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DC CIRCUIT ANALYSIS Version 1.4, March 1995 Copyright 1991-1995, Arthur Tanzella All Rights Reserved The "DC Circuit Analysis" program is an educational tool for introducing the user to the concepts of Direct Current (DC) circuits in general, and digital computer circuits in particular. Circuits are created and evaluated on the computer screen. This program is not intended to be a design tool, and as such does not properly handle some analog circuits, such as operational amplifiers. This documentation can function as a tutorial to learn about semiconductors, logic, and digital computer circuits. Numerous sample circuits are used throughout this documentation and can be displayed and evaluated using this program. ACKNOWLEDGEMENTS I would like to take this opportunity to thank the following people who are my good friends, and have contributed significantly to this program. Their contributions were in the testing of the program and in their suggestions to make this program and this documentation easier to use and read. Warren Cella Ken Hanawalt Art Silverstein Mike Weisfield Bill Locke I would also like to thank Bill Locke for contributing subroutines to solve a matrix of simultaneous equations. LICENSE AGREEMENT DC Circuit Analysis is a "Shareware Program" and is provided at no charge to the user for a one week evaluation period. Feel free to share it with your friends, but please do not give it away altered or as part of another system. The essence of "user-supported" software is to provide personal computer users with quality software without high prices, and yet to provide incentive for programmers to continue to develop new products. If you find this program useful and continue to use the program after the one week evaluation period, you are requested to send a registration payment of $15 (US) to: Arthur Tanzella 4613 Clubvue Drive Pittsburgh, PA 15236-4803 USA Print out and fill in the "REGISTER.DOC" file. Send it with the $15 (US) registration fee to the above address to register this program. The $15 (US) registration fee will license one copy for use on any one computer at any one time. You must treat this software just like a book. An example is that this software may be used by any number of people and may be freely moved from one computer location to another, while there is no possibility of it being used at one location while it's being used at another. Treat the software just like a book that cannot be read by two people in two different locations simultaneously. Users of DC Circuit Analysis must accept this disclaimer of warranty: "DC Circuit Analysis is supplied as is. The author disclaims all warranties, expressed or implied, including, without limitation, the warranties of merchantability and of fitness for any purpose. The author assumes no liability for damages, direct or consequential, which may result from the use of DC Circuit Analysis." Commercial users of DC Circuit Analysis must register and pay for their copies of DC Circuit Analysis within 30 days of first use or their license is withdrawn. Site-License arrangements may be made by contacting Arthur Tanzella at the above address. Anyone distributing DC Circuit Analysis for any kind of remuneration must first contact Arthur Tanzella at the address above for authorization. This authorization will be automatically granted to distributors recognized by the Association of Shareware Professionals (ASP) as adhering to its guidelines for shareware distributors, and such distributors may begin offering DC Circuit Analysis immediately. However, Arthur Tanzella must still be advised so that the distributor can be kept up-to-date with the latest version of the DC Circuit Analysis program. You are encouraged to pass a copy of DC Circuit Analysis along to your friends for evaluation. Please encourage them to register their copy if they plan to continue using it. All registered users will receive a copy of the latest version of the DC Circuit Analysis program when they register. If you have any comments or problems with this program, you can contact me at the address above or send an E-mail message via CompuServe to Arthur Tanzella 71175,76. All registered users will receive support for a minimum of three months from the time they registered.ASP OMBUDSMAN The author is a member of the Association of Shareware Professionals (ASP). The ASP wants to make sure that the shareware principle works for you. If you are unable to resolve a shareware-related problem with an ASP member by contacting the member directly, the ASP can probably help you. The ASP Ombudsman can help you resolve a dispute or problem with an ASP member, but does not provide technical support for members' products. Please write to the ASP Ombudsman at 545 Grover Road, Muskegon, MI 49442 or send an E-mail message via CompuServe to ASP Ombudsman 70007,3536. GETTING STARTED The DC Circuit Analysis program contains over 100 files occupying approximately 800 KB of disk space, and is compressed into a single self- extracting file called "INSTALL.EXE." This file was created using the LHarc version 2.11 program, which is a copyright reserved freeware program written by Haruyasu Yoshizaki. To run the program requires a 286 or later (386, 486, or Pentium) processor, an EGA or VGA graphics' adapter with 256 KB of RAM installed, and a color monitor. It also requires between 300 KB and 350 KB of available RAM after DOS, drivers and Terminate and Stay Resident (TSR) program are loaded. The actual amount of RAM required depends on the complexity of the circuit. If Expanded Memory (EMS) is installed, only 300 KB of RAM is required. You can use the CHKDSK or MEM command to decide if you have enough available RAM to run this program. To start the DC Circuit Analysis you must be in the directory containing this program. Typically, the program is stored in the C:\DC14 directory. Use the DOS "CD" (Change Directory) command to change the default directory to the program directory as follows: CD \DC14 To start the program type "DC" with or without parameters as follows: DC or DC filename.DC or DC filename.DC x If no parameters are specified after the "DC" command, the first (help) screen of the online tutorial will be displayed. This tutorial contains all the information in this document, and allows access in a Hyper-Text like fashion. The cursor keys (or mouse) can be used to highlight keywords on the screen. The ENTER key will display another screen of information whose subject corresponds to the selected keyword. The PGDN key, or selecting the "More" keyword, will display the next screen of information. The PGUP key will display the previous screen. The F1 key will display the first screen of the tutorial. From the first screen the "Table of Contents" keyword will display a screen containing the Table of Contents that will allow you to jump directly to the desired section. The "Index" keyword will display a screen containing many different keywords. The ESC key will exit the Tutorial and return you to the DC Circuit Analysis program. The F5 key will allow you to return to the tutorial at the same screen previously displayed. To return to the main menu, press the ESC key. Press ENTER to display the "Select Sample Circuit" screen. This screen contains three menus. From left to right they are the Circuits, Directories, and Drives menus. Each menu contains a sorted list of items. You use the LEFT and RIGHT cursor keys to move from one menu to another. From within a menu you can use the UP and DOWN cursor keys to highlight an item. The PGUP and PGDN key will page through this directory. Alternatively, you can start to type out the entry to highlight the desired item. Use the ENTER key to select the highlighted item. In the Directories (middle) menu, selecting the ".." item will move you up one directory in the tree. Whenever you change the directory, the path displayed on the second line in blue will change along with the Circuits menu. In the Drives menu, you should not select a floppy drive that does not contain a diskette. Otherwise, DOS will display an "Abort, Retry, or Fail" menu. Finally, ESC will exit this menu without selecting a sample circuit. At the opening menu you can select "Exit" to exit the program without modifying the sample circuit. If a filename is specified on the command line, and it does not exist, the program will display the "Modify Circuit" screen that allows you to create a new circuit. By convention, circuit files have the extension "DC." To exit this screen, press the ESC key. When exiting from the opening menu, you can choose to Save the Circuit or Exit without saving the circuit. If you choose to save the circuit, it will be stored in the file (filename.DC) specified on the command line when you started the program. If a problem occurs during the writing of the file, you will be prompted to enter a new filename. If the file specified on the command line already exist, the program will display the opening menu. Your choices are: Analyze Circuit Modify Circuit Select Sample Circuit Save Circuit As Save Circuit Exit "Analyze Circuit" will evaluate the circuit, calculating, and displaying voltages at interconnect nodes. It will also calculate and display the current and its direction across each resistor in the circuit. Finally, it will decide if any components are overloaded. If you want to analyze a circuit and exit without modifying the circuit, add any character following the filename on the command line as follows: DC filename.DC x Sample circuit files are located in the "DC" subdirectory under the default directory. You must prefix sample filenames with "DC\" to use files in this subdirectory as follows: DC DC\filename.DC x As an example, let's look at the "RESIST1.DC" sample circuit. Start the program by typing the following: DC Select "RESIST1.DC" from the select sample circuit menu. This file actually contains three separate resistor circuits. The simplest circuit is on the left, and the circuits gradually become more complex as you move to the right. Notice that voltages at interconnect nodes are displayed in green, and currents across resistors are displayed in orange. Further notice, that an arrow prefixes the current indicating the direction of the current, always pointing from a larger voltage to a smaller voltage. The ESC or F10 key is used to exit.BASIC ELECTRICAL THEORY Electrical potential is measured in Volts (V). Electrical current is measured in Amperes or Amps (A). Electrical resistance is measured in Ohms (Ω). Electrical power is measured in Watts (W). Conductors are usually metal wires made of copper or aluminum, and are used to conduct electricity. These metals have a very small resistance measured in milliohms (0.001 ohms) per foot of wire, depending on the diameter of the wire. The DC Circuit Analysis program assumes that wires used to connect components have zero resistance. This assumption is valid if short distances (less than a few feet) are involved. Insulators are usually made of materials like rubber and plastic, and are used to insulate wires. Insulators have very high resistance (millions of ohms). Resistors are components that allow electrical current to flow, but resist the current converting some of it into heat. Resistors are typically made from carbon, and have resistance measured in ohms or Killohms (1,000 ohms). A potentiometer is a variable resistor with three connection points. The top and bottom connections are to a fixed resistor. The middle connection can make contact at different locations along this resistor. Hence, the sum of the resistance between the middle connection and the top connection, and the resistance between the middle connection and the bottom connection, is the same as the resistance between the top and the bottom connection. Other basic electrical components include capacitors and inductors. Capacitors are constructed of two large surface area conductors separated by a thin insulator. Capacitors are typically used in an Alternating Current (AC) circuit to filter selective frequencies. They can also be used to stabilize a DC voltage from voltage spikes. Inductors are wires wrapped into a coil. When electrical current spirals through an inductor, it creates a magnetic field. Inductors are primarily used in AC circuits to produce oscillators. Inductors have the opposite effect of capacitors on a circuit. Inductors can also be used to create electromagnets. If two inductors are wrapped around the same iron core, they form a transformer. Transformers are used to raise or lower AC voltages. It is possible to create an electrical potential by passing an inductor through a magnetic field. This is how an electrical generator works. Batteries are electrical devices that use chemicals to produce an electrical potential. The battery has an excess of electrons (negatively charged) at its negative pole, and a shortage of electrons at its positive pole. Both generators and batteries can be used to supply power to an electrical circuit. This program represents the power supply using fixed voltage nodes established at +10V, +5V, 0V (ground), -5V, or -10V. In a steady state DC circuit, capacitors act like an insulator, unless the DC voltage is more than the capacitor rated voltage. Inductors on the other hand, act like wires or resistors with small resistance values. Consequently, the DC Circuit Analysis program does not support capacitors, inductors or transformers. This program assumes a steady state DC circuit and uses the following equation to calculate voltage and current through out the circuit: V = I R where: V is the potential measured in Volts I is the current measured in Amps R is the resistance measured in Ohms Every component in the circuit is reduced to its characteristic resistance, and the voltage potential across the component is calculated based on the current flow using this equation. The actual equation implemented in DC Circuit Analysis is a derivation of V=IR for multiple resistors connected to the same node. The assumption is that the total current entering a node is equal to the total current exiting that node (ΣI=0). The following equation is used to calculate the voltage at each node: N Σ Vi/Ri i=0 V = ────────── N Σ 1/Ri i=0 where: V is the calculated voltage at a specified node N is the number of resistors connected to that node Ri is the resistance of each resistor Vi is the voltage at the node on the other end of each resistor A double precision matrix of simultaneous equations is used to calculate the voltage at each node. The effective resistance of each semiconductor is calculated based on the voltage at each node. The calculation is continually repeated until the voltage at each node converges (barely changes). The convergence criterion used by the program varies with the speed of the computer. The convergence criteria ranges from a stringent value of 1.0e-10 (0.0000000001) Volts for fast computers, to a relaxed value of 1.0e-8 (0.00000001) Volts for slow computers. The more stringent the convergence criteria the longer this program may take to calculate voltage and current, and the more accurate the results are. You can override the convergence value and explicitly set it external to the program using the DOS environmental variable "DC_DV" as follows: SET DC_DV=1.0e-8 Electrical power is calculated using the following equation: P = V I or P = I² R where: P is the calculated power in Watts V is the potential across a component measured in Volts I is the current passing through the component measured in Amps I² is the current squared (current multiplied by itself) in Amps² R is the resistance of the component measured in Ohms Power is calculated to decide if various components are overloaded. All resistors in the library are assumed to be standard ¼ Watt resistors. As an example, using the equation I = V/R, a 100 ohm resistor connected to a 10 Volt source and ground has a current of 0.1 Amps passing through it. Using the power equation P = VI, the power through this resistor is 1 Watt that exceeds its rated value of a ¼ Watt. Therefore, this component (resistor) is overloaded. USING THE PROGRAM The DC Circuit Analysis program automatically detects and uses the following: a math coprocessor, a two or three button mouse, and EMS (Expanded) memory. These items are not required, but if found, will improve the performance of the program. DC Circuit Analysis supports a mouse if one is installed with either the MOUSE.SYS or MOUSE.COM driver. However, a mouse is not required. Tthe left mouse button is equivalent to the ENTER key and is used to select items. The right mouse button is equivalent to the ESC key and is used to exit screens. If the mouse has three buttons, the middle button is supported in in the Modify Circuit screen to display the Library of Components screen, and to switch pages of library components. Let us now analyze the "RESIST2.DC" sample circuit. This file contains two sample circuits, one with a potentiometer, and the other with a switch. Use the LEFT and RIGHT cursor keys are used to select an adjustable component. Adjustable components with blue back grounds show they have been selected. A mouse can be used to select an adjustable component. The ENTER key or the left mouse button will toggle the selected switch, or increment the selected potentiometer in 10% increments. All switches are Single-Pole Double-Throw. When a switch is selected: The HOME, PGUP, and UP cursor keys will position the switch in the up position. The END, PGDN, and DOWN cursor keys will position the switch in the down position. When a potentiometer is selected: The UP and DOWN cursor keys will increment or decrement the potentiometer in 1% increments. The PGUP and PGDN keys will increment or decrement the potentiometer in 10% increments. The HOME key sets the potentiometer to 99%, and the END key sets it to 1%. The "p" key will plot a graph of the first eight interconnect node voltages (labeled A through H in yellow) versus the potentiometer voltage. The program will automatically calculate voltages at every node as it adjusts the potentiometer. If you have a fast computer, the potentiometer will be adjusted in 1% increments from 1% to 99%. Slower computers will use larger increments between 2% and 5%. Since the program must continually calculate the circuit until it converges for each time the potentiometer is incremented, plots can take up to ten minutes, depending on the complexity of the circuit and the speed of the computer. A math coprocessor can speed up the calculation, but is not required. The DOS environmental variable "DC_PLOT" can be used to explicitly set the potentiometer increments external to the program as follows: SET DC_PLOT=5 Once the program completes this calculation, the plot will be displayed on the screen. Press any key to exit the plot and return to the analysis screen. Subsequent "p" commands will instantly redisplay the plot without recalculation. Therefore, you can press "p" to toggle between the plot and the analysis screen. You can also adjust the potentiometer on the analysis screen as you toggle between the two screens. Interconnect nodes, connected to fixed voltage or switches, are treated as though they are fixed nodes with the corresponding voltage, therefore the program does not explicitly display a voltage next to these nodes. Interconnect nodes connected to other interconnect nodes are combined for calculational purposes into a single interconnect node and the calculated voltage is displayed only at the node created first. Finally, the "w" key writes the Analysis or Plot screen into a PC Paintbrush compatible file called DC.PCX. If the DOS environmental variable TMP is defined, the DC.PCX file will be written to the directory identified by the TMP variable, otherwise it will be written to the default directory. Now let's exit (ESC) this sample circuit and look at modifying a circuit. Let's start with the existing circuit RESIST1.DC. After selecting this circuit from the "Select Sample Circuit" menu, you should save it under a different name using the "Save Circuit As" menu. To modify the circuit you should select "Modify Circuit" from the opening menu. Now let's modify the first circuit on the left. Let's change the 10V fixed voltage node to 5V fixed voltage node. Use the cursor keys or the mouse to move the cursor over the 10V fixed voltage icon. Hold the CTRL key and the BACKSPACE key down simultaneously to delete the 10V fixed voltage icon. Now press F4, or the middle button on the mouse, to display the library of components. If you have a slow disk drive, it may take a few seconds to display this screen, because it must read the library file containing the icons. A 256 KB disk cache, such as SMARTDRV (see your MS-DOS manual), would speed up the display of this screen. Use the cursor keys or mouse to move the white box to the 5V fixed voltage icon. Press ENTER or the left mouse button to select this icon. The Modify Circuit screen will now reappear. Use the cursor keys or mouse to move the icon to the same location that the 10V fixed voltage icon was in. Press ENTER or the left mouse button to lock it in place. Beware that if you attempt to locate the icon too close to an existing icon on the screen, you will get the message: "ERROR - Component Overlaps Another Component." If this occurs, press any key to clear the message, move the icon to another location, and press ENTER or the left mouse button. Icons must have some space between them. They cannot be touching. Think of each icon as having an invisible rectangular outline that encompasses the icon. If you need to move an icon, locate the cursor on top of the icon and press the F3 key. Then use the cursor keys or mouse to move the icon to a new location and press ENTER or the left mouse button to lock it in place. We now must connect the 5V fixed voltage node to the top of the resistor. Locate the cursor over the bottom circle (connection point) of the 5V fixed voltage node, and press ENTER or the left mouse button. The icon will turn red. Now locate the cursor over the top portion of the resistor and press ENTER or the left mouse button. The program will draw a wire (line) between the two connection points. You must always select a node (interconnect, fixed, or switch) before selecting a component (or IC) to make a connection. You can use the same procedure to disconnect (remove) a wire. You can connect two nodes together in any order. You can press F1 for a brief help message. For additional help, press F1 a second time to receive a full screen of help. This screen identifies the different types of nodes and components in the library. Finally, press F6 to analyze the circuit and see the results of your modification. F6 allows you to switch between the "Analyze Circuit" and "Modify Circuit" screens. Now is a good time for you to attempt to build your first circuit from scratch. Exit the program and type the following: DC DC\TEST2.DC Now build a simple resistor circuit of your choosing. Then go to analyze your circuit. Let's look at the RESIST3.DC sample circuit for an example of a complex resistor network. BASIC SEMICONDUCTOR THEORY Besides resistors, there are electrical components called semiconductors. They get their name from the fact that sometimes they act as a conductor, a resistor, or an insulator depending on the circumstance. Semiconductors are typically made of materials like silicon or germanium. There are two types of semiconductor materials, Positive type (P-type) material, and Negative type (N-type) material. Typically, a semiconductor starts with a chemical group IV element (with four outer electrons), such as silicon. This material must be formed into a nearly perfect crystal. A small quantity of a group III element (with three outer electrons), such as boron, is added to create P-type material. This material is positive because there is a slight shortage of electrons. (Electrons are negative, so their absence makes the material positive). Adding a small quantity of a group V element (with five outer electrons), such as phosphorus, creates N-type material. Other elements can also be used to form semiconductors. ┌─────┬─────┐ (+) ───┤ P │ N ├─── (-) └─────┴─────┘ The simplest semiconductor is formed by joining P-type material and N-type material to form a P-N junction. This class of semiconductors includes diodes and rectifiers. The P-N junction is characterized by the fact that electrons can flow (forward) from the N-type material to the P-type material easier than (in reverse) from the P-type material to the N-type material. There is a forward voltage required, called the threshold voltage, for the electrons to flow from the N-type to the P-type material. A typical threshold voltage for a silicon diode is approximately 0.6 Volts. For electrons to flow in the opposite direction usually requires a much higher voltage, (50 Volts or larger). In reality, electrons travel from a negative source, containing an excess of electrons, to a positive source, containing a shortage of electrons. By convention, electrical current is assumed to flow in the opposite direction, from a positive source to a negative source. This convention was established long before the discovery of the electron. When a diode is reversed biased, the current remains constant until the voltage reaches the break down voltage. At the break down voltage the current increases rapidly until the diode over heats destroying the diode. When the diode is forward biased, the current increases exponentially until the voltage reaches the threshold voltage. At the threshold voltage the diode will over heat destroying the diode. The equation used to calculate the current in a P-N junction is as follows: I = Irev exp(K V) where: I is the calculated current when the diode is forward biased Irev is the theoretical current when the diode is reversed biased exp() is the exponential function "e" raised to the power of K V K is a constant approximately equal to 39 for silicon V is the forward biased voltage A simple method for estimating the resistance of a forward biased diode, is to set the effective resistance of the diode in such a way to maintain a constant voltage drop across the diode equivalent to the threshold voltage. Eventually, the diode will overload and burn out if too much current passes through it. The symbol for a diode looks like a triangle pointing to a vertical line, as crudely represented below. Conventional electrical current flows in the direction that the triangle points. │\ │ (+) ───┤ >├─── (-) │/ │ Diode The DIODE1.DC and DIODE2.DC circuits illustrate the characteristics of a diode. When plotting DIODE2.DC, the resulting curve is characteristic for the current increasing expedientially as the voltage across the diode approaches the threshold voltage. This brings us to the next class of semiconductors, called transistors. The name Transistor is derived from "Transient Resistor." There are two types of transistors, NPN and PNP, which are constructed of three semiconductor materials sandwiched together. The middle layer is called the "Base," and the outer two layers are called the "Emitter," and "Collector." The thicknesses of each layer are not equal. The Collector is the thickest layer, and the Base is the thinnest layer. ┌───────┬─┬─────┐ Collector ───┤ N │P│ N ├─── Emitter └───────┴┬┴─────┘ Base ┌───────┬─┬─────┐ Collector ───┤ P │N│ P ├─── Emitter └───────┴┬┴─────┘ Base This class of transistor is called a "bipolar" transistor, because current flows through the transistor using two different methods. In N-type material, current flows as electrons move through the material. In P-type material, current flows as "holes" move through the material. The symbol for a bipolar transistor is a three-prong icon as crudely represented below. The prong with an arrow head is always the Emitter and it points in the direction the (conventional) current flows. The Emitter in an NPN transistor points away from the Base, and the Emitter in a PNP transistor points toward the Base. │ / Collector │ / Emitter │/ │ / Base ───┤\ Base ───┤└ │ \ │\ │ ┘ Emitter │ \ Collector NPN PNP I will only discuss the NPN transistor. The PNP transistor works identically, except that the direction of the current is reversed. The Base-Emitter junction acts like a P-N junction diode, but with a slightly higher threshold voltage of approximately 0.7 Volts. When the Base-Emitter junction is reversed biased (the Emitter voltage is larger than the Base voltage), the transistor is considered "Off," and very little current can flow through the transistor. When the Base-Emitter junction is forward biased (the Base voltage is larger than the Emitter voltage), the resistance between the Collector and Emitter depends on the current flowing between the Base and Emitter. The more current through the Base-Emitter junction, the smaller the resistance, and therefore the larger the current flowing between the Collector and Emitter. The ratio of current flowing between the Collector and Emitter, and the current flowing between the Base and Emitter, is called the current gain designated "Hfe," and is typically about 100. Therefore, bipolar transistors are current amplifiers. The difference between the different bipolar transistors is primarily the amount of current they can handle before overloading. Computer circuits are designed to be fast, not powerful. The resistance between the Base and the Emitter (Rbe) is calculated using the same method for calculating the resistance for a diode. The resistance between the Collector and the Emitter (Rce) is calculated as follows: Rce = Rbe/Hfe where: Rce = calculated resistance between the Collector and the Emitter Rbe = effective resistance between the Base and the Emitter Hfe = current gain The TRANNPN.DC and TRANPNP.DC sample circuits illustrate the characteristics of bipolar transistors. A special type of transistor designed for high power and high gain (Hfe) is called a darlington. It is essentially two bipolar transistors back to back on the same piece of silicon. It is characterized by a threshold voltage that is typically twice that of a bipolar transistor and has an effective current gain (Hfe) about a 1,000 instead of a 100. The TRANDNPN.DC and TRANDPNP.DC sample circuits illustrate the characteristics of darlingtons. Note: when a darlington is turned On, there is a minimum voltage across the Collector and Emitter equivalent to the threshold voltage of a transistor (0.7 Volts). A typical transistor in a computer circuit can only handle about 10 milliamps (mA) of current. A typical medium range transistor, like the 2N2222, can handle up to ½ Amp. A typical power darlington, like the TIP100, can handle up to 8 Amps. Gate Gate │ │ ┌─────┴─────┐ ┌─────┴─────┐ │ metal │ │ metal │ ├───────────┤ ├───────────┤ │ glass │ │ glass │ ├───┬───┬───┤ ├───┬───┬───┤ Source ───┤ P │ │ P ├─── Drain Source ───┤ N │ │ N ├─── Drain ├───┘ N └───┤ ├───┘ P └───┤ │ │ │ │ └─────┬─────┘ └─────┬─────┘ │ │ Substrate Substrate P-Channel N-Channel The last type of transistor to discuss is called the Metal Oxide Semiconductor (MOS). It is a type of Field Effect Transistor (FET). This transistor is similar to a bipolar transistor (NPN or PNP) with the addition of a metal "Gate" over the "Substrate." The Gate is separated from the Substrate by a thin insulator, usually SiO2 (glass). The symbols for these types of transistors are crudely represented below: Gate ──┐├─── Source │├─── Drain │ ──> Substrate │ <── Substrate │├─── Drain Gate ──┘├─── Source PMOS NMOS When a positive voltage of at least 2 Volts is applied between the Gate and a P-type Substrate, the electrons in the Substrate are pulled toward the Gate allowing current to flow between the two N-type materials called the "Source" and the "Drain." This is called an N-channel MOS (NMOS) transistor. The larger the voltage, the less resistance between the Source and the Drain. The resistance is inversely proportional to the voltage (less the 2 Volt threshold voltage) squared as illustrated in the following equation: K R = ────── (V-2)² where: R = The calculated resistance between the Source and the Drain K = A constant, approximately 5,000 Ohms/Volt² V = Voltage potential between the Gate and the Substrate. A similar P-channel MOS (PMOS) transistor exists, but requires a negative voltage between the Gate and the N-type Substrate for current to flow between the P-type Source and Drain. The TRANPMOS.DC and TRANNMOS.DC sample circuits illustrate the characteristics of MOS type transistors. Unlike bipolar transistors that are current amplifiers, MOSFETs are voltage amplifiers. LOGIC Before we can discuss actual computer circuits, we must first discuss the concept of logic. There are only two logical values: "TRUE" and "FALSE." There are three fundamental logical operators from which all other logical operators can be derived. They are "NOT," "AND," and "OR." The NOT operator works as follows: If it is NOT TRUE, it must be FALSE. Conversely, if it is NOT FALSE, it must be TRUE. All of the inputs must be TRUE for the AND operator to be TRUE. Any of the inputs can be TRUE for the OR operator to be TRUE. The following table summarizes these fundamental logical operators: ╔═══════════════╦═══════════════════════════╗ ║ Input ║ Output ║ ╟───────┬───────╫────────┬─────────┬────────╢ ║ A │ B ║ NOT A │ A AND B │ A OR B ║ ╠═══════╪═══════╬════════╪═════════╪════════╣ ║ FALSE │ FALSE ║ TRUE │ FALSE │ FALSE ║ ║ FALSE │ TRUE ║ TRUE │ FALSE │ TRUE ║ ║ TRUE │ FALSE ║ FALSE │ FALSE │ TRUE ║ ║ TRUE │ TRUE ║ FALSE │ TRUE │ TRUE ║ ╚═══════╧═══════╩════════╧═════════╧════════╝ Besides the fundamental logical operators, there are three additional logical operators that are commonly used and can be derived from the three fundamental operators. They are "NAND," "NOR," and Exclusive OR "XOR." The NAND operators is the same as "NOT AND." In other words, the result of the AND operator is complemented by the NOT operator. The logical equation for the NAND operator is the following: A NAND B = NOT (A AND B) Similarly, the NOR operator is the same as "NOT OR." The logical equation for the NOR operator is the following: A NOR B = NOT (A OR B) The Exclusive OR is similar to the OR operator, except only one input is allowed to be TRUE at a time for the answer to be TRUE. In other words, the answer is TRUE if one or the other input is TRUE, but not both. The logical equation for Exclusive OR (XOR) is the following: A XOR B = (A OR B) AND NOT (A AND B) or A XOR B = (A OR B) AND (A NAND B) The following table summarizes the NAND, NOR, and XOR logical operators: ╔═══════════════╦═══════════════════════════════╗ ║ Input ║ Output ║ ╟───────┬───────╫───────────┬─────────┬─────────╢ ║ A │ B ║ A NAND B │ A NOR B │ A XOR B ║ ╠═══════╪═══════╬═══════════╪═════════╪═════════╣ ║ FALSE │ FALSE ║ TRUE │ TRUE │ FALSE ║ ║ FALSE │ TRUE ║ TRUE │ FALSE │ TRUE ║ ║ TRUE │ FALSE ║ TRUE │ FALSE │ TRUE ║ ║ TRUE │ TRUE ║ FALSE │ FALSE │ FALSE ║ ╚═══════╧═══════╩═══════════╧═════════╧═════════╝ I will now discuss the DeMorgan's theorem. This theorem states that if you invert the input and output of the AND operator, you obtain the same results as the OR operator. Conversely, if you invert the input and output of the OR operator, you obtain the same results as the AND operator. In addition, there are corollaries to this theorem. The logical equations for this theorem and its corollaries are listed below: A AND B = NOT ( (NOT A) OR (NOT B) ) A AND B = (NOT A) NOR (NOT B) A OR B = NOT ( (NOT A) AND (NOT B) ) A OR B = (NOT A) NAND (NOT B) A NAND B = (NOT A) OR (NOT B) A NOR B = (NOT A) AND (NOT B) The DeMorgan's theorem can be extremely useful when designing logic circuits. It is actually possible to derive the three fundamental logical operators, NOT, AND, and OR using a single logical operator, and subsequently derive all logical operators from this single logical operator. (The original computer designers only had one or two logical operator circuits to work with). This logical operator can be either an NAND or a NOR logical operator. The following logical equations illustrate this capability: NOT A = A NAND A A AND B = NOT (A NAND B) A OR B = (NOT A) NAND (NOT B) A NOR B = NOT ( (NOT A) NAND (NOT B) ) A XOR B = NOT ( ( (NOT A) NAND (NOT B) NAND (A NAND B) ) NOT A = A NOR A A AND B = (NOT A) NOR (NOT B) A OR B = NOT (A NOR B) A NAND B = NOT ( (NOT A) NAND (NOT B) ) A XOR B = (A NOR B) NOR ( (NOT A) NOR (NOT B) ) How does this discussion on logic help explain how digital computers work? A digital computer is a "Binary" computer. Binary computers deal with only two states: TRUE or FALSE, 1 or 0, On or Off, Voltage or Ground. Binary computers do not use varying voltages to represent values, instead they use simple On/Off circuits. This means that binary computer circuits do not require precision electrical components. The decimal numbering system we are familiar with uses ten different digits (0 through 9), and is called base 10. A binary computer represents numbers using base 2, which only has two digits "0" and "1." In base 10, the least significant (right most) digit is multiplied by 1, the next digit by 10, 100, 1000, etc. In base 2, the least significant digit is multiplied by 1, the next by 2, 4, 8, etc. So the decimal number 9 can be represented by the binary number 1001. (A binary digit is called a bit.) The Exclusive OR logical operator is the fundamental basis for a binary adder. Once you have the ability to add two numbers together, you can than subtract two numbers by converting one number to its negative value and adding it to the other number. Negative numbers are represented by using a method called "Twos Compliment." This method represents a negative one by the largest possible number (all binary ones). Therefore, when you add positive one and negative one you get zero (and carry out). To convert a number to its negative value you must invert each digit using the NOT logical operator, and add one via carry in. You can multiply two numbers by using a series of shifts and additions similar to long hand multiplication. Finally you can divide two numbers by using a series of shifts and subtractions. LOGIC GATES We finally get to the good stuff. It is time to start building circuits that can perform the various logical operations discussed above. Circuits that perform logical operations are usually called "Logic Gates." We will start with the simplest circuit using diodes. Using only diodes and resistors we can build the AND and OR logic gates. The sample circuits DIODEAND.DC and DIODEOR.DC illustrate these logic gates. In these circuits the switches are the inputs, where 5 Volts represents a TRUE value, and ground (0 Volts) represents a FALSE value. The DIODEAO.DC depicts a circuit with two ANDs and one OR logical operator that solve the following equation: E = (A AND B) OR (C AND D) where E is the output This sample circuit illustrates some limitations to pure diode logic gates. The first limitation is that the output voltage is not regenerated (reset to 0 or 5 Volts) after each logic gate, therefore the TRUE output of the AND gate can be as little as 2.8 Volts, instead of 5 Volts as illustrated in the previous example. The reduced voltage is due to the Resistor-Diode- Resistor circuit between the input diodes and the output stage. To make matters worse, the TRUE output of the OR gate can be as little as 2.2 Volts. The second limitation is that diode circuits cannot function as a logical NOT operator. If we look back to the sample circuit of the NPN transistor (TRANNPN.DC), we see that a single transistor can function as a logical NOT operator. When the input is 5 Volts the output is 0 Volts, and vice versa. DTL By combining the Diode AND circuit for input and the Transistor NOT circuit for output, we form the Diode-Transistor Logic (DTL) NAND gate, as depicted in the sample circuit DTLNAND.DC. It was necessary to add a diode between the Diode AND circuit and the transistor because the threshold voltage of the transistor and the diode is almost the same. This diode protects against false triggering of the transistor. This circuit has the advantage that the output voltage of each gate is always regenerated, so there is no limit to how many gates can be connected in series. By removing one of the input diodes, the NAND gate now functions as a NOT gate (or Inverter). The DTLNOT.DC sample circuit illustrates the NOT gate. The PLTDTL.DC sample circuit allows you to vary the input voltage to see how this circuit responds. If you use the "p" command, you can plot the voltage at each node as the input voltage varies from 0 Volts to 5 Volts. When the input is approximately 0.5 Volts, the output of the logic gate will change. The logic AND gate can be formed by combining the NAND gate with the NOT gate. It is not necessary to use diodes in the internal NOT gate, when a single transistor will suffice. The sample circuit DTLAND.DC illustrates this circuit. The DTL OR gate does not use the Diode OR gate as an input stage. If a Diode OR was used, current would be allowed to flow through the input stage into the remainder of the circuit. The DTL NAND gate isolates the input current from the remainder of the circuit. To provide the same isolation for the DTL OR gate, the OR gate is created using three NOT gates and an AND gate as defined by DeMorgan's theorem: A OR B = NOT ( (NOT A) AND (NOT B) ) Two DTL NOT gates are used as an input stage, and the transistors' Collectors and Emitters are tied together to form an AND gate. A third DTL NOT gate (a single transistor) is used for the output stage. The final NOT gate is required to provide a consistent output voltage independent of whether one or both inputs are in the On position. The sample circuit DTLOR.DC illustrates this circuit. By adding another NOT gate to the output stage of the OR gate, we form the DTL NOR gate as illustrated in the DTLNOR.DC sample circuit. Finally, the Exclusive OR (XOR) gate is illustrated in the DTLXOR.DC sample circuit, and uses the DTL AND, OR, and NAND gates to solve the Exclusive OR equation discussed earlier. The traditional icons for the AND, OR, and NAND gates are used in this program. If you press the F1 key twice, a full screen help message will appear identifying the icons used for logical gates. TTL This brings us to the next family of logic gates called Transistor- Transistor Logic (TTL). The original TTL logic circuits used a multiple Emitter transistor for input, and a pair of transistors arranged one above the other for output. The upper transistor is only On when the output is TRUE, and the lower transistor is only On when the output is FALSE. This output configuration of transistors is called the "Totem-Pole" output. The multiple Emitter transistor, which could only be manufactured in an Integrated Circuit (IC) chip, performs the same basic function as the Diode AND gate used in the DTL NAND gate. Today's TTL circuits actually use diodes for their input stage, just like the DTL circuits. Therefore, the sample TTL circuits in this program use diodes for input, instead of the multiple Emitter transistor. However, the rest of the TTL circuit is characteristic of the original TTL circuits. The sample circuits TTLNOT.DC, TTLNAND.DC, and TTLAND.DC depicts the TTL NOT, NAND and AND logic gates. Notice that the TRUE output is not 5 Volts, but 4 Volts. The PLTTTL.DC sample circuit is configured with a potentiometer for input and the voltage at each node can be plotted using the "p" option. The sample circuits TTLOR.DC and TTLNOR.DC illustrate the TTL OR and NOR gates. The input stage of these circuits is similar to the corresponding DTL input stages, and the output stage contains the standard TTL totem-pole output. The Exclusive OR (XOR) gate is illustrated in the TTLXOR.DC sample circuit, and uses the TTL AND, OR, and NAND gates to solve the Exclusive OR equation discussed earlier. Besides the standard logic gates, TTL circuits offer a three-state gate that can turn Off both transistors in the totem-pole output stage. Three state gates are typically used when the output of many gates is connected together on a bus, and only one gate is allowed to be active at a time. The TTL3NOT.DC sample circuit is an example of a TTL three state gate. The top switch is connected to the data input. Only when the bottom switch is Off, will the output be enabled. In general, TTL circuits are faster than DTL circuits. Over the years several variations of TTL circuits have evolved. These variations include Low-power (L), Schottky (S), Low-power Schottky (LS), and Advanced Low- power Schottky (ALS or F) circuits. Of these variations, the LS series is the most commonly available since it is faster, cheaper, and requires less power than the original TTL circuits. ┌─────┬─────┐ (+) ───┤metal│ N ├─── (-) └─────┴─────┘ A "Schottky Diode" is a surface barrier diode composed of a metal (such as gold) and N-type material. This diode is faster than a silicon diode and has a threshold voltage about 0.3 Volts or half the threshold voltage of a silicon diode. The SKDIODE.DC sample circuit illustrates the operating characteristics of a Schottky Diode. The Schottky Diode symbol is crudely depicted below: ┌┐ │\ │ (+) ───┤ >├─── (-) │/ │ └┘ Schottky Diode The Low-power Schottky (LS) series logic gate employs Schottky Diodes between the Base and Collector junction of each transistor preventing the transistor from fully saturating (fully turned On). By not fully saturating the transistor, it can switch from On to Off much faster. These transistors are called "Schottky Transistors" and are crudely depicted below: ┌┐ ┌┐ │ / Collector │ / Emitter │/ │ / Base ───┤\ Base ───┤└ │ \ │\ │ ┘ Emitter │ \ Collector └┘ └┘ NPN PNP The SCHOTTKY.DC sample circuit illustrates operating characteristics of the Schottky transistor. The input stage of the LS series gates uses Schottky diodes instead of conventional diodes or multiple Emitter transistors. The LS series also uses Schottky diodes for negative input voltage protection. The LSNOT.DC sample circuit depicts a typical LS series NOT gate. The PLTLS.DC sample circuit is configured with a potentiometer for input and the voltage at each node can be plotted using the "p" option. The sample circuits LSNAND.DC and LSAND.DC depict the LS NAND and AND logic gates. Note that when an LS gate output is TRUE the output voltage is approximately 4 Volts. When an LS gate output is FALSE the output voltage is approximately 0.3 Volts. The sample circuits LSOR.DC and LSNOR.DC illustrate the LS OR and NOR gates. The LS XOR circuit is similar to the DTL and TTL XOR circuit, except it uses LS gates. In addition to the standard logic gates, LS circuits offer a three-state gate that can turn Off both transistors in the totem-pole output stage. Three state gates are typically used when the output of many gates are connected together on a bus, and only one gate is permitted to be active at a time. The LS3NOT.DC sample circuit is an example of a LS three state gate. The bottom switch is connected to the data input. Only when the top switch is On, will the output be enabled. Note: the output may oscillate in this program when the output is disabled. ECL The last family of logic gates that use bipolar transistors is called Emitter-Coupled Logic (ECL). ECL gates maintain a partial current in each transistor preventing them from saturating or turning Off. This makes ECL gates the fastest logic gates on the market. Also, the difference in voltage between TRUE and FALSE, is approximately 1 Volt. The typical ECL circuit consists of a differential amplifier input stage, a bias circuit, and an Emitter-follower output. Traditional ECL circuits operate using ground and -5.2 Volts for power supply. However, they can operate at 5 Volts and ground like other logic gates. All the sample circuits in this program use the 5 Volts and ground power supply for ECL logic gates. The basic ECL gate is an OR-NOR gate, which is characterized by a dual complementary output. The ECLORNOR.DC sample circuit illustrates this logic gate. You may notice that an input device labeled "ECL" is inserted between the switch and the circuit input. This device consists of three resistors and is required to convert 5 Volts and ground from a switch to input voltages that are compatible with ECL circuits. If this circuit was not installed, the ECL node voltages would not be characteristic of ECL circuits. The ECLNOT.DC sample circuit illustrates the simplest of the ECL circuits, with a single input and the traditional dual complementary outputs. The PLTECL.DC sample circuit, is the same NOT gate, but with a potentiometer for input to illustrate the effects of varying the input voltage, on the output voltage. The ECL AND-NAND gate is derived using the OR-NOR gate as described by DeMorgan's theorem: A AND B = (NOT A) NOR (NOT B) A NAND B = (NOT A) OR (NOT B) The ECLNAND.DC sample circuit illustrates the ECL AND-NAND gate. Both input stages start with a switch, followed by a switch-to-ECL converter, followed by an ECL NOT gate. The outputs of the OR-NOR gate must be reversed, since the NOR output (top) becomes the AND output, and the OR output (bottom) becomes the NAND output. The ECL Exclusive OR gate also has dual complementary outputs and is constructed using only NOT and OR-NOR gates. You must reverse the OR-NOR gate outputs, since OR becomes NXOR, and NOR becomes XOR. The sample circuit ECLXOR.DC illustrates this circuit which can also be represented by the logical equation: A XOR B = (A NOR B) NOR ( (NOT A) OR (NOT B) ) Note: the ECLXOR.DC sample circuit uses 100 components. This is the most complex sample problem provided and will take the longest amount of time to evaluate. ECL gates are the fastest logic gates on the market, but they also require the most power. Hence, it is difficult to pack a lot of ECL gates on a single integrated circuit chip without overheating the chip. CMOS The last family of logic gates I will discuss are called Complementary Metal Oxide Semiconductors (CMOS). The term complementary refers to the use of two types of transistors in the output circuit in a configuration similar to the totem-pole output in TTL. The PMOS transistor is on top, and the NMOS transistor is on the bottom. The CMOSNOT.DC sample circuit illustrates the NOT gate, which is the simplest of the CMOS gates. The PLTCMOS.DC sample circuits illustrates the effects of varying input voltage on this gate. CMOS circuits can operate using a wide variety of power supply voltages. Since the threshold voltage for the PMOS and NMOS transistors is 2 Volts, the minimum power supply that CMOS circuits can use is approximately 3 Volts. On the other hand, the power supply can be as large as 15 Volts. This makes battery driven circuits very practical, since the circuits will continue to operate as the battery gradually runs down. The CMOS NAND gate consists of four transistors, two PMOS transistors in parallel, and two NMOS transistors in series, as illustrated by the CMOSNAND.DC sample circuit. Both NMOS transistors must be On for the output to be FALSE (0 Volts). The CMOS AND gate is the same circuit followed by a CMOS NOT gate as illustrated in the CMOSAND.DC sample circuit. The CMOS NOR gate also consists of four transistors, however the two PMOS transistors are in series, and the two NMOS transistors are in parallel, as illustrated CMOSNOR.DC sample circuit. Both PMOS transistors must be On for the output to be TRUE (5 Volts). The CMOS OR gate is the same circuit followed by a CMOS NOT gate as illustrated in the CMOSOR.DC sample circuit. The CMOS Exclusive OR gate is similar to the DTL and TTL Exclusive OR gates, except it uses CMOS AND, NAND, and OR gates as illustrated in the CMOSXOR.DC sample circuit. CMOS gates are characterized by requiring very little power because the MOS transistors use voltage to trigger, instead of current. The same reason that explains their low power consumption, also explains why CMOS gates are the slowest logic gates (when the transistors are physically the same size as the bipolar transistors in the previous logic families). The speed of a circuit is limited by the size and spacing of the components, and the speed of light. The speed of the electrons flowing through a circuit approaches the speed of light, which is the theoretical speed limit. However, today's CMOS technology use very small transistors, with very thin insulators between the Gate and Substrate of the transistor, and the Gates are now made out of semiconductor material instead of aluminum metal. Therefore today's CMOS logic gates can be fast. Because of their low power consumption, they can be more densely packed on an integrated circuit chip. As an example, the Intel 486 processor is based on CMOS technology, contains more than a million transistors on a single chip, and can operate at speeds up to 66 MHz (million cycles/second). The Intel Pentium processor contains more than 3 million transistors and can operate at 3.3 Volts with speeds up to 100 MHz. INTEGRATED CIRCUITS (IC) After the invention of semiconductors, the next major invention was the Integrated Circuit (IC) chip, which places multiple semiconductor components on a single semiconductor wafer. An entire circuit constructed of resistors, capacitors, diodes, and transistors can be etched on to a single chip. All the components are made from semiconductor P-type and N-type material, and are connected together with a metal conductor, like aluminum. The resistor can be made of either P-type or N-type material. By varying the thickness of this material and by winding it back and forth in a small area, different resistance values can be achieved. Diodes are formed by the junction of P-type and N-type material. Schottky diodes are formed by the junction of a metal like gold with N-type material. Capacitors are typically reverse biased diodes, which are characterized by small reverse biased voltages. NPN bipolar transistors are constructed by embedding N-type material for both the Emitter and the Collector into a P-type Base. (To make PNP transistors, replace N-type with P-type and vice versa). CMOS transistors are similar to bipolar transistors, except there is a metal or semiconductor (P-type or N-type) Gate over the Base of the transistor separated by a thin insulator of SiO2 (glass). The original ICs only contained a few components, possibly a single logic gate. As the technology improved, the components became smaller, and more gates were placed on a single chip. Eventually the ability to dissipate the heat became the limiting factor. Using today's CMOS technology, over a million transistors can be placed on a single IC chip. In the DC Circuit Analysis program, the term "Integrated Circuit" (IC) takes on a slightly different meaning. The DC Circuit Analysis library contains both basic components (like resistors, diodes, and transistors) and Integrated Circuits (like DTL NOT, TTL NAND, and CMOS NOR gates), which are circuits created using the DC Circuit Analysis program, saved in a file with a "DCL" extension, and referenced in the library. The DC.DCL file contains all the parameters and screen locations for each item in the library. (See the section below that describes this file format). Each IC is stored in a separate file. As an example, the DTL NOT gate is stored in the file DTLNOT.DCL located in the DCL sub-directory. You can view this circuit by changing to the DCL subdirectory in the Select Sample Circuit menu. From the Directories menu select the ".." item to move up one directory, then select the "DCL" item to display the library circuits. From the Circuits menu select "DTLNOT.DCL." You will notice that there is no power supply, no switches for input, and all the nodes are set to 0 Volts. The first nodes created correspond to the connection points. By convention, the connections are in the following order: power supply, ground, inputs, and outputs. DCL files are not always easy to read, since they use the fewest number of nodes necessary for the library. Nodes can be moved around on the screen, but if you delete one of the connection nodes, you cannot simply recreate it. Since the order in which the nodes were created is essential to maintain compatibility with the DC.DCL file. Please do not modify the DCL library files. USER DEFINED ICs Why did I discuss DCL files? Because you can create your own circuits and add them to the library. The last eight icons in the library are reserved for your use. They are stored in the files DCL\U1.DCL through DCL\U8.DCL. The connection nodes are already created and organized on the screen in a pattern matching the icon connection points. All you have to do is add your circuits to these files. You can embed other Ics into your circuit, the only limitation is the 100 total components which includes the components within each IC and the IC icon itself. You can move the nodes around the screen, but please do not delete them. If you make a mistake in your user defined IC file, you can start all over by copying the DCL\USER.DCL file into the file you were working on. This file provides a good starting point. Please do not modify the DCL\USER.DCL file. MISCELLANEOUS EXAMPLES Let's look at some miscellaneous examples. Since my primary intention of writing this program was to introduce you to computer circuits, I will discuss some common computer circuits. Due to the limitation of 100 components and the computer overhead to analyze complex circuits, I can only discuss a few simple circuits. To reduce the time required to analyze these circuits, only CMOS technology will be used for these sample circuits. How does computer memory work? The basis for all computer memory is the Set-Reset (S-R) Latch, which consists of two NAND gates that are cross connected. The SRLATCH.DC sample circuit illustrates the S-R Latch. This circuit has two inputs and two outputs. The output of the top NAND gate is the normal output, and the output of the bottom NAND gate is the complemented output. The top switch Sets the latch to TRUE, when it is in the Off position. The bottom switch Resets the latch to FALSE, when it is in the Off position. When both switches are in the On position, the circuit "remembers" what it was last set to. However, the initial output of this circuit is unknown and will oscillate in this program until it is either Set or Reset using one of the switches. Both switches should not be in the Off position, since both outputs (which are suppose to be opposites of each other) will both become TRUE. The Data Latch is an improvement on the Set-Reset Latch. The DLATCH.DC sample circuit illustrates the Data Latch. This circuits consists of four NAND gates, where the two NAND gates on the right form the familiar Set- Reset Latch described above. The top switch is the data input, and the bottom switch is the enable input. When the bottom switch is On, the input data is stored in the latch. When the bottom switch is Off, the input data is ignored, and the circuit remembers its last setting. The Data Flip-Flop is an example of a Master-Slave Flip-Flop. It consists of two latches connected in series and is illustrated in the FLIPFLOP.DC sample circuit. The first (Master) latch is a standard Data Latch as described above. The second (Slave) latch is a Set-Reset Latch with enable. When the enable input is On, the value of the Data input is stored in the first latch. When the enable input is Off, the value stored in the first latch is transferred to the second latch. Applications for Flip- Flops include binary counters. Initially, the output of the Flip-Flop is unknown an will oscillate in this program until the lower switch changes. The next set of circuits I will discuss are adders. I will start with the Half-Adder. This circuits adds two binary numbers together and has two outputs: Sum and Carry. The Half-Adder is a variation on the Exclusive OR circuit. The HALFADDR.DC sample circuit illustrates the Half-Adder, as described by the following logical equations: Sum = A XOR B Carry = A AND B The truth table for a Half-Adder is as follows: ╔═══════╦════════════╗ ║ Input ║ Output ║ ╟───┬───╫─────┬──────╢ ║ A │ B ║ Sum │ Carry║ ╠═══╪═══╬═════╪══════╣ ║ 0 │ 0 ║ 0 │ 0 ║ ║ 0 │ 1 ║ 1 │ 0 ║ ║ 1 │ 0 ║ 1 │ 0 ║ ║ 1 │ 1 ║ 0 │ 1 ║ ╚═══╧═══╩═════╧══════╝ The Full-Adder is essentially two Half-Adders in series. The Full-Adder has three inputs: A, B, and Carry (C) from the previous least significant digit. It also has two outputs: Sum and Carry. Full-Adders can be connected in series to handle larger numbers. The FULLADDR.DC sample circuit illustrates a Full-Adder, as described by the following logical equations: Sum = (A XOR B) XOR C Carry = (A AND B) OR (A AND C) OR (B AND C) The truth table for a Full-Adder is as follows: ╔═══════════╦════════════╗ ║ Input ║ Output ║ ╟───┬───┬───╫─────┬──────╢ ║ A │ B │ C ║ Sum │ Carry║ ╠═══╪═══╪═══╬═════╪══════╣ ║ 0 │ 0 │ 0 ║ 0 │ 0 ║ ║ 0 │ 0 │ 1 ║ 1 │ 0 ║ ║ 0 │ 1 │ 0 ║ 1 │ 0 ║ ║ 0 │ 1 │ 1 ║ 0 │ 1 ║ ║ 1 │ 0 │ 0 ║ 1 │ 0 ║ ║ 1 │ 0 │ 1 ║ 0 │ 1 ║ ║ 1 │ 1 │ 0 ║ 0 │ 1 ║ ║ 1 │ 1 │ 1 ║ 1 │ 1 ║ ╚═══╧═══╧═══╩═════╧══════╝ Due to limitations of this program, it is not practical to attempt to show more complex logic circuits. If you would like to learn more about computer logic circuits, I recommend you invest in the "Logic Circuit Analysis" program that I wrote. It is cable of handling 1,000 logic gates, which is enough to model an entire 4-bit Arithmetic Logic Unit (ALU). Sometimes it is necessary to interface computer circuits to the outside world. The first circuit I will discuss is a Digital to Analog (D/A) converter. The simplest D/A consists of a resistor circuit. The DTOA.DC sample circuit is an example of a D/A. The top switch is the most significant digit and the bottom switch is the least significant digit. If you turn Off all the switches, and then turn only one switch On at a time, you will notice that the top switch adds 2.5 Volts (½ the power supply voltage), the second switch adds 1.25 Volts (¼ the power supply voltage), the third switch 0.625 Volts, and the last switch 0.3125 Volts (or 1/16 the power supply voltage). This circuit can easily be interfaced with CMOS logic gates, but not with the other family of logic gates. That is because CMOS logic is the only logic family with full 0 to 5 Volt output. The next circuit is a CMOS Analog Switch. The ANALOGSW.DC sample circuit illustrates this circuit. It uses a CMOS NOT circuit and a pair of MOS transistors. However, they are configured such that the switch can turn both transistors On, or both Off. When they are both On, they will provide a small resistance allowing current to flow in either direction. A typical use of analog switches is to multiplex multiple analog signals into a single Analog to Digital converter. This brings us to Solid State Switches. Sometimes it is necessary for a digital circuit to control an electrical device, such as a light bulb, or a motor. The SSSW.DC and SSPOWSW.DC sample circuits illustrate solid state switches capable of switching loads up to ½ Amp and 8 Amps respectively. The first circuit uses a 2N2222 transistor to switch up to a ½ Amp load, and the second circuit adds a TIP100 power darlington to switch up to an 8 Amp load. The 100 ohm resistor represents the load in both cases. Higher voltages can be controlled, but the resistor values must be changed and you will have to use larger Wattage resistors. (All resistors in this library are only rated at ¼ Watts). The final sample circuit, SSRPOWSW.DC is a Solid State Reversible Power Switch which uses four power transistors (two NPN and two PNP) for its output. This circuit can turn the load On and Off, as well as reverse the power applied to the load. The top switch is the On/Off switch, and the bottom switch is the Forward/Reverse switch. In this circuit each TTL AND gate controls one 2N2222 transistor. The 2N2222 transistor controls both the PNP power transistor and the NPN power transistor located in the opposite corners. The TTL logic assures that all four power transistors are not turned On at the same time, but can all be turned Off. The reverse biased diodes are required to protect the power transistors when this circuit is used to control a motor. In addition, you should add a capacitor across the motor. I hope you enjoyed this tutorial and will continue to use this program to explore other Direct Current (DC) circuits. This program allows you to try some circuits without actually building the circuit. SPECIFICATIONS REQUIREMENTS ──────────── IBM-PC or compatible computer with a 286 or later processor 800 KB of disk space 300 KB minimum available RAM, (after DOS, drivers and TSR) 350 KB maximum available RAM required when there is no EMS EGA or VGA graphics adapter with 256 KB of RAM installed Color Monitor SUPPORTS (but not required) ─────────────────────────── Mouse (2 or 3 button) with MOUSE.SYS or MOUSE.COM device driver. If a Math coprocessor installed, the program will run faster. If 64 KB of Expanded Memory (EMS) is available, it will be used. DOS ENVIRONMENTAL VARIABLES ─────────────────────────── TMP Sets location of DC.PCX and DC.DC file, otherwise written to the default directory. Example: SET TMP=D:\ MONITOR Can be set to EGA or VGA. The program will automatically detect if an EGA or VGA adapter is installed. The MONITOR variable will override the automatic detection. Example: SET MONITOR=EGA EMS Can be set to OFF or NO to override auto-detection so not to use EMS memory even if it is available. Example: SET EMS=OFF DC_DV Used to override the convergence criteria. If it takes a long time to display calculation results, you may want to set this variable to 1.0e-8. This may speed up the program but reduce the accuracy of the results. Example: SET DC_DV=1.0e-8 DC_PLOT Used to override the potentiometer increments used during plotting. This value may range from 1% to 5%. Example: SET DC_PLOT=5 PROGRAM LIMITS ────────────── 112 Library Entries 100 Components per circuit, including ICs and their components 250 Nodes per circuit 750 Connections per circuit 8 User Definable Circuits 8 Connection terminals per IC 5 Connections per node. SUMMARY OF KEYS TUTORIAL SCREEN Cursor Keys - Highlight the desired keyword ENTER - Select the highlighted keyword PGDN - Display next screen PGUP - Display previous screen F1 - Display opening tutorial screen ESC - Exit tutorial OPENING MENU Cursor Keys - Highlight the desired item HOME - Highlight "Analyze Circuit" END - Highlight "Exit" F5 - Display tutorial ENTER - Select the highlighted item SELECT SAMPLE CIRCUIT MENU PGUP, PGDN - Display additional pages of sample circuits Cursor Keys - Highlight the desired sample circuit HOME - Highlight the first sample circuit on this page END - Highlight the last sample circuit on this page ENTER - Select the highlighted sample circuit ESC, F10 - Exit menu without selecting a sample circuit ANALYZE CIRCUIT LEFT and RIGHT - Highlight Adjustable Component (Switch or Potentiometer) Switch: UP, PGUP, HOME - Set to up position DOWN, PGDN, END - Set to down position ENTER - Toggle Switch Potentiometer: HOME - Set to 99% ENTER, PGUP - Increment by 10% UP - Increment by 1% DOWN - Decrement by 1% PGDN - Decrement by 10% END - Set to 1% F5 - Display tutorial F6 - Edit circuit p - Plot node voltage vs. potentiometer voltage w - Save screen into PC Paintbrush compatible file F10, ESC - Exit MODIFY CIRCUIT F1 - Help (Second F1 for full screen help) F2 - Redraw screen F3 - Move a Component (Node or IC) F4 - Access Library of Components F5 - Display tutorial F6 - Analyze circuit Cursor Keys - Move Cursor CTRL-BACKSPACE - Delete Component (Node or IC) ENTER - Make a Connection, or Lock Component in position F10, ESC - Exit LIBRARY OF COMPONENTS F1 - Help (Second F1 for full screen help) Cursor Keys - Highlight Component (Node or IC) PGUP, PGDN - Switch Pages of Library Components ENTER - Select Component F10, ESC - Exit LIBRARY The Library is based on the following components: Resistors are standard values, ¼ Watts, 5% carbon resistors Potentiometers are linear and are rated at 2 Watts Silicon Diodes are 1N914 high speed switching Diodes (10 mA) Schottky Diodes can carry up to 20 mA NPN Transistors are 2N2222 500 mA, with Hfe = 150 PNP Transistors are 2N2904 500 mA, with Hfe = 150 NPN Darlingtons are TIP100 8 Amp, with Hfe = 2000 PNP Darlingtons are TIP105 8 Amp, with Hfe = 3000 PMOS and NMOS transistors are standard CMOS transistors ICs are circuits created using the DC Circuit Analysis program and made available in the library. The Library contains the following items: Type Description ───── ─────────────────────────────────────────────── INODE Interconnect Node VNODE Fixed Voltage Node, 0 Volts (Ground) VNODE Fixed Voltage Node, 5 Volts VNODE Fixed Voltage Node, -5 Volts VNODE Fixed Voltage Node, 10 Volts VNODE Fixed Voltage Node, -10 Volts SNODE Switch Node, 5 Volts and 0 Volts (Ground) SNODE Switch Node, 10 Volts and -10 Volts R Resistor, 100 Ohms, ¼ Watts R Resistor, 130 Ohms, ¼ Watts R Resistor, 240 Ohms, ¼ Watts R Resistor, 470 Ohms, ¼ Watts R Resistor, 750 Ohms, ¼ Watts R Resistor, 1,000 Ohms, ¼ Watts R Resistor, 1,600 Ohms, ¼ Watts R Resistor, 2,000 Ohms, ¼ Watts R Resistor, 3,000 Ohms, ¼ Watts R Resistor, 3,900 Ohms, ¼ Watts R Resistor, 4,700 Ohms, ¼ Watts R Resistor, 10 Kilohms, ¼ Watts R Resistor, 20 Kilohms, ¼ Watts R Resistor, 47 Kilohms, ¼ Watts R Resistor, 100 Kilohms, ¼ Watts R Resistor, 1,000 Kilohms, ¼ Watts R Resistor, 100 Ohms, ¼ Watts R Resistor, 130 Ohms, ¼ Watts R Resistor, 240 Ohms, ¼ Watts R Resistor, 470 Ohms, ¼ Watts R Resistor, 750 Ohms, ¼ Watts R Resistor, 1,000 Ohms, ¼ Watts R Resistor, 1,600 Ohms, ¼ Watts R Resistor, 2,000 Ohms, ¼ Watts R Resistor, 3,000 Ohms, ¼ Watts R Resistor, 3,900 Ohms, ¼ Watts R Resistor, 4,700 Ohms, ¼ Watts R Resistor, 10 Kilohms, ¼ Watts R Resistor, 20 Kilohms, ¼ Watts R Resistor, 47 Kilohms, ¼ Watts R Resistor, 100 Kilohms, ¼ Watts R Resistor, 1,000 Kilohms, ¼ Watts POT Potentiometer, 1 Kilohms, 2 Watts POT Potentiometer, 10 Kilohms, 2 Watts DIODE Switching Diode, 1N914 10 milliamps DIODE Switching Diode, 1N914 10 milliamps DIODE Switching Diode, 1N914 10 milliamps DIODE Switching Diode, 1N914 10 milliamps PMOS PMOS Transistor, (CMOS) 10 milliamps NMOS NMOS Transistor, (CMOS) 10 milliamps NPN NPN Transistor, 2N2222 500 milliamps, Hfe=150 NPN NPN Transistor, 2N2222 500 milliamps, Hfe=150 PNP PNP Transistor, 2N2904 500 milliamps, Hfe=150 PNP PNP Transistor, 2N2904 500 milliamps, Hfe=150 IC Integrated Circuit, DNPNL.DCL, NPN Darlington IC Integrated Circuit, DNPNR.DCL, NPN Darlington IC Integrated Circuit, DPNPL.DCL, PNP Darlington IC Integrated Circuit, DPNPR.DCL, PNP Darlington IC Integrated Circuit, DTLNOT.DCL, DTL Inverter (NOT) IC Integrated Circuit, TTLNOT.DCL, TTL Inverter (NOT) IC Integrated Circuit, CMOSNOT.DCL, CMOS Inverter (NOT) IC Integrated Circuit, ECLNOT.DCL, ECL Differential output IC Integrated Circuit, ECL116.DCL, ECL Differential input & output IC Integrated Circuit, ECLOR.DCL, ECL 2-In OR/NOR IC Integrated Circuit, ECLOR3.DCL, ECL 3-In OR/NOR IC Integrated Circuit, ECLAND.DCL, ECL 2-In AND/NAND IC Integrated Circuit, DTLAND.DCL, DTL 2-In AND IC Integrated Circuit, DTLAND3.DCL, DTL 3-In AND IC Integrated Circuit, DTLOR.DCL, DTL 2-In OR IC Integrated Circuit, DTLOR3.DCL, DTL 3-In OR IC Integrated Circuit, DTLNAND.DCL, DTL 2-In NAND IC Integrated Circuit, DTLNAND3.DCL, DTL 3-In NAND IC Integrated Circuit, DTLNOR.DCL, DTL 2-In NOR IC Integrated Circuit, DTLNOR3.DCL, DTL 3-In NOR IC Integrated Circuit, TTLAND.DCL, TTL 2-In AND IC Integrated Circuit, TTLAND3.DCL, TTL 3-In AND IC Integrated Circuit, TTLOR.DCL, TTL 2-In OR IC Integrated Circuit, TTLOR3.DCL, TTL 3-In OR IC Integrated Circuit, TTLNAND.DCL, TTL 2-In NAND IC Integrated Circuit, TTLNAND3.DCL, TTL 3-In NAND IC Integrated Circuit, TTLNOR.DCL, TTL 2-In OR IC Integrated Circuit, TTLNOR3.DCL, TTL 3-In NOR IC Integrated Circuit, CMOSAND.DCL, CMOS 2-In AND IC Integrated Circuit, CMOSAND3.DCL, CMOS 3-In AND IC Integrated Circuit, CMOSOR.DCL, CMOS 2-In OR IC Integrated Circuit, CMOSOR3.DCL, CMOS 3-In OR IC Integrated Circuit, CMOSNAND.DCL, CMOS 2-In NAND IC Integrated Circuit, CMOSNND3.DCL, CMOS 3-In NAND IC Integrated Circuit, CMOSNOR.DCL, CMOS 2-In NOR IC Integrated Circuit, CMOSNOR3.DCL, CMOS 3-In NOR IC Integrated Circuit, DTLXOR.DCL, DTL Exclusive OR IC Integrated Circuit, TTLXOR.DCL. TTL Exclusive OR IC Integrated Circuit, CMOSXOR.DCL, CMOS Exclusive OR IC Integrated Circuit, ECLXOR.DCL, ECL Exclusive OR/NOR IC Integrated Circuit, ECLIN.DCL, Switch to ECL Input IC Integrated Circuit, DTOA.DCL, Digital to Analog Converter IC Integrated Circuit, SCHOTTKY.DCL, NPN Schottky Transistor IC Integrated Circuit, SCHOTTKR.DCL, NPN Schottky Transistor Diode 20 mA Schottky Diode Diode 20 mA Schottky Diode Diode 20 mA Schottky Diode Diode 20 mA Schottky Diode IC Integrated Circuit, User.DCL, Reserved IC Integrated Circuit, User.DCL, Reserved IC Integrated Circuit, User.DCL, Reserved IC Integrated Circuit, User.DCL, Reserved IC Integrated Circuit, U1.DCL, User Defined IC IC Integrated Circuit, U2.DCL, User Defined IC IC Integrated Circuit, U3.DCL, User Defined IC IC Integrated Circuit, U4.DCL, User Defined IC IC Integrated Circuit, U5.DCL, User Defined IC IC Integrated Circuit, U6.DCL, User Defined IC IC Integrated Circuit, U7.DCL, User Defined IC IC Integrated Circuit, U8.DCL, User Defined IC SAMPLE CIRCUITS The following examples can be found in the \DC14\DC sub-directory: Filename Description ─────────── ─────────────────────────────────────────────── ANALOGSW.DC CMOS Analog Switch CMOSAND.DC CMOS 2-In AND CMOSNAND.DC CMOS 2-In NAND CMOSNOR.DC CMOS 2-In NOR CMOSNOT.DC CMOS Inverter (NOT) CMOSOR.DC CMOS 2-In OR CMOSXOR.DC CMOS Exclusive OR DIODE1.DC Sample Diode Circuits DIODE2.DC Plot of Diode Circuit DIODEAND.DC 2-In Diode AND DIODEAO.DC Two 2-In Diode AND, and One 2-In Diode OR DIODEOR.DC 2-In Diode OR DLATCH.DC Data Latch DTLAND.DC DTL 2-In AND DTLNAND.DC DTL 2-In NAND DTLNOR.DC DTL 2-In NOR DTLNOT.DC DTL Inverter (NOT) DTLOR.DC DTL 2-In OR DTLXOR.DC DTL Exclusive OR DTOA.DC Digital to Analog Converter ECLNAND.DC ECL 2-In AND/NAND ECLNOT.DC ECL Driver with Differential Output ECLORNOR.DC ECL 2-In OR/NOR ECLXOR.DC ECL Exclusive OR FLIPFLOP.DC Data Flip-Flop FULLADDR.DC Full Adder HALFADDR.DC Half Adder LS3NOT.DC TTL Low-Power Schottky (LS) Three State Inverter LSAND.DC TTL Low-Power Schottky (LS) 2-In AND LSNAND.DC TTL Low-Power Schottky (LS) 2-In NAND LSNOR.DC TTL Low-Power Schottky (LS) 2-In NOR LSNOT.DC TTL Low-Power Schottky (LS) Inverter (NOT) LSOR.DC TTL Low-Power Schottky (LS) 2-In OR PLTCMOS.DC Plot of CMOS Inverter (NOT) PLTDTL.DC Plot of DTL Inverter (NOT) PLTECL.DC Plot of ECL Driver with Differential Output PLTLS.DC Plot of TTL Low-Power Schottky (LS) Inverter (NOT) PLTTTL.DC Plot of TTL Inverter (NOT) RESIST1.DC Sample Resistor Circuits RESIST2.DC Sample Potentiometer Circuit RESIST3.DC A very complex resistor network SCHOTTKY.DC NPN Schottky Transistor SKDIODE.DC Schottky Diode SRLATCH.DC Set-Reset Latch SSPOWSW.DC 8 Amp Solid State Switch SSRPOWSW.DC 8 Amp Reversible Solid State Switch SSSW.DC ½ Amp Solid State Switch STEPPER.DC Stepper Motor Driver Circuit TRANDNPN.DC NPN Darlington TRANDPNP.DC PNP Darlington TRANNMOS.DC NMOS Transistor TRANNPN.DC NPN Transistor TRANPMOS.DC PMOS Transistor TRANPNP.DC PNP Transistor TTL3NOT.DC TTL Three State Inverter TTLAND.DC TTL 2-In AND TTLNAND.DC TTL 2-In NAND TTLNOR.DC TTL 2-In NOR TTLNOT.DC TTL Inverter (NOT) TTLOR.DC TTL 2-In OR TTLXOR.DC TTL Exclusive OR DC.DCL FILE FORMAT DC.DCL contains the specifications for each library entry. There is one line for each entry as follows: TYPE NL NC NP --- Locations x y --- --- Parameters --- where TYPE is: INODE - Interconnection Node VNODE - Fixed Voltage Node SNODE - Switch Voltage Node R - Resistor POT - Potentiometer DIODE - DIODE PMOS - P-channel CMOS transistor NMOS - N-channel CMOS transistor NPN - NPN bipolar transistor or darlington PNP - PNP bipolar transistor or darlington IC - Integrated Circuit - Stored in separate files NL: Number of Locations NC: Number of Connections must be less then or equal to NL NP: Number of Parameters --- Locations x y --- Locations specified in x y pairs relative to upper left corner of icon. The first NC locations are the connections, any additional locations are for Resistor current, Potentiometer % turns, or INODE Voltage labels. --- Parameters --- The number and type of parameters depends on the TYPE as follows: TYPE NL NC NP Locations Parameters ───── ── ── ── ─────────────────────────── ─────────────────────────── INODE 2 1 0 connection, Voltage Label none VNODE 1 1 1 connection Fixed Voltage SNODE 1 1 2 connection Up Voltage, Down Voltage R 3 2 2 First, Second, Amp Label Resistance, Rated Wattage POT 4 3 2 Top, Bottom, Middle, % Label Resistance, Rated Wattage DIODE 2 2 3 Plus, Negative Vth, Amp, HiZ Resistance PMOS 4 4 4 Gate, Source, Base, Drain Vth, Ohms/Volt², Amp, HiZ R NMOS 4 4 4 Gate, Source, Base, Drain Vth, Ohms/Volt², Amp, HiZ R NPN 3 3 4 Emitter, Base, Collector Vth, Hfe, Amp, HiZ R PNP 3 3 4 Emitter, Base, Collector Vth, Hfe, Amp, HiZ R IC ? ? -1 +V, -V, Inputs, Outputs dcl\filename.DCL Up to Eight Connections Integrated Circuits (ICs) files are stored in the \DC14\DCL sub-directory. ICs are all predefined DC Circuits that contain Components or other ICs. DC AND DCL FILE FORMATS Files with the extension "DC" are sample circuit files located in the DC sub-directory. Files with the extension "DCL" are library (IC) circuit files located in the DCL sub-directory. Both files contains circuit created by the DC Circuit Analysis program, and have the same format: The first line contains two numbers as follows: NC NN where NC = Number of Components or ICs NN = Number of Nodes (Interconnect, Fixed, or Switch) The next NC lines contains the components, one per line as follows: LIB ROW COL N N1 N2 ... where LIB = Library entry (0-111) ROW = Screen row location of icon (0-299) COL = Screen column location of icon (0-79) N = Number of connection terminals N1, N2, ... = Node corresponding to each connection Nodes are numbered starting with 100 The next NN lines contains the nodes, one per line as follows: LIB ROW COL N C1 CC1 C2 CC2 where LIB = Library entry (0-111) ROW = Screen row location of icon (0-299) COL = Screen column location of icon (0-79) N = Number of connections C1, C2, ... = Component (0-99), or Node CC1, CC2, ... = Connection on component or Node C1, C2, ...