Figure 7.1 b - John Wiley & Sons · Fundamentals of Electric Circuit Analysis, by Clayton Paul Figure 7.1 Illustration of a switching operation in a first-order RL circuit: (a) the

Fundamentals of Electric Circuit Analysis, by Clayton Paul

Figure 7.1 Illustrationof a switching operation in afirst-order RL circuit:(a) the physicalconfiguration, (b) the circuitfor t > 0 (in steady state),(c) the transition to steadystate in the t > 0 circuit, (d)the natural solution for theinductor current, illustratingthe time constant T, (e) thetotal solution for the inductorcurrent, showing the naturaland forced components ofthat solution, and ( f ) thesolution for the inductorvoltage.


Figure 7.2 Reducing all first-order circuits containing an inductor to (a) a Theveninequivalent and (b) a Norton equivalent, and (c) determining the forced solution for theinductor current from the Norton equivalent circuit.


Figure 7.3Example 7.1.


Figure E7.1Exercise Problem 7.1.


Figure 7.4 The first-order RC circuit: (a) the physical circuit, (b) the response of thecapacitor voltage, and (c) determining the forced solution for the capacitor voltage.


Figure 7.5 Reducing all first-order circuits containing a capacitor to (a) a Nortonequivalent and (b) a Thevenin equivalent, and (c) determining the forced solution for thecapacitor voltage from the Thevenin equivalent circuit.






Figure 7.7 The second-order series RLC circuit: (a) the physical circuit, (b)determining the differential equations for the inductor current and capacitor voltage usingthe differential operator impedances, (c) determining the forced solutions for the inductorcurrent and capacitor voltage, and (d ) the t = 0+ circuit (immediately after switch closure)for determining the derivatives of the inductor current and capacitor voltage at t = 0+.


Figure 7.8Plots of the overdamped,underdamped, andcritically dampedsolutions of Example 7.3for (a) the inductorcurrent, and (b) thecapacitor voltage.


Figure 7.9 The second-order parallel RLC circuit: (a) the physical circuit, (b)determining the differential equations for the inductor current and capacitor voltage usingthe differential operator impedances, (c) determining the forced solutions for the inductorcurrent and capacitor voltage, and (d ) the t = 0+ circuit (immediately after switch closure)for determining the derivatives of the inductor current and capacitor voltage at t = 0+.


Figure 7.10The unit impulse function: (a) u(t), (b) u(t – t0), and (c) Au(t).


Figure 7.11The unit impulsefunction: (a) δ (t),(b) approximating theunit impulse as asequence of pulseswhose width shrinksto zero but whose arearemains unity,(c) Aδ (t), and(d ) δ (t – t0).


Figure 7.12The Laplace-transformed circuitelements: (a) theresistor, (b) theinductor, (c) apreferred equivalentcircuit of the inductor,(d ) the capacitor, (e) apreferred equivalentcircuit of the capacitor.


Figure 7.13The Laplace-transformed circuitfor mutual inductance:(a) the time-domaincircuit, (b) oneLaplace-transformedequivalent circuit, and(c) the preferredLaplace-transformedequivalent circuit.


























Figure 7.20Solution of the first-order RLcircuit with the Laplacetransform method: (a) thetime-domain circuit, (b) theLaplace transformed circuit,(c) using superposition todetermine the portion of theresponse due to the inductorinitial current and the portionof the response due to theopen-circuit voltage source(which represents the effect ofthe actual sources in thecircuit), (d ) plot of theinductor current response, and(e) plot of the inductor voltageresponse.




Figure 7.22Solution of the first-order RC circuit withthe Laplace transformmethod: (a) the time-domain circuit,(b) the Laplacetransformed circuit,(c) plot of thecapacitor voltageresponse, and (d ) plotof the capacitorcurrent response.




























Figure 7.32 Viewing a circuit with one independent source and zero initial conditionsas a single-input (the source), single-output (the desired voltage or current) system in (a)the time domain, and (b) the Laplace transform domain.




















Figure 7.39PSPICE plots of theinductor current forExample 7.31.


Figure 7.40Modeling an impulsefunction as a pulse.




Figure 7.42Results for the capacitorvoltage in Example 7.32:(a) unit step response,(b) unit impulse response,and (c) unit impulseresponse showing thebeginning time behavior.




Figure 7.44MATLAB plotsof the inductorcurrent ofExample 7.33.


Figure 7.45MATLAB plotsof the capacitorvoltage impulseresponse inExample 7.34.


Figure 7.46MATLAB plotsof the capacitorvoltage stepresponse inExample 7.34.


Figure 7.47 A light flasher: (a) the physical circuit, and (b) the resulting waveform ofthe capacitor voltage.


Figure 7.48Illustration of theeffect of aconnection cable’scapacitance andinductance on thetransmittedwaveforms: (a)the physicalcircuit, (b) anequivalent circuit,(c) the Laplacetransformedcircuit, and (d )the PSPICE nodelabeling.


Figure 7.49The PSPICEsimulation of the loadvoltage of the circuitin Fig. 7.48 Showing(a) the ringing forR=0Ω caused by thecable’s capacitanceand inductance, andthe load voltage for(b) R=100Ω, and (c)R=250Ω.


Figure 7.50Illustration ofcrosstalk betweentransmission linescaused by theirmutual capacitanceand inductance:(a) the physicalconfiguration, and(b) an equivalentcircuit with typicalvalues and nodesnumbered for usein PSPICE.


Figure 7.51The PSPICEsimulation of the near-end crosstalk voltage.


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Figure 7.1 b - John Wiley & Sons · Fundamentals of Electric Circuit Analysis, by Clayton Paul Figure 7.1 Illustration of a switching operation in a first-order RL circuit: (a) the