EME106 Intro to Engineering II Spring 2010 Lecture 10: Analysis of Electrical Systems Today: Review of Electrical Components Ohm’s Law Applications Study of the Line following Robot Circuit. Tuesday: Circuit Board Etching Thursday: Tour of Union Solutions Depart: 2:00 p.m. Return: 3:20 p.m. Introduction to Electrical Circuit Analysis: What is Electricity? Electricity is a controlled flow of electrons along a some path. Electrons are the negatively charged particles that are found orbiting all elementary particles of matter we know as atoms. Atoms are extremely small. A single grain of table salt literally contains 1018 atoms. Electrons even smaller. Normally an atom’s electrons are bond to the atom by the attraction of the negatively charged electron to the positively charged nucleus of the atom. However, for some substances, when the literally billions upon billions of atoms are packed closely enough together with specific structure or lattice, the outer most electrons of the atom are freed to move between different atoms with very little effort. Materials in which this occurs are generally called “conductors”. The general movement of these “free” electrons along a prescribed path of such material is called “electron flow” or “electricity”. Being able to harness this extremely minuscule particle along with many trillions of its twins to act with the same general motion makes electricity a powerful phenomenon which can be put to many different uses. What is Charge? Charge refers to a property of matter which describes a force of repulsion or attraction to other matter which also has charge. Elementary particles such as electrons are said to be negatively charged, protons are positively charged, neutrons have no charge. Alike charged particles repel each other. Oppositely charged particles attract each other. Controlling these “forces” allow us to interact with and manipulate the response and action of particles. Charge is measured in units of coulombs. A coulomb is defined in terms of the force one charged object exerts on another. F F A charge of 1 coulomb exerts a - force of 8.988 x109 N on another - 1 coulomb charge located 1 meter away from it in air. In comparison one electron has a charge of -1.6x10-19 C. 1m When electrons with their charge are coaxed to move in along the same path of conducting material, this flow of charge is called electric current. We commonly distinguish two different types of electric current. Alternating current (AC): the movement of electric charge back and forth in a periodic motion (usually sinusoidal). This is the kind of current used for most most electrical distribution systems. Direct current (DC): the movement of electric charge in only one direction. This is most commonly associated with electrical power provided by batteries and that current used in digital electronic devices. Devices such as batteries and generators are able to set up Voltage + + + + + flows of electric current. Their ability to set up this flow is measured as a quantity called electric potential or a quantity you are more commonly used to calling “voltage”. Voltage is Current actually a measure of the electric potential. When a voltage exists between locations and a conducting material or path is available between the two locations, an electric current will light flow. Studies of electrical flow or “current” and electric potential or “voltage” show that for many difference conducting Current materials, the current flow is directly proportional to the electric potential. In other words, the larger the electrical potential, the larger the current flow for a specific conducting material. This relationship is called Ohm’s Law. Ground V I R The proportional constant between “current” and “voltage” is called resistance and is measured in units of ohms (Ω). The value of resistance depends upon the material that is used to form the conducting path and the shape and length of the material path. Different materials have different resistivity. The geometry of the material path affects the resistance. In general, a longer path has more resistance…while a path with a larger cross section has less resistance. All material offer some resistance to flow of current. What are the best conducting materials? Silver, Aluminum, Copper, Gold, SuperConductors…. R=100 Ω Example 1: A 12 Volt battery is connected across + a 100 ohm resistance. 12 V I What current flows? - Solution: V 12 V V I R I 012 A . R 100 More complicated circuits may include many resistance values. Designing electric circuits means that we need to be able to predict current flow through different circuits. Rules for Resistance Networks: ------------------------------------------------------------------------------------------------- Resistors in series: Req = R1 + R2 + R3 = Σ Ri R1 R2 R3 REQ --------------------------------------------------------------------------------------------------- 1 1 1 Resistors in Parallel: Req = = 1 1 1 Ri R1 R1 R2 R3 REQ R2 R3 ---------------------------------------------------------------------------------------------- Example 2: The following resistance network can be reduced to an equivalent resistance of what value? 20 Ω 50 Ω 40 Ω 10 Ω 30 Ω REQ Example 2 Solution: The following resistance network can be reduced to an equivalent resistance of what value? 20 Ω 50 Ω 40 Ω 10 Ω 30 Ω Resistors in parallel: 1 1 1 60 R20||30 12 1 1 1 1 3 2 5 R20 R|30 20 30 60 60 50 Ω 40 Ω R20||30 = 12 Ω 10 Ω Resistors in series: REQ R50 R40 R20||30 R10 50 40 12 10 112 REQ Example 3: 100 Ω VA What is the voltage at point A. + I 50 V 100 Ω 100 Ω - Solution: Start by replacing system with an equivalent resistance network. 100 Ω 100 Ω REQ = 150 Ω 100 Ω 1 1 100 REQ R100 100 100 150 1 1 1 1 2 R100 R100 100 100 then the circuit can be simplified as, where the overall current may be found using Ohm’s Law, V I R . REQ =150 Ω V 50 V I 0333 A . R 150 + I 50 V - then the voltage drops from 50 V to VA as the 0.333 A current passes through the 100 Ω resistor. V IR 100 Ω VA 50V VA ( 0333 A )( 100 ) . VA 50 333 167 V . . + I 50 V I R100||100=50 Ω - Common Circuit Components: There are many electrical components, but the vast majority of them will include such components as Resistors Capacitors Inductors or Coils Batteries Diodes Bulbs Transistors Switches Integrated Circuit Chips Crystals LEDs Fuses Motors Voltage regulators Relays Systems of real electrical components are modeled as electrical circuit diagrams: R1 R C 2 2 + C1 vo(t) R3 L1 - R4 where each component can be modeled mathematically for its behavior. Resistor: Capacitor: Inductor or Coil: 1 dI Principle: VA VB IR VA VB Idt VA VB L C dt VA VA VA I C I R I L VB VB Resistors: Resistors are electrical components which dissipate electrical energy as heat. Important ratings for a resistor are it Resistance (in Ohms) and its Power rating (in Watts) Resistors use a color code to identify the resistance of component. The most common type of resistors used are 1/4 watt metal or metal oxide film resistors. This is what you see on many printed circuit board assembly. The gold or silver bar represents a tolerance level of the resistor. The other three color bars give you the resistance value. To find the resistance of the one shown here (bars from left to right: Orange, White, Red, Gold) can be found as Color Bar: Value: st 1 Digit: Orange 3 2nd Digit: White 9 Multiplier: Red 102 Accuracy: Gold 5% from the Handbook of tables for Applied Engineering Science by Bolz and Tuve Capacitors: Capacitors are electrical components that store charge. Capacitors are commonly used for applications which require: a) filtering applications b) voltage stabilization c) voltage spike suppression d) rapid release of energy and current e) oscillation circuitry Capacitors can be used as power storage devices which don't generally hold a lot of energy, they then can charge and discharge very quickly and can be recharged an almost unlimited number of times. They are small, light weight, and inexpensive and usually have a disk or barrel shape. Important characteristics to consider when selecting a capacitor include type ( electrolytic, tantalum, ceramic have slightly different ), capacitance (in farads), maximum voltage, and directionality (unidirectional or bidirectional). If you were to attempt to measure the ability of a capacitor to build up a stored charge, it is proportional to the charge already held by the capacitor. Which means the time response of the voltage across the capacitor follows an exponential time response function. What this means, is it takes time to charge a capacitor, but an empty capacitor charges faster than one which is already partially charged. It doesn’t happen instantaneously. As an example, when the switch in the circuit below is closed, the output voltage V across the capacitor, builds up as shown by the graph below. RC is called the time constant. Potential difference (V) R Vo – Vo/e + C V VO - RC 2RC 3RC Time (t) There are a variety of different types of capacitors. The large barrel-shaped electrolytic capacitors usually have the rating labeled on the case. Smaller capacitors including both tantalum and ceramic capacitors more commonly use a three digit code to indicate their size. The larger capacitor give both the capacitance and the maximum voltage rating. from the website http://www.electronics-tutorials.ws/capacitor/ Diodes and LEDs: A diode is a semiconductor component which allows current to pass through it in only one direction. Common uses of diodes are in a) overvoltage protection circuits b) AC voltage rectification circuits c) high voltage gain circuits Diodes are identified by a system which uses numbers and letters to identify different types of semiconductor devices. This is the same system used for identification of transistors and many other semiconductor components. The first number in the system indicates the number of junctions in the semiconductor device and is a number, one less than the number of active elements. A 1 designates a diode; 2 designates a transistor, and 3 designates a tetrode (a four-element transistor). The letter "N" following the first number indicates a semiconductor. The 2- or 3-digit number following the letter "N" is a serialized identification number. A diode is a directional device. Diodes distinguish one end of the diode from the other (anode from cathode). Manufacturers generally code the cathode end of the diode with a "k," "+," "cath," a color dot or band, or by an unusual shape (raised edge or taper). In some cases, standard color code bands are placed on the cathode end of the diode. This serves two purposes: (1) it identifies the cathode end of the diode, and (2) it also serves to identify the diode by number. Light emitting diodes (LED) usually distinguish the negative lead (anode) by a flattened part of the LED’s base. Length of the LED legs will usually have the longer leg as the cathode, but not always, so check its polarity. Be careful when placing diodes in a circuit. In some circuits, incorrect orientation of the diode can result in a short circuit condition and can cause damage to components. In the case of LEDs, they should always be used in conjunction with a current limiting resistor. Transistors: Transistors are semiconductor devices which primarily serve one of two main functions. In the majority of applications they will function as an electrically controlled switch. In other applications they may be used for current or voltage amplification. We will only be considering their use in switching applications. There are several different types of transistors but we will only disucss one type here. BJTs are Bipolar Junction Transistors and come in two flavors: PNP and NPN. Both flavors of BJT have three input lets called the Emitter, Base, and Collector. In each case, the transistor acts like a switch when there exists adequate current flow through the base. The main difference between the two flavors is the direction of the current flow with respect to the base. NPN transistors turn on when sufficient current flows into the base (usually achieved by applying a positive voltage to the base). When this is the case, the path from the Collector to the Emitter behaves as if it is a conducting circuit. If the current flow into the base is below a specified current level, then the path from the Collector to the Emitter is blocked, and no current flows. PNP transistors works when current flows out of the base (which is usually achieved by holding the voltage level of the base close to ground). When this happens current is allowed to flow from the Emitter to the Collector as if it were an shorted circuit circuit. PNP NPN Typical circuit applications of NPN and PNP switching circuits are shown below . R1 R1 + Rload + C E On Off B B - - On C Off E NPN R2 PNP R2 Rload The main concept is when you supply a small current flow to the base, you can induce a larger current flow through the Collector. For switching, the current flow is effectively saturated. The resistances R1 and R2 are used in conjunction with the transistor gain to limit the current through the load and transistor. Proper selection of these resistances can make the transistor function as an amplifier instead of a switch. Line Following Robot Circuit: A complete circuit of the line-following controller is given below. You should examine this circuit and attempt to identify the different electrical components that are present. +9 VDC R1 EME 106: Intro to Engineeirng II Lecture 11: Homework 1) For the Resistance shown, calculate the voltages at TP1 and TP2. R1=2 kΩ R2 = 10 kΩ (evenly split) R3 = 7.5 kΩ TP1 TP2 R4 = 7.2 kΩ R5 = 4.3 kΩ R6 = 4.1 kΩ R2 R3 R4 R5 R6 9V 9V 9V 2) For the LM393 Linear Comparitor IC: R7 R8 Pins 2,3,5 and 6 are the inputs TP1 TP2 Pins 1 and 7 are the outputs Fill in the truth table for this chip. (consult your Data sheets on Lecture 10) A Inputs A out B inputs B out Bout B- B+ A- < A+ B- < B+ LM393 A- = A+ B- = B+ Aout A- A+ A- > A+ B- > B+ 3) What is the purpose of Resistors R7 and R8? If typical current to the LED is 10 to 20 mA and they have a voltage drop across the LED of 1.8 V, what size should the resistors be for a 9 V input? Input (what this means is the chosen resistor should allow a current flow of 10 to 20 mA for a voltage drop of 7.2 volts.) Output to Motor 4) Will the transistor turn On when the Input goes High or Low? Does turning transistor On or Off turn the motor On or Off? Explain how you know these answers.