Figure 6.1 a A ωt b A ωt c A ωt φ d A ωt A ωt A ωt A ωt · 2000-06-21 · Figure 6.1...

Fundamentals of Electric Circuit Analysis, by Clayton Paul

Figure 6.1 Illustration of sinusoidal waveforms: (a) A sin ωt, (b) A cos ωt, (c) Asin(ωt + φ ), and (d ) the relation between sin and cos: A sin ωt = A cos(ωt – 90°), A cosωt = A sin(ωt + 90°).

Figure 6.2A general periodic function: x(t) = x(t ± nT ).

Figure 6.3Representing (a) aperiodic function(a square wave) as(b) the sum ofsinusoidalcomponents.

Figure 6.4Representing aperiodic sourcewaveform as the sumof its sinusoidalcomponents so thatsuperposition can beused to determinethe response to thatperiodic waveform.

Figure 6.5An example of a circuit that is driven by a sinusoidal source.

Figure 6.6Representation of a complex number as a vector in two-dimensional space.

Figure 6.7 Illustration of (a) the sum and (b) the difference of two complex numbersas the addition and subtraction of vectors.

Figure 6.8 Representation of a complex exponential source as the connection of twosources (series for a voltage source and parallel for a current source) using Euler’s identity.

Figure 6.9 The key to the phasor method: in order to determine the response to eithera sine or a cosine source, replace the source with the complex exponential source and usesuperposition.

Figure 6.10 Solution of the circuit of Fig. 6.5 by replacing the original source withthe complex exponential source and using Euler’s identity and superposition.

Figure E6.4Exercise Problem 6.4.

Figure 6.11The phasor impedances for (a) the resistor, (b) the inductor, and (c) the capacitor.

Figure 6.12 Illustration of converting (a) the time-domain circuit to (b) its phasor, orfrequency-domain, equivalent.

Figure 6.13Example 6.4.

Figure 6.22Illustration of averagepower delivered to anelement: (a) the time-domain relation forthe element, (b) plotof the instantaneouspower, and (c) theaverage powerdelivered to anelement in terms of itsphasor voltage andphasor current.

Figure 6.24Illustration of the power relations for a resistor.

Figure 6.25Illustration of the power relations for an inductor.

Figure 6.26Illustration of the power relations for a capacitor.

Figure 6.28Illustration of the concept of power factor.

Figure 6.30Illustration of a power transmission line connecting a source to a load.

Figure 6.31Illustration of thetypical source-loadconfiguration fordeterminingmaximum powertransfer.

Figure 6.32Illustration of theprinciple ofsuperposition ofaverage powerfor sinusoidalsources ofdifferentfrequencies.

Figure 6.35Application of a current source having a periodic waveform to a resistor.

Figure 6.37Use of rms voltages and currents in phasor circuits.

Figure 6.39Interpreting a phasorquantity in the timedomain as theprojection of therotating phasor on thereal axis (for a cosine)or on the imaginaryaxis (for a sine).

Figure 6.40An exampleillustrating thevisualization ofphasor voltages andcurrents in a phasordiagram: (a) thetime-domain circuit,(b) the phasor circuit,and (c) the phasordiagram.

Figure 6.41Element impedances for computing transfer functions where p = jω.

Figure 6.42 Viewing a linear system or electric circuit in block diagram form:(a) time domain, and (b) frequency domain.

Figure 6.45 Illustration of series resonance: (a) the series LC circuit, (b) the phasorequivalent, and (c) a plot of the magnitude of the series impedance versus radian frequencyshowing that the impedance is zero at ω0 = 1/√ LC, where the series combination acts likea short circuit.

Figure 6.46 Illustration of parallel resonance: (a) the parallel LC circuit, (b) thephasor equivalent, and (c) a plot of the magnitude of the parallel admittance versus radianfrequency showing that the admittance is zero at ω0 = 1/√ LC where the parallelcombination acts like an open circuit.

Figure 6.47 Illustration of the magnitude of the transfer function for (a) a lowpassfilter, (b) a highpass filter, (c) a bandpass filter, and (d ) a bandreject filter.

Figure 6.48Circuit implementation of(a) a lowpass filter, (b) ahighpass filter, (c) a bandpassfilter, and (d ) a bandrejectfilter.

Figure 6.49An op-amp (active) bandpass filter.

Figure 6.50Representation of athree-phase powersource: (a) the circuitmodel, (b) the phasordiagram, and (c) physicalconstruction of athree-phase generator.

Figure 6.51Two common loadconnections: (a) thewye-connected load,and (b) the delta-connected load.

Figure 6.54PSPICE plots of thefrequency response of thebandpass filter of Fig. 6.53:(a) magnitude (in decibels),(b) magnitude (absolute),and (c) phase (degrees).

Figure 6.57 MATLAB plots of the frequency response of the bandpass filter of

6.53: (a) magnitude (in decibels), and (b) phase (degrees).

Figure 6.58AM radio transmission.

Figure 6.59Design of a filter for AM radio transmissions: Example 6.31.

Figure 6.60Illustration of thephenomenon of crosstalkbetween wire-connectedcircuits: (a) the physicalconfiguration of two pairsof closely spaced wires,(b) magnetic field coupling,(c) electric field coupling,(d) a lumped-circuit modelof the interaction betweenthe two circuits, and (e)typical element valuesalong with the PSPICEnode labeling.

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Figure 6.1 a A ωt b A ωt c A ωt φ d A ωt A ωt A ωt A ωt · 2000-06-21 · Figure 6.1...

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