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{{projectinfo|Tutorial| Building a Three-Input Digital AND Function |b2TUT4_1DigiTUT1_5.png|In this project, the basic concepts of digital circuit simulation in RF.Spice A/D are demonstrated, and a simple voltage divider logical AND circuit is modeled built and examined.|

*[[CubeCAD]]Digital Circuit*VisualizationLogic Gate*[[EM.Tempo#Lumped Sources | Lumped Sources]]Live Simulation*[[EM.Tempo#Scattering Parameters and Port Characteristics | S-Parameters]] Live Digital Timing Diagram *[[EM.Tempo#Far Field Calculations in FDTD | Far Fields]] Binary State Transition*[[Advanced Meshing in EM.Tempo]] Propagation Delay|All versions|{{download|http://www.emagtech.com/contentdownloads/project-file-download-repository|EMProjectRepo/DigitalLesson1.Tempo zip Digital Lesson 1|[[EM.Cube]] 14.8}} }}

=== Placing Digital Parts === Open the "'''Parts Bin'''" by selecting the "'''Add Part'''" tab of the "'''Toolbox'''" or the left side panel. By defaultTo build your first digital circuit, the "'''Function'''" tab of the Part Bin is active. This means that parts are sorted based on their function. Open the "'''Digital Components'''" menu and select the "'''Gates...'''" item as shown below. All the logic gate parts and devices are listed in the Part Bin. Scroll down the list and find and select “'''74LS10D'''”, which is a three-input NAND gate. Either double-click the part's name or click the "'''Place Part'''" button at the bottom of the Parts Bin to place the device on your schematic. The program may ask which section of the package you want to select. Accept all need the defaults. Repeat the same procedure as above and find and select “'''74LS04D'''”, which is an logic inverter. You can also locate following parts by filtering. Click the button labeled "'''Extended Filter...'''" in the middle of the Add Part tab of the Toolbox. This opens up the '''Select Device Dialog'''. Type in part of the device's name into the "Name" field of the Filters. For instance, typing "74LS" or "LS10" will show only devices that contain that text somewhere in the name.:

[[File:b2TUT4_4Digital input and output ports are generic and virtual parts.png|thumb|300px|You can get them from the "'''Digital Input Dialog]][[File:b2TUT4_6I/O'''" submenu of the "'''Parts Menu'''".png|thumb|300pxOr you can easily place them in your circuit by typing the keyboard shortcut {{key|N}} for '''Digital Output Dialog]]Input''' and the keyboard shortcut {{Notekey|Unlike analog and mixed-mode circuits that are excited using voltage or current sources, digital circuits require "O}} for '''Digital Input PortsOutput'''" which . Similar to all other parts or devices, digital input and output ports have property dialogs that can only take either be accessed by double-clicking on them. By default, the digital input and output takes 1-bit binary or hexadecimal datain decimal format (rather then hexadecimal).The keyboard shortcut for the NAND gate is {{key|Alt+A}} , and keyboard shortcut for the inverter gate is {{key|Alt+O}}.

Digital input and output ports are generic and virtual parts. {{Note|You can get them from the "'''Digital I/O'''" submenu of the the "'''Parts Menu'''". Or you can easily place them in your circuit by typing the keyboard shortcut "'''N'''" for '''Digital Input''' and the keyboard shortcut "'''O'''" for '''Digital Output'''. Use the keyboard shortcut "N" to place your first input port to the left of the NAND gate. Then press use the keyboard's "'''SPACE'''" {{key|Space}} bar to "Repeat Place Device" and place your second input port and repeat one more time to define the third input. Next, use the keyboard shortcut "O" to place your output port to the right of the inverter gate. }}

{{Note<table><tr><td> [[File:b2TUT4_4.png|In analog and mixed-mode circuits, you measure node voltages and device currentsthumb|360px|Digital Input Dialog. In digital circuits, you probe only binary or hexadecimal data at "''']] </td><td> [[File:b2TUT4_6.png|thumb|360px|Digital Output Ports'''"Dialog.}} ]] </td></tr></table>

Similar to all other parts or device, digital input and output ports have property dialogs that can be accessed by double-clicking on them. The Your project workspace at this point should like the figure below shows the property dialog of the digital input and output, respectively. By default, the digital input takes 1-bit binary data in decimal format (rather then hexadecimal).:

Your circuit at this point should like the figure below:<table>{| border="0"|-| valign="top"|<tr><td> [[File:b2TUT4_5DigiTUT1 1.png|420pxthumb|500px|The digital parts placed in the Schematic Editor.]]</td>|-</tr>|}</table>

Finally, use one the wiring methods you learned in the earlier analog tutorial lessons to connect all the parts and I/O ports. At the end, you should have a digital circuit similar to the figure shown at the beginning of this lessonbelow. Straight wires can always be drawn by simply clicking on device pins and dragging a line out of the pins. For drawing bent lines and multi-segment lines, sometimes you have to use the '''Wire Tool'''.

=== Testing the Digital Circuit by Stepping Manually ===<table>{{Note<tr><td> [[File:DigiTUT1 2.png|In thumb|550px|The finished digital circuit simulations, device propagation delays are typically in the order of nanoseconds. It is important to set the step size of the simulation so that each step still allows you to see the resulting changes without slowing the simulation too much. A step size of 20ns is suggested but can be adjusted from there.}}]] </td></tr></table>

== Testing the Digital circuit simulation is a time domain simulation. Furthermore, it is an event-driven simulation. It means that the simulation engine waits for changes in the input(s) of the circuit and then updates the digital state of various nodes in response to those state changes. You can run a time domain simulation in three different modes: '''Step''', '''Walk''' or '''Run'''. "Stepping" increments time a single time step at a time. "Walking" is faster than stepping and increments time Circuit by multiple steps at a time determined using a "Walk Factor". "Running" is equivalent to the analog live simulation and continues indefinitely until you pause it or stop it and reset. The first thing you always do in a [[Digital Simulation|digital simulation]] is to set the time step size. Note that "'''Step Size'''" is different from "'''Step Ceiling'''". Step size specifies how large each time step of the simulation is when using the "Simulation Stepping" feature. Step Size does not factor into the simulation when running the engine in "'''Walk'''" or "'''Run'''" modes, where the simulation engine itself decides how large a step to take. On the other hand, Step Ceiling is the maximum value that you specify for the automatically calculated time step when a simulation is "Walked" or "Run".Manually ==

To set the step sizeDigital circuit simulation is a time domain simulation. Furthermore, go to '''Simulate Menu''' it is an event-driven simulation. It means that the simulation engine waits for changes in the input(s) of the circuit and select then updates the "digital state of various nodes in response to those state changes. You can run a time domain simulation in three different modes: '''Time Options...Step'''" to open the Simulation Time Options Dialog. Or click the button labeled ", '''...Walk'''" on the or '''[[Toolbars#Main_Toolbar|Main Toolbar]]Run''' on the left of the Run button as shown in the figure below. You can also use the keyboard shortcut "Ctrl+IStepping" increments time a single time step at a time. "Walking" is faster than stepping and increments time by multiple steps at a time determined using a "Walk Factor". "Running" is equivalent to open this dialog, which the analog live simulation and continues indefinitely until you pause it or stop it and reset. The first thing you always do in a digital simulation is shown below: to set the time step size.

{{Note| border="0"|-| valign="top"|[[File:b2TUT4_7In digital circuit simulations, device propagation delays are typically in the order of nanoseconds.png|thumb|left|480px|Simulation Portion It is important to set the step size of Main Menu]]| valign="bottom"|[[File:b2TUT4_8the simulation so that each step still allows you to see the resulting changes without slowing the simulation too much.png|thumb|left|270px|Simulation Time Options Dialog]]|-|A step size of 20ns is suggested but can be adjusted from there.}}

Set the "'''Time Step'''" to 20n, leave the "'''Walk Factor'''" at the default value of 2 and close the dialog. Now start the [[Digital Simulation|digital simulation]] by "Stepping" your digital circuit. Click the "'''Step'''" [[File:b2Step_Toolb2TUT4_8.png]] button of the '''[[Main toolbar|Main Toolbarthumb|300px|The Simulation Time Options dialog.]]Also note that "''' or select "Step" from the "'''Simulate MenuSize'''" or simply use the keyboard shortcut is different from "'''Ctrl+HStep Ceiling'''". The simulation Step size specifies how large each time will increase to 20ns, and the output’s value will change to 0. Note that all your three input have initial values step of 0. The state of your circuit is shown in the figure below on the left. Next, change the value of Input 1 to 1 and leave the Input 2 and Input 3 at 0. During a live simulation, you can change is when using the values of inputs by clicking on their "'''Up'''" and "'''Down'''Simulation Stepping" arrow buttons at their right endfeature. Note that by changing Step Size does not factor into the input values, the output doesn't change immediately. This is because you simulation when running the engine is waiting for you to step the time to compute the next state of the circuit. Click the in "'''StepWalk'''" [[File:b2Step_Tool.png]] button or type "'''Ctrl+HRun'''" one more time. The simulation time increases to 40nsmodes, but where the output’s value stays at 0. This is expected as simulation engine itself decides how large a three-input AND circuit requires all three inputs step to be 1 to have an output of 1take. The state of On the circuit at t = 40s other hand, Step Ceiling is shown below in the middle figure. Finally, change the values of Input 2 and Input 3 to 1. Step maximum value that you specify for the automatically calculated time step when a simulation to 60ns. This time, the output changes to 1 as shown below in the figure on the rightis "Walked" or "Run".

{| border=To set the step size, go to '''Simulate Menu''' and select the "0'''Time Options...'''"to open the Simulation Time Options Dialog. Or click the button labeled {{key|-| valign="bottom"|[[File:b2TUT4_9.png|thumb|..}} on the '''Main Toolbat''' on the left|360px|State of Circuit at t = 20ns]]| valign="bottom"|[[File:b2TUT4_10the Run button as shown in the figure below.png|thumb|left|360px|State of Circuit at t = 40ns]]| valign=You can also use the keyboard shortcut "bottomCtrl+I"|[[Fileto open this dialog, which is shown below:b2TUT4_11.png|thumb|left|360px|State of Circuit at t = 60ns]]|-|}

Note that at each time step, the state of all the wire including the output <table><tr><td>[[File:b2TUT4_7.png|thumb|640px|The "Simulation" portion of the NAND gate is displayed on the circuitMain Menu.]]</td></tr></table>

Set the "'''Time Step'''" to 20n, leave the "'''Walk Factor'''" at the default value of 2 and close the dialog. Now start the digital simulation by "Stepping" your digital circuit. Click the "'''Step'''" [[File:b2Step_Tool.png]] button of the '''Main Toolbar''' or select "Step" from the "'''Simulate Menu'''" or simply use the keyboard shortcut {{key|Ctrl+H}}. The simulation time will increase to 20ns, and the output’s value will change to 0. Note that all your three inputs have initial values of 0. The state of your circuit is shown in the figure below on the left. Next, change the value of Input 1 to 1 and leave the Input 2 and Input 3 at 0. During a live simulation, you can change the values of inputs by clicking on their {{key|Up Arrow}} and {{key|Down Arrow}} buttons at their right end. Note that by changing the input values, the output doesn't change immediately. This is because the engine is waiting for you to step the time to compute the next state of the circuit. Click the "'''Step'''" [[File:b2Step_Tool.png]] button or type {{key|Ctrl+H}} one more time. The simulation time increases to 40ns, but the output’s value stays at 0. This is expected as a three-input AND circuit requires all three inputs to be 1 to have an output of 1. The state of the circuit at t === Using Live Digital Timing Diagrams ===40s is shown below in the middle figure. Finally, change the values of Input 2 and Input 3 to 1. Step the simulation to 60ns. This time, the output changes to 1 as shown below in the figure on the right. Note that at each time step, the state of all the wires including the output of the NAND gate is displayed on the circuit. The binary states are shown in small black box labels. You can also tell the state of a wire from its color. Blue is 0 and red is 1.

<table><tr><td>[[B2File:DigiTUT1_3.Spice A/D]] allows you to view the state png|thumb|550px|State of your the digital inputs and outputs graphically in real time using "'''Live Timing Diagrams'''". The timing diagrams appear circuit at the bottom of the Workshop just like a regular graph. However, these are interactive "live" graphs that change and expand t = 20ns with every time stepIn1 = In2 = In3 = 0. For this part of the lesson, you keep the value of "Time Step" at 20ns. First, reset your simulation engine by clicking the "'''Stop]]</td></Reset'''" tr><tr><td>[[File:b2Stop_ToolDigiTUT1_4.png]] button |thumb|550px|State of the [[Main toolbar|Main Toolbardigital circuit at t = 40ns with In1 = 1 and In2 = In3 = 0.]], or using the keyboard shortcut "'''Ctrl+E'''"</td></tr><tr><td>[[File:DigiTUT1_5. Also reset the values png|thumb|550px|State of all the three inputs to 0digital circuit at t = 60ns with In1 = In2 = In3 = 1. ]]</td></tr></table>

To activate the timing diagrams, click the "'''Show/Hide == Using Live Digital Timing Diagrams'''" [[File:b2Timing_Tool.png]] button of the '''[[Schematic toolbar|Schematic Toolbar]]'''. Nothing happens immediately because you haven't started a [[Digital Simulation|digital simulation]] yet. Here is the game plan that you will follow next. You will set the values of each input to 1 sequentially, one at a time. You will increment three time steps between any two actions or events. Then, you will revert the values of the three inputs back to 0 sequentially, one at a time, in the reverse order, until all the three inputs are 0 again. The following table shows the timing of the events: ==

[[RF.Spice A/D]] allows you to view the state of your digital inputs and outputs graphically in real time using "'''Live Timing Diagrams'''". The digital timing diagram appears at the bottom of the Workshop just like a regular graph. However, these are interactive "live" graphs that change and expand with every time step. For this part of the lesson, you keep the value of "Time Step" at 20ns. First, reset your simulation engine by clicking the "'''Stop/Reset'''" [[File:b2TUT4_13b2Stop_Tool.png|thumb|800px]]button of the Main Toolbar. Also reset the values of all the three inputs to 0.

To activate the timing diagrams, click the "'''Show/Hide Live Digital Timing Diagrams'''" [[File:b2TUT4_14b2Timing_Tool.png|thumb|400px|Property Dialog of the NAND Gate]]button of the '''Schematic Toolbar'''. Nothing happens immediately because you haven't started a digital simulation yet. Here is the game plan that you will follow next. You will set the values of each input to 1 sequentially, one at a time. You will increment three time steps between any two actions or events. Then, you will revert the values of the three inputs back to 0 sequentially, one at a time, in the reverse order, until all the three inputs are 0 again. The following table shows the timing of the events:

Start the [[Digital Simulation|digital simulation]] with all zero inputs and increment three time steps to 60ns. You will see that four timing diagrams appear at the bottom of the Workshop, one for each input and one for the output. In general every input and output port will have a timing diagram. Then, change the value of Input 1 to 1. Step again and you will see that the timing diagrams immediately get updated because the input states have now changed. Increment two more time steps to 120ns. Then, change the value of Input 2 to 1. Follow this recipe according to the above event table with 60ns intervals until all inputs are set to 0 again. The timing diagrams get updated after each change of state and the final diagrams are shown in the figure abovebelow. With a closer look at the output Note that your timing diagram, you will be able may expand too long to see fit into the propagation delay between the input and output portsbottom graph window. For exampleIn that case, at t = 180ns, when all three inputs are 1, you would expect to see click on the title of the output graph window tab to jump at 1. However, make it take about 20ns for this to happen (at t = 200ns)the active window. To understand this, double-The toolbar changes accordingly. Then click on the NAND gate to open up its property dialog as shown above. You will see that 74LS10D has a "'''Low-to-High Propagation DelayZoom Out Horizontal'''" [[File:b2ZoomOutHoriz_Tool.png]] button of 9ns and a "'''High-the Graph Toolbar to-Low Propagation Delay'''" of 10ns. The 74LS04D Inverter has similar propagation delays. When Input 3 jumps to 1 at t = 180ns, it takes shrink the NAND gate a propagation delay of 10ns to fall from its 1 state down to 0. Similarly, diagram until it takes has the Inverter gate an additional propagation delay of 9ns to rise from its 0 state up to 1. This makes a total delay of 19ns as you can see from the graphright size for viewing.

[[File:b2TUT4_16.png|thumb|400px]] [[File:b2TUT4_15.png|thumb|360px|Property Dialog of Digital Source]]Since digital simulations take place in == Analyzing the time domain, you can also run a transient test on them. Recall from previous tutorial lessons that unlike live simulations, [[tests]] are preplanned simulation. In other words, in a test, the inputs are completely known and will not change during the period of time when the simulation engine is doing its job. At the end of a test, you will see the final results. Contrast this to a live [[Digital Simulation|digital simulation]], when the engine waits for you to make your next move. Then it responds to your action. For transient test of digital circuit, [[B2.Spice A/D]] offers another type of digital input called a "'''Digital Source'''". A digital source is indeed the same as a digital input except for the fact that it contains a preloaded "'''Time-Value Array'''". This means that a digital source knows in advance what values it will take at certain times during the simulation.Propagation Delays ==

At this pointWith a closer look at the output timing diagram, go back you will be able to your circuit see the propagation delay between the input and delete output ports. For example, at t = 180ns, when all the three digital inputs. Select each part and press are 1, you would expect to see the keyboard's '''Delete Key'''output to jump at 1. NextHowever, from it takes about 19ns for this to happen (at t = 199ns). To understand this, double-click on the NAND gate A2 and inverter gate A4 to open up their property dialogs as shown below. You will see that the generic NAND gate has a "'''Parts MenuLow-to-High Propagation Delay''', select the " of 11ns and a "'''Digital I/OHigh-to-Low Propagation Delay''' submenu and then select " of 7ns. The generic inverter gate has a "'''Digital SourceLow-to-High Propagation Delay'''". Place the source in your circuit at the location where you used to have Input 1 of 12ns and connect it to the same wire. Use the keyboarda "'s ''High-to-Low Propagation Delay'SPACE Bar''' to duplicate the digital source twice and place them at the locations " of the old Input 2 and 3. Your digital circuit should now look like the opposite figure8ns.

Double-click the first digital source to open its <table><tr><td> [[File:DigiTUT1 6.png|thumb|540px|The property dialog as shown below. In the table titled "'''Edit Time-Value Array'''", enter the binary values of the source as a function of time according to the state table shown in the previous sectiongeneric NAND gate. Enter time in nanoseconds and use the values in "Input 1" column for the first digital source]] </td></tr><tr><td> [[File:DigiTUT1 8. Similarly, open the png|thumb|540px|The property dialogs dialog of the second and third digital sources and enter their time-value arrays using the values in the "Input 2" and "Input 3" columns of the above generic inverter gate.]] </td></tr></table, respectively. >

{{Note|The "Time-Value" array When Input 3 jumps to 1 at t = 180ns, it takes the NAND gate A2 a propagation delay of 7ns to fall from its 1 state down to 0. Similarly, it takes the Inverter gate A4 an additional propagation delay of 12ns to rise from its 0 state up to 1. This makes a digital source total delay of 19ns as you can be conveniently loaded see from a text filethe graph.}} At t = 240ns, the reverse of these events happens and gate A2 and A4 undergo the opposite transition types. The total propagation delay is still 19ns, and therefore, the output drops from 1 to 0 at t = 259ns. These events are summarized in the table below. {| borderclass="0wikitable"

| valign! scope="bottomcol"|Time[[File:b2TUT4_17.png|thumb! scope="col"|left|220px|Edit Graph Dialog]]A2 Transition Type! scope="col"| valignA2 Transition Delay! scope="bottomcol"|A4 Transition Type[[File:b2TUT4_18.png! scope="col"|thumb|left|220pxA4 Transition Delay! scope="col"|Edit Axis Dialog]]Total Delay

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