Transient Circuits

1
Chapter 3

• Transient Circuits

2
Objectives

• Discuss the form and notation for a time-varying
  voltage and/or current.
• State Ohms law for a resistance in terms of
  time-varying voltage and current.
• Define the three passive circuit parameters and
  discuss each one in terms of energy dissipation
  or energy storage.

3
Objectives

• State and apply the different forms of the
  voltage-current relationships for an inductance
  and a capacitance.
• For piecewise linear voltage or current
  functions, calculate and plot the waveforms of
  voltage, current, and power for inductance and
  capacitance.
• Determine the energy stored in an inductance and
  a capacitance.

4
Objectives

• Draw the initial equivalent circuits for an
  inductance and a capacitance for the case of no
  initial energy and for when there is initial
  energy stored.
• Solve for the initial values of voltage and
  current in a circuit with inductance and
  capacitance.

5
Objectives

• Draw the final steady-state equivalent circuits
  for inductance and capacitance when all
  excitations are dc.
• Solve for the final values of voltage and current
  in a circuit with inductance and capacitance when
  all excitations are dc.
• Determine the voltage or current response of a
  first-order circuit with dc sources and sketch
  the waveforms.

6
3-1 Basic Circuit Parameters
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Resistance with Instantaneous Time-Varying
Voltage and Current
8
Inductance with Instantaneous Time-Varying
Voltage and Current
9
Capacitance with Instantaneous Time-Varying
Voltage and Current
10
Capacitor and Voltage of Example 3-1
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Waveforms of Example 3-1.
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Waveforms of Example 3-3
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Waveforms of Example 3-4
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3-2 Boundary Conditions for Energy Storage
Elements
15
Initial Equivalent Circuits for Unfluxed
Inductance and Uncharged Capacitance
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Initial Equivalent Circuits for Fluxed Inductance
and Charged Capacitance
17
Steady-State DC Equivalent Circuits for
Inductance and Capacitance
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Circuit of Example 3-5 and its Initial Equivalent
Circuit
19
Circuit of Example 3-6 and its Steady-State DC
Equivalent Circuit
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Circuit of Example 3-7 and its Initial Equivalent
Circuit
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3-3 First-Order Circuits with DC Excitations

• dy/dt (1/t)y K
• y A Be-t/t
• t RC
• t L/R

22
Circuit Forms of Example 3-8
23
Inductor Voltage and Loop Current of Example 3-8
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Circuit Forms of Example 3-9
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Loop Current and Capacitor Voltage of Example 3-9
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Circuit Forms of Example 3-10
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Loop Current and Capacitor Voltage of Example 3-10
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3-4 Inductance and Capacitance Combinations

• Inductors in Series
• Inductors in Parallel
• Capacitors in Series
• Capacitors in Parallel

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Inductances in Series (given no mutual inductance)
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Inductances in Parallel (given no mutual
inductance)
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Capacitances in Series
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Capacitances in Parallel