ENGR 2405: Circuit AnalysisClass 1: Basic ConceptsCollege of Engineering, University of North Texas

EENG 2610, Class 1

*HW #1

Chp 1: 1,2,8,9,10,20,41Chp 2: 5,12,16,17,37,39,47,62,2FE2,2FE8

Due: Fri, 1/30

*Electro-technology is driving force in all engineering disciplineCircuit analysis is fundamental to electro-technologyPower GridMotherboard of Computer Integrated Circuits (IC chips)

*Basic Strategy in Circuit AnalysisTypical Electric Circuit

*International System of Units SI Standard System

*Standard SI PrefixesSI prefixes used to form decimal multiples and submultiples of SI units.These standard prefixes are employed throughout our study of electric circuits.

*Basic QuantitiesElectric Charge (unit: coulomb) Q, q, q(t) (1C = 6.241509745 x 10^18 electrons)(1e = 1.6021176462 x 10^-19 C)The most elementary quantity in electric circuit analysisCharged particle in matter: electron (-), proton (+), neutron (no charge) Electric CircuitA pipeline where electric charge can be transferred from one point to anotherAn interconnection of electrical components, each of which we will describe with a mathematical modelElectric Current (unit: ampere) i, i(t) The time rate of change of charge:1 A = 1 C/s (A: ampere, C: coulomb, s: second)Conventional current flow represents the movement of positive charges, even though in metallic conductors current flow is resulted from the motion of electrons, negative charge.I = 2 A means 2 C of charge pass from left to right each second

Must specify both magnitude and direction:

*Basic QuantitiesTwo types of current we will study in this courseAlternating current (AC)Direct Current (DC)Voltage (or potential) between two points in a circuit (unit: volt)Defined as the difference in energy level of a unit charge located at each of the two points:

The energy required to move a unit positive charge is the defined voltage1 V = 1 J/C = 1 Nm/C (V: volt, J: joule, C: coulomb, N: newton, m: meter)

The + and signs define a reference direction for VA unit charge moved between A and B will have energy changeMust specify both magnitude and direction

ACDC

*Basic QuantitiesEnergy and Energy Transfer W, w(t)

When the element is absorbing energy, a positive current enters the positive terminal and leaves via the negative terminal.When the element is supplying energy, a positive current enters the negative terminal and leaves via the positive terminal.A negative current in one direction is equivalent to a positive current in the opposite direction, and vice versa. Similarly for voltage.

*Basic QuantitiesPower (unit: watt) P, p(t)Defined as the time rate of change of energy:

The change in energy in a period of time:

1 W = 1J/s = 1 VA (W: watt, J: joules, V: volt, A: ampere)Passive Sign Convention Sign Convention for PowerVariables for the current and voltage should be arranged as shown in the figure:Current enters an element via positive voltage reference point

If the sign of power is positive, power is being absorbed by the element; if the sign is negative, power is being supplied by the element.Power:

*Example 1.2: Determine whether the elements are supplying or receiving power and how much

*Circuit ElementsIn general, all elements will be terminal devices that are completely characterized by the current through the element and the voltage across it.Active or passive elementsActive element is capable of generating energy.Passive element cannot generate energy.Passive ElementsResistor, Capacitor, InductorWe will define these in coming classesIndependent Voltage SourceMaintain a specified voltage between its terminals regardless of the current through it.Independent Current SourceMaintain a specified current between its terminals regardless of the voltage across its terminals.Independent sources normally supply energy, but they can also absorb energy

*Circuit ElementsDependent (or Controlled) SourcesUnlike independent sources, dependent (or controlled) sources generate a voltage or current that is determined by a voltage or current at a specified location in the circuit.Four different types of dependent sources:Voltage ControlledSourcesCurrentcontrolledSources

*Example 1.7: Use power balance to compute I0The Principle of Conservation of EnergyTellegens Theorem: Power supplied in a circuit network is exactly equal to the power absorbed. Electrical circuits satisfy this principle.

ENGR 2405: Circuits AnalysisClass 2: Ohms Law, Kirchhoffs LawsCollege of Engineering, University of North Texas

EENG 2610, Class 1

Ohms LawOhms LawDefines a passive element Resistor R (unit: ohm)It only absorbs power; converts electrical energy to thermal energyOhms Law: The voltage across a resistor is directly proportional to the current flowing through it:1 = 1 V/A (: ohm, V: volt, A: ampere)

Linear approximationActual v-I relationshipLinear range

Ohms LawPower absorbed by a resistor

Conductance G (unit: siemens S)1 S = 1 A / V

Two specific values of resistanceShort Circuit Open Circuit

Example 2.1: Determine voltage, current, and power absorbed by resistor

Some Important ConceptsLumped-Parameter Circuit Wires in circuits are assumed perfect conductorInterconnections in circuits have zero resistanceWire doesnt consume energy; energy in circuits is lumped in each circuit element.NodeA point of connection of two or more circuit elements.A node is one end of a circuit element together with all the perfect conductor that are attached to it.LoopA loop is any closed path through the circuit in which no node is encountered more than once.BranchA branch is a portion of a circuit containing only a single element and the nodes at each end of the element.

Kirchhoffs Current Law (KCL)KCLThe algebraic sum of the currents ENTERING any node is zero:

Example 2.5: Write all KCL equationsOur sign convention for KCL: - The algebraic sign of the current is plus if the current is entering the node - The algebraic sign of the current is minus if the current is leaving the node

Example 2.7: Write KCL equations for the circuit below.

Closed Surface as Super-NodeSuper-NodeIf some set of elements are completely contained within a surface that is interconnected, the surface is called super-node.Generalized KCL for Super-NodeThe algebraic sum of the currents entering any closed surface (or super-node) is zero.Write KCL equations for super-nodes

Kirchhoffs Voltage Law (KVL)KVLThe algebraic sum of the voltages around any loop is zero:

Voltage is defined as the difference in energy level of a unit positive charge located at each of the two points. KVL is based on the conservation of energy: the work required to move a unit charge around any loop is zero.

Our Sign Convention for KVLAs moving around a loop, the algebraic sign of voltage is positive in KVL equation if encounter the plus sign first, and the algebraic sign of voltage is negative in KVL equation if encounter the minus sign first.

Example 2.9: Using KVL equation to find

Convention for Voltage NotationDouble-subscript notationVab = Va Vb

+ and notation

Arrow notationUse an arrow between two points, pointing from negative node to positive node.KVL can be applied to a closed path even if part of the closed path is the arrow notation.

Example 2.11: Use KVL to find Vae and Vec

*This course is your first course in Electrical Engineering. Its very important to master the materials that you will learn in this course to become a good Electrical Engineer. This course is the foundation to almost all other EE courses that you will take in the future.

Even though you may not have noticed, electrical technology is one of the most fundamentally important technologies in this world and we have been relying on electrical technology for our daily life.*Give some example: For example 2x10^3 m = 2 km, 2x10^9 m = 2 Gm, *Show on white board: equivalent circuit for negative current.*