EE 213
Basic Circuit Analysis II
Spring 2014
Lecture Summary

Lecture 1: (1/15) Course Outline and introduction. Sinusoids: properties and motivation for using in circuit analysis. Operations on sinusoids.

Lecture 2: (1/17) Real sinusoids. Review complex numbers. Complex sinusoids and phasors. Steady state sinusoidal analysis (SSSA), impedence. Procedure for finding output voltage/ current.

Lecture 3: (1/22) SSSA for circuits, phasors, impedence, review KVL (mesh analysis), KCL (node analysis). SSSA circuit examples (using matlab to solve equations.

Lecture 4: (1/24) Sinusoids and (matlab plots),. Review steps for Steady State Sinusoidal Analysis (SSSA). Frequency response and computation using circuit analysis. Transfer function and examples.

Lecture 5: (1/27) Frequency response and computation using circuit analysis. Transfer function and examples. Using matlab to plot transfer function. Example, second order circuit, bandpass filter, (frequency response).

Discussion Section: (1/28) Homework problems, sinusoids, phasors, transfer function. (will be posted).

Lecture 6: (1/29) Review calculation of transfer function from circuit analysis. Thevenin and Norton equivalent circuits. Example. Power of sinusoid and power from circuit elements. Maximum power transfer.

Lecture 7: (1/31) Review power of sinusoid and power from circuit elements and Maximum power transfer. Introduction to operational amplifiers. Pin diagram and internal circuitry. Study of input/output behavior of op amps and applications, terminal characteristics. PS 1 due.

Lecture 8: (2/3) Matrix and MATLAB review. Matrix addition, multiplication, inversion. Solving systems of linear equations. Introduction to operational amplifiers. amplifier with and without feedback.

Lecture 9: (2/5) Opamp circuit application; inverting amplifier without and with feedback. Ideal opamp characteristics; current into each input is 0 and no voltage drop across inputs. Passive and active circuits. Advantages of active circuits; amplifier gains, don't need inductors, outputs buffered (can build filters in cascade). SSSA with op amps. Example. Introduction to Laplace Transform.

Discussion Section: (2/7) Homework problems, sinusoidal steady state analysis, power, transfer function.

Lecture 10: (2/10) More realistic model for Opamp. Analysis of inverting amplifier with feedback. Introduction to Laplace Transform. Motivation: alternate way of analyzing circuits, generalizes sinusoidal steady state analysis, Laplace Transforms can also handle initial conditions. Laplace transform definition.

Lecture 11: (2/12) Laplace Transform pair; evaluating integral, properties, building tables. Examples. Properties; linearity, time shift, time scaling. Using properties to compute Laplace Transform. Impulse signal and properties.

Discussion Section: (2/14) Homework problems, Laplace Transforms; computation by integrating, properties, tables, and symbolic MATLAB.

Lecture 12: (2/19) Impulse signal, sifting integral property, and Laplace Transform of impulse signal. Laplace transform and examples. Derivative property and derivation. Application to circuits (capacitor and inductor relationships). Application to solving differential equations. Initial Value Theorem and Final Value Theorem. Derivation and examples.

Lecture 13: (2/21) Laplace Transform, region of convergence, example. Inverse Laplace Transform, using tables. Rational functions; poles, zeros. Finding inverse Laplace Transform of rational functions; making rational funciton proper, partial fraction expansion, taking inverse Laplace Transform. Residue method for rational function with simple poles. Example. PS 3 due.

Lecture 14: (2/24) Laplace Transform and Inverse Laplace Transform, using tables and properties. Rational functions; poles, zeros. Finding inverse Laplace Transform of rational functions; making rational funciton proper, partial fraction expansion, taking inverse Laplace Transform. Residue method for rational function with simple poles/ repeated poles. Complex poles. Examples.

Lecture 15: (2/26) Transfer function. Poles and zeros. Region of convergence. Zero state response (ZSR). Computing ZST; find transfer function, compute Laplace Transform of input, find output, find inverse Laplace Transform. Examples. 2nd order circuits; underdamped, critically damped, overdamped cases.

Lecture 16: (2/28) Zero State Response (ZSR) using Laplace Transform. Examples. 2nd order circuits; underdamped, critically damped, overdamped cases. Step response, impulse response, arbitrary respons. Using Laplace Transform to find solutions to Linear Constant Coefficient Differential Equations.

Lecture 17: (3/3) Zero State Response (ZSR) using Laplace Transform. Alternate method of computing ZSR using convolution integral. Convolution integral: definition, commutative property. Computing convolution integral for RC circuit with decaying exponential input. PS 4 due. Lecture 18: (3/5) Convolution procedure. Computing convolution integral for RC circuit with pulse input. Step response and relation to impulse response. Natural response and relation to step response. Using MATLAB to perform numeric convolution.

Discussion Section: (2/14) Review for exam.

Lecture 19: (3/7) Convolution procedure. Example (natural response of RC circuit). Ways of getting zero state response; Laplace transform, convolution, properties. Convolution properties; commutative, associative, distributive, time shift.

Lecture 20: (3/10) Convolution example. Total response; Zero state response, zero input response. Using Laplace Transform to get total response. Handling initial conditions; voltage across capacitor, current through inductor. Example.

Exam 1: (3/12)

Lecture 21: (3/14) Total response, zero input response. Handling initial conditions. Examples. PS 5 due.

Lecture 22: (3/17) Total response, zero input response. Handling initial conditions. Example. Introduction to state space methods.

Discussion Section: (3/19) Total response and convolution integral.

Lecture 23: (3/21) Introduction and motivation to state space methods. Replace capacitors with current sources and inductors with voltage sources. Conduct circuit analysis to get first order vector differential equations with output equation. Identify A,b,c,and d. Example.

Lecture 24: (3/31) State space methods. Replace capacitors with current sources and inductors with voltage sources. Conduct circuit analysis to get first order vector differential equations with output equation. Identify A,b,c,and d. Examples.

Lecture 25: (4/2) State space method. Example. Getting Laplace Transform of output from A, b, c, d. Get transfer function from state space solution. PS 6 due.

Lecture 26: (4/4) Review state space equations. Getting transfer function, impulse response, step response, and frequency response from state space realization. Getting total response (direct using Laplace Transform, state space method, linear constant coefficient differential equations). Getting state space realization from linear constant coefficient differential equations. Example. Review first order systems (transfer function): lowpass filter, circuit realization, pole, impulse response, step response.

Lecture 27: (4/7) First order system: high pass filter, circuit realization, pole/zero, impulse response, step response. Second order system: low pass filter, circuit realization, poles, step response (over damped, critically damped, under damped), frequency response. Repeat for high pass filter, bandpass filter.

Lecture 28: (4/9) Bounded input/ bounded output stability. Determining stability, region of convergences (ROC), ROC must include jw axis. Example of unstable circuit. Introduction to filter design, frequency selective filters. Ideal lowpass filter, approximation to ideal frequency response, tolerance (passband, stopband). How to design filters; design stage to approximate transfer function (look at magnitude), realization using cascade of filters. PS 7 due.

Lecture 29: (4/11) Introduction to filter design, frequency selective filters. Approximation to ideal frequency response; use approximation filter given specifications, circuit implementation using a case of biquad filters and first order filter. Bode plots; finding an approximation based on poles and zeros. Magnitude and phase plots. Magnitude plots using dB scale. Simple pole plots.

Lecture 30: (4/14) Bode plots; finding an approximation based on poles and zeros. Simple poles, pair of complex poles. Find plots of magnitude and phase for rational transfer functions. Filter design; approximation to ideal frequency response. Introduction to Butterworth filters.

Lecture 31: (4/16) Butterworth filter design. Lowpass filters. Properties; monotonic decreasing,poles on unit circle, high frequency rolloff, Maximally flat in passband (first 2n-1 derivatives at 0 are 0). Pole structure for even and odd order filter. Circuit implementation using biquads and first order circuits in series. PS 8 due.

Discussion Section: (4/17) Convolution, total response, state space mathods.

Lecture 32: (4/21) Frequency selective filter design. Design approximating magnitude of transfer function. Butterworth filter design, MATLAB commands. Butterworth filter properties, filter implementation using biquads and possibly first order filter in cascade. Chebyshev 1 filter design.

Discussion Section: (4/22) Convolution, total response, state space mathods.

Exam 2: (4/23)

Lecture 33: (4/25) Review step response; initial value theorem, Final value theorem. Magnitude and frequency scaling. Frequency selective filters; lowpass, highpass, bandpass filters. MATLAB commands. Implementing Sallen Key biquads with equal capacitance values. Implementing first order circuits.

Lecture 34: (4/28) Exam 2 discussion; state space methods, zero input response. Introduction to Fourier Transforms. Motivation and definition. Fourier Transform Pair. Conditions for existence of Fourier Transform. Example; left sided and right sided decaying exponential signals.

Lecture 35: (4/30) Fourier Transform pair. Properties; linearity, time shift, scaling, duality, convolution. Examples; impulse signal, sinusoid signal, pulse signal, sinc signal. PS 9 due.

Lecture 36: (5/2) Fourier Transform pair, properties. Circuit examples; left sided signal, sinusoid signal. Introduction to periodic signals. Frequency content of periodic signals. Passing periodic signals through circuits.

Discussion Section: (5/2) Filter design, state space, zero input response.

Discussion Section: (5/5) Filter design, Fourier Transforms, solving circuit problems using Fourier Transforms.

Discussion Section: (5/15) Review for final.