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## Final Exam Review

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**Final Exam Review**Dr. Holbert April 28, 2008 EEE 202**Don’t Forget the Essentials**• Verify voltage polarity and current direction • Obey the passive sign convention • The Fundamentals: Ohm’s Law; KCL; KVL • Series/Parallel Impedance combinations EEE 202**Circuit Analysis Techniques**• All these circuit analysis techniques have wide applicability: DC, AC, and Transient • Voltage and Current Division • Nodal and Loop/Mesh Analyses • Source Transformation • Superposition • Thevenin’s and Norton’s Theorems EEE 202**AC Steady-State Analysis**• AC steady-state analysis using phasors allows us to express the relationship between current and voltage using an Ohm’s law-like formula: V = IZ • A phasor is a complex number that represents the magnitude and phase of a sinusoidal voltage or current x(t) = XM cos(ωt+θ) ↔ X = XMθ Time domain Frequency Domain EEE 202**Impedance Summary**• Z is called impedance(units of ohms, Ω) • Impedance is (often) a complex number, but is not technically a phasor • Impedance depends on frequency, ω EEE 202**x is the real part**y is the imaginary part z is the magnitude q is the phase angle imaginary axis y z real axis q x Complex Numbers Polar: z q = A = x + jy :Rectangular EEE 202**X(j)ejt = X(s)est**Y(j)ejt = Y(s)est H(j) = H(s) Transfer Function • Recall that the transfer function, H(s), is • The transfer function in a block diagram form is • The transfer function can be separated into magnitude and phase angle information (s=jω) H(j) = |H(j)| H(j) EEE 202**Bode Plots**• Place system function in standard form • The terms should appear as: (1 + s) • Magnitude and phase behavior of terms • Constant gain term (K): • with poles/zeros at the origin: find ω0dB • without poles/zeros at origin: use 20 log10(K) dB • Poles and zeros of the form (1 + j) • Sketching the magnitude and phase plots • Reverse: Bode plot to transfer function EEE 202**Bode Plot Sketch Summary**ωp Gain 0 dB –20 dB ω Phase One Decade 0° –45° –90° ω Pole at ωbreak=1/ EEE 202**Bode Plots of Common Filters**Gain Gain Low Pass High Pass Frequency Frequency Band Pass Band Reject Gain Gain Frequency Frequency EEE 202**Our vocabulary has expanded further with several new terms,**including: Resonant frequency Quality factor (Q) Decibels (dB) and decade Active vs. passive filter Phase shift lead/lag RMS current/voltage Bandwidth Break freq., corner freq., cutoff freq., half-power frequency Notch filter Butterworth filter FFT Some Terminology & Quantities EEE 202**Course Summary**• Bottom line for the semester—can you perform a comprehensive analysis of a given electrical network by determining (as appropriate): • the dc and/or ac output of the circuit • the system response to a step or impulse input • the network transfer function(s) • the system characteristics such as the poles and zeros, and the type of damping exhibited • the frequency response by sketching a Bode plot (magnitude and phase) of the system function • the type of filtering the circuit performs, if any EEE 202