Embedded Systems. Copyright 2000 Ken Arnold 1. Outline. Embedded Hardware. Fluid Flow Analogies. Schematic Conventions. Voltage = Pressure
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1 Embedded Hardware Background: Electronics & Digital Logic Ken Arnold Outline Electronic Schematic Conventions Basic Electronics & Logic Circuit Concepts Fluid Flow Analogies Transistors, Switches Logic Symbols Boolean Algebra Timing Diagram and Notation Copyright 2006 Ken Arnold 1 Copyright Ken Arnold 2 Schematic Conventions Flow is Left to Right: Inputs on Left, Outputs on Right Arrows Show Positive Current Flow As opposed to electron flow Black Dots on Crossing => Connection Fluid Flow Analogies Voltage is like fluid Pressure (Volts) Current is like fluid Flow Rate (Amps) Resistance is like an Aperture (Ohms) Limits Current Flow Power Dissipation (Watts) Copyright Ken Arnold 3 Copyright Ken Arnold 4 Basic Circuit Concepts Voltage = Pressure Voltage, Current, Resistance Ohm s Law: V = I * R Power Dissipation: P = I*V = I 2 *R = V 2 /R Equivalent Fluid Circuit Analogies for: Diode Switch Transistors Copyright Ken Arnold 5 Copyright Ken Arnold 6 Copyright 2000 Ken Arnold 1
2 Resistance = Restriction Complete Circuit Ohm s Law: Note that V and E are both used to represent voltage Copyright Ken Arnold 7 Copyright Ken Arnold 8 Diode Analogy Diode Analogy Copyright Ken Arnold 9 Copyright Ken Arnold 10 Simple Switch Transistor Switch NPN BJT SPST switch Shown Open (Off) Off==Open On==Closed SPST==Single Position Single Throw Copyright Ken Arnold 11 Copyright Ken Arnold 12 Copyright 2000 Ken Arnold 2
3 Circuit Simplification Kirchoff s Laws I Bat =? V Bat = 3.3V I R1 =? R2 I R2 =? R1 + V R1 =? - R3 I R3 =? V=? Sum of Currents Into a Node = 0 Sum of Voltages Around a Loop = 0 Series Rs: Ra, Rb Requiv = Ra + Rb Parallel Rs: Requiv = 1/(1/Ra+1/Rb) IBat=? VBat= 3.3V IR1=? R2 IR2=? R1 + - VR1=? R3 IR3=? V=? Copyright Ken Arnold 13 Copyright Ken Arnold 14 Simplify Combine Parallel R Simplify Combine Series R V Bat = 3.3V R1 R total = R1 + R eq = 3.3K V= (R eq / (R1 + R eq ))*V Bat = (1.1/3.3)*3.3 = 1.1V R eq = R2 R3 = 1/((1/R2)+(1/R3)) = 1.1K Copyright Ken Arnold 15 Copyright Ken Arnold 16 Example Circuit - Solved Transistor Inverter 1->0 I Bat = 1mA V Bat = 3.3V I R1 = 1mA R2 I R2 = 0.5mA R1 + V R1 = 1mA* - = 2.2V R3 V= 1.1V I R3 = 1.1V/ = 0.5mA Copyright Ken Arnold 17 Copyright Ken Arnold 18 Copyright 2000 Ken Arnold 3
4 Transistor Inverter 0->1 NMOS Inverter Copyright Ken Arnold 19 Copyright Ken Arnold 20 CMOS Inverter Common Logic Symbols Copyright Ken Arnold 21 Copyright Ken Arnold 22 Inverted Output Symbols Boolean Algebra Similar to Algebra Identities Associative Commutative Distributive Simplification Notation OR = + = AND = = & NOT = x = -x Some New Rules Copyright Ken Arnold 23 Copyright Ken Arnold 24 Copyright 2000 Ken Arnold 4
5 Simplification Rules - 1 Simplification Rules - 2 a AND 0 = 0 a OR 0 = a a AND 1 = a a OR 1 = 1 Copyright Ken Arnold 25 Copyright Ken Arnold 26 Simplification Rules - 3 Idempotent Rules Simplification Rules - 4 Complementary Rules Copyright Ken Arnold 27 Copyright Ken Arnold 28 Simplification Rules - 5 Commutative Rules Involution Rule Copyright Ken Arnold 29 Copyright Ken Arnold 30 Copyright 2000 Ken Arnold 5
6 Associative Rules Distributive - 1 Copyright Ken Arnold 31 Copyright Ken Arnold 32 Distributive - 2 Simplification Copyright Ken Arnold 33 Copyright Ken Arnold 34 Simplification (cont d) DeMorgan Equivalence Copyright Ken Arnold 35 Copyright Ken Arnold 36 Copyright 2000 Ken Arnold 6
7 DeMorgan Equivalence 2 Notation Conventions Bubbles on Gates Mean Inverted Logic Alternative, Inverted Logic: DeMorgan Equivalents AND Inverted I/Os same as OR gate OR Inverted I/Os same as AND gate Copyright Ken Arnold 37 Copyright Ken Arnold 38 Tri-State Logic Timing Diagram Notation Copyright Ken Arnold 39 Copyright Ken Arnold 40 Timing Diagram Notation 2 Buses and Multiplexing Copyright Ken Arnold 41 Copyright Ken Arnold 42 Copyright 2000 Ken Arnold 7
8 Bus Timing Logic Output V vs. I Logic ONE: Logic ZERO: Copyright Ken Arnold 43 Copyright Ken Arnold 44 Summary Circuits & Logic Review Symbols and Notation Basic Circuit Concepts Fluid Flow Analogies Switches and Logic Boolean Algebra For more information: MIT Open Courseware: Circuits and Electronics Computational Structures Maxfield, BeBop to the Boolean Boogie Gonick, The Cartoon Guide to Physics Arnold, Embedded Controller Hardware Design Circuits: on-line references Copyright Ken Arnold 45 Copyright Ken Arnold 46 Copyright 2000 Ken Arnold 8
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