ECE 3025 Homework 3: Charged Lines and Short Pulses - Voltage Analysis, Assignments of Guiding Electromagnetic Systems

Download ECE 3025 Homework 3: Charged Lines and Short Pulses - Voltage Analysis and more Assignments Guiding Electromagnetic Systems in PDF only on Docsity! ECE 3025 Homework 3: Charged Lines and Short Pulses 1. As a practical joke, you charge up a long, skinny parallel-plate capacitor to 200 V and leave it in your friend’s sock drawer. While charged, your friend begins rummaging for socks and touches the end of the capacitor with his 100Ω finger which happens to be perfectly matched to the transmission line model of these parallel plates: 50 cm 0.5 mF Capacitor T-line Characteristics: C = 1 mF/m, L = 10 H/m finger How long does the discharge last? Draw sketches of the voltage across the length of the capac- itor (as a function of position) for the following moments in time: t = 0, t = T2 , t = T , t = 3T 2 , and t = 2T . 2. Switching Network 1: The circuit below is switched according to these sequential switching states: • State 0: Both switches are open and all lines are uncharged. • State 1: Immediately after switch A is closed. • State 2: Switch A has been closed for a while. • State 3: Immediately after switch B is closed. • State 4: Switch B has been closed for a while. • State 5: Immediately after switch A is opened. • State 6: Switch A has been open for a while. + - 24 V Z0 Z0 Z0 Z0 Z0 Z0 A B + + ++ + - - -- - VX VY VAV0 V + V - VB Fill out the following table according to these switching states. Note that V + is measured at the generator side and V − is measured at the load side: V0 V + V − VA VB VX VY State 0 0 0 0 0 0 0 0 State 1 State 2 State 3 State 4 State 5 State 6 0 0 0 0 0 0 0 3. Switching Network 2: The circuit below represents a high-speed digital interconnect that is switched according to the following states: • State 0: Both switches are open and both lines are uncharged. • State 1: Immediately after switch A is closed. • State 2: Switch A has been closed for a while. • State 3: Immediately after switch B is closed. • State 4: Switch B has been closed for a while. + - 20 V Z0 Z0 Z0Z0 Z0 4Z0 A B C ++ + - - - VMV1 V1 + V2 V2 - 2