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EE3301 Electrical Network Analysis

EE3301 Electrical Network Analysis. Dr. Jeanne Pitz. Electrical Network Analysis. Analysis and design of RC, RL, and RLC electrical networks Sinusoidal steady state analysis of passive networks using phasor representation mesh and nodal analyses

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EE3301 Electrical Network Analysis

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  1. EE3301 Electrical Network Analysis Dr. Jeanne Pitz

  2. Electrical Network Analysis • Analysis and design of RC, RL, and RLC electrical networks • Sinusoidal steady state analysis of passive networks using phasor representation • mesh and nodal analyses • Introduction to the concept of impulse response and frequency analysis using the Laplace transform. • Prerequisites: MATH 2420 ( integral & differential eq) • PHYS 2326 (electricity & magnetism) . • Corequisite: EE 3101 (ENA lab)

  3. Course Logistics • Homework will be assigned but NOT collected. • There will be a quiz every Wed. closed book and notes. • It will cover the material that has already covered and the homework. No quiz on test days. • 3 Tests are scheduled during the semester. • They are NOT comprehensive. • The date will not be changed but what’s covered may be modified. • The grade will be based on 4 tests • The 4th will be the percentage based on the sum of the quizzes 10 best quizzes.

  4. Course Logistics: Schedule

  5. Chapter 1 • Overview • International units • Voltage and Current Definitions • “Ideal” circuit element • Power and energy

  6. homework • Read chapter 1 esp. pages 10-18 • Work problems: • 1.14 a-d • 1.18 a-c • 1-25 a-e • 1-26 • Answers are in the back of the book.

  7. Circuit language • Voltage is measured across two points • Current is measured through an element • Scale factor prefix smaller than 1 • Milli (m) – 10-3 • Micro (m) - 10-6 • Nano (n) – 10-9 • Pico (p) – 10-12 • Scale factor prefix larger than 1 • Kilo( K) – 103 • Mega( M) – 106 • Giga (G)– 109 • Terra (T) – 1012

  8. Definitions in circuit theory • Voltage is the energy per unit charge of separating a pos and neg charge, that is the potential difference between two points • Current is the rate of change of charge • Current and voltage sign passive convention + -

  9. Conventions in circuit theory • Voltage is joules per coulomb, the energy required to move a positive charge of 1colomb through the element. • Power is i(t)*v(t)

  10. definitions • Power is the time rate of delivering or absorbing energy • In terms of voltage and current:

  11. Other facts • Current and voltage are VECTOR quantities having both magnitude and direction • If you compute power with the passive sign convention • Positive power is absorbed • Negative power is supplied • Energy is neither created or destroyed; it must be conserved. • The charge on an electron is 1.6022 X 10 -19 coulombs

  12. Power sign conventions • P is pos = vi if the current is entering the positive terminal. • See fig 1.6 for other cases v(t) + i(t) -

  13. Problem 1-14 pg 20 a, b + a. V=125V I= 10 A =1250 W B->A Supplied by B Absorbed by A v(t) i(t) A B - b. V=5V I= -240A W= 1200W A->B. Supplied by A Absorbed by B

  14. Prob 1-18 a. Find the power at 625 s =0.625ms Work out the exponents: 1600*0.625ms=1000ms = 1.00s 400*0.625 ms = 0.25s 1000*0.625 ms = 625ms = .625 s

  15. Prob 1-18 b E

  16. Solution in book

  17. Chapter 2 • Voltage and current sources • Independent, dependent • Electrical resistance • Ohm’s law • Resistive Circuits • Circuit models • Kirchhoff's law • Analysis of independent vs. dependent current sources

  18. homework • Read pages 24-48 • Make sure you understand the examples • Look it the following homework problems • 2.2, 2.4, 2.5, 2.7, 2.112.13, 2.1, 2.18 2.19, 2.22, 2.28 2.34, 2.35, 2.36, 2.37

  19. Ideal Sources • Ideal Voltage sources: can supply as much current as the circuit requires. • Ideal Current sources : supplies current regardless of the voltage across it. • Independent Sources: don’t rely on any other circuit parameters • Dependent Sources : depend on some parameter in the circuit.

  20. Sources: voltage + • DC Independent Voltage source: • Constant value regardless of what is attached. The sign indicates it’s polarity (positive on top) + - 5V -

  21. Sources: current • DC Current source : independent • arrow show it’s direction • Constant value regardless of what is attached. • Current flows around the loop. 10A

  22. Dependent Voltage Sources • Dependent DC Voltage source : dependent on some parameter in the circuit. + + -  5 V -

  23. Dependent current Sources • Dependent DC Current source : dependent on some parameter in the circuit. + 25a A a -

  24. Assessment problem 2.1 a. What value of ib makes this circuit valid: b. What power is associated with the 8A source: a, b, -2 P8A 2 16 W Current entering + node

  25. Networks in Electrical Engineering • A network is an interconnection of components such as sources, resistors inductors and capacitors. • In studying first, DC (direct current) circuits composed only of resistors and sources, we can learn the basics of electricity, that will be useful with more complex circuits. • In Direct current circuits the voltage or current is assumed to be constant overtime. • For example the 4V supply never varies with time. Similarly for the current sources they are considered 2A and 4A for all time.

  26. R Resistors and Ohm’s Law • Resistance is the property of a component to impede the flow of current. • Such a component is called a “resistor”. • The symbol for a resistor with resistance R is shown below. • Ohms law relates the current through the resistor to the voltage across it. V=I*R

  27. v + - i Circuit Elements • Resistors • resist the flow of current • Obey ohm’s law • Voltage and current relationships • V=ir ohms law. • R is usually considered a constant. • but can be temperature dependent

  28. R Resistors: Current and Voltage conventions • The conventions for signs are as follows. Ir Vr + - Vr= Ir* R

  29. Single loop analysis • Ohm’s law : the voltage across a resistor is directly proportional to the current flowing through it. • For simple resistors R is constant so • v=i*R • In DC analysis the voltage (or current ) is constant so on a plot of I vs. V, the slope is 1/R i 1/R v

  30. Conductance • If we use the reciprocal of ohms we get Conductance which is measured in “siemens” S. • some literature uses “mho” • G= 1/R • Mho : 

  31. Prob 2.11 v=i*r =>r=v/i Slope m = Δy/Δx; on this graph y is current in mA and x is V Find slope from 2 points: (54,2m) (108,4m): m=(4-2)mA/(108-54)V=1/R R=26K

  32. R1 R2 Adding resistors series vs parallel • Series share the same current • RT = R1 + R2 • Parallel share the same voltage • 1/RT= 1/R1 +1/R2 • RT= R1*R2/(R1 + R2) I V + R1 R2 - -

  33. Circuit Models • Some terminology • Branch – a portion of the circuit containing a single element and the nodes at either end of the element. • Node – a point connecting two or more elements. • Loop – a closed path in which no node is encountered more than once (except the starting point).

  34. Loops, nodes, branches node - 8V + Vx 6V 4A - + * - 2A branch - 6V + + 4V - - 2V + 6A Closed loop node

  35. Kirchhoff’s laws • Current law • Sum of currents entering or leaving a node is 0, taking direction into account • Voltage law • Sum of voltages around a closed loop is 0 taking polarity into account

  36. Circuit convention rules • Sum of voltages around a closed loop is 0. • Sum of currents at a node is 0. • Power passive sign convention: • Arrange I and v so magnitude are positive then if the sign of power is positive it being absorbed; if the sign of power is negative it being supplied. + v(t) i(t) -

  37. Problem 1-22 Vx 6V 2A 4A - 8V + - + + - • proceed in a loop; Add the voltage if you reach the + terminal first; subtract if you reach the – terminal first. • 0 = -8V + Vx - 6V - 4V • Vx= 18V - 6V + + 4V - - 2V + 6A

  38. Analysis with dependent sources • Write the equations using the “parameter” specified. • Then another equation setting the parameter • Solve the equations simultaneously

  39. Example

  40. Example assessment 2.9 • Solve for current i1 write a kvl loop equation around the outside loop. • Voltage v: kvl around the outside loop, solve for v

  41. Power calculations: assessment 2.9 c,d

  42. Voltage and current division • Voltage divides across resistors in series in proportion to their values. • Vt = V1 + V2 = I R1 + I R2 • Current divides through resistors in proportion to their values. • It= I1 + I2 =V/R1 + V/R2

  43. Chapter 3 • Resistors in series • Resistors in parallel • Voltage divider circuits • Current divider circuits • Measuring voltage • Measuring current • Measuring resistance • Wheatstone bridges • (skip section 3.7)

  44. Adding Resistors in Series • Two resistors connected at a single node • Write Kirchhoff's law around the loop:

  45. Adding Resistors in Parallel • Parrallel connected elements have the same voltage • Write Kirchhoff's current law at node a.

  46. Adding Resistors in Parallel

  47. Example Assessment Problem 3.1 • Find the voltage v • Find the power delivered by the current source • Find the power dissipated by the 10  resistor.

  48. Solution • a. solve for Req then v = 5A*Req • b. solve for power delivered by the 5A source

  49. Solution • Find the power dissipated by the 10  resistor To find V1 across the 10 + 6 resistors we must first determine the current in 30 and 7.2 then find current in the 10 branch V1

  50. Solution • Now we have the current in the branch we can find voltage in the 10  and power is v*i.

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