Fundamentals of Electric Circuits
6th Edition
ISBN: 9780078028229
Author: Charles K Alexander, Matthew Sadiku
Publisher: McGraw-Hill Education
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Question
Chapter 16.4, Problem 9PP
a.
To determine
Find the transfer function
b.
To determine
Find the expression of impulse response
c.
To determine
Find the expression of output voltage
d.
To determine
Find the expression of output voltage
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A system is described by the differential equation (see attached).
a)What is the order of the system. How many poles does the system's transfer function have. How many states are needed to describe the system completely.b) Determine the system's transfer function, Y(s)/U(s) (the poles of the system are at ―1, ― 2, and ―4);c) Determine matrices A, B, C, and D to describe the system in state-space form x' = Ax + Bu, y = Cx + Du.
The differential equations below represent systems where x is the input and y is the output.
Determine
a) the transfer function of the given systems,
b) whether the following systems are stable, or unstable, and
c) the number of roots with positive real part
a. Find the circuit’s input, or driving-point, impedance, Zi, in the s-domain.
Chapter 16 Solutions
Fundamentals of Electric Circuits
Ch. 16.2 - Determine vo(t) in the circuit of Fig. 16.6,...Ch. 16.2 - Prob. 2PPCh. 16.2 - Prob. 3PPCh. 16.3 - For the circuit shown in Fig. 16.12 with the same...Ch. 16.3 - Prob. 5PPCh. 16.3 - The initial energy in the circuit of Fig. 16.17 is...Ch. 16.4 - Prob. 7PPCh. 16.4 - Prob. 8PPCh. 16.4 - Prob. 9PPCh. 16.5 - Obtain the state variable model for the circuit...
Ch. 16.5 - Prob. 11PPCh. 16.5 - Prob. 12PPCh. 16.6 - For what value of is the circuit in Fig. 16.29...Ch. 16.6 - Prob. 14PPCh. 16.6 - Prob. 15PPCh. 16.6 - Synthesize the function Vo(s)Vin=2ss2+6s+10 using...Ch. 16 - Prob. 1RQCh. 16 - The current through an RL series circuit with...Ch. 16 - Prob. 3RQCh. 16 - Prob. 4RQCh. 16 - Prob. 5RQCh. 16 - Prob. 6RQCh. 16 - Prob. 7RQCh. 16 - Prob. 8RQCh. 16 - Prob. 9RQCh. 16 - Prob. 10RQCh. 16 - The current in an RLC circuit is described by...Ch. 16 - The differential equation that describes the...Ch. 16 - Prob. 3PCh. 16 - If R = 20 , L = 0.6 H, what value of C will make...Ch. 16 - The responses of a series RLC circuit are vc(t) =...Ch. 16 - Prob. 6PCh. 16 - Prob. 7PCh. 16 - Prob. 8PCh. 16 - Prob. 9PCh. 16 - The step responses of a series RLC circuit are Vc...Ch. 16 - The step response of a parallel RLC circuit is v =...Ch. 16 - Prob. 12PCh. 16 - Prob. 13PCh. 16 - Prob. 14PCh. 16 - For the circuit in Fig. 16.38. calculate the value...Ch. 16 - The capacitor in the circuit of Fig. 16.39 is...Ch. 16 - If is(t) = 7.5e2t u(t) A in the circuit shown in...Ch. 16 - Find v(t), t 0 in the circuit of Fig. 16.41. Let...Ch. 16 - The switch in Fig. 16.42 moves from position A to...Ch. 16 - Find i(t) for t 0 in the circuit of Fig. 16.43.Ch. 16 - In the circuit of Fig. 16.44, the switch moves...Ch. 16 - Find the voltage across the capacitor as a...Ch. 16 - Obtain v (t) for t 0 in the circuit of Fig....Ch. 16 - The switch in the circuit of Fig. 16.47 has been...Ch. 16 - Calculate v(t) for t 0 in the circuit of Fig....Ch. 16 - Prob. 26PCh. 16 - Find v (t) for t 0 in the circuit in Fig. 16.50.Ch. 16 - For the circuit in Fig. 16.51, find v(t) for t 0.Ch. 16 - Prob. 29PCh. 16 - Find vo(t), for all t 0, in the circuit of Fig....Ch. 16 - Prob. 31PCh. 16 - For the network in Fig. 16.55, solve for i(t) for...Ch. 16 - Using Fig. 16.56, design a problem to help other...Ch. 16 - Prob. 34PCh. 16 - Prob. 35PCh. 16 - Prob. 36PCh. 16 - Prob. 37PCh. 16 - The switch in the circuit of Fig. 16.61 is moved...Ch. 16 - Prob. 39PCh. 16 - Prob. 40PCh. 16 - Prob. 41PCh. 16 - Prob. 42PCh. 16 - Prob. 43PCh. 16 - Prob. 44PCh. 16 - Find v(t) for t 0 in the circuit in Fig. 16.68.Ch. 16 - Prob. 46PCh. 16 - Determine io(t) in the network shown in Fig....Ch. 16 - Prob. 48PCh. 16 - Find i0(t) for t 0 in the circuit in Fig. 16.72....Ch. 16 - Prob. 50PCh. 16 - In the circuit of Fig. 16.74, find i(t) for t 0.Ch. 16 - Prob. 52PCh. 16 - In the circuit of Fig. 16.76, the switch has been...Ch. 16 - Prob. 54PCh. 16 - Prob. 55PCh. 16 - Calculate io(t) for t 0 in the network of Fig....Ch. 16 - Prob. 57PCh. 16 - Prob. 58PCh. 16 - Find vo(t) in the circuit of Fig. 16.82 if vx(0) =...Ch. 16 - Prob. 60PCh. 16 - Prob. 61PCh. 16 - Using Fig. 16.85, design a problem to help other...Ch. 16 - Consider the parallel RLC circuit of Fig. 16.86....Ch. 16 - The switch in Fig. 16.87 moves from position 1 to...Ch. 16 - For the RLC circuit shown in Fig. 16.88, find the...Ch. 16 - For the op amp circuit in Fig. 16.89, find v0(t)...Ch. 16 - Given the op amp circuit in Fig. 16.90, if v1(0+)...Ch. 16 - Prob. 68PCh. 16 - Prob. 69PCh. 16 - Using Fig. 16.93, design a problem to help other...Ch. 16 - Prob. 71PCh. 16 - The transfer function of a system is H(s)=s23s+1...Ch. 16 - Prob. 73PCh. 16 - Design a problem to help other students better...Ch. 16 - Prob. 75PCh. 16 - For the circuit in Fig. 16.95, find H(s) =...Ch. 16 - Obtain the transfer function H(s) = VoVs for the...Ch. 16 - Prob. 78PCh. 16 - For the circuit in Fig. 16.97, find: (a) I1/Vs (b)...Ch. 16 - Refer to the network in Fig. 16.98. Find the...Ch. 16 - Prob. 81PCh. 16 - Prob. 82PCh. 16 - Refer to the RL circuit in Fig. 16.101. Find: (a)...Ch. 16 - A parallel RL circuit has R = 4 and L = 1 H. The...Ch. 16 - Prob. 85PCh. 16 - Prob. 86PCh. 16 - Prob. 87PCh. 16 - Prob. 88PCh. 16 - Develop the state equations for the circuit shown...Ch. 16 - Prob. 90PCh. 16 - Prob. 91PCh. 16 - Prob. 92PCh. 16 - Prob. 93PCh. 16 - Prob. 94PCh. 16 - Prob. 95PCh. 16 - Prob. 96PCh. 16 - A system is formed by cascading two systems as...Ch. 16 - Determine whether the op amp circuit in Fig....Ch. 16 - It is desired realize the transfer function...Ch. 16 - Prob. 100PCh. 16 - Prob. 101PCh. 16 - Synthesize the transfer function...Ch. 16 - Prob. 103CPCh. 16 - Prob. 104CPCh. 16 - Prob. 105CP
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- Which of the following is the H (s) transfer function of the system whose block diagram is given? s / (4s + 3)4 s / (3s + 1)4 s / (3s + 2)s / (s + 4)4 s / (s + 1)3 s / (s + 4)arrow_forwardIf the transfer function V2(s) / V1(s) = s / s^2+5s+4, then find the Z. (It may contain R,L,C components). ..arrow_forwardFind the transfer function, G(s) = X3(s) / F(s), for the translational mechanical networkarrow_forward
- In control systems analysis, transfer functions are developed that mathematically relate the dynamics of a system’s input to its output. A transfer function for a robotic positioning system is given by G(s) = C(s) N(s) = s3 + 12.5s2 + 50.5s + 66 s4 + 19s3 + 122s2 + 296s + 192 where G(s) = system gain, C(s) = system output, N(s) = system input, and s=Laplace transform complex frequency. Use a numericaltechnique to find the roots of the numerator and denominator and factor these into the form G(s) = (s + a1)(s + a2)(s + a3) (s + b1)(s + b2)(s + b3)(s + b4) where ai and bi = the roots of the numerator and denominator,arrow_forwardA state space representation for the transfer function given below, The value of C will be A_[6 1] B_[5 6] C_[6 5] D_[1 6]arrow_forwardThe transfer function of a system is given as follows:A)permanent status error find ESSB)Perform the Inverse Laplace transformation of Y(s)C)graph of the time-dependent change of y (t)draw and show that the ESS you found are correct.arrow_forward
- Obtain the transfer function of the given electrical system below expressed in Laplace form s . Let i(t) be the input of the system and the voltage across R4 be the output of the system.arrow_forwardA second order discrete time system is described by the transfer functionG (Z) =Y (Z)/R (Z) =1/Z2+3/4Z+1/8Determine the response of the system to a unit sample sequence.arrow_forwardGiven Figure 1 below, (a) simplify the block diagram and obtain the transfer function, (b) obtain the solution by Laplace.arrow_forward
- Find the transfer function of the given electrical system below from the state equation. Assume v(t) be the input of the system and the voltage across C be the output of the system. Let X1 be the current flowing on L1, X2 be the voltage across C and X3 be the current flowing on L2.arrow_forward1) In the electrical circuit given in the figure, v (t) -input and vC2 (t) -output, a) Draw the Laplace equivalent of the system and obtain the transfer function. (In your transactions, consider the initial values as zero.). b) Draw the appropriate graph tree and write the equation of state for the system.arrow_forwardObtain the transfer functions X1(s)/U(s) and X2 (s)/U(s) of the mechanical system.arrow_forward
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