1 ELEC130 Electrical Engineering 1 Week 3 Module 2 DC Circuit Tools

5 March, 1999Lecture 32 Administration Items zTutorials - Will be held in ES 210 this week. yAnswers tutorial 1 will be revised yIntroduction to Electronic Workbench - Revised document yFaculty PC’s Rm. ES210 - Go to Diomedes xLogin: cstudentnumber xPassword: access keys on students card + daymonth (ddmm) of birth yUse Drive u: to save your work zLaboratory - THIS WEEK in EE 103(a) zAllocation of Laboratory and Tutorial Times xNO more changes after Friday 12 March pm xIf you cannot make your time, please ask for alternative zQuiz 1 - THIS WEEK

5 March, 1999Lecture 33 Survey Results zSubject Home Page: - through Dept. Pages yhttp:// xThen to Undergraduate studies xThen to Course Information/Syllabus xThen to Subject Web Pages yFrom the web site you have the option to save the file in power point yYou are expected to read the specified text references to build the background information to the topic areas we are covering. You should think of the lecture as an opportunity to reflect on your reading and clarify difficult concepts.

5 March, 1999Lecture 34 Survey Results (cont.) zCurrent Sources yDC power supply, transistors zConductance - Parallel Resistance's zVoltage and Current Division zWhy - Delta - tutorial 1 Question 19 part 4 yFloyd pg. 309 Example 8-19 pg. 312 zSuperposition

5 March, 1999Lecture 35 Conductance zSometimes easier to use inverse of resistance called conductance G = R -1 ySymbol: G yUnits:Siemens S (mhos) zNB: Useful when resistors are connected in parallel xGeq = G 1 + G G n x1/Req = 1/R 1 + 1/R /R n zCase of two parallel resistance's: xReq = R 1 R 2 /(R 1 + R 2 ) VsVs R1R1 I1I R2R2 I2I2

5 March, 1999Lecture 36 Week 2 Summary cont. zVoltage Divisionz Current Division R2R2 R1R1 I1I1 I2I2 IsIs + - I R1R1 R2R2 V1V1 +_+_ V2V2 +_+_ VsVs

5 March, 1999Lecture 37 Survey (cont.) zCurrent Sources yDC power supply, transistors zConductance - Parallel Resistance's zVoltage and Current Division zWhy - Delta - tutorial 1 Question 19 part 4 yFloyd pg. 309 Example 8-19 pg. 312 zSuperposition

5 March, 1999Lecture 38 Wye Delta Transformations z Need to find equivalent resistance to determine current. HOW? (They are not in series, not in parallel) z Use Y to  transformation

5 March, 1999Lecture 39 Survey zCurrent Sources yDC power supply, transistors zConductance - Parallel Resistance's zVoltage and Current Division zWhy - Delta - tutorial 1 Question 19 part 4 yFloyd pg. 309 Example 8-19 pg. 312 zSuperposition

5 March, 1999Lecture 310 Week 2 Summary (cont.) zSuperposition: If a linear circuit is excited by more that one independent source, then the total response is simply the sum of the responses of the individual sources. zVoltage sources - short circuit zCurrent source - open circuit

5 March, 1999Lecture 311 Power Calculations z Power is not linear! z Superposition will not work directly! yWith 2 A source opened P’ 1 = 25 W yWith 10 V Source shorted P’’ 1 = 1 W yTotal P = P’ + P’’ = 26 W (incorrect) z Must calculate current by superposition and then work out power yI’ = 5 A & I’’ = -1 A yTotal I = I’ + I’’ = 4 A yPower P = 4 2 R = 16 W

5 March, 1999Lecture 312 Example Week 3 zFind I ? zDetermine V BC ? zWhat power is delivered by 4V source ? I V BC C

5 March, 1999Lecture 313 Week 3 zHow does the current in the load change if R L is (say) doubled?

5 March, 1999Lecture 314 Thevenin’s Theorem zAny linear network with a pair of terminals can be replaced by a circuit comprised of a voltage source in series with a resistor. zThe observed voltages and currents in the load will be the same using the “Thevenin equivalent” circuit as would be seen using the original circuit.

5 March, 1999Lecture 315 Thevenin’s Components zV Th Thevenin Voltage y‘open circuit’ voltage yV Th is the voltage which would appear across the terminals of the original and equivalent circuit if those terminals are open circuited. z R Th Thevenin Resistance yIndependent sources inactivated yR Th is the total resistance seen when looking into the original circuit with sources inactivated yCan also be obtained by observing the short circuit current. R Th = V Th / I sc.

5 March, 1999Lecture 316 Steps to finding the Thevenin Equivalent zStep 1Determine the two points from which the Thevenin is to be found. NB:Polarity – zStep 2Find open circuit voltage across these two points by removing the Load (resistance) V Th = V o/c zStep 3Find R Th by looking from the two points into the circuit after replacing all independent sources zStep 4Draw the Thevenin Equivalent –Voltage source in series with a resistor

5 March, 1999Lecture 317 Example Week 3 zFind I ? zDetermine V BC ? zWhat power is delivered by 4V source ? zWhat is the Thevenin Equivalent circuit between A & B ? I V BC C

5 March, 1999Lecture 318 Norton’s Theorem zAny linear network with a pair of terminals can be replaced by a circuit comprised of a current source in parallel with a resistor. zThe observed voltages and currents in the load will be the same using the “Norton equivalent” circuit as would be seen using the original circuit.

5 March, 1999Lecture 319 Norton’s Components zI N Norton Current y‘short circuit’ current yI N is the current which would appear through the terminals of the original and equivalent circuit if those terminals are short circuited. z R N Norton Resistance yindependent sources inactivated yR N is the total resistance seen when looking into the original circuit with sources inactivated yCan also be obtained by observing the open circuit voltage. R N = V oc / I N.

5 March, 1999Lecture 320 Steps to finding the Norton Equivalent zStep 1Determine the two points from which the Norton is to be found. NB:Polarity – zStep 2Find the short circuit current through these two points by putting a short across them I N = I s/c zStep 3Find R N by looking from the two points into the circuit after replacing all independent sources zStep 4Draw the Norton Equivalent –Current source in parallel with a resistor

5 March, 1999Lecture 321 Example Week 3 zFind I ? zDetermine V BC ? zWhat power is delivered by 4V source ? zWhat is the Thevenin Equivalent circuit between A & B ? zWhat is the Norton Equivalent circuit between A & B ? I V BC C

5 March, 1999Lecture 322 Relationship between Thevenin & Norton zA particular circuit can be represented by Thevenin or Norton equivalent. Therefore Thevenin and Norton equivalent circuits must be the same. zHence R eq = R th = R N zR Th = V Th / I sc = V Th / I N V Th = R N I N zR N = V oc / I N = V Th / I N I N = V Th / R Th