Topic: Microwave Engineering
A lossless T-junction two way power divider has a source impedance, input transmission line impedance and output port load impedance of 50Ω. Find the output characterization impedances so that the input power is divided in a 2:1 ratio.
- A. $Z_1 = 150\Omega$, $Z_2 = 75\Omega$
- B. $Z_1 = 50\Omega$, $Z_2 = 100\Omega$
- C. $Z_1 = 60\Omega$, $Z_2 = 120\Omega$
- D. $Z_1 = 30\Omega$, $Z_2 = 60\Omega$
Answer: A. $Z_1 = 150\Omega$, $Z_2 = 75\Omega$
Explanation: Since the divider is lossless, $P_1^+ = P_2^- + P_3^-$. The division ratio is $\alpha = P_2^-/P_3^- = Z_{03}/Z_{02} = 2/1$. For matching at port 1, $Z_{01} = \frac{Z_{02}Z_{03}}{Z_{02}+Z_{03}}$. Thus, $Z_{02} = Z_{01}(1 + 1/\alpha) = 50(1 + 1/2) = 75 \Omega$ and $Z_{03} = Z_{01}(1 + \alpha) = 50(1 + 2) = 150 \Omega$.