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## EE202 Supplementary Materials for Self Study

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**EE202 Supplementary Materialsfor Self Study**Circuit Analysis Using Complex Impedance Passive Filters and Frequency Response**Acknowledgment**Dr. Furlani and Dr. Liu for lecture slides Ms. Colleen Bailey for homework and solution of complex impedance Textbook: Nilsson & Riedel, “Electric Circuits,” 8th edition**Steady-State Circuit Response to Sinusoidal Excitation -**Analysis Using Complex Impedance**Household Circuit Breaker Panel**240V Central Air 120V Lighting, Plugs, etc.**Single Frequency**Sinusoidal Signal**Sinusoidal Signal**Amplitude Peak-to-peak Root-mean-square Frequency Angular Frequency Period**Trigonometry Functions**Appendix F**Other Periodic Waveforms**Fundamental and Harmonics**Resistor Only Circuit**I=V/R, i(t)=v(t)/R Instantaneous Response**R-L Circuit**Transient Steady-state**Phase Shift**Time Delay or Phase Angle: t / T *2 or *360-degree**Phasor – Complex Number**Z Real(Z)+j Imag(Z) Y Imag(Z) tan-1(Y/X) X Real(Z) Reference**Observations**Single Frequency for All Variables Phasor Solution of Diff Eq. Algebraic equation Extremely simple Phase Delay between variables Physical Measurements Real part of complex variables v = Real{V}; i = Real{I}**Impedance in Series**Complex Impedance Resistance, Reactance**Example**=5000 rad/sec**Apply ZL=jL, ZC=1/j C**Zab=90+j(160-40)=90+j120=sqrt(902+1202)exp{jtan-1(120/90)} =150 53.13 degree I=750 30 deg / 150 53.13 deg = 5 -23.13 deg=5exp(-j23.13o)**Impedance in Parallel**Complex Admittance Conductance, Susceptance**Example**=200000 rad/sec**Apply ZL=jL, ZC=1/j C**Series: Use Z; Parallel: Use Y Y=0.2 36.87 deg; Z=5 -36.87 deg V=IZ=40 -36.87 deg**Kirchhoff’s Laws**Same Current at a Node Addition of current vectors (phasors) Voltage Around a Loop or Mesh Summation of voltage vectors (phasors)**Voltage divider**Vo=36.12-j18.84 (V)**Find VTh**Vx=100-I*10, Vx=I*(120-j40)-10*Vx; solve Vx and I VTH=10Vx+I*120=784-j288 (V)**Find ZTh**Calculate Ia Determine Vx Calculate Ib ZTh=VT/IT=91.2-j38.4 (Ohm)**Transformer**Time differentiation replaced by j**AC Sine Wave, Ideal Transformer**Voltage and Current Power Conserved**Transformer**• Power Applications • Convert voltage • vout=(N2/N1) vin • Signal Applications • Impedance transformation • Xab=(N1/N2)2 XL • Match source impedance with load to maximize power delivered to load**Frequency Response of Circuits**• Analysis Over a Range of Frequencies • Amplifier Uniformity • Filter Characteristics • Low pass filter • High pass filter • Bandpass filter • Equalizer**RC Filters**High Pass Low Pass