..2 nt Crcut Bascs KVL, KCL, Ohm's Law LED Outputs Buttons/Swtch Inputs VOLTAGE AND CRRENT..4 Current and Voltage Current / Voltage Analogy Charge s measured n unts of Coulombs Current Amount of charge flowng through a n a certan Measured n = Coulombs per second Current s usually denoted by the varable, I Voltage Electrc energy Analogous to mechancal potental energy (.e. ) Must measure ponts Measured n Volts (V) Common reference pont: Ground (GND) = 0V Often really connected to the ground Hgher Potental Conductve Materal (A Wre) Hgher Potental Lower Potental Lower Potental V 5V Charge = Water Voltage Source = Water Pressure v v 2 2 v GND
Meet The Components Most electronc crcuts are modeled wth the followng components Resstor Measures how well a materal conducts electrons Capactor & Inductor Measures materal's ablty to store charge and energy Transstor Basc amplfcaton or swtchng technology.5 Transstor Krchhoff's Laws Common sense rules that govern current and voltage Krchhoff's Current Law (KCL) Krchhoff's Voltage Law (KVL) Krchhoff's Current Law (KCL) The current flowng a locaton (a.k.a. node) must equal the current flowng of the locaton or put another way The sum of current at any locaton must An electronc component (e.g. resstor, transstor, etc.) 2 4 KCL says.6 Krchhoff's Current Law Remnder: KCL says Start by defnng a for each current It does not matter what drecton we choose When we solve for one of the currents we may get a current "Negatve" sgn smply means the drecton s of our orgnal ndcaton In the examples to the rght the top two examples the drectons chosen are fne but physcally n volaton of KCL but KCL helps us arrve at a consstent result snce solvng for one of the current values ndcates The of and 2 are the same They always flow n the drecton of each other (f one flows n the other flows out or vce versa) 2 KCL says mples 2 KCL says mples 2 KCL says 2 KCL says.7 Krchhoff's Laws Krchhoff's Voltage Law (KVL) The sum of voltages around a (.e. walkng around and returnng to the ) must equal 0 Defne "polarty" of voltage and then be consstent as you go around the loop obvously when you solve you may fnd a voltage to be negatve whch means you need to flp/reverse the polarty v KVL says: v v 2 v 4 2 v 4 KVL says: v 2 2 v 5.8 v 5
.9.0 A Bref Summary Nodes KCL and KVL are and no matter what knd of devces are used The yellow boxes could be ANY electronc devce: resstors, batteres, swtches, transstors, etc KVL and KCL wll stll apply In a few mnutes, we'll learn a law that only apples to resstors (or any devce that can be modeled as a resstor) Some KVL or KCL equatons may be Wrtng the equaton for loop {v,v2,v} and {v,v4,v5} may be suffcent and wrtng {v,v2,v4,v5} may not be necessary But as a novce, feel free to KVL says: v v 2 v =0 v v 2 v 4 v 5 =0 v v 4 v 5 =0 (Def.) An electrc node s the juncton of devces connected by wres voltage at any pont of the node How many nodes exst n the dagram to the rght? 9 2 8 4 5 6 7 se KCL to solve for, 4, and 6 se KVL to solve for v, v8, v5 Practce KCL and KVL NODE D A 2V Hnt: Fnd a node or loop where there s only one unknown and that should cause a domno effect 9 A 9 9V 5V 2 8 v 8 NODE A A 4 v 4 v 5 4V NODE C 0.5A 8 5 NODE B 6 6 7 V 5V. Resstance and Ohms Law Measure of how hard t s for current to flow through the substance Resstance = How much do you have to put to get a certan to flow Measured n Ohms (Ω) Ohm's Law I = or V = R => I http://usc.scout.com/2/92696.html http://www.zmbo.com/photos/marquselee/oregonvsc/9qqqbuy88z Large Resstance R Small Resstance Schematc Symbol for a Resstor Ohm's Law ONLY apples to resstors (or devces that can be modeled as a resstor such as swtches and transstors).2
Seres & Parallel Resstance Seres resstors = one after the next wth no other dvergent path Parallel resstors = Spannng the same two ponts Seres and parallel resstors can be combned to an equvalent resstor wth value gven as shown Seres Connectons R R eff R=R= Parallel Connecton R eff R R eff = For only 2 resstors, ths smplfes to:. Solvng Voltage & Current Gven the crcut to the rght, let = 5V, R = 400 ohms, = 600 ohms Solve for the current through the crcut and voltages across each resstors (.e. V and V2) Snce everythng s n, KCL teaches us that the current through each component must be the, let's call t = Ths alone lets us compute V and V2 snce Ohm's law says V = and V2 = V = and V2 = Though unneeded, KVL teaches us that VV2=0 or that = V V2 v dd _ V R v v2 2.4 Voltage Supply Drawngs The voltage source () n the left dagram (.e. the crcle connected to the "Rest of Crcut") s shown n an alternate representaton n the rght dagram (.e. the trangle labeled "") In the left dagram we can easly see a KVL loop avalable There s stll a KVL loop avalable n the rght dagram _ V R Both are drawngs of the same crcut (.e. they are equvalent) Rest of Crcut Actual connecton wll be drawn lke ths.5 Shortcut: Voltage Dvders A shortcut applcaton of KVL, KCL, and Ohm's law when two resstors are n seres (must be n seres) When two resstors are n seres we can deduce an expresson for the voltage across one of them () = / ; (2) V = *R; () V2 = * Substtutng our expresson for nto (2) and () 2 2 2 2 The voltage across one of the resstors s proportonal to the value of that resstor and the total seres resstance If you need 0 gallons of gas to drve 500 mles, how much gas you have you used up after drvng 200 mles? Gas =, Mleage = V tot R V V2 Voltage Dvder Eqn: If two resstors R and are n seres then voltage across R s: V = Memorze ths. We wll use t often!.6
.7.8 Solvng Voltage & Current Solvng Voltage & Current Reconsderng the crcut to the rght wth = 5V, R = 400 ohms, = 600 ohms Solve for the current through the crcut and voltages across each resstors (.e. V and V2) We can use the voltage dvder concept to mmedately arrve at the value of V2 2 _ V R Consder the crcut on the rght What s the relatonshp between V and V? Can you solve for the voltage V (n terms of Vs, R,, R)? Vs _ V R V R Can you solve for the voltage V2 (n terms of Vs, R,, R)?.9.20 A Problem Gven the followng parameters Vs=5V, R=4, = 2, R = 2 and R4 = 0 ohms. Can we use the voltage dvder concept to mmedately solve the voltage across or do we need to frst do some manpulaton? What about R4? Frst, fnd the total equvalent resstance (R eq ) seen by Vs and then solve for the voltage across each resstor LEDS AS OTPTS AND SWITCHES/BTTONS AS INPTS Frst collapse ths to a sngle equvalent resstance, R eq
Generatng Inputs & Measurng Outputs Where do nputs to a dgtal crcut orgnate? sually as from another dgtal crcut (.e. SB connectng to your laptop's man processng system) For our class rght now: A controlled by a human (can be on or off) How wll we know what voltage s comng out of a dgtal crcut? Could use a voltmeter or osclloscope (don't be afrad to use the equpment n our lab!) are commonly used to show the status of a dgtal output to a human A button or swtch (nput stmulus) Input Some dgtal processng/ control An LED Output Each key on your keyboard s essentally a dgtal nput generated by a push button (pressed or not pressed) The status ndcator on the Caps Lock button s smply an LED controlled by a dgtal output..2 (LghtEmttng) Dodes The smplest output we can control s an LED (Lghtemttng dode) whch s lke a tny lght bulb An LED glows ('on') when current through t (.e. when there s a voltage across t) LEDs are polarzed meanng they only work n one Longer leg orentaton ( leg must be at hgher voltage) LED Schematc Symbol Shorter leg http://www.custobots.com/stes/def ault/fles/magecache/product_full/p roducts/solarbotcsredled.gf 5V 0V Current flows = LED on 5V 0V BACKWARDS!! No Current flows = LED off.22 Longer leg connects to the sde wth the hgher voltage Shorter leg connects to the sde wth the lower voltage 0V 0V 5V 5V No voltage dfferental = No Current flows = LED off Man Pont: To be 'on', there must be a voltage dfference across the LED makng current flow. Need for Seres Resstor wth LEDs Problem: LEDs may allow too much current to flow whch may blow out the LED Soluton: se a seres resstor to lmt current Amount of current wll determne of LED R then and thus LED brghtness = V/R = (VsV LED ) / R sually R s a few hundred ohms ( ohms) No current lmtaton BAD Choose resstor to lmt current A dgtal (gate) output wll usually serve as our voltage source that can be ether '0' (0V) or '' (5V) Doesn't matter where resstor s placed as long as t s n seres Man Pont: LED's should always be connected wth a currentlmtng resstor Longer leg LED Schematc Symbol Breadboard vew.2 Shorter leg LED Connecton Approaches When lettng a dgtal output control an LED, the value (.e. '0' = low or '' = hgh voltage) that causes the LED to lght up depends on how the crcut s wred Ths box represents a dgtal output (e.g. your Arduno) that can generate a hgh () or low (0) voltage. What dgtal output value must be present for the LED to be on? Note: Gates can often (take n) more current than they can (push out), so opton 2 may be preferred but let's not worry about ths now let's use opton Opton 0 LED on LED off GND Model of dgtal output LED s on when gate outputs '' R Opton 2 LED off LED on LED s on when gate outputs '0' Man Pont: LED's can lght for ether a logc '' or '0' output t depends on how they are wred..24
Swtch and PushButton Inputs Swtches and pushbuttons can be n one of two confguratons: or Swtches can be opened or closed and then n that poston untl changed Pushbuttons are open by and requre you to push them to close the crcut (they then open when you release) Can be used as an nput to dgtal devce.25 Example pushbuttons Example swtch Swtches and Pushbuttons Important Note : We can model a button or swtch as a resstor of ether 0 ohms or nf. (very large) ohms When open a SW/PB looks lke an resstance (no current can flow) When closed a SW/PB looks lke a (R=0) and no voltage drops across t Queston: What voltage does an open or closed swtch (pushbutton) generate? Answer:. Important Note 2: SW or PBs don't produce dgtal 0's or 's, they control what voltage (PWR/GND) s connected to your devce SW SW SW SW = =.26 R=nf. (open crcut) R=0 (wre) V =?? V =?? Connectng a Swtch Swtches only the voltage gong nto a devce, they do not produce a voltage (0V or 5V) by themselves Opton : Attach one sde to GND and the other sde to the devce When the swtch=open, nothng s connected to the devce (a.k.a. ) A floatng nput may sometmes appears as zero, and other tmes as a one. We need the nputs to logc gates to be n ether the 0 or state not floatng Opton 2: When swtch closed => resstance connecton from power to ground = current flow BAD!!! (Ths s known as a "short crcut"). Vn = floatng = unknown Vn.27 Opton : Bad (floatng) Swtch Closed = 0V (Logc 0) to nput Swtch Open =??? (does not work) nlmted current flow when closed Opton 2: Bad (short crcut) Swtch Open = =5V (Logc ) to nput Swtch Closed = Short Crcut (does not work) Preferred Wrng of Swtches Soluton: Put GND on the far sde and a "pullup" resstor at the nput sde "Pullup resstor" used to hold the nput hgh unless somethng s forcng t to a zero SW open => Arduno nput looks lke nf. Resstance n seres wth Rp. Thus through Rp and thus no voltage drop across Rp Vn = SW closed => Drect wre from GND to nput nput = Also current flowng from to GND s lmted by Rp preventng a short crcut. sually Rp s large (0k ohms) to lmt current Analogy: Ths Photo by nknown Author s lcensed under CC BYSA Rp Vn Preferred: se a pullup resstor To calculate Vn: Vn = V RP Vn = RP = snce n wth resstance of Arduno nput Thus, Vn = Man Pont: Buttons & swtches should have GND connected to one sde & a pullup resstor on the other.28
Power & Ground Connectons Easy mstake when you're just learnng to wre up crcuts: Wre the nputs & outputs but forget to connect power and ground All crcuts and chps requre a connecton to a power source and ground Dgtal crcuts (aka "gates") Swtches Buttons Actual connecton Rest of Crcut GND wll be drawn lke ths.29 Summary KCL and KVL apply to ALL electronc devces Ohm's law apples ONLY to resstors and governs the relatonshp between the current through and the voltage across a resstor A resstor network can be collapsed to a sngle equvalent resstance by applyng seres and parallel transformatons If two or more resstors are n seres, the voltage across any of those resstors can be quckly found by applyng the voltage dvder equaton LEDs are used as dgtal outputs and must be wred n the correct drecton Swtches can be modeled as a small (0) resstance when closed or large (nf.) resstance when open.0