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Exam #2 Review

Exam #2 Review. Dr. Holbert March 26, 2008. 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. Circuit Analysis Techniques.

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Exam #2 Review

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  1. Exam #2 Review Dr. Holbert March 26, 2008 EEE 202

  2. 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

  3. 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

  4. Transient Circuit Analysis • First and second order circuit responses • Differential equation approach • Laplace transform approach • Inspection (step-by-step) method • Bottom line: Using appropriate techniques can you find v(t) and/or i(t) in transient RLC circuits? EEE 202

  5. RLC Characteristics ELI and the ICE man EEE 202

  6. Circuit ODE Solutions • Determine the circuit differential equation(s) • Find the forced (particular) and natural (complementary) solutions • First-order vs. second-order circuits • First-order: find time constant (=RC; =L/R) • Second-order: Compute the natural frequency, 0, and the damping ratio,  (or compute the roots, s1,2, of the characteristic equation) • Transient and steady-state waveforms EEE 202

  7. Damping Summary EEE 202

  8. Laplacian Domain • Determining the Laplace transform from • The defining integral • Transform pairs in conjunction with properties u(t) ↔ 1/s e-at ↔ 1/(s+a) • Circuit element representations in s domain • Finding the transfer function • Performing the inverse Laplace transform to find the time-domain response • Three possible cases based on poles EEE 202

  9. IC(s) IL(s) + + 1/sC sL i(0) s VC(s) VL(s) + – v(0) s – – Laplacian of Circuit Elements Using Ohm’s Law, impedance (Z) can be defined via: V = I Z EEE 202

  10. System X(s) ↔ x(t) Y(s) ↔ y(t) H(s) ↔ h(t) Input Output Transfer Function • The transfer function, H(s), is the ratio of some output variable (y) to some input variable (x) • The transfer function is shown in block diagram form as (where h(t) is the impulse response) EEE 202

  11. Our vocabulary has expanded with several new terms, including: Phasor & impedance Impulse (delta) and step functions Transfer function Impulse response Poles and zeros Initial and final value theorems Linearity and time invariance Convolution integral Period, frequency, and amplitude Characteristic equation Over/under damped Some Terminology & Quantities EEE 202

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