ECE166 hwk1-Fall 2010-new

ECE166 hwk1-Fall 2010-new - ECE 166 Microwave Circuits and...

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1 ECE 166 – Microwave Circuits and Systems Homework #1 – Due Thursday, October 7, 2010 (This problem is to show you how the voltage and impedance change along the line. You need a plotting routine, MATLAB for example,. to plot the voltages vs. the z-axis.). Problem 1: Consider a load with =0.5(-80deg) and f = 2.5 GHz in an FR-4 medium with eff =4.0 and Z 0 = 50 . The forward wave is V o + =1 V(rms) defined at the load (z=0) . a) Determine the wavelength of the transmission medium. b) Determine the load impedance in Ohms. c) Determine the total voltage at the load (complex number). This is V load and is not V o + . d) Find the location of the voltage and current maximum, and the voltage and current minimum on the line. Determine their amplitudes. Calculate the VSWR. Use the Crank diagram for your solution. e) Calculate the forward power (P+), the backward power (P-) and the power dissipated in the load. f) Determine the voltage, current and impedance at z = 0, -0.05 , -0.1 , -0.15 , -0.2 , -0.25 , -0.3 from the load. You can use the impedance equation on page 5. See how much the impedance changes vs. position! g) Plot the voltage and current magnitudes for two wavelengths from the load. Assume a lossless line. h) Plot the voltage and current magnitudes for two wavelengths from the load assuming a line loss of 0.3 dB/cm ( you will need to convert this to Np/cm to use in the exponential ). For |V 0 +
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