1. 5. RC and RL First-Order Circuits
CIRCUITS by Ulaby & Maharbiz
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3. Transient Response
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4. Non-Periodic Waveforms
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Non-Periodic Waveforms
Step Function
Ramp Function
Square Pulse
Exponential

5. Non-Periodic Waveforms: Step Function
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Non-Periodic Waveforms: Step Function

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7. Non-Periodic Waveforms: Ramp Function
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Non-Periodic Waveforms: Ramp Function

8. Waveform synthesis as sum of two ramp functions
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9. Non-Periodic Waveforms: Pulses
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Non-Periodic Waveforms: Pulses

10. Waveform Synthesis 1. Pulse 2. Trapezoid
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11. Non-Periodic Waveforms: Exponentials
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Non-Periodic Waveforms: Exponentials

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13. Passive element that stores energy in electric field
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Capacitors
Passive element that stores energy in electric field
Parallel plate capacitor
For DC, capacitor looks like open circuit
Voltage on capacitor must be continuous (no abrupt change)

14. Various types of capacitors
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Various types of capacitors

15. Capacitors in Fingerprint Imager
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16. Tech Brief 11: Supercapacitors
A new generation of capacitor technologies, termed supercapacitors or ultracapacitors, is narrowing the gap between capacitors and batteries. These capacitors can have sufficiently high energy densities to approach within 10 percent of battery storage densities, and additional improvements may increase this even more. Importantly, supercapacitors can absorb or release energy much faster than a chemical battery of identical volume. This helps immensely during recharging. Moreover, most batteries can be recharged only a few hundred times before they are degraded completely; supercapacitors can be charged and discharged millions of times before they wear out. Supercapacitors also have a much smaller environmental footprint than conventional chemical batteries, making them particularly attractive for green energy solutions.
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17. Energy Stored in Capacitor
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18. Energy Storage Comparison
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19. Capacitor Response: Given v(t), determine i(t), p(t), and w(t)
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Capacitor Response: Given v(t), determine i(t), p(t), and w(t)
C =

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RC Circuits at dc
At dc no currents flow through capacitors: open circuits

21. Use KVL, current same through each capacitor
Capacitors in Series
Use KVL, current same through each capacitor
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22. Capacitors in Parallel
Use KCL, voltage same across each capacitor
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23. Voltage Division
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24. Passive element that stores energy in magnetic field
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Inductors
Passive element that stores energy in magnetic field
Solenoid Wound Inductor
At dc, inductor looks like a short circuit
Current through inductor must be continuous (no abrupt change)
Note: voltage divider with capacitors

25. Inductor Response to
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26. Use KVL, current is same through all inductors
Inductors in Series
Use KVL, current is same through all inductors
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27. Inductors in Parallel Voltage is same across all inductors
Inductors add together in the same way resistors do
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28. RL Circuits at dc At dc no voltage across inductors: short circuit
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RL Circuits at dc
At dc no voltage across inductors: short circuit

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30. Response Terminology Source dependence Time dependence
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Response Terminology
Source dependence
Natural response – response in absence of sources
Forced response – response due to external source
Complete response = Natural + Forced
Time dependence
Transient response – time-varying response (temporary)
Steady state response – time-independent or periodic (permanent)
Complete response = Transient + Steady State

31. Natural Response of Charged Capacitor
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Natural Response of Charged Capacitor
(a) t = 0− is the instant just before the switch is moved from terminal 1 to terminal 2
(b) t = 0 is the instant just after it was moved;
t = 0 is synonymous with t = 0+
since the voltage across the capacitor cannot change instantaneously, it follows that

32. Solution of First-Order Diff. Equations
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Solution of First-Order Diff. Equations
τ is called the time constant of the circuit.

33. Natural Response of Charged Capacitor
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Natural Response of Charged Capacitor

34. General Response of RC Circuit
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General Response of RC Circuit

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Solution of

36. Example 5-10: Determine Capacitor Voltage
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Example 5-10: Determine Capacitor Voltage

37. Example 5-10 Solution (a) Switch was moved at t = 0 At t = 0
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Example 5-10 Solution
(a) Switch was moved at t = 0
At t = 0
(b) Switch was moved at t = 3 s
At t > 0

38. Example 5-11: Charge/Discharge Action
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Example 5-11: Charge/Discharge Action

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Example 5-11 (cont.)

40. Example 5-12: Rectangular Pulse
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Example 5-12: Rectangular Pulse

41. Natural Response of the RL Circuit
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Natural Response of the RL Circuit

42. General Response of the RL Circuit
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General Response of the RL Circuit

43. Example 5-13: Two RL Branches
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At t=0
Cont.

44. Example 5-13: Two RL Branches (cont.)
After t=0:
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45. RC Op-Amp Circuits: Ideal Integrator
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46. Example 5-15: Square-Wave Signal
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47. RC Op-Amp Circuits: Ideal Differentiator
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48. Example 5-16: Pulse Response
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Example 5-16: Pulse Response

49. Multisim Example
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50. All rights reserved. Do not copy or distribute
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Summary