107_22 - 1 Electrical Engineering Technology EET 107...

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Unformatted text preview: 1 Electrical Engineering Technology EET 107 Introduction to Circuit Analysis #22 Professor Robert Herrick Purdue University © EET 107 - 22 Introduction to Circuit Analysis 2 Electrical Engineering Technology Parallel Circuits - continued Purdue University © EET 107 - 22 Introduction to Circuit Analysis 3 Overview Ø KCL – Quick Review Ø Current divider rule Ø Current Sources Ø Current Sources in Parallel Purdue University © EET 107 - 22 Introduction to Circuit Analysis 4 Overview Ø KCL – Quick Review Ø Current divider rule Ø Current Sources Ø Current Sources in Parallel Purdue University © EET 107 - 22 Introduction to Circuit Analysis 5 KCL - Simple Node node I1 uWhat uI1 I2 flows in must flow out = I2 Purdue University © EET 107 - 22 Introduction to Circuit Analysis 6 KCL – Alternate Form node I1 I2 Ø I1 into the node is considered + Ø I2 out of the node is considered - Ø I1 - I2 = 0 Purdue University © EET 107 - 22 Introduction to Circuit Analysis 7 KCL – Simple or Voltage Node Σ Iinto = Σ Iout node I1 I2 I3 I4 I1 = I2 + I3 +I4 or alternate form Σ Iinto − Σ Iout = 0 I1 - I2 - I3 -I4 = 0 Purdue University © EET 107 - 22 Introduction to Circuit Analysis 8 KCL - Super Node Ι1 Ι2 Ι3 electronic circuit Ι4 I1 - I2 - I3 - I4 = 0 Purdue University © EET 107 - 22 Introduction to Circuit Analysis 9 Overview Ø KCL – Quick Review Ø Current divider rule Ø Current Sources Ø Current Sources in Parallel Purdue University © EET 107 - 22 Introduction to Circuit Analysis 10 Parallel Circuit - current divider node 6A + 1A 2A 3A - Current divides at a connecting node ! node Above could be a simple or voltage node. Purdue University © EET 107 - 22 Introduction to Circuit Analysis 11 Parallel Circuit - current divider 6A + 1A 2A 3A - Current divides in a parallel circuit based upon branch conductance! Purdue University © EET 107 - 22 Introduction to Circuit Analysis 12 Parallel Circuit - current divider G = 1/R 6A + - 1A 2A 3A 6Ω 3Ω 2Ω Branch Purdue University © Rê EET 107 - 22 Gé Ié Introduction to Circuit Analysis 13 CDR – Conductance View IT E + - I1 R1 GT Purdue University © G1 I2 I3 R2 R3 Ι1 / G1 = ΙΤ / GΤ G1 I1 = • IT GT EET 107 - 22 CDR Introduction to Circuit Analysis 14 CDR – Resistance View 6A + - RT 1Ω 1A 2A 3A 6Ω 3Ω 2Ω ΙΤ • RΤ = Ι1 • R1 = Ι2 • R2 = Ι3 • R3 6A • 1Ω = 1A • 6Ω = 2A • 3Ω = 3A • 2Ω 1A 3A Purdue University © EET 107 - 22 Introduction to Circuit Analysis 15 Parallel Circuit - current divider rule IT E I1 I2 I3 R1 + - R2 R3 RT Purdue University © Ι1 l R1 = ΙΤ l RΤ RT I1 = • IT R1 EET 107 - 22 CDR Introduction to Circuit Analysis 16 Parallel Circuit - current divider 6A IT + E - RT 1Ω I1 6Ω R1 3Ω 2Ω RT 1Ω I1 = • IT = • 6 A = 1A R1 6Ω Purdue University © EET 107 - 22 Introduction to Circuit Analysis 17 Parallel Circuit - current divider 6A IT E + - RT 1Ω I2 6Ω 3Ω R2 2Ω RT 1Ω I2 = • IT = • 6A = 2A R2 3Ω Purdue University © EET 107 - 22 Introduction to Circuit Analysis 18 Parallel Circuit - current divider 6A IT E + - RT 1Ω R3 I3 6Ω 3Ω 2Ω RT 1Ω I3 = • IT = • 6 A = 3A R3 2Ω Purdue University © EET 107 - 22 Introduction to Circuit Analysis 19 Parallel Circuit - current divider Ix 6A IT E + - 6Ω RT 1Ω Purdue University © 3Ω R2 2Ω Rx 1.2Ω 1.2 RT 1Ω Ix = • IT = • 6A = 5A Rx 1.2Ω EET 107 - 22 Introduction to Circuit Analysis 20 Parallel Circuit - current divider 12A E + - Ix 6Ω RT 2Ω 12Ω 6Ω 4Ω Left resistor not not included ! RT 2Ω Ix = • IT = • 12 A = 2 A Rx 12Ω Purdue University © EET 107 - 22 Introduction to Circuit Analysis 21 Parallel Circuit - 2 branch CDR R1 I2 = • IT R1 + R2 Only works for two branches A branch current equals the resistance of the other branch divided by sum of the other branch resistances times the input current. branch Purdue University © EET 107 - 22 Introduction to Circuit Analysis 22 Parallel Circuit - 2 branch CDR IT 6A I2 R1 + - R2 3Ω 6Ω No need for RT R1 3Ω I2 = • IT = • 6A = 2A R1 + R2 9Ω Purdue University © EET 107 - 22 Introduction to Circuit Analysis 23 Overview Ø KCL – Quick Review Ø Current divider rule Ø Current Sources Ø Current Sources in Parallel Purdue University © EET 107 - 22 Introduction to Circuit Analysis 24 Ideal DC Voltage Source ® Voltage is a fixed 5V DC value 5V + - ® E always 5V unloaded and loaded ® Ideally 0Ω internal resistance ® Looks like an ideal short short Purdue University © EET 107 - 22 Introduction to Circuit Analysis 25 Ideal DC Voltage Source 5V + - RL Except RL = ? Purdue University © + VL - VL = 5V Cannot be a short (0 Ω) Ω) EET 107 - 22 Introduction to Circuit Analysis 26 Real DC Voltage Source - model R E + - + VL - Real Source Model ® E - ideal DC voltage source ® R - fixed series resistance ® R - represents a real source’s internal resistance ® R << RLOAD to be effective voltage source ® VL - load voltage across real voltage source Purdue University © EET 107 - 22 Introduction to Circuit Analysis 27 Ideal DC Current Source Symbol ® “I” represents current ® é represents conventional current direction I ® Current is a fixed DC value ® Needs load to produce “I” ® “I” does not vary with load ® Ideally internal resistance looks like an open open Purdue University © EET 107 - 22 Introduction to Circuit Analysis 28 Ideal DC Current Source IL 3A 3Α IL 3A IL = 0A undefined undefined o p e n 3Ω Purdue University © + 9V - IL = 3A VL = 3A x 3Ω = 9V EET 107 - 22 Introduction to Circuit Analysis 29 Real DC Current Source - model IL I R RL + VL - Real Source Model ® I - ideal DC current source ® R - fixed parallel resistance ® R - represents a real source’s internal resistance ® R >> RL to be effective current source ® IL - load current from real current source Purdue University © EET 107 - 22 Introduction to Circuit Analysis 30 Real DC Current Source - model IL I R RL + VL - R IL = ×I R + RL Purdue University © EET 107 - 22 IL = ? IL < I Introduction to Circuit Analysis 31 Real DC Current Source - example RL IL 10mA 1kΩ RL + VL - IL --------- ---------------- short VL -------------- 10mA 0V 1Ω 9.99mA 9.99mA 10Ω 9.90mA 9.90mA 99mV 100Ω 9.09mA 9.09mA 909mV 9.99mV Careful of load resistance ! IL changed little - VL changed allot ! Purdue University © EET 107 - 22 Introduction to Circuit Analysis 32 Real DC Current Source - example 3 mΑ 3mA 2 mΑ IL 1kΩ 6kΩ 2kΩ + + VL 4V - 3kΩ IL = 6kΩ / 9kΩ x 3mA = 2mA 2-branch CDR VL = 2mA x 2kΩ = 4V Purdue University © EET 107 - 22 Introduction to Circuit Analysis 33 Application – DC model of BJT BJT C C IB B β dc IB + − B 0.7V E E BJT collector acts like a current source of β dcIB. Silicon BE junction acts like a 0.7V voltage supply. Purdue University © EET 107 - 22 Introduction to Circuit Analysis 34 Application: 4-20 mA Control Loops long cable run lossy connectors same I I 1. Noise spikes on twisted pair wire cancel 2. Same I with varying resistance (connectors, etc.) Purdue University © EET 107 - 22 Introduction to Circuit Analysis 35 Converting from V to I Control Loop Control Signals: 1V to 5V or 4mA to 20mA Iload / β 1 to 5 V control signal BJT Current Booster Iload 4 to 20 mA control loop load 250 Ω Circuit converts voltage control to current control. voltage current Negative feedback amplifier with BJT current boost. Purdue University © EET 107 - 22 Introduction to Circuit Analysis 36 Multiple Parallel Current Sources 6A 4A 2A 3Ω INET = + 6A + 4A - 2A = 8A 3Ω 8A Purdue University © into top node EET 107 - 22 Introduction to Circuit Analysis 37 Overview Ø KCL – Quick Review Ø Current divider rule Ø Current Sources Ø Current Sources in Parallel Purdue University © EET 107 - 22 Introduction to Circuit Analysis ...
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This note was uploaded on 02/22/2012 for the course ECET 107 taught by Professor Staff during the Fall '08 term at Purdue.

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