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The Analysis And Design Of Linear Circuits 8th Edition Roland E. Thomas, Albert J. Rosa, Gregory J. Toussaint - Solutions

5–27 Find the Fourier coefficients, cyclic frequency, and radian frequency of the following sinusoids:(a) v(t) = 24 cos (200πt + 36.9) V(b) i(t) = 240 cos (120πt − 90)A
5–23 (a) Plot the waveform of each sinusoid in Problem 5–22 by hand.(b) Use Multisim to produce the waveform in Problem 5–22(a).(c) Use MATLAB to produce the waveform in Problem 5–22(b).
5–22 Find the period, frequency, amplitude, time shift, and phase angle of the following sinusoids.(a) v1ðtÞ = 240 cos ð120πtÞ − 240 sinð120πtÞ V(b) v2ðtÞ = −30 cos ð50 kπtÞ + 40 sinð50 kπtÞ V
5–18 The amplitude of an exponential waveform is 12 V at t =0 and 7 V at t = 3 ms. What is its time constant?
5–16 An exponential waveformdecays to 50%of its initial ðt = 0Þ amplitude in 20 μs. Find the time constant of the waveform.
5–15 Write expressions for the derivative ðt > 0Þ and integral (from 0 to t) of the exponential waveform iðtÞ = 100 e−2500t u t ð Þ mA.
5–11 Using its pulse voltage source, generate on Multisim a waveform vðtÞ that starts at t = 2ms and consists of a pulse train of 1-V pulses with a 1-ms pulse width that repeat every 4 ms.
Characterize the composite waveform obtained as the difference of two exponentials with the same amplitude
Characterize the composite waveform obtained by multiplying sin ω0t by an exponential.
Characterize the composite waveform obtained by multiplying the ramp rðtÞ=TC times an exponential
Asinusoid has a period of 5 μs. At t = 0 the amplitude is 12 V. The waveform reaches its first positive peak after t =0 at t =4 μs. Find its amplitude, frequency, and phase angle
Write an equation for the waveform obtained by integrating and differentiating the following signals:(a) υ1(t) = 30 cos(10t−60) V(b) υ2(t) = 3 cos(4000πt)−4 sin(4000πt) V
(a) An exponential waveform has υð0Þ = 1:2 V and υð3Þ = 0:5 V. What are VA and TC for this waveform?(b) An exponential waveform has υð0Þ = 5 V and υð2Þ = 1:25 V. Find the value of υðtÞ at t = 1 s and t =4 s?(c) An exponential waveform has υð0Þ = 5 V and an initial ðt = 0Þ slope
5-3 Waveform Partial Descriptors (Sect. 5–6)Given a complete description of a basic or composite waveform:(a) Classify the waveform as periodic or aperiodic and causal or noncausal.(b) Find the applicable partial waveform descriptors.(c) Use appropriate software tools to calculate applicable
5-2 Composite Waveforms (Sect. 5–5)Given an equation, graph, or word description of a composite waveform:(a) Construct an alternative description of the waveform.(b) Find the parameters or properties of the waveform.(c) Generate the composite waveforms in MATLAB or Multisim and use them
5-1 Basic Waveforms (Sects. 5–2, 5–3, and 5–4)Given an equation, graph, or word description of step, ramp, exponential, or sinusoid waveforms:(a) Construct an alternative description of the waveform.(b) Find the parameters or properties of the waveform.(c) Construct new waveforms by
Battery Design A satellite requires a battery with an open-circuit voltage vOC ¼36 Vand a Thevenin resistance RT 10 V. The battery is to be constructed using series and parallel combinations of one of two types of cells. The first type has vOC¼9V, RT¼ 4V, and a weight of 30 grams. The second
Design the interface circuit in Figure P3–87 so that ROUT¼50Vand the voltage delivered to the 50-Vload is v ¼2.5 V. Hint: Use an L-pad.
Design the interface circuit in Figure P3–85 so that the voltage delivered to the load is 2.5 V.
A practical source delivers 50 mA to a 300-V load. The source delivers 12 V to a 120-V load. Find the maximum power available from the source.
A 100 V-load needs 10 mA to operate correctly.Design a practical power source to provide the needed current. The smallest source resistance you can practically design for is 50 V, but you can add any other series resistance if you need to.
When a 5-kV resistor is connected across a two-terminal source a current of 15 mA is delivered to the load. When a second 5-kV resistor is connected in parallel with the first, a total current of 20mAis delivered. Find the maximum power available from the source.
A nonlinear resistor is connected across a two-terminal source whose Thevenin equivalent is vT¼ 5Vand RT¼ 500V.The i-v characteristic of he resistor is i ¼ 104 (v þ2 v3.3). Use the MATLAB function solve to find the operating point for this circuit and determine the voltage across, the current
The Thevenin equivalent parameters of a practical voltage source are vT ¼ 30 V RT ¼ 300 V. Find the smallest load resistance for which the load voltage exceeds 10 V.
The i-v characteristic of the active circuit in Figure P3–58 is 5v + 500i ¼ 100. Find the output voltage when a 500-V resistive load is connected.
A certain linear circuit has four input voltages and one output voltage vO. The following table lists the output for different values of the four inputs. Find the input-output relationship for the circuit. Specifically, find an expression for vO in terms of the four input voltages.vS1(V) vS2(V)
Alinear circuit is driven by an independent voltage source vS¼ 10 V and an independent current source iS ¼ 10 mA. The output voltage is vO¼ 2Vwhen the voltage source is on and the current source off. The output is vO¼ 1Vwhen both sources are on. Find the output voltage when vS ¼ 20 Vand iS¼
A linear circuit containing two sources drives a 100-V load resistor. Source number 1 delivers 1Wto the load when source number 2 is off. Source number 2 delivers 4Wto the load when source number 1 is off. Find the power delivered to the load when both sources are on. Hint: The answer is not 5 W.
(a) Use the superposition principle to find vO in terms of vS,iS, and R in Figure P3–42.(b) Use MATLAB and node-voltage analysis to verify your answer symbolically.AppendixLO1
Use Figure P3–24 and MATLAB to solve the following problems:(a) Using mesh-current analysis, find a symbolic expression for iA in terms of the circuit parameters.(b) Computer the ratio iA/vS.(c) Find a symbolic expression for the equivalent resistance of the circuit by combining resistors in
6. Build, test, and implement the database and applications The purpose of this chapter is to build on the Tiers of Software Development and to provide a framework for the life cycle of most software development projects. This is important prior to explaining the details of the user interface and
5. Design the database and accompanying applications The purpose of this chapter is to build on the Tiers of Software Development and to provide a framework for the life cycle of most software development projects. This is important prior to explaining the details of the user interface and analysis
4. Convert business requirements to system requirements The purpose of this chapter is to build on the Tiers of Software Development and to provide a framework for the life cycle of most software development projects. This is important prior to explaining the details of the user interface and
3. Gather business requirements The purpose of this chapter is to build on the Tiers of Software Development and to provide a framework for the life cycle of most software development projects. This is important prior to explaining the details of the user interface and analysis tools that are
2. Define that system’s goals The purpose of this chapter is to build on the Tiers of Software Development and to provide a framework for the life cycle of most software development projects. This is important prior to explaining the details of the user interface and analysis tools that are
1. Determine the need for a system to assist a business process The purpose of this chapter is to build on the Tiers of Software Development and to provide a framework for the life cycle of most software development projects. This is important prior to explaining the details of the user interface
11-1 Network Functions (Sects. 11–1 and 11–2)Given a linear circuit:(a) Find specified network functions and locate their poles and zeros.(b) Select the element values to produce specified poles and zeros.
11-2 Network Functions, Impulse Response, and Step Response (Sects. 11–3 and 11–4)(a) Given a first- or second-order linear circuit, find its impulse or step response.(b) Given the impulse or step response of a linear circuit, find the network function.(c) Given the impulse or step response of
11-3 Network Functions and the Sinusoidal Steady-State Response (Sect. 11–5)(a) Given a first- or second-order linear circuit with a specified input sinusoid, find the sinusoidal steadystate response.(b) Giventhe networkfunction,impulse response, or step response, find the sinusoidal steady-state
11-4 Network Functions and Convolution (Sect. 11–6)(a) Given the impulse response of a linear circuit, use the convolution integral to find the response to a specified input.(b) Use the convolution integral to derive properties of linear circuits.
11-5 Network Function Design and Evaluation (Sect.11–7)(a) Design alternative circuits that realize a given network function and meet other stated constraints.(b) Use software to visualize and simulate alternative designs.(c) Evaluate alternative designs using stated criteria and select the best
A simple series RC circuit shown in Figure 11–2 is driven by a charging exponential source. If R=10 kΩ and C =0:01 μF, the network function isFind the zero-state response υ2ðtÞ when the input is υ1ðtÞ = 10(1−e−5000t) u(t) V. Identify the natural and forced components of your answer.
(a) Find the transfer functions of the circuits in Figure 11–7.(b) Find the driving-point impedances seen by the input sources in these circuits.(c) Using R = 1kΩ, C = 1μF, and L = 1 H, show that all three circuits have the same transfer function. Then show that their driving-point impedances
(a) Show that the two OP AMP circuits in Figure 11–8 have a transfer function TVðsÞ = V2ðsÞ=V1ðsÞ of the same form.(b) Select standard values from the inside rear cover so that the transfer functions found in(a) each have a pole at s = −10,000.(c) Using the values found in (b), find the
(a) Find the input impedance seen by the voltage source in Figure 11–9.(b) Find the voltage transfer function TVðsÞ =V2ðsÞ=V1ðsÞ of the circuit.(c) Locate the poles and zeros of TVðsÞ for R1 = 10 kΩ,R2 = 20 kΩ,C1 = 0:1 μF, and C2 =0:05 μF. +1 R ww V(s) Cs FIGURE 11-9 C25 R ww +o V($)
For the circuit of Figure 11–10, (a) find the voltage transfer function TVðsÞ =V2ðsÞ=V1ðsÞ and the driving-point impedance ZðsÞ, and (b) locate the poles and zeros of the transfer function when R1 =R2 =1 kΩ,L= 10 mH, and C =0:1 μF. +1 Ls R ee w 1 C's V(s) V(8) R IGURE 11-10
Find the driving-point impedance seen by the voltage source in Figure 11–11. Find the voltage transfer function TVðsÞ =V2ðsÞ=V1ðsÞ of the circuit. The poles of TVðsÞ are located at p1 = −1000 rad=s and p2 = −5000 rad=s. If R1 =R2 =20 kΩ, what values of C1 and C2 are required? +- R +3
Suppose that capacitor C1 in the circuit of Figure 11–11 suddenly became shorted. What effect would it have on the circuit’s voltage transfer function? +1 R 13: R2 ww V(s) C28 FIGURE 11-11 V(8)
Suppose that capacitor C2 in the circuit of Figure 11–11 suddenly became open-circuited.What effect would it have on the circuit’s voltage transfer function? +1 R 13: R2 ww V(s) C28 FIGURE 11-11 V(8)
For the circuit in Figure 11–12 find the input impedance ZðsÞ =V1ðsÞ=I1ðsÞ, the transfer impedance TZðsÞ =V2ðsÞ=I1ðsÞ, and the voltage transfer function TVðsÞ =V2ðsÞ=V1ðsÞ. 1(s) V(8) (+ 1+ Cs IA(S) ww A R RIB(s) IB(S)) FIGURE 11-12 V2(8) Cs
For the circuit shown in Figure 11–12, insert a follower at pointAand find the transfer function TVðsÞ =V2ðsÞ=V1ðsÞ. Compare your result with that found in Example 11–5 for the same transfer function. I(3) V(s) (+ 1+ Cs IA(S) FIGURE 11-12 www R A R IB(S)) = V(5) Cs
Find the voltage transfer function TVðsÞ =V2ðsÞ=V1ðsÞ of the circuit in Figure 11–13 HH VA(s) R R Vc(s) VD(s) ww VB(s) +1 V(s) FIGURE 11-13 V(s) +3 + C28 Vc(s)
Consider the dependent-source circuit shown in Figure 11–13 with R1 = R2 = R and C1 = C2 = C and the resulting transfer function under those conditions shown in the example immediately above.(a) Select values for μ, R, and C so that the transfer function has purely imaginary poles at s =
(a) Find the voltage transfer function TVðsÞ =V2ðsÞ=V1ðsÞ of the circuit in Figure 11–14.(b) What are the conditions on μ that will ensure the circuit is stable? R www V(s) Cs HH Vx(s) +11 FIGURE 11-14 V(3) (3)
Figure 11–17 shows two cascade connections involving the same two stages but with their positions reversed. Do either of these connections involve loading? If not, use the chain rule to find the overall transfer function. V(s) R ww Cs R Cs V(3) R3 (a) ZIN(S) R R V(s)+ Cs R33 ZT(s) (b) FIGURE
Figure 11–18 shows two cascade connections involving the same two stages but with their positions reversed. Does either of these connections involve loading? Find their voltage transfer functions and, if loading is present, determine the condition necessary to minimize the effect. + Rs w V(s) ww
Find the response υ2ðtÞ in Figure 11–20 when the input is υ1ðtÞ = δðtÞ. Use the element values R1 =10 kΩ,R2 =12:5 kΩ,C1 =1 μF, and C2 =2 μF. R ww V(8) ww V(s) Cs Cs R +1 FIGURE 11-20 19
A certain circuit has the following voltage transfer function:Find the circuit’s impulse response h(t). Tv (s)=- 10's (s+10) (s+10)
The impulse response of a linear circuit is h(t) = 200e−100tu(t). Find the output when the input is a unit ramp r(t) = tu(t).
The impulse response of a circuit is h (t)= 100e−20tu(t). Find the output when the input is a step function x(t) = u(t).
Find the impulse response of the circuit in Figure 11–21. V(f) 1+ 9 www 1 1 F FIGURE 11-21 ww o+ V2(f)
The element values for the circuit in Figure 11–23 are R1 =10 kΩ,R2 = 100 kΩ, C1 =C2 = 0:1 μF, and υ1ðtÞ = uðtÞV. Find the response υ2ðtÞ. R www V(s) +3 FIGURE 11-23 R w + C28 V2(3)
Design a circuit that will produce the following step response output: 02 (1)= [1-e-1000u(t) V
The step response of a linear circuit is gðtÞ = 5½1−e−200t uðtÞ. Find the output waveform when the input is xðtÞ = ½12e−200t uðtÞ. Use the inverse Laplace function to visualize(plot) the response yðtÞ.
A particular circuit has the following voltage transfer function:Find the circuit’s step response g t ð Þ, impulse response h t ð Þ, step response transform G s ð Þ, and impulse response transform H s ð Þ. Tv(s)= s+5 S+10
Three time-domain parameters often used to describe the step response are rise time, delay time, and overshoot. Rise timeðTRÞ is the time interval required for the step response to rise from 10% to 90% of its steady-state value gð∞Þ. Delay timeðTDÞ is the time interval required for the step
The impulse response of a circuit is h(t)= 8000(600t−1)e−800tu (t). Find and plot the step response. Find approximate values for the rise time, delay time, and overshoot.
Find the steady-state output inFigure11–27(a) for a general input υ1ðtÞ =VAcosðωt + ϕÞ.Then for L= 1mH, R= 100 Ω, and v1ðtÞ = 10 cos ð100 k t + 135Þ V, find v2SSðtÞ.Finally, use Multisim to verify your result. Ls m 1+1 +V(s) R V(s) (a) FIGURE 11-27
Find the steady-state output in Figure 11–28 for a general input υ1ðtÞ =VAcos ðωt + ϕÞ V. R w R 1/Cs + V(s) 10 FIGURE 11-28 V($) 10
A sensitive piece of electronic equipment is interfered with by a 60Hz hum.A manufacturer claims his simple circuit can effectively eliminate that noise. The manufacturer’s specification sheet does not show what components make up the design, but rather, lists the transfer function asand claims
Rather than purchasing the device in Example 11–14, design a circuit to achieve the transfer function given. (Hint: Use a series RLC circuit with the output voltage taken appropriately.)
The impulse response of a linear circuit is:(a) Find the sinusoidal steady-state response when x(t) = 5 cos 1000t.(b) Repeat (a) when x(t) = 5 cos 3000t. h(t)=5000 [2e-1000 cos 2000t-e-1000t sin 2000t]u(t).
The transfer function of a linear circuit is TðsÞ = 5ðs + 100Þ=ðs + 500Þ. Find the steady-state output for(a) xðtÞ = 3 cos 100t(b) xðtÞ = 2 sin 500t
The impulse response of a linear circuit is hðtÞ = δðtÞ−100 e−100t uðtÞ. Find the steady-state output for(a) xðtÞ = 25 cos 100t(b) xðtÞ = 50 sin 100t
A linear circuit has an impulse response hðtÞ = 2e−tuðtÞ and an input xðtÞ = e−2tuðtÞ.Find the zero-state response using(a) The s-domain process in Eq. (11–23)(b) The t-domain convolution integral in Eq. (11–24)
A linear circuit has an impulse response hðtÞ = e−100tuðtÞ and an input xðtÞ = t uðtÞ.(a) Find the zero-state response using the t-domain convolution integral.(b) Validate your answer using both the s-domain process and MATLAB.(c) Which method was the easier to use?
A linear circuit has an impulse response hðtÞ = e−10tuðtÞ and an input xðtÞ = 5uðtÞ. Find the zero-state response using the t-domain convolution integral.
Use time-domain and s-domain convolution to find the zero-state response when hðtÞ = xðtÞ = 2e−t ½ uðtÞ
Use the convolution integral to find the zero-state response for hðtÞ = 2uðtÞ and xðtÞ = 5½uðtÞ−uðt−2Þ.
Use the convolution integral to find the zero-state response for hðtÞ = 2uðtÞ and xðtÞ = 5½uðtÞ−uðt−2Þ.
Repeat Example 11–19 by mathematically, not geometrically, computing the convolution integral. Verify that the result is equivalent to the answer found for Example 11–19.You may use MATLAB
Design an RC circuit to realize the following transfer function T(s) = 200 s+1000
Design an RL circuit to realize the following transfer function: T(s)= 200 s+1000
Design an RC circuit to realize the following transfer function T(s)= 500 s+10,000
Design an active RC circuit to realize the following transfer function T(s)= 2000 S+1000
Design an active RL circuit to realize the following transfer function T(s)= 2000 S+1000
Design a circuit to realize the following transfer function using only resistors, capacitors, and OP AMPs: Tv(s)=- (s+) 3000s (s +1000) (s+4000)
Design a circuit to realize the following transfer function using only resistors, capacitors, and no more than one OP AMP. Tv(s) = 10 (s+103)2
Design an active RC prototype circuit to realize the following transfer function T(s)=-100+50 s+100
Design a circuit to realize the transfer function given in Example 11–20 using inverting OP AMP circuits.
Design a circuit to realize the following transfer function using only resistors, capacitors, and no more than one OP AMP. Tv(s)= -10% (s+10)
Magnitude scale the circuit in Figure 11–40 so all resistances are at least 10 kΩ and all capacitances are less than 1 μF. 1 1 ww 3 www 4000 1000 + + 1st stage. FIGURE 11-40 2nd stage
Select a magnitude scale factor for each stage in Figure 11–36 so that both capacitances are 0:01 μF and all resistances are greater than 10 kΩ. 1000 2 4000 -2nd stage 3rd stage 1st stage- FIGURE 11-36
Select a magnitude scale factor for the OP AMP circuit in Figure 11–39. + V(s) 5000 w 1 100 w 100 FIGURE 11-39 + V(8)
Find a second-order realization of the transfer function given in Example 11–20.
Design a second-order circuit to realize the following transfer function: Tv (s)= 106 (s+10)
Design a second-order circuit to realize the following transfer function using practical, standard values: Tv(s)= 2x1010 s+10s +10%
Given the step response g(t) = +- [1 + 4e−500t] u(t),(a) Find the transfer function T(s).(b) Design two RC OP AMP circuits that realize the T(s) found in part (a).(c) Evaluate the two designs on the basis of element count, input impedance, and output impedance.
The following transfer function was realized in different ways in Figures 11–37, 11–41, and 11–45:Compare the various designs in a table similar to Table 11–1. Which would you recommend if (a) There was no power available?(b) There was a desire not to invert the output and to avoid using
There is a need to realize the following transfer function using practical standard values:In researching distributers’ catalogs, the manufacturer of the circuit shown in Figure 11–48, claimed it could produce the desired transfer function. Element values were not provided, but your supervisor

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