Circuits & Electronics
Circuits & Electronics ECE 3710
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This 0 page Class Notes was uploaded by Cassidy Effertz on Monday November 2, 2015. The Class Notes belongs to ECE 3710 at Georgia Institute of Technology - Main Campus taught by Staff in Fall. Since its upload, it has received 17 views. For similar materials see /class/233899/ece-3710-georgia-institute-of-technology-main-campus in ELECTRICAL AND COMPUTER ENGINEERING at Georgia Institute of Technology - Main Campus.
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Date Created: 11/02/15
Lecture 1 Circuits Currents and Voltages ECE 3710 Fall 2011 Georgia HH Tech Ermgj rmrr rm School of Electrical and Computer Engineering Text Key Sections 12 13 in the book Current and Voltage The quot uid ow analogy The pipes are the METALLIC WIRES The owing water is the CURRENT The pump is the BATTERY The water pressure is the VOLTAGE The valves are the SWITCHES Current Reference Direction 9 Conceptually current is the rate of ow of charge through a crosssectional area of a conductor Current is the sum of components of moving charge Current Components Keep in mind charge can actually be negative electrons or positive holes which tend to move in opposite directions Negati e Charg Negative Charge Positive Charge The Standard Convention We will assume that a positive charged current ows In reality electrons are owing This means that current into the positive terminal of a device means it is dissipating energy Current ow out of the positive terminal means it is an energy source Current s Relation to Charge Current is de ned as the rate of ow of electrons dql coulombs it AmpereAmp t sec and Similarly qltrgt filtrgtdrqltr1gt Example Qt can be an arbitrary function oftime for tgtO Find it qt 10 e sot Simply differentiate qt to get it it M 50e50t dt DC and AC Current Current can be either Direct DC or Alternating AC it it i l I time time Voltage 0 The energy that is transferred to an element per unit charge that ows through it Therefor the units are JC or VOLTS V A voltage always has two terminals A polarity is indicated by the and and is termed a quotvoltage drop Diodes Voltage Regulators and Recti er Circuits ECE 3710 Fal 2011 Georgia HH 69 Tech Emcgj tmtf tm School of Electrical and Computer Engineering Text Key Sections 101 102 103 and 106 in the text A Voltage Regulating Circuit Occasionally there is a need for a circuit that will produce a speci c constant output voltage while operating from a variable voltage source Usually in reality this is the case we need a very precise voltage to run our device or chip yet the value of the source turbines turning in a nuclear plant a chemical battery solar cells windmills etc is producing a non constant voltage As we make the jump into digital circuit we need very discrete speci c voltages L The quotIdealquot Diode I V01 VDgt0 0Nsh0rt vDlt0 0FF0pen I l I Y Y Reverse Bias Forward Bias How Would We Make a Diode When we want to have a circuit element that has a nonlinear IV curve meaning it doesn t follow ohms law we use an active solidstate device The current elements that we have used have been considered gassive elements We ll start with active solid state devices next lecture Diode Example 1 1000 Solve the circuit Start by picking a state for the diode then solve the circuit and make sure the choice quotmakes sense 7 Diode Example 1 1000 10V VD Assume the diode is OFF Incorrect A 10V FORWARD bias would mean VD that that the diode is ON Diode Example 1 1000 10V 390 Assume the diode is ON Correct A positive current owing into the ID positive terminal the diode is ON Example with Diodes 4kQ D1 D2 a 10v 6kQ 3V Analyze the above circuit assuming each diode is ideal Lets start by making assumptions for the state ON or OFF of D1 and D2 10 Example with Diodes D1 OFF D2 ON I 3V mA This makes sense for D2 positive D2 current owin throu h it 60009 g g This is wrong a 7V would mean 10 VD1 3V gt VDI 7V the diode would be ON 11 Example with Diodes 4kQ lDl 10V 6kQ E 3V D1 ON D2 OFF 10V This makes sense for D2 positive iD2 m 1 current owing through it This makes sense for D2 reverse V02 3V 6V 3V biased so OFF 12 The quotIdealquot Zener Diode I Y Reverse Bias These devices are always placed in a circuit such that they are reverse biased A Basic Regulator Circuit v v v D 0 D VSS 2 What happens if the voltage Vss gets too large The Zener Diode will become a short and remove the excess voltage 15 Recti er Circuits with Diodes A recti er circuit converts a sinusoidal input voltage to a DC output voltage These circuits form the basis of power supplies for basic household devices and battery charging circuits We usually like to transmit power in the form of AC such as 60 Hz on a wall outlet but our devices will operate on DC power Complex Impedances ECE 3710 Fall 2011 Georgia HH Tech Emgj mm m School of Electrical and Computer Engineering Text Key Sections 52 and 53 in the book Why Use Complex Impedances In this lecture we nd that by using complex notations of sources and resistances we can solve for the steadystate response of a circuit much simpler than by using differential equa ons We will introduce the concept of a complex impedance which can be an inductor capacitor or resistor L Impedance of an Inductor Suppose we have the current through an inductor given by iL t Imsinat 6 Voltage across the inductor can be expressed as di t vL t L L wLIm cosat6 dt Now we can express the phasors for the current and voltage IL Im46 90quot VL wLIm L6 wLL90 xIm L6 90quot 4 Impedance of an Inductor VL wLIm 46 4900 gtlt Im 46 90 The phasor for the current VL wLL90 gtlt IL VL jaLgtltIL Ohm s Law in phasor form VLZLgtltILgt ZLij 5 The impedance of an inductor Impedance of an Inductor Z L ij Does this make sense to us to is the radial frequency of the source coswt6 The lower the frequency the lower the d o l derivative of the current which means the V t L impedance lowers until eventually being 0 L a short for a DC signal Impedance of a Capacitor Solving the phasor voltage and current for a capacitor we can similarly nd an expression for the impedance of a capacitor VC ZCIC ZC iL 90 wC ij Impedance of a Resistor Does a resistor have a complex impedance WU A W VV VR RIR No the voltage and current are inphase 10 PN Junction Diode and BJT Transistor ECE 3710 Fall 2011 Georgia HH Tech Emgj mm tm School of Electrical and Computer Engineering Text Key Supplemental The Circuit Diode In the previous lecture we talked about a diode which is a device that only allows current to ow in one direction Diodes are Z VD nonlinear VD gt 0 Sim This device does not obey Ohm s Law which states V lt 0 Open there should be a linear relationship between D voltage and current 3 How Do We Make a Diode How do we make a device that has a nonlinear response ie the current distinctly changes at a certain threshold voltage Ultimately we want the voltage to change the resistance Lets look back at what resistance is The Resistance of a Material pL A What could the voltage change 1 u is a measure of how easily mobile charge can p move in the material n is a measure of how how many mobile charges there are in the material We will use voltage to change the number of mobile charges n in the material This is how we get a nonlinear device 5 P and N type Silicon If we put in an element that has one less electron we make the Si have mobile positive charge and it is ptype If we put in an element that has one extra electron we make the Si have mobile negative charge and it is ntype What happens if we smash together a p type Si and an ntype silicon The Resistance of a PN Junction Lets take a look at the resistance of a PN junction Iquot39 l 1 ll 2 ll 3 l l l l LowR HighR LowR This center region is called the depletion region because it is quotdepletedquot of charge and is the key to making the diode high or low resistance 10 What Happens When You Bias the Diode VDltO VDgtO l The barrier at junction is removed A Forward Biased Diode What can we say about the ow of current through the diode Positive current ows to the right and negative current to the left Do these two components of the current add or subtract to each other NPN Transistor BJT Base 1 Input Signal L T JunctionZ Junction 1 Emitter O Collector 07 Circuit Elements and Ohm s Law ECE 3710 Fall 2011 Georgia HH Tech Emgj mm m School of Electrical and Computer Engineering Text Key Sections 16 in the book Circuit Elements We make the jump from generic circuit elements to speci c elements with unique functions within the circuit Conductors Voltage Sources Current Sources Resistors DC and AC Independent Voltage Sources 5V 3cos2Ttt These voltage sources are said to be independent because their output does not depend on any other voltage or current in the circuit 7 Ground Plane on a PCB What is a oating ground Dependent Voltage Sources A dependent voltage source is one where the voltage across the terminals is a function of other voltages or currents in the circuit Can be a voltage G x V or controlled or current controlled source G is a constant called the gain garameter 10 DC and AC Independent Current Sources 3A 4sin50nt Resistors An element which disrupts slows the flow of current R ohms Q Resistance is the parameter that de nes the relationship between the current flow and the voltage drop ie how much energy is dissipated by an element 16 Resistivity p Resistivity is the material property that makes the difference between conductors and insulators 1 p 61M u is a measure how easily electrons ow through a material n is the amount of free electrons in a material Resistivity is the parameter of choice when trying to change how resistive an element is conductor insulator semiconductor as opposed to simply keeping the same material but reducing the dimensions 18 Ohm s Law the relation between V and I viR The voltage drop across an ideal resistor is linearly proportional to the amount of current owing through it V This relationship won t always be linear the transistor Trans Resistor 19 NodeVoltage and MeshCurrent Analysis ECE 3710 Fall 2011 Georgia HH 69 Tech Emgj mm tm School of Electrical and Computer Engineering Text Key Sections 24 and 25 in the book How Do We Solve This N R1 R2 V2 R3 vlo v NV M3 Can t Combine Resistances Can t do Dividers Node Voltage Analysis Start by de ning a reference node Next we label the voltages at each node The negative reference polarity is the reference node Next we strategically solve for each of the node voltages Node1 NodeVoltage Example R1 Node3 R539 Node Voltage Example Suppose that we know the values of all the node voltages 0 How do we nd the voltage across R3 vx Assuming that the left hand side is the positive reference NodeVoltage Example R1 Node 1 Assume we know all node voltages we can draw KVL across the loop Node Voltage Example Looking at KVL we can write the solution around the loop nng0 What do we know about V3 It s the node voltage at Node 3 What do we know about V2 It s the node voltage at Node 2 NodeVoltage Example Rim V vzv3 v vy v2 v1 v2 v1 O VV R2 R3 R539 Write an expression for Vy and V2 in terms of the node voltages V1V2 and V3 V3 A Few Notes on our Choices N R1 v1 O V MAI 3 v3 R4 39 R5 L REference Make the reference V1 is the source voltage 10 node ground
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