# Download PDF Pragmatic Logic (Synthesis Lectures on Digital Circuits and Systems)

It is placed in the desired position by left clicking the mouse. The same window is open again to select a new component. If we wish to place another DC voltage source we select it and press the OK button. Now we place the resistors, otherwise we press the Close button. We click on the Basic icon in the Component toolbar. The window in Fig. There are two possibilities to choose a resistor.

TTL logic parts. In the resistor set we can only place resistors with predetermined commercial values. In our example we can use both sets. Thus, after placing R1 we are returned to the same window to select the following component and there we press the Close button. To place R2 in a vertical position we select it with the mouse and press Control-R. See Fig. We repeat with R3. Finally, we have to place a ground symbol, which it is available from the sources icon. The last one is used in digital circuit simulation.

The schematic page with the components is shown in Fig. To wire up the components we place the pointer in the upper end of the DC power source, we click the left mouse button to start the wire, then drag the pointer to the left end of R1 and left click again. A wire connecting the voltage source and resistor R1 has been created. Now, connect the remaining elements. The complete circuit is shown in Fig. In this figure, node numbers are shown next to each node. Node numbers or names are displayed if we select in the main menu Edit Properties which opens the dialog window shown in Fig.

The next step is to change the values of resistor R1. We click on the 1K values and the window of Fig. In the same way we change the value of the source V1 to 10 V. The final circuit is shown in Fig. Finally, save the circuit as Example The circuits saved have an extension ms11, indicating that the design was done on Multisim 11 the latest version as of this writing. We are now ready to simulate our circuit. This type of analysis is performed even when a different type of analysis is chosen such as AC or transient.

This type of analysis calculates the node voltages and the currents through the voltage sources. This action takes us to the window shown in Fig. We select I v1 and V 2 as our variables, then. The variables selected are now displayed in the right window see Fig. Now press the Simulate button and after the analysis is run, Multisim displays the values of the variables selected before I v1 and V 2 shown in Fig. There we see that the current through the voltage source is -4 mA, indicating that the current is leaving the positive terminal in the voltage source, and that the voltage at node 2 is 2 volts.

Multisim provides a set of instruments that can be positioned in the circuit diagram to make measurements. These instruments can be used to measure voltages, currents, resistance and dB, among other more advanced measurements that we will cover along the book. The first type of measurement instruments we cover are the voltmeter and the ammeter. These instruments are available in the Indicator icon in the Components toolbar. If we click on this icon we obtain the window of Fig. The voltmeters are shown in Fig. We see that there are four choices. All of them are voltmeters and the only difference is the position of the pins and the positive input.

Associated with these voltmeters there is associated a resistance which is the internal resistance of them. An ideal voltmeter has associated an infinite resistance but a real one has a finite resistance. Now we run the simulation with the Run icon or with the Run button, both seen in Fig. After using any one of the Run options, after a few moments after the values are shown in the voltmeter window, we can stop the simulation by clicking on the Stop icon located next to the Run icon we can see the voltages across resistors R1 and R2, which are 8 V and 2 V, respectively, as shown in Fig.

The voltage across R2 is the voltage at node 2 obtained in Section 2. The voltage across R1 is the difference of the node voltages 1 and 2 which at Section 2. The other type of measurement instrument that can be used is the ammeter. Ammeters are also available in the Indicator set. An ammeter has to be inserted in the circuit. Thus, if we wish to measure the current across resistors R1 and R3, we have to insert them in the circuit as can be seen in Fig. An ideal ammeter has a zero internal resistance. A real one has a very small associated resistance.

This resistance can be changed in the Value tab of the ammeter which opens by double clicking on the ammeter element in the schematic diagram. We run the simulation by using the Run icon or the Run button of Fig. Besides the voltmeter and ammeter just discussed, there is another instrument to measure voltage, current, resistance, and dBs.

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It is available in the Instruments toolbar of Fig. The first one of the instruments is a Multimeter. When we click on the Multimeter icon and one of them is displayed on the circuit diagram see Fig. When we double click on the Multimeter symbol we get a window see Fig. For the circuit we have been using, we place two multimeters, one to measure the voltage across R3 and another one to measure the current through R1.

The circuit is shown in Fig. We run the simulation in the same way as before by clicking on the Run icon and after a few seconds we obtain the result shown in Fig. The results agree with those obtained previously with the Voltmeter and Ammeter. The measurement of resistance follows the same format as before and a measurement is shown in Fig.

In this case, as it is in a real lab, we do not need to have a power supply but we also have to click on the Run button to measure resistance. A powerful instrument from the Instruments toolbar is the Oscilloscope. This instrument allows us to see the signals waveforms. In this chapter we have only used DC signals, however, when we use AC signals, this instrument is very useful. To see how the oscilloscope can be used let us consider the circuit of Fig.

This circuit is a simple resistive voltage divider excited by a voltage sine wave available as an AC voltage source. After wiring up the circuit use the run button and open the oscilloscope window by pressing the oscilloscope icon on the schematic diagram. We see the sine wave moving as in a real oscilloscope. The oscilloscope is internally connected to the ground node so it is not necessary to connect the negative inputs to ground. The oscilloscope has a time base that can be adjusted for a proper display of the signals. It also has two input Scales, A and B, that can be adjusted for a better visualization of the signals.

The scales for channels A, B, and the time base can be adjusted by left clicking on. There also two cursors that can be positioned with the mouse for proper signal amplitude measurements. The Wattmeter is available in the Instruments toolbar and it is used to measure power dissipation in a device. It measures current and voltage and calculates the product of them to compute power.

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This instrument has an ammeter and a voltmeter that have to be properly connected. As an example we consider the circuit of Fig. We can see that the power through resistor R1 is 32 mW. Unfortunately, the wattmeter does not work correctly in all Multisim versions, for example, version The last element in the Instruments toolbar is the Probe.

This instrument can be used to measure voltage, current, and frequency for either a DC or an AC signal. To the circuit of Fig. Probe and run the simulation to obtain the results shown in Fig. There we see that the voltage at that node is 2 VDC and that the current passing through that wire is 4 mA. Multisim has the capability to wire a schematic on a breadboard in the same way we build the circuit on a breadboard. This feature enables novice simulation users to breadboard their schematic and to check if the circuit was correctly wired. To use this Multisim feature, we click on the Show Breadboard icon of Fig.

This icon will produce the breadboard on the Multisim drawing space as can be seen in Fig. To use the breadboard we have first to draw a schematic diagram of the circuit. We show the procedure with a simple RC circuit. Let us consider the circuit of Fig. As can be seen it is composed of an AC voltage source, a resistor, and a capacitor. We have added a ground symbol to comply with the need of having it for the simulation. Now we click on the Show Breadboard icon to obtain the breadboard view, shown in Fig. Here we see an empty breadboard with all the components. The green arrows at both ends of the blue tray are used to scroll the components.

To place the components on the breadboard we click on any of them and place it on the breadboard. We place the three components on the breadboard as shown in Fig. If we need to rotate them to place them in the required position we right click on the component and select Orientation 90 Clockwise or 90 Counter CW.

If we go back to the schematic drawing we see that the three components have turned green. This means that they are on the breadboard. Now on the breadboard we wire up the circuit as required. To place a wire we left click on a point in the breadboard and move the cursor to the other point where we wish to place the wire as can be seen in Fig. We repeat this procedure until we are finished wiring. The finished circuit is shown in Fig. To check if we wired it correctly, we go back to the schematic drawing and note that the circuit elements and connections are now green indicating that the breadboard circuit was wired up correctly.

If there are wrong connections, these connections will remain in red. It will produce an output as shown in Fig. We see there that there are no connectivity errors. Multisim Educational license has the capability to draw pictorial diagrams and then simulate them. It has resistors, capacitors, inductors, diodes, transistors, among another few components, as can be seen in Fig. An example shows how we can use this feature. The circuit shown in Fig.

Transistor pins can be obtained from manufacturer data sheets, in this case for the bipolar transistor, the pins are ordered from left to right as EBC emitter-base-collector. We perform a transient analysis and the input and output waveforms are shown in Fig. We note a small gain in the amplifier in addition to a phase shift. Multisim can display results of a simulation in its powerful Grapher. Results of any analysis, with exception of the DC Operating Point one, can be plotted in the Grapher.

To show how the Grapher works let us use again the circuit of Fig. There we select the source V1 that it is going to be swept. In the Output tab see Fig. We then press the Simulate button. The results are displayed in Fig. There we see that the voltage at node 2 changes from 2 V to 20 V when the DC voltage source changes from 10 V to V. Figure 2. A npn BJT is shown in the symbol window. Some devices, such as transistors and operational amplifiers, are modeled by equivalent circuits consisting, among other elements, by controlled sources.

Multisim has four types of controlled sources available. They are: 1. The left element is to be positioned at the controlling nodes. As an example consider the circuit of Fig. This circuit is composed by an independent DC voltage source with a value of 10 v, three resistors, and a VCVS whose voltage is 7 times the voltage drop across resistor R2.

A window appears where we select the variables we wish to find out. We add all of them and press the Simulate button. Then, the circuit is simulated and a window showing the values of all the variables selected is displayed as shown in Fig. The ICIS is a current source whose value depends upon the value of a current in other branch.

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The Multisim symbol is shown in Fig. The sensing element is located at the left side and it must be inserted in the circuit. Let us consider the circuit in Fig. This circuit is drawn in Multisim as shown in Fig. Note that because of the controlling current is pointing downward, the sensing element has to be connected accordingly downward.

We select all of them and click the Simulate button. After the simulation is finished we see the window with the node voltages and the current through the DC voltage source shown in Fig. A voltage controlled current source is a current source whose current is controlled by a voltage drop in a pair of nodes. It is denoted in Multisim with a letter G, and thus it is also referred as a G-source.

The Multisim symbol for a G-source is presented in Fig. Example 2. The circuit in Fig. The Multisim circuit is shown in Fig. Note that the signs in the sensing element and the controlling voltage must coincide. Its symbol is shown in Fig. This is a controlled source whose voltage value is controlled by the current through another branch.

The circuit of Fig. Its Multisim diagram is given in Fig. In this chapter we presented the first few circuits analyzed in Multisim. Although our circuits have been restricted to circuits containing resistors and independent and controlled sources, the main purpose of the chapter is to introduce the reader to the Multisim simulation environment.

We also introduced measurement instruments. They were used to measure voltage, current, and resistance. In the next chapters we will cover other types of analysis with circuits containing inductors, capacitors, transistors, etc. More interesting types of analysis can be performed in such cases.

Repeat Exercise 2. Using a multimeter, obtain the equivalent resistance between: a nodes 1 and ground, and b nodes 2 and 4. Using the breadboard, wire up the circuit shown. Then, obtain the dc node voltages and branch currents. Change the dc voltage source V1 to an AC voltage source.

Use an oscilloscope to plot the input and output waveforms. At which scale we see the amplitude of the input voltage? And for the output voltage? In the circuit shown we are using a virtual diode from the Diodes library. Use the oscilloscope and a probe to measure the peak voltage. Compare the peak voltage in both instruments and explain. In the circuit shown, use the Multisim Grapher to obtain the waveforms in the input and output nodes. Use a VCVS in the circuit shown and obtain the node voltages. Note the signs in the controlling voltage Vx. Time Domain Analysis Transient Analysis One of the most useful analyses in electronic circuits is the transient analysis which is a time domain analysis.

The purpose of this analysis is to apply a waveform to the circuit and observe its response versus time. Some of the parameters to watch are the overflow, rise time, delay, etc. In this chapter we treat in detail how to perform a transient analysis.

Furthermore, in this chapter we introduce capacitors and inductors, where the relationships between voltage and current are integro-differential equations. This fact makes that circuits composed of inductors and capacitors, besides resistors, have very interesting properties. In addition, the functions that these circuits can perform are quite varied and useful, when compared to resistive circuits.

The chapter is organized as follows. Section 3. Fourier analysis is described in Section 3. Capacitors and inductors are designated with the letters C and L, respectively. Their Multisim symbols are shown in Fig. In this figure, electrolitic capacitors explicitly have a polarity. This is only important when we apply an initial condition to these elements. As a rule, when we put any one of these components in a schematic, the left-hand node is the positive one. So if we rotate them, it is useful to watch where the positive node is moving to.

To apply an initial condition we select the element inductor or capacitor to open its window where we write the initial condition value. Example 3. It is worth mentioning that for an inductor the initial condition is a current while for a capacitor it is a voltage. In addition, the use of initial conditions is only valid for transient analysis. It is also possible to define coupled inductors in the form of transformers, transformers with a tap, and variable inductors and capacitors. Next, we give a description of each of these sources. Its parameters are described in Table 3. Table 3.

## Circuit Analysis with Multisim

It keeps increasing its value during TD2 s to reach the value V2 when it begins to decrease in value with a time constant TC2. The rise time RT is the time it takes to change its value from V1 to V2 where it stays for PW s and finally it changes its value back to V1. PER is the period of the signal. The coordinates of each break point are given depending upon the desired form of the signal. They can also be given in a file. There is an option to repeat the data given during the simulation. A sine wave signal is displayed in Fig.

Its parameters are listed in Table 3. The AC sine wave obeys. The frequency modulated signal FM is shown in Fig. Its parameters are given in Table 3. It is a source used for noise analysis. We have to specify the bandwidth, the temperature, and the equivalent resistance. A typical waveform is shown in Fig. The amplitude modulated signal AM is shown in Fig. It only exists for voltage sources. The parameters are given in Table 3. The AM source single-frequency amplitude modulation source generates an amplitude modulated waveform. Transient analysis is the name of the analysis in the time domain.

The data we need to enter is Starting time for simulation. In a transient analysis, Multisim solves numerically a set of differential equations. The time step is adjusted to ensure a successful convergence of the solution. To this purpose, we have the option to give a maximum time step TMAX. Alternatively, we can also define the maximum number of. An example will show how a transient analysis is performed. It has a period of 8 sec and a duty cycle of 5 sec. The rise and fall times are both equal to 1 nsec. We perform a transient analysis from sec in the dialog window of Fig.

We plot the input signal and the voltage across resistor R2. The results are shown in Fig. Due to the time constants, we see that the output signal takes almost 5 sec to reach its maximum value. A transient analysis allows the specification of initial conditions in capacitors and inductors. For inductors the initial condition is a current and for capacitors it is a voltage. Initial condition can be given by double clicking on the element. This opens a window where the initial condition desired value is entered.

The dialog window of Fig. The parameters for the. The plot of Fig. Often we wish to know the value of the signal displayed at a certain time. To do this we use anyone of the two available. In a plot, cursors are enabled by clicking on the cursor icon in the toolbar of the plot. The cursor icon is shown in Fig. When we click on the cursor icon, a small green triangle appears on top of the vertical axis which corresponds to one of the two cursors available.

They can be positioned on the desired position along the horizontal axis by clicking on it and moving it with the mouse. The same procedure applies to cursor number 2. As an example we use the plot available in Fig. Once the cursor icon is clicked we can move the cursors to the desired position, as shown in Fig. We also see that a small window appears showing the coordinates of the point where each of the cursor is positioned. Also available are the differential, the inverse of the differential, the minimum and maximum values for the coordinates, and the offset values.

Cursors are disabled by clicking on the cursor icon again. Multisim has available a set of virtual instruments that behave in the same way as the real ones in the laboratory. They are available from the Instruments toolbar of Fig. Here we discuss two of them: the Oscilloscope and the Distortion Analyzer. The oscilloscope is a very useful and important instrument in the laboratory.

Two channel and a four channel oscilloscopes are available as seen in Fig. The operation of both oscilloscopes is very similar. Their operation is illustrated with the circuit of Example 3. An oscilloscope has been added to the schematic of the circuit in Example 3. When we double click on the oscilloscope symbol we open the window of Fig.

The output is shown in Fig. There we see the output waveform. We can see that there are cursors at both ends of the plot. These cursors can be used to show signal values at different time points in the plot. The cursors can be positioned with the arrows in the top left corner of the instrument panel.

The values of the signal at each cursor position as well as the difference between those values is displayed next to the arrows see Fig. Note that the oscilloscope only displays when the Run button is clicked on. The analysis that runs when this is done is a Transient Analysis with the conditions established in the dialog window that is displayed when we choose SimulateInteractive Simulation Settings.

The window is shown in Fig. This is also the case for the Voltmeter, Ammeter, and Multimeter introduced in Chapter 2. Figure 3. The Distortion Analyzer is selected by clicking on it on the Instruments toolbar, placing it alongside the circuit and wiring it to the desired node in the circuit. The Distortion Analyzer window is shown in Fig.

Here we give the Fundamental Frequency for the distortion measurement. The THD is very large because the input signal is a square signal rich in harmonic content. Multisim has the capability to perform a Fourier analysis to the signals in the circuit being simulated. Thus, we can obtain a harmonic decomposition for either a voltage or current in the circuit. This type of analysis receives the name of its creator Jean Fourier , who developed the mathematical basis to express any periodic function as a sum of sine waves.

This action opens the dialog window of Fig. In this window we specify the fundamental frequency for the Fourier analysis and the number of harmonics we wish to see as well as the final time TSTOP for the analysis. We can also specify the way we wish to see the results either Display phase, Display as a bar graph, or Normalize graphs. We use the simple circuits of Fig. The input data is given in Fig. Since the frequency of the sine source is 1 KHz, we choose this frequency as the fundamental frequency in the Fourier analysis. Also, we calculate the first 20 harmonics.

Finally, we perform the transient analysis for 2 msec. After running the Fourier analysis we see the Grapher window where there is a spreadsheet see Fig. Here, we see the DC component value, the number of harmonics calculated, the THD Total Harmonic Distortion , the magnitude and phase of each of the harmonics, and finally the normalized magnitude and phase of each of the harmonics.

THD is calculated with the harmonics calculated in the analysis, thus, the more harmonics we choose to calculate, the more accurate is the result of THD. Since the signal analyzed is a sine wave we only see a single component, a very small THD, and the harmonic components are negligible. Now, let us consider the circuit in Fig. The input signal is a Pulse signal.

We repeat in Fig. The Grapher window shows the spreadsheet with the output data. Since we have a square signal at the input we now have a very large THD. From this information we can see that the DC component is 0. The first few harmonic components and the corresponding total harmonic distortion are also included in Fig. From this data we see that the THD is In this section we present some examples using the concepts and analyses covered in this chapter. Thus, it has a frequency of Hz, and the pulse width is 2 msec.

We make a transient analysis from 0 to 10 msec, as seen in the dialog window of Fig. The input and output waveforms are shown in Fig. We see that even though the input signal is a square wave with a great deal of harmonic components, the output resembles a sine wave. This is due to the fact that the circuit is filtering a large number of harmonics. We then perform a Fourier analysis. Since the period of the input signal is 4 msec, the frequency is Hz.

We request 10 harmonic components. We choose as the output variable the voltage V 3. The dialog window is that of Fig. The results are presented in Fig. In the spreadsheet we see that the output signal has a THD of The inductor and the capacitor have initial conditions. We add the delay to observe the effect of the initial conditions on the response.

The initial conditions are added by double clicking on the reactive elements and selecting the Initial conditions square and entering the initial condition for the current in the inductor and the voltage in the capacitor, as shown in Fig. We perform a transient analysis and measure the independent input current and the current through the inductor. To measure the currents we add dummy voltage sources in series with the inductor and the current source as shown in Fig. The positive terminal in the dummy voltage source is connected to the current source because the current in a voltage source enters the positive terminal.