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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 logical AND circuit is built and examined.|

*Binary State Transition*Propagation Delay|All versions|{{download|http://www.emagtech.com/contentdownloads/project-file-download-repository|ProjectRepo/DigitalLesson1.zip Digital Tutorial Lesson 1|[[RF.Spice A/D]] R15}} }}

In this tutorial you will use generic inverter gates and two-input NAND gates to build a three-input AND circuit. You will learn how to define digital inputs and outputs and use [[RF.Spice]]'s live digital timing diagrams. It is assumed that by this time you have already completed the first few analog tutorial lessons and are comfortable with navigating the [[RF.Spice A/D]] Workshop.

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<td> [[File:DigiTUT1 2.png|thumb|540px550px|The finished digital circuit.]] </td>

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 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.

To set the step size, go to '''Simulate Menu''' and select the "'''Time Options...'''" to open the Simulation Time Options Dialog. Or click the button labeled {{key|...}} on the '''[[Main toolbar|[[Main toolbar|[[Main toolbar|[[Main toolbar|[[Main toolbar|[[Main toolbar|[[Main toolbar|[[Main toolbar|[[Main toolbar|[[Main toolbar|Main Toolbar]]]]]]]]]]]]]]]]]]]]Toolbat''' on the left of the Run button as shown in the figure below. You can also use the keyboard shortcut "Ctrl+I" to open this dialog, which is shown below:

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_Tool.png]] button of the '''[[Main toolbar|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 = 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.

[[File:DigiTUT1_3.png|thumb|500px550px|State of the digital circuit at t = 20nswith In1 = In2 = In3 = 0.]]

[[File:DigiTUT1_4.png|thumb|500px550px|State of the digital circuit at t = 40nswith In1 = 1 and In2 = In3 = 0.]]

[[File:DigiTUT1_5.png|thumb|500px550px|State of the digital circuit at t = 60nswith In1 = In2 = In3 = 1.]]

[[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:b2Stop_Tool.png]] button of the [[Main toolbar|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: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:

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 below. Note that your timing diagram may expand too long to fit into the bottom graph window. In that case, click on the title of the graph window tab to make it the active window. The toolbar changes accordingly. Then click the "'''Zoom Out Horizontal'''" [[File:b2ZoomOutHoriz_Tool.png]] button of the [[Graph toolbar|Graph Toolbar]] to shrink the diagram until it has the right size for viewing.  {{Note|The timing diagram updates only when there is a change of states of the inputs.}}

== Analyzing the Propagation Delays == With a closer look at the output timing diagram, you will be able to see the propagation delay between the input and output ports. For example, at t = 180ns, when all three inputs are 1, you would expect to see the output to jump at 1. However, it takes about 20ns 19ns for this to happen (at t = 200ns199ns). To understand this, double-click on the NAND gate A2 and inverter gate A4 to open up its their property dialog dialogs as shown abovebelow. You will see that 74LS10D the generic NAND gate has a "'''Low-to-High Propagation Delay'''" of 9ns 11ns and a "'''High-to-Low Propagation Delay'''" of 10ns7ns. The 74LS04D Inverter generic inverter gate has similar propagation delays. When Input 3 jumps to 1 at t = 180ns, it takes the NAND gate a propagation delay of 10ns "'''Low-to fall from its 1 state down to 0. Similarly, it takes the Inverter gate an additional propagation delay -High Propagation Delay'''" of 9ns 12ns and a "'''High-to rise from its 0 state up to 1. This makes a total delay -Low Propagation Delay'''" of 19ns as you can see from the graph. {{Note|The timing diagram updates only when there is a change of states of the inputs8ns.}}

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