Download 1st Order Transients

EE 2260 Lecture 6
1st Order Transients
Reading: 7.5 – 7.6
HW #6: AP: 7.7, 7.8, 7.10
7.5 Sequential Switching
Example 7.11
Solution.
a) iL (0  )  6 A (use source transformation or find Vth and Rth while treating 3 ohm as a
load)
Equivalent resistance = 9||18 = 6 
Time constant = (150 / 6)  103  25 ms
b) At t = 35 ms,
Time constant = (150 / 9)  10 3  16.67 ms
1/τ = 59.99 ms-1 = 60 ms-1
c) To find the energy across 18 ohm resistor, we need to know either the voltage across it
or current through it.
[ wind 
1 2
Li ]
2
Example 7.12
Note that this may be a switched capacitor circuit where the switch can be implemented
by a transistor. Switched capacitor circuits are used in filters, amplifiers, charge pump
(DC-DC converter), or switched-mode power supplies.
Solution.
Initial v = 0
Final v = 400 V
Time constant = 10 ms
At t = 15 ms,
Initial:
Final v = 0
Time constant =5 ms
Note that the exponential function is shifted by 15 ms.
b)
c) The capacitor will reach 200 V at two distinct times during charging and discharging
cycles.
The first time,
7.6 Unbounded Response (with dependent sources, and negative time constant)
Example 7.13
Solution.
a) Find the Thevenin equivalent resistance
Note that the equivalent resistance is -5k and not a physical component. Having -5k
resistance creates unbounded response.
[Setting up the differential equation]
[short-cut: What is the initial value? What is  = RThC ?]
Note that this exponential grows without bounds as time increases.
b) After a certain time period, the voltage across the capacitor will exceed the capacitor
limit. The result of which is a short circuit through the capacitor (dielectric/insulator
becomes conductor).