1.

7.3 A directional coupler has the scattering matrix given below. Find the return loss, coupling factor, directivity, and insertion loss. Assume that the ports are terminated in matched loads.

2. For clarity, first write the S-parameters of a single coupler and then solve for the case when 2 couplers are cascaded.

7.4 Two identical 90° couplers with C= 8.34 dB are connected as shown below. Find the resulting phase and amplitudes at ports 2' and 3', relative to port 1.

3.

7.8 Design a three-port resistive divider for an equal power split and a 100 Ω system impedance. If port 3 is matched, calculate the change in output power at port 3 (in dB) when port 2 is connected first to a matched load, and then to a load having a mismatch of Γ = 0.3. See the figure below.

4. You can use the equations 7.37 (a) – (c) from pozar.

7.10 Design a Wilkinson power divider with a power division ratio of P3/P2 = 1/3 and a source impedance of 50 Ω.

5. Hint: Your need to use the even and odd-mode analysis like always. The line of symmetry will be a vertical line passing from port 1 to port 3.

7.31 Find the scattering parameters for the four-port Bagley polygon power divider shown below.