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