LectRFEEE 2021 Final Exam Review Dr. Holbert April 28, 2008

LectRFEEE 2022 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

LectRFEEE 2023 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

LectRFEEE 2024 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 = I Z A phasor is a complex number that represents the magnitude and phase of a sinusoidal voltage or current x(t) = X M cos(ωt+θ) ↔ X = X M  θ Time domainFrequency Domain

LectRFEEE 2025 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 ElementImpedance Resistor Z R = R = R  0  Inductor Z L = sL = jωL = ωL  90  Capacitor Z C = 1/(sC) = 1/(jωC) = –1/(ωC)  90 

LectRFEEE 2026 Complex Numbers x is the real part y is the imaginary part z is the magnitude  is the phase angle  z x y real axis imaginary axis Polar: z   = A = x + jy :  Rectangular

LectRFEEE 2027 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  ) H(j  ) = H(s) X(j  ) e j  t = X(s) e st Y(j  ) e j  t = Y(s) e st

LectRFEEE 2028 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 ω 0dB without poles/zeros at origin: use 20 log 10 (K) dB –Poles and zeros of the form (1 + j  ) Sketching the magnitude and phase plots Reverse: Bode plot to transfer function

LectRFEEE 2029 Bode Plot Sketch Summary PlotPole (–) or Zero (+) Gain (mag- nitude) Rolloff at ω break =1/  ; slope of ±20 dB/decade PhaseAsymptotic shift of ±90° with ±45°/dec slope and ±45° cross-over at ω break ω Pole at ω break =1/  Gain Phase ω 0° –45° –90° One Decade 0 dB –20 dB ωpωp

LectRFEEE Bode Plots of Common Filters Frequency High Pass Frequency Low Pass Frequency Band Pass Frequency Band Reject Gain

LectRFEEE Some Terminology & Quantities 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

LectRFEEE 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