EE201 Lecture 21 P 1 Waveform Generation Use RL or RC circuit to obtain a specific waveform Response is controlled by a switch Recall general solution for RL or RC circuits with sources x t x x to x e t to Suppose two excitation levels are required to activate turn off or turn on a switch x t1 X1 e g turn on iL t1 3 A x t2 X2 e g turn off iL t2 1 A EE201 Lecture 21 P 2 The time required for circuit to go from one excitation level to the other is t2 t1 ln X1 x 21 1 X2 x This is the elapsed time formula Example Plot vc t for the circuit below when the switch is activated three times closed opened closed 6 k 12 u t V 3 k 0 5 mF v t C EE201 Lecture 21 P 3 Initially switch is open as shown and it closes when vc t equals 9 V Switch opens again when vc t equals 5 V vc 0 0 V General solution for RC circuit vC t vC vC to vC e t to t ta switch closes t tb switch opens t tc switch closes Step 1 Find waveform for 0 t ta when open vC 0 0 V vC 12 V RTH 6 k RTHC 3 s vC t 12 1 e t 3 V EE201 Lecture 21 P 4 How long is this solution valid Use elapsed time formula 21 1 0 12 ta 0 3 ln 9 12 4 16 sec Step 2 Find waveform for ta t tb when closed vC ta vC ta 9 V vC 4 V RTH 2 k RTHC 1 s vC t vC vC to vC e t to vC t 4 5e t ta 1 V How long to go from 9 V to 5 V Use elapsed time formula 21 1 9 4 tb ta 1 ln 1 61 sec 5 4 EE201 Lecture 21 P 5 Step 3 Find waveform for tb t tc when reopens vC tb vC tb 5 V vC 12 V RTH 6 k RTHC 3 s vC t vC vC to vC e t to vC t 12 7e t tb 3 V How long to go from 5 V to 9 V 5 12 tc tb 3 ln 2 54 sec 9 12 EE201 Lecture 21 P 6 Step 4 Plot solutions to obtain complete waveform vC t tc ta 9 6 5V tb 3 2 4 9V 6 8 t s Period time interval for waveform to repeat itself tc ta 4 15 sec Waveform frequency 1 4 15 s 0 24 Hz
View Full Document
Unlocking...