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## ET4631 Electronic Circuit Analysis

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**ET4631Electronic Circuit Analysis**David Morrisson, MS,MBA**1. Evaluate and compare several circuit analysis methods.**2. Incorporate the energy storage effects of capacitors and inductors into circuit models to predict the voltages and currents at times, t = 0+ and t = ∞ . 3. Apply Laplace transform methods to obtain complete solutions for first-order and second-order circuits. 4. Transform a circuit into the s-domain, derive the transfer function, and predict the output, given the input. 5. Analyze a system containing several circuit blocks and multiple feedback loops. 6. Transform a circuit into the jω-domain and perform phasor analysis to determine voltages and currents. 7. Predict the frequency response of a circuit using the Bode method. 8. Calculate and compare the Fourier transform versus the frequency spectrum for several different periodic waveforms. Introduction**Unit 1: BASIC CIRCUIT LAWS**Unit 2: CIRCUIT ANALYSIS METHODS Unit 3: CAPACITIVE AND INDUCTIVE TRANSIENTS, EQUIVALENT CIRCUITS, AND INITIAL, FINAL, AND FIRST-ORDER CIRCUITS Unit 4: LAPLACE TRANSFORMS Unit 5: CIRCUIT ANALYSIS WITH LAPLACE TRANSFORMS – Part 1 Unit 6: CIRCUIT ANALYSIS WITH LAPLACE TRANSFORMS – Part 2 Unit 7: TRANSFER FUNCTIONS Unit 8: SINUSOIDAL STEADY-STATE ANALYSIS Unit 9: FREQUENCY RESPONSE ANALYSIS AND BODE PLOTS Unit 10: WAVEFORM AND FOURIER ANALYSIS Unit 11: COURSE REVIEW AND FINAL EXAM Agenda**Unit 1: BASIC CIRCUIT LAWS**Upon completion of this unit, students are expected to: Define circuit quantities and apply the relevant voltage-current relationship. State and apply Ohm’s law, KCL, and KVL. Determine the equivalent resistance of a passive circuit containing only resistors. Apply and compare the voltage divider rule versus the current divider rule. Define the dependent source models and discuss their significance in circuit modeling Agenda**Unit 1: BASIC CIRCUIT LAWS**Upon completion of this unit, students are expected to: Define circuit quantities and apply the relevant voltage-current relationship. State and apply Ohm’s law, KCL, and KVL. Determine the equivalent resistance of a passive circuit containing only resistors. Apply and compare the voltage divider rule versus the current divider rule. Define the dependent source models and discuss their significance in circuit modeling. Overview**Basic Components(Passive Components)**• Battery (energy source) • Resistors • Impede the flow of electrons. • Coils (inductors) • Store energy in a magnetic field. • Capacitors • Store energy in an electrostatic field (electrons on one side, voids on the other).**Two Fundamentals of Electronics**• Moving electrons create magnetic fields. • Moving or changing magnetic fields cause electrons to move.**Basic Types of Current**• Direct Current (dc) • Electrons move in one direction. • Can fluctuate (pulse or ripple dc) in magnitude, but still only in one direction. • Alternating Current (ac) • Electrons reverse direction with some regularity. • Constant fluctuation from positive-zero-negative.**Components of Electricity**• Voltage E (Pressure) • Current I (Atoms) • Resistance R (Opposition)**Ohm’s Law**• Mathematical relationship between components. • E = I * R**Alternating Current Defined**In alternating current (ac), electrons flow back and forth through the conductor with some periodicity.**Power**• Power is the ability to do work. • Work is basically making something move. • Force over a distance or • Pressure over a distance • If something doesn’t move, there is no work produced. • Heat produced is also a measure of work.**Power in Electricity**• The force is Voltage. • The things being moved are electrons. • Power therefore is Voltage times Current. • Power is measured in Watts.**Power in DC**12 volts pushing 2 amps = 24 W (watts). 1.5 volts pushing 300 milliamps = 450 milli W. This is great for dc, but what about ac when the voltage and current are constantly changing?**Power in ACFinding the Effective Voltage**• The voltage used in power calculations in ac is the equivalent dc voltage value that would do the same amount of work (or heat). • A simple average of ac voltage is not quite good enough. • A weighted average called Root Mean Square (RMS) is more accurate.**Important Points about RMS**• RMS is the equivalent value of dc voltage to do the same work. • RMS is used in Power and Ohm’s Law formulas. • The RMS voltage is 0.707 times the peak voltage.**Resistors**• Values measured in Ohms. • From fractions to millions. • (kilo = 1,000; meg = 1,000,000) • Ability to handle heat (or power or current). • Physical size (1/4, 1/2, 1, 2, … watt)**Resistors**• Material • Carbon • Most common • High values (Ohms) • High precision • Low power • Wire • Long, thin wire wound in a coil • Not so common anymore • Low values (Ohms) • Low precision • High power • Lots of inductance (a coil of wire)**Resistors in CircuitsSeries**Looking at the current path, if there is only one path, the components are in series.**Resistors in CircuitsParallel**• If there is more than one way for the current to complete its path, the circuit is a parallel circuit.**Resistors in CircuitsParallel Challenge**Make a circuit with 3 resistors in parallel, calculate the equivalent resistance. • R1 = 330 ohm • R2 = 10 k-ohm • R3 = 4.7 k-ohm**Resistors in CircuitsMixed**If the path for the current in a portion of the circuit is a single path, and in another portion of the circuit has multiple routes, the circuit is a mix of series and parallel.**Resistors in CircuitsMixed**Start with a relatively simple mixed circuit. It is using: • R1 = 330 • R2 = 4.7 k • R3 = 2.2 k R1 R3 R2**Resistors in CircuitsMixed**Take the parallel segment of the circuit and calculate the equivalent resistance: R1 R3 R2**Resistors in CircuitsMixed**• Look at the simplified circuit as shown here. The parallel resistors have been replaced by a single resistor with a value of 1498 ohms. • Calculate the resistance of this series circuit: R1 RE=1498**Resistors in CircuitsMixed**• In this problem, divide the problem into sections, solve each section and then combine them all back into the whole. • R1 = 330 • R2 = 1 k • R3 = 2.2 k • R4 = 4.7 k R1 R2 R4 R3**Resistors in CircuitsMixed**Looking at this portion of the circuit, the resistors are in series. • R2 = 1 k-ohm • R3 = 2.2 k-ohm R2 R3**Resistors in CircuitsMixed**Substituting the equivalent resistance just calculated, the circuit is simplified to this. • R1 = 330 ohm • R4 = 4.7 k-ohm • RE = 3.2 k-ohm • Now look at the parallel resistors RE and R4. R1 RE R4**Resistors in CircuitsMixed**Using the parallel formula for: RE = 3.2 k-ohm R4 = 4.7 k-ohm R4 RE**Resistors in CircuitsMixed**The final calculations involve R1 and the new RTotal from the previous parallel calculation. R1 = 330 RE = 1.9 k R1 RTotal**Resistors in CircuitsMixed**R1 = 330 ohm RTotal = 2,230 R2 = 1 k-ohm = R4 = 4.7 k-ohm R3 = 2.2 k-ohm**Or KCL for short**• Based upon conservation of charge – the algebraic sum of the charge within a system can not change. Kirchhoff’s Current Law Where N is the total number of branches connected to a node.**Or KVL for short**• Based upon conservation of energy – the algebraic sum of voltages dropped across components around a loop is zero. Kirchhoff’s Voltage Law Where M is the total number of branches in the loop.**Determine I, the current flowing out of the voltage source.**Use KCL • 1.9 mA + 0.5 mA + I are entering the node. • 3 mA is leaving the node. V1 is generating power. Example 1**Suppose the current through R2 was entering the node and the**current through R3 was leaving the node. • Use KCL • 3 mA + 0.5 mA + I are entering the node. • 1.9 mA is leaving the node. V1 is dissipating power. Example 2**If voltage drops are given instead of currents, you need to**apply Ohm’s Law to determine the current flowing through each of the resistors before you can find the current flowing out of the voltage supply. Example 3**For power dissipating components such as resistors, passive**sign convention means that current flows into the resistor at the terminal has the + sign on the voltage drop and leaves out the terminal that has the – sign. Example 3 (con’t)**I1 is leaving the node.**I2 is entering the node. I3 is entering the node. I is entering the node. Example 3 (con’t)**Find the voltage across R1. Note that the polarity of the**voltage has been assigned in the circuit schematic. • First, define a loop that include R1. Example 4