0.1Introduction:Students taking this course must be able to perform the- mesh- loop- nodalmethods for DC and AC steady-state circuit analysis on circuits containing- Resistors, Capacitors, Inductors- Op Amps- Ideal Transformers- Mutual Inductance- Independent Voltage and Current Sources- Dependent Voltage and Current Sources Students must be able to load these circuits into SPICE and determine the currents and voltages throughout the circuit.Node Voltage Example:0.2Perform phasor analysis to determine Vo. Since the frequency of the source is not specified, leave impedances in terms of j = p.vs(t) = cos(t) V2 4 0.5 F2 H+vo(t)-Show that ( )V Vpp pVo s s 222 2 2123 33 99033 tan Show v0(t) = .33cos(2t-9.46) V , when =20.3Mesh Current Example:Perform phasor analysis to determine CVˆ. Assume v)602cos(5)( ttvs.Write a SPICE program to also find this value.Show that 101.tan1)01(.5.0ˆˆ122scVV Show vc(t) = 0.6410cos(t-75.1439) v , when =2601000ixvs1K10K1FixvC1000ixvs1K10Kvc1FVixix012340.4* This SPICE program solves the review example* that contains a current controlled voltage sourceV1 1 0 AC 5 0VIX 2 3 AC 0 0R1 1 2 1KR2 3 4 10KC1 4 0 1UHIX 3 0 VIX 1000.AC LIN 1 60 60.PRINT AC VM(4,0) VP(4,0).ENDComplex Number and Phasor Notation Review:Why are complex numbers used in circuit analysis?0.5Important Facts: - For a linear circuit driven by a sinusoidal source (input), the steady-state voltages and currents everywhere in the circuit will have the same frequency as the input.- The only changes between the source current and voltage, and everywhere else in the circuit, is the magnitude and phase of the sinusoids.Therefore, a single complex number can be used to represent the critical quantities ofthe sinusoidal current and voltages.A t A A A jAcos( ) e cos( ) sin( ) jIn phasor analysis the frequency of the input (source) is used to compute impedances,and only the magnitudes and phases are computed for the output (dependent) quantities.Complex Number Plane:Each point in the complex number plane represents a sinusoid for a single frequency.0.6 REIMabrSketch 10cos(2t + 30) in time, and in the complex number plane.Each point in the complex number plane can also represent a path in a circuit from areference point (input) to another point of interest (output). Recall first circuit example: ( )V Vpp pVo s s 222 2 2123 33 99033 tanFor =2: ( ) ( )(. . ) ( )V V H j V H V Ho s s s 21 0 33 9
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