107_17 - 1 Electrical Engineering Technology EET 107...

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Unformatted text preview: 1 Electrical Engineering Technology EET 107 Introduction to Circuit Analysis Lecture # 17 Professor Robert Herrick Purdue University © EET 107 - 17 Introduction to Circuit Analysis 2 Summary Thévenin’s Theorem Voltage Supplies in Series Diode Models Purdue University © EET 107 - 17 Introduction to Circuit Analysis 3 Thévenin’s Theorem or What’s in the Box Modeling Purdue University © EET 107 - 17 Introduction to Circuit Analysis 4 Why Model? Model Complex Devices and Circuits into Components Useful for Circuit Analysis Purdue University © EET 107 - 17 Introduction to Circuit Analysis 5 Thévenin’s Theorem Linear Bilateral Circuit RTH ETH Supplies, resistors, lamps, switches, etc. Thévenin Model Purdue University © EET 107 - 17 Introduction to Circuit Analysis 6 Measuring Thévenin Voltage Open Circuit or No Load voltage No ETH = VOC = VNL Linear Bilateral Circuit RTH red lead voltmeter Supplies, resistors, lamps, switches, etc. Purdue University © red lead E TH black lead EET 107 - 17 voltmeter black lead Introduction to Circuit Analysis 7 Finding Thévenin Resistance Measure two of the following Iload, Vload, Rload Then calculate RTH Linear Bilateral Circuit RTH Iload + Vload − Purdue University © + VRTH − Rload ETH EET 107 - 17 Iload + Vload − Rload Introduction to Circuit Analysis 8 Example – Find Thévenin Open Circuit Voltage Linear Bilateral Circuit red lead 10 V voltmeter Supplies, resistors, lamps, switches, etc. Test Circuit Purdue University © + black lead − ETH = VOC = 10 V 10 EET 107 - 17 Introduction to Circuit Analysis 9 Example – Find Thévenin Resistance Loaded circuit RTH ETH + VRTH − Iload + Vload 8V − 10 V Rload 4k Vload = 8 V Rload = 4kΩ Iload = 8V / 4kΩ = 2mA VRTH = 10 V – 8 V = 2 V RTH = 2V / 2mA = 1kΩ 1k Purdue University © EET 107 - 17 Introduction to Circuit Analysis 10 Example –Thévenin Model 1 k RTH ETH Model works for any load ! + VRTH − 10 V Attach any load and find Iload & Vload any Purdue University © EET 107 - 17 Introduction to Circuit Analysis 11 Example – Find Thévenin Resistance ETH + VRTH − Attach 1kΩ load 5 mA 1 k RTH Iload + + Vload − 10 V Rload 1k 5V - and find Vload & Iload Iload = 10V / 2kΩ = 5 mA Vload = 1kΩ • 5mA = 5 V Same as if solved with original circuit ! Purdue University © EET 107 - 17 Introduction to Circuit Analysis 12 Voltage Supplies in Series & Voltage Supply Modeling Purdue University © EET 107 - 17 Introduction to Circuit Analysis 13 Voltage Supplies in Series - AIDING + VSW − I1 E1 1.5 V I2 E2 1.5 V + Vlamp − Vlamp = E1 + E2 = 1.5V + 1.5V = 3V Purdue University © EET 107 - 17 Introduction to Circuit Analysis 14 Voltage Supplies in Series - OPPOSING I1 E1 Series OPPOSING OPPOSING E2 I2 Vlamp = −E2 + E1 = −1.5V + 1.5V = 0V Purdue University © EET 107 - 17 Introduction to Circuit Analysis 15 Battery Charging Circuit + VRbattery − + VRgen − Egen 0.06 Rgen Igen + Vgen 14 V − Generator charger model Purdue University © 0.94 Rbattery Ibattery Ebattery 12 V Dead battery model EET 107 - 17 Introduction to Circuit Analysis 16 Battery Charging Circuit + VRbattery − + VRgen − Egen 14 V 0.06 Rgen Igen + 0.94 Rbattery Ibattery V gen Ebattery 12 V 13.88 V − Enet = +14V – 12V = 2V (CW) RT = 0.06Ω + 0.94Ω = 1Ω Igen = 2V / 1Ω = 2A Vgen = +14V – 0.06Ω (2A) = 13.88V 13.88V Purdue University © EET 107 - 17 Introduction to Circuit Analysis 17 Modeling Diodes as A Voltage Supply with Series Resistance Purdue University © EET 107 - 17 Introduction to Circuit Analysis 18 Diode Models short 0.7 V I (mA) rdiode 0.7 V I (mA) I (mA) short V (V) open 0 (a) Ideal Purdue University © V (V) 0 0.7 (b) 2nd approximation EET 107 - 17 V (V) 0 0.7 (c) 3rd approximation Introduction to Circuit Analysis 19 Ideal Diode VD Esupply 6V I D VD R 10 + VR − Esupply 6V I D R 10 + VR − VR = 6.0V I = 6V / 10 = 600mA VD = 0V Purdue University © EET 107 - 17 Introduction to Circuit Analysis 20 Diode – 2nd Approximation VD 0.7 V Esupply 6V I D VR = +6V – 0.7V = 5.3V R 10 + VR − I = 5.3V / 10Ω = 530mA VD = 0.7V Purdue University © EET 107 - 17 Introduction to Circuit Analysis 21 Diode – 3rd Approximation +VD− 0.7 V Esupply I D rDIODE 0.2 6V R 10 + VR − Enet = +6V – 0.7V = 5.3V RT = 0.2Ω + 10Ω = 10.2Ω I = 5.3V / 10.2Ω = 0.52A VR = (0.52A) (10Ω) = 5.2V 5.2V VD = 0.7V + (0.2Ω) (0.52A) = 0.7V + 0.104V = 0.804 V 0.804 Purdue University © EET 107 - 17 Introduction to Circuit Analysis 22 Summary of Model Results Diode model Ideal 2nd approximation 3rd approximation I (A) 0.60 0.53 0.52 VR (V) 6.0 5.3 5.2 VD (V) 0.0 0.7 0.8 2nd Approximation Looks Reasonable Purdue University © EET 107 - 17 Introduction to Circuit Analysis 23 Zener Diode Purdue University © EET 107 - 17 Introduction to Circuit Analysis 24 Zener Diode – Voltage Regulator I (mA) VZ V (V) 0 0.7 Zener region (a) Symbol (b) Characteristic curve Used as a voltage regulator – fixed voltage VZ. Purdue University © EET 107 - 17 Introduction to Circuit Analysis 25 Zener Diode Models Reverse biased Reverse biased rZ VZ VZ I (mA) I (mA) VZ VZ 0 0 V (V) rZ (b) 2nd approximation (a) Ideal Purdue University © EET 107 - 17 Introduction to Circuit Analysis 26 Zener Diode – Ideal Example +VR− E 9V I R 100 Purdue University © +VR− VOUT + VD − E 9V I VOUT R 100 VZ 6V + VD − VR = 9V – 6V = 3V I = 3V / 100Ω = 30mA VOUT = 6V 6V EET 107 - 17 Introduction to Circuit Analysis 27 Zener Diode – 2nd Approximation VOUT +VR− R 100 E 9V I VZ 6V rZ 2Ω + VD − Enet = +6V – 3V = 3V RT = 2Ω + 100Ω = 102Ω I = 3V / 102Ω = 29.4mA VR = 29.4mA (100Ω) = 2.94V VOUT = +9V – 2.94V = 6.06V 6.06V VD = 6V + 29.4mA (2Ω) = 6V + 0.059V = 6.059 V 6.059 Purdue University © EET 107 - 17 Introduction to Circuit Analysis 28 Zener Diode – Comparison VOUT +VR− R 100 E 9V I VZ 6V rZ 2Ω + Ideal Model VOUT = Vz = 6.00V 6.00V VD − Purdue University © 2nd Approximation VOUT = 6.06V 6.06V EET 107 - 17 Introduction to Circuit Analysis 29 Appropriate Model VOUT +VR− R 100 E 9V I VZ 6V rZ 2Ω + VD Simplest model possible that gives reasonable results for the situation. − Simpler model – simpler circuit. Purdue University © EET 107 - 17 Introduction to Circuit Analysis 30 Summary Thévenin’s Theorem Voltage Supplies in Series Diode Models Purdue University © EET 107 - 17 Introduction to Circuit Analysis ...
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