The input to the circuit shown in Figure SP 14-1 is the voltage of the voltage source \(v_{\mathrm{i}}(t)\). The output is the voltage across the capacitor \(v_{\mathrm{o}}(t)\). The input is the pulse signal specified graphically by the plot. Use PSpice to plot the output \(v_{\mathrm{o}}(t)\) as a function of \(t\). Hint: Represent the voltage source using the PSpice part named VPULSE.
Read more
Table of Contents
1
Electric Circuit Variables
1.2
Electric Circuits and Current
1.3
Systems of Units
1.5
Power and Energy
1.7
How Can We Check . . . ?
2
Circuit Elements
2.1
How Can We Check . . . ?
2.2
Engineering and Linear Models
2.4
Resistors
2.5
Independent Sources
2.6
Voltmeters and Ammeters
2.7
Dependent Sources
2.8
Transducers
2.9
Switches
3
Resistive Circuits
3.2
Kirchhoffs Laws
3.3
Series Resistors and Voltage Division
3.4
Parallel Resistors and Current Division
3.5
Series Voltage Sources and Parallel Current Sources
3.6
Circuit Analysis
3.7
Analyzing Resistive Circuits Using MATLAB
3.8
How Can We Check . . . ?
4
Methods of Analysis of Resistive Circuits
4.11
How Can We Check . . . ?
4.2
Node Voltage Analysis of Circuits with Current Sources
4.3
Node Voltage Analysis of Circuits with Current and Voltage Sources
4.4
Node Voltage Analysis with Dependent Sources
4.5
Mesh Current Analysis with Independent Voltage Sources
4.6
Mesh Current Analysis with Current and Voltage Sources
4.7
Mesh Current Analysis with Dependent Sources
4.8
The Node Voltage Method and Mesh Current Method Compared
4.9
Circuit Analysis Using MATLAB
5
Circuit Theorems
5.2
Source Transformations
5.3
Superposition
5.4
Thevenin s Theorem
5.5
Nortons Equivalent Circuit
5.6
Maximum Power Transfer
5.8
Using PSpice to Determine the Thevenin Equivalent Circuit
5.9
How Can We Check . . . ?
6
The Operational Amplifier
6.1
How Can We Check . . . ?
6.3
The Ideal Operational Amplifier
6.4
Nodal Analysis of Circuits Containing Ideal Operational Amplifiers
6.5
Design Using Operational Amplifiers
6.6
Operational Amplifier Circuits and Linear Algebraic Equations
6.7
Characteristics of Practical Operational Amplifiers
7
Energy Storage Elements
7.11
How Can We Check . . . ?
7.2
Capacitors
7.3
Energy Storage in a Capacitor
7.4
Series and Parallel Capacitors
7.5
Inductors
7.6
Energy Storage in an Inductor
7.7
Series and Parallel Inductors
7.8
Initial Conditions of Switched Circuits
7.9
Operational Amplifier Circuits and Linear Differential Equations
8
The Complete Response of RL and RC Circuits
8.1
How Can We Check . . . ?
8.3
The Response of a First-Order Circuit to a Constant Input
8.4
The Response of a First-Order Circuit to a Constant Input
8.5
Stability of First-Order Circuits
8.6
The Unit Step Source
8.7
The Response of a First-Order Circuit to a Nonconstant Source
9
The Complete Response of Circuits with Two Energy Storage Elements
9.1
Roots in the Complex Plane
9.11
How Can We Check . . . ?
9.2
Differential Equation for Circuits with Two Energy Storage Elements
9.3
Solution of the Second-Order Differential EquationThe Natural Response
9.4
Natural Response of the Unforced Parallel RLC Circuit
9.5
Natural Response of the Critically Damped Unforced Parallel RLC Circuit
9.6
Natural Response of an Underdamped Unforced Parallel RLC Circuit
9.7
Forced Response of an RLC Circuit
9.8
Complete Response of an RLC Circuit
9.9
State Variable Approach to Circuit Analysis
10
Sinusoidal Steady-State Analysis
10.1
Op Amps in AC Circuits
10.11
The Complete Response
10.12
Using MATLAB to Analyze Electric Circuits
10.2
Sinusoidal Sources
10.3
Phasors and Sinusoids
10.4
Impedances
10.5
Series and Parallel Impedances
10.6
Mesh and Node Equations
10.7
Thevenin and Norton Equivalent Circuits
10.8
Superposition
10.9
Phasor Diagrams
11
AC Steady-State Power
11.1
The Ideal Transformer
11.11
How Can We Check . . . ?
11.3
Instantaneous Power and Average Power
11.4
Effective Value of a Periodic Waveform
11.5
Complex Power
11.6
Power Factor
11.7
The Power Superposition Principle
11.8
The Maximum Power Transfer Theorem
11.9
Coupled Inductors
12
Three-Phase Circuits
12.2
Three-Phase Voltages
12.3
The Y-to-Y Circuit
12.4
The D-Connected Source and Load
12.5
The Y-to-D Circuit
12.6
Balanced Three-Phase Circuits
12.7
Instantaneous and Average Power in a Balanced Three-Phase Load
12.8
Two-Wattmeter Power Measurement
12.9
How Can We Check . . . ?
13
Frequency Response
13.2
Gain, Phase Shift, and the Network Function
13.3
Bode Plots
13.4
Resonant Circuits
13.6
Plotting Bode Plots Using MATLAB
13.8
How Can We Check . . . ?
14
The Laplace Transform
14.1
Stability
14.11
Partial Fraction Expansion Using MATLAB
14.12
How Can We Check . . . ?
14.2
Laplace Transform
14.3
Pulse Inputs
14.4
Inverse Laplace Transform
14.5
Initial and Final Value Theorems
14.6
Solution of Differential Equations Describing a Circuit
14.7
Circuit Analysis Using Impedance and Initial Conditions
14.8
Transfer Functions
14.9
Convolution
15
Fourier Series and Fourier Transform
15.12
Convolution and Circuit Response
15.14
How Can We Check . . . ?
15.2
The Fourier Series
15.3
Symmetry of the Function f (t)
15.5
Exponential Form of the Fourier Series
15.6
The Fourier Spectrum
15.7
Circuits and Fourier Series
15.9
The Fourier Transform
16
Filter Circuits
16.3
Filters
16.4
Second-Order Filters
16.5
High-Order Filters
16.7
How Can We Check . . . ?
17
Two-Port and Three-Port Networks
17.2
T-to-P Transformation and Two-Port Three-Terminal Networks
17.3
Equations of Two-Port Networks
17.4
Z and Y Parameters for a Circuit with Dependent Sources
17.5
Hybrid and Transmission Parameters
17.6
Relationships Between Two-Port Parameters
17.7
Interconnection of Two-Port Networks
17.8
How Can We Check . . . ?
Textbook Solutions for Introduction to Electric Circuits
Chapter 14 Problem DP14-6
Question
The input to each of the circuits shown in Figure DP 14-6 is the voltage \(v_i\)(t), and the output is the voltage \(v_o\)(t). Choose one of the circuits shown in Figure DP 14-6 and design it to have the step response
\(v_0(t)=\left(\frac{4}{3} e^{-20 t}-\frac{1}{3} e^{-5 t}\right) u(t) \mathrm{V}\)
Solution
The first step in solving 14 problem number 123 trying to solve the problem we have to refer to the textbook question: The input to each of the circuits shown in Figure DP 14-6 is the voltage \(v_i\)(t), and the output is the voltage \(v_o\)(t). Choose one of the circuits shown in Figure DP 14-6 and design it to have the step response \(v_0(t)=\left(\frac{4}{3} e^{-20 t}-\frac{1}{3} e^{-5 t}\right) u(t) \mathrm{V}\)
From the textbook chapter The Laplace Transform you will find a few key concepts needed to solve this.
Visible to paid subscribers only
Step 3 of 7)Visible to paid subscribers only
Subscribe to view the
full solution
full solution
Title
Introduction to Electric Circuits 9
Author
James A. Svoboda, Richard C. Dorf
ISBN
9781118477502
Answer: The input to each of the circuits shown in Figure DP 14-6 is the voltage vi(t)
Chapter 14 textbook questions
-
Chapter 14: Problem 0 Introduction to Electric Circuits 9
-
Chapter 14: Problem 0 Introduction to Electric Circuits 9
The circuit shown in Figure SP 14-2 is at steady state before the switch closes at time t = 0. The input to the circuit is the voltage of the voltage source, \(12 \mathrm{~V}\). The output of this circuit is the voltage across the capacitor v(t). Use PSpice to plot the output v(t) as a function of t. Use the plot to obtain an analytic representation of v(t), for t > 0. Hint: We expect \(v(t)=A+\mathbf{B} e^{-t / \tau}\) for t > 0, where A, B, and \(\tau\) are constants to be determined.
Read more -
Chapter 14: Problem 0 Introduction to Electric Circuits 9
The circuit shown in Figure SP 14-3 is at steady state before the switch closes at time t = 0. The input to the circuit is the current of the current source, 4 mA. The output of this circuit is the current in the inductor, i(t). Use PSpice to plot the output i(t) as a function of t. Use the plot to obtain an analytic representation of i(t) for t > 0. Hint: We expect \(i(t)=A+B e^{-t / \tau}\) for t > 0, where A, B, and \(\tau\) are constants to be determined.
Read more -
Chapter 14: Problem 0 Introduction to Electric Circuits 9
The input to the circuit shown in Figure SP 14-4 is the voltage of the voltage source \(v_i\)(t). The output is the voltage across the capacitor \(v_o\)(t). The input is the pulse signal specified graphically by the plot. Use PSpice to plot the output \(v_o\)(t) as a function of t for each of the following cases: (a) C = 1 F; L = 0.25 H; \(R_1\) = \(R_2\) = 1:309 \(\Omega\) (b) C = 1 F; L = 1 H; \(R_1\) = 3 \(\Omega\); \(R_2\) = 1 \(\Omega\) (c) C = 0.125 F; L = 0.5 H; \(R_1\) = 1 \(\Omega\); \(R_2\) = 4 \(\Omega\) Plot the output for these three cases on the same axis. Hint: Represent the voltage source, using the PSpice part named VPULSE.
Read more -
Chapter 14: Problem 0 Introduction to Electric Circuits 9
The input to the circuit shown in Figure SP 14-5 is the voltage of the voltage source vi(t). The output is the voltage vo(t) across resistor R2. The input is the pulse signal specified graphically by the plot. Use PSpice to plot the output vo(t) as a function of t for each of the following cases: (a) C = 1 F; L = 0.25 H; \(R_1\) = \(R_2\) = 1:309 \(\Omega\) (b) C = 1 F; L = 1 H; \(R_1\) = 3 \(\Omega\); \(R_2\) = 1 \(\Omega\) (c) C = 0.125 F; L = 0.5 H; \(R_1\) = 1 \(\Omega\); \(R_2\) = 4 \(\Omega\) Plot the output for these three cases on the same axis. Hint: Represent the voltage source, using the PSpice part named VPULSE.
Read more -
Chapter 14: Problem 0 Introduction to Electric Circuits 9
Design the circuit in Figure DP 14-1 to have a step response equal to \(v_o\) = \(5te^{-4t}\) u(t) V Hint: Determine the transfer function of the circuit in Figure DP 14-1 in terms of k, R, C, and L. Then determine the Laplace transform of the step response of the circuit in Figure DP 14-1. Next, determine the Laplace transform of the given step response. Finally, determine values of k, R, C, and L that cause the two step responses to be equal.
Read more -
Chapter 14: Problem 0 Introduction to Electric Circuits 9
Design the circuit in Figure DP 14-1 to have a step response equal to \(v_o\) = \(5e^{-4t}\) sin (2t)u(t) V Hint: Determine the transfer function of the circuit in Figure DP 14-1 in terms of k, R, C, and L. Then determine the Laplace transform of the step response of the circuit in Figure DP 14-1. Next, determine the Laplace transform of the given step response. Finally, determine values of k, R, C, and L that cause the two step responses to be equal.
Read more -
Chapter 14: Problem 0 Introduction to Electric Circuits 9
Design the circuit in Figure DP 14-1 to have a step response equal to \(v_o\) = \(5(e^{-2t} - e^{-4t})\)u(t) V Hint: Determine the transfer function of the circuit in Figure DP 14-1 in terms of k, R, C, and L. Then determine the Laplace transform of the step response of the circuit in Figure DP 14-1. Next, determine the Laplace transform of the given step response. Finally, determine values of k, R, C, and L that cause the two step responses to be equal.
Read more -
Chapter 14: Problem 0 Introduction to Electric Circuits 9
Show that the circuit in Figure DP 14-1 cannot be designed to have a step response equal to \(v_o\) = 5(e^{-2t} + e^{-4t}\)u(t) V Hint: Determine the transfer function of the circuit in Figure DP 14-1 in terms of k, R, C, and L. Then determine the Laplace transform of the step response of the circuit in Figure DP 14-1. Next, determine the Laplace transform of the given step response. Notice that these two functions have different forms and so cannot be made equal by any choice of values of k, R, C, and L.
Read more -
Chapter 14: Problem 0 Introduction to Electric Circuits 9
The input to the circuit shown in Figure DP 14-5 is the current i(t), and the output is the current \(i_o\)(t). Determine the values of R, L, and C that cause the impulse response of this circuit to be \(i_o\)(t) = \((k_1 e^{-2000t) + k_1 e^{-8000t})\)u(t) A where \(k_1\) and \(k_2\) are unspecified constants.
Read more -
Chapter 14: Problem 0 Introduction to Electric Circuits 9
The input to each of the circuits shown in Figure DP 14-6 is the voltage \(v_i\)(t), and the output is the voltage \(v_o\)(t). Choose one of the circuits shown in Figure DP 14-6 and design it to have the step response \(v_0(t)=\left(\frac{4}{3} e^{-20 t}-\frac{1}{3} e^{-5 t}\right) u(t) \mathrm{V}\)
Read more -
Chapter 14: Problem 0 Introduction to Electric Circuits 9
The input to each of the circuits shown in Figure DP 14-6 is the voltage \(v_i(t)\), and the output is the voltage \(v_0(t)\). Choose one of the circuits shown in Figure DP 14-6 and design it to have the step response \(v_0(t)=5\left(e^{-10 r}-e^{-15 t}\right) u(t) \mathrm{V}\)
Read more -
Chapter 14: Problem 0 Introduction to Electric Circuits 9
The input to each of the circuits shown in Figure DP 14-6 is the voltage \(v_i(t)\), and the output is the voltage \(v_{\mathrm{e}}(t)\). Choose one of the circuits shown in Figure DP 14-6 and design it to have the step response \(v_o(t)=\left(1-e^{-20 t}-20 t e^{-20 c}\right) u(t) \mathrm{V}\)
Read more -
Chapter 14: Problem 0 Introduction to Electric Circuits 9
DP 14-9 The input to each of the circuits shown in Figure DP 14-6 is the voltage \(v_i(t)\), and the output is the voltage \(v_0(t)\). Choose one of the circuits shown in Figure DP 14-6 and design it to have the step response \(v_0(t)=e^{-10 t} \sin (40 t) u(t) \mathrm{V}\)
Read more -
Chapter 14: Problem 0 Introduction to Electric Circuits 9
The input to each of the circuits shown in Figure DP 14-6 is the voltage \(v_i(t)\), and the output is the voltage \(v_{\mathrm{a}}(t)\). Choose one of the circuits shown in Figure DP 14-6 and design it to have the step response \(v_0(t)=e^{-10 t} \cos (40 t) u(t) \mathrm{V}\)
Read more