1. Show that it is impossible to construct a three-port network that is lossless, reciprocal, and matched at all ports. Is it possible to construct a nonreciprocal three-port network that is lossless and matched at all ports?

1- A lossless transmission line of characteristic impedance 50 ohm is to be matched to a load impedance of 100+j47.5 ohm using short circuited stub tuner. Find the required lengths using Smith Chart. Attach your Smith Chart! 2- Consider the transistor amplifier amplifier at 3 GHz with s-parameters shown below. Design input and output matching network for max gain at 3 GHz. Zo-50 ohms. The output matching network must be LC based (give L and C values in ohms). The input matching network will be shorted shunt stub (give the lengths in wavelengths). Attach two Smith Charts for input and output matching. S = 0.82– 80°, S, = 10.0Z – 20°, S,, = 0, S„ = 0.5 – 40° MNL 502 MNs 3- Design a microwave transistor oscillator at 3 GHz. The MOSFET has S-parameters at 3.0 GHz given by (Z, =502) S,=0.77Z – 62°, S, =5.4/128.916°, S, =0.087Z44°, S„=0.56 – 89.319°. a) plot source and load stability circles on the Smith Chart and choose r, to sustain oscillation. b) using the same Smith Chart, design the…

Problem 2 A lossless transmission line has a characteristic impedance of 50 2. A power supply with a generator resistance of 50 2 is connected to the beginning of the line, supplying an AC voltage of V₂ (t) = 10 cos(at +) volts to the line. This transmission line is ended with a matched load of 50 Q. (1) What is the voltage reflection coefficient at the load? (2) What is the impedance of this line when viewed at 1/3 wavelength from the load resistor (z = -1/3 2)? (3) What is the average power delivered to the load?

For problems 15 and 17 A transmission line has the following per unit length parameters. R' = 0 Q/m, L' =0.4µH /m, G' = 0S /m,C' =150 pF / m Problem [15] Is this a lossless or a lossy transmission line? Problem [16] Calculate the characteristic impedance of this line at 500 MHz Problem [17] Calculate the wavelength on this line at 500 MHz