Electric Circuits Plus Mastering Engineering with Pearson eText 2.0 - Access Card Package (11th Edition) (What's New in Engineering)
11th Edition
ISBN: 9780134814117
Author: NILSSON, James W., Riedel, Susan
Publisher: PEARSON
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Question
Chapter 13, Problem 4P
a.
To determine
Derive the s-domain impedance of the series combination
b.
To determine
Find the numerical values of poles and zeroes.
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Introduction
The circuit of Fig. 1 is required to be modeled using a state - space representation, where 2
states will be used, based on the number of the energy - storing elements of the circuit, the
capacitor and the inductor.
u(t)
+
ΙΩ
www
13
F
5 Ω it (t)
www
vc(t) 1 H
Figure 1: LCR circuit
The input signal to the circuit is the voltage u(t) in Volts and the output signal is the voltage
across the capacitor, vc(t).
Questions
1. Choice of system states:
Choose appropriate signals for the 2 states of the
system.
x₁(t) = i₁(t)
x₂ (t) =
5. State transition matrix:
(t), which is defined as,
Calculate analytically the state transition matrix
(t) = et = L¯¹{(sI – A)¯¹}
Show that the answer is the following,
1
e-4t cos(√2t) -
e-4 sin(√2 t)
1
e
-4t
√2
(t) = et
-3
1
-4t sin (√2 t)
e
COS
-4t cos (√2t) + -
e
sin(√2 t)
2-4t sin(√2 t)|
Calculate the following:
(SI - A)-1=
Use the completion - in - the-square technique (CASE 3) to calculate the inverse Laplace:
L¯¹{(SI - A)¯¹} =
Chapter 13 Solutions
Electric Circuits Plus Mastering Engineering with Pearson eText 2.0 - Access Card Package (11th Edition) (What's New in Engineering)
Ch. 13.2 - The parallel circuit in Example 13.1 is placed in...Ch. 13.3 - Prob. 2APCh. 13.3 - The energy stored in the circuit shown is zero at...Ch. 13.3 - The dc current and dc voltage sources are applied...Ch. 13.3 - Prob. 6APCh. 13.3 - Using the results from Example 13.7 for the...Ch. 13.3 - The energy stored in the circuit shown is zero at...Ch. 13.4 -
Derive the numerical expression for the transfer...Ch. 13.5 - Find (a) the unit step and (b) the unit impulse...Ch. 13.5 - The unit impulse response of a circuit is
υo(t) =...
Ch. 13.7 - The current source in the circuit shown is...Ch. 13.7 - For the circuit shown, find the steady-state...Ch. 13 - Prob. 1PCh. 13 - Prob. 2PCh. 13 - Prob. 3PCh. 13 - Prob. 4PCh. 13 - An 2 kΩ resistor, a 6.25 H inductor, and a 250 nF...Ch. 13 - A 250 Ω resistor is in series with an 80 mH...Ch. 13 - Find the poles and zeros of the impedance seen...Ch. 13 - Find the poles and zeros of the impedance seen...Ch. 13 - Prob. 9PCh. 13 - The switch in the circuit in Fig. P13.10 has been...Ch. 13 - Find Vo and υo in the circuit shown in Fig. P13.11...Ch. 13 - Prob. 12PCh. 13 - Prob. 13PCh. 13 - Find the time-domain expression for the current in...Ch. 13 - Prob. 15PCh. 13 - Prob. 16PCh. 13 - The make-before-break switch in the circuit in...Ch. 13 - Prob. 18PCh. 13 - Prob. 19PCh. 13 - There is no energy stored in the circuit in Fig....Ch. 13 - Prob. 21PCh. 13 - There is no energy stored in the circuit in Fig....Ch. 13 - Prob. 23PCh. 13 - Prob. 24PCh. 13 - Prob. 25PCh. 13 - Prob. 26PCh. 13 - Prob. 27PCh. 13 - Prob. 28PCh. 13 - Prob. 29PCh. 13 - Prob. 30PCh. 13 - There is no energy stored in the capacitance in...Ch. 13 - The switch in the circuit seen in Fig. P13.32 has...Ch. 13 - Prob. 33PCh. 13 - Prob. 35PCh. 13 - There is no energy stored in the circuit in Fig....Ch. 13 - Prob. 37PCh. 13 - Prob. 38PCh. 13 - Prob. 39PCh. 13 - Prob. 40PCh. 13 - Prob. 41PCh. 13 - Prob. 42PCh. 13 - Prob. 43PCh. 13 - Prob. 44PCh. 13 - Prob. 45PCh. 13 - The op amp in the circuit shown in Fig. P13.46 is...Ch. 13 - Prob. 47PCh. 13 - Prob. 48PCh. 13 - Prob. 49PCh. 13 - Find the transfer function H(s) − Vo/Vi for the...Ch. 13 - Prob. 51PCh. 13 - Prob. 52PCh. 13 - Prob. 53PCh. 13 - Prob. 54PCh. 13 - The operational amplifier in the circuit in Fig....Ch. 13 - Prob. 56PCh. 13 - The operational amplifier in the circuit in Fig....Ch. 13 - Find the transfer function Io/Ig as a function of...Ch. 13 - Prob. 60PCh. 13 - Prob. 61PCh. 13 - Prob. 62PCh. 13 - Prob. 66PCh. 13 - Prob. 69PCh. 13 - The input voltage in the circuit seen in Fig....Ch. 13 - Find the impulse response of the circuit shown in...Ch. 13 - Assume the voltage impulse response of a circuit...Ch. 13 - Prob. 75PCh. 13 - Prob. 76PCh. 13 - Prob. 77PCh. 13 - The transfer function for a linear time-invariant...Ch. 13 - The transfer function for a linear time-invariant...Ch. 13 - Prob. 80PCh. 13 - The op amp in the circuit seen in Fig. P13.81 is...Ch. 13 - Prob. 82PCh. 13 - Prob. 83PCh. 13 - Prob. 84PCh. 13 - There is no energy stored in the circuit in Fig....Ch. 13 - Prob. 86PCh. 13 - Prob. 87PCh. 13 - Prob. 89PCh. 13 - Prob. 90PCh. 13 - The switch in the circuit in Fig P13.91 has been...Ch. 13 - The parallel combination of R2 and C2 in the...Ch. 13 - Show that if R1C1 = R2C2 in the circuit shown in...
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