input impedance, we divide both the numerator and denominator by Z0:
Zin_norm = (ZL/Z0) * (1 + j * tan(beta * lambda/4)) / (1 + j * ZL/Z0 * tan(beta * lambda/4))
Therefore, the correct answer is option d. (YL / 4).
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