EEE161 Applied Electromagnetics Laboratory 2

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Dr. Milica Marković Applied Electromagnetics Laboratory page 1 EEE161 Applied Electromagnetics Laboratory 2 Instructor: Dr. Milica Marković Office: Riverside Hall 5026 Email: milica@csus.

Review using phasors to derive and calculate voltages and currents in simple series and parallel circuits. 3.

1 Dr. Milica Marković Applied Electromagnetics Laboratory page 1 EEE161 Applied Electromagnetics Laboratory 2 Instructor: Dr. Milica Marković Office: Riverside Hall milica@csus.edu Web: milica 1 Learning Objectives In this lab you will 1. Learn how to simulation a circuit in ADS using AC Simulation and display phasors on a polar plot. 2. Review using phasors to derive and calculate voltages and currents in simple series and parallel circuits. 3. Define Kirchoff s Voltage Law (KVL) and Kirchoff s Current Law (KCL) in both frequency and time domains. 4. Describe how are the equations in the time and frequency domain different? How are they the same? 5. Proove that KVL and KCV are valid in both frequency in time domain. 6. Design a simple circuit to fit specifications. (a) Gustav Robert Kirchoff (b) Keysight s cartoon. Figure 1: The first two steps to plot a signal as a function of angle.

2 Dr. Milica Marković Applied Electromagnetics Laboratory page 2 2 Series RC Circuit - Hand Calculations Q Calculate on paper the magnitude and phase of the current and voltages in a series RC circuit if the source voltage is v s = cos ωt, R=1 kω, C=0.159 pf, f=1 GHz. Answer the following questions: 1. What are the magnitude, phase and time delay of the source voltage. 2. What are the magnitude, phase and time delay of the voltage across the resistor. 3. What are the magnitude, phase and time delay of the voltage across the capacitor. 4. Sketch the phasor diagram of the three voltages. 5. On the phasor diagram, what is the angle between the vector of voltage on the capacitor and resistor? Why? 6. Explain why the voltage magnitudes on capacitor and resistor do not add up. For example, in Figure 6, the voltage magnitude across the resistor is about 0.5V and the voltage magnitude across the capacitor is about 0.85V. 0.85V+0.5V 1V. Why? Does that mean that the KVL doesn t work? Hint: Think about KVL in frequency domain. You are using phasors now. Write the equation for KVL using phasors. Write an equation that describes this addition. What kind of equation is this? What kind of numbers do you have to use to describe this addition? Which domain is this equation in? 7. Sketch the voltage on the capacitor and resistor as a function of time. What is the total voltage equal to at any time instance? For example, look at the time instance t=0, t=0.5 ns, then calculate the voltages on resistor, capacitor and input voltage. What can you conclude? Hint: Look at the Figure 6 and marker m1. At that time, voltage on a capacitor is zero, and votage on the resistor and source are 0.5V. Write an equation that describes this addition. What kind of equation is this? What kind of numbers do you have to use to describe this addition? Which domain is this equation in? In the following section, we will simulate a series RC circuit in ADS. 3 Accessing ADS First you will open ADS on Hydra. If you are loged in on Windows computer, you will login remotely to hydra.ecs.csus.edu, by using Start, All programs, Remote Desktop. Make sure that you are logging in to ECS domain with ECS\yourusername and ECS password. If you are in RVR 3009, you are loged in on Unix computers. Click on The following instructions assume that you are already on Hydra. 1. Select Start, All programs, Advanced Design System 2015 (or the current installed version, for example Advanced Design System 2016)

3 Dr. Milica Marković Applied Electromagnetics Laboratory page 3 2. ADS windows opens, wait several minutes, especially if the entire lab is logging on at the same time. You should see several windows open, the top one Getting Started with ADS. Close that window. 3. From window: Advanced Design System 2015 (Main) click on the icon W+ to create the new workspace. ( Later when you are returning to work again on ADS you would select W- open a workspace). 4. New Workspace Wizard window opens. Click on Next. 5. Worskpace name: Name the workspace (for example Phasorlab_wrk). Create in: T:\ADS2015-HOME drive. Click Next then Finish. 6. Click on the schematic icon in Advanced Deisng System 2015 (Main) window. Schematic icon is the white icon with a resistor under a capacitor. 7. New Schematic window opens. Cell: Problem1B (or something like that). Schematic Design Templates: wizard_templates:gs_ac In the next section, using the circuit diagram in Figure 2(a) as a guide, reproduce the voltages on capacitor and resistor as shown in Figure 2(b). Note that the figures you will get will not look exactly like the figures below because the circuit in Figure 2 is similar but not exactly the same as your circuit. 4 Simulation of Series RC Circuit in ADS Once the circuit diagram is open: 1. You should see an AC source, a 1kOhm resistor and the gear icon on your schematic. 2. Make sure that at the top left corner Lumped-Components section is selected. 3. Select the top left choice for the capacitor C. Do not select C-Model, select just C. Click on it and drag it to the place where you want the series resistor. Click on the Arrow icon on the top of the window (or escape) to stop placing capacitors on your schematic. If you placed more than one resistor click on the X icon on the top of the window, then on extra capacitors to remove them. Again click on the arrow (or escape) to continue. Note that the default value for the capacitor is 1 pf. Click on the C=1 pf, then change it to pf. 4. To add the current probe, go to the Lumped-Components drop-down menu and change it to Probe Components. Select the top left choice I_Probe. Place it between the source and the circuit. 5. Double click on AC gear icon on the schematic. AC Small Signal Simulation:1 opens. On the frequency tab (default) Change the Sweep Type to Single point. Set the frequency to 1GHz. The default frequency is usually 1GHz, but check that this is so.

4 Dr. Milica Marković Applied Electromagnetics Laboratory page 4 6. Click on the icon Name, WirePin Label window opens. Write vin, then click on the wire that connects the source and the circuit. 7. Click on the gear icon on top menu to simulate the circuit. 8. Data window shows two windows, one shows the magnitude of the output voltage as a function of frequency, and the other phase as a function of frequency. In this case we simulated only one frequency point, so there is really no sweep. 9. Click on the icon that shows a 4by3 table from the Palette and place it on the Data window. This opens a rectangular x-y plot on data window. Plot Traces&Attributes Window appears. Click on Vout then Add. A window opens reminding you that you are accessing a variable that is complex, e.g. it has a magnitude and the phase information. Select Time Domain Signal. 10. Repeat step 9 for vin. 11. To plot the voltage on the resistor R1 (from Figure 1, you will need to write an equation from one or the other element, depending on how your circuit was connected), one needs to write an equation in Data Window. Click on Eqn con from the Palette. Enter Equation windows open. Write the equation as shown in Figure2:vr=1000*, then click on the variable I_Probe1.i from the right window and select Insert. This will place I_Probe1.i in your equation. Note that you have other variables such a freq in the same window. 12. To place Vr on the time-domain graph, double click on the graph, then select from Datasets and Equations pull-down menu Equations instead of Problem 1, then select Vr, click Add, and select Time Domain Signal. You should see a graph as shown in Figure 2(b).

5 Dr. Milica Marković Applied Electromagnetics Laboratory page 5 (a) Series RC Circuit in ADS Schematic Diagram (b) Voltages as a function of time Figure 2: Create a circuit diagram and display voltages.

6 Dr. Milica Marković Applied Electromagnetics Laboratory page To plot phasors of voltages, select the icon from the Palette that looks like a target. A window Plot Traces & Attributes opens. Select Vout and vin and add them to the plot. If you want to increase the size of dots representing the voltages, double click on the dot, a Trace Options windows opens. Select larger thickness of the point, for example 3. You should see a graph as shown below in Figure 3(a). To make a plot as shown in Figure 3(b), click on the top dropdown menu: Insert, then select Line. (a) Polar plot display in Ads (b) Polar plot with voltage vectors drawn in. Figure 3: Displaying signals on a polar plot.

Dr. Milica Marković Applied Electromagnetics Laboratory page 7 14. To plot time domain plots as a function of angle in radians or degrees, you have to define angle as ωt.

7 Dr. Milica Marković Applied Electromagnetics Laboratory page To plot time domain plots as a function of angle in radians or degrees, you have to define angle as ωt. Since this is a frequency-domain simulation, we have to define time as t=ts(freq). ts() performs frequency to time transform. Select Equation from the pallete menu, place it on the Data Display. In a window that opens, write equation as defined in Figure 4(a). Now we will replace time with the equation for omega on x-axis of the rectangular plot. Place the rectangular plot on the Data Display, select the voltage you want to plot as a function of angle, and select Time-Domain signal Figure 4(b). Then, select the pull-down menu (an upside down triangle) as shown in figure 5(a) and select Equation, as shown in Figure 5(b), then select omega. When you select OK, new window opens as shown in Figure 5(c). Select Time-Domain Signal and click OK. You should now see the window as shown in Figure 5(d). When you click OK, voltage as a function of angle in radians is displayed, as shown in Figure 5(e). Now you can plot all voltages as shown in Figure You can now repeat the process for angle in degrees, or you can directly change the graph in radians. Click on omega, then multiply omega with the conversion factor 180/π. (a) Define equation for angle. (b) Place the rectangular plot on the Data Display. Figure 4: The first two steps to plot a signal as a function of angle.

(c) Voltage as a function (d) Voltage as a

8 Dr. Milica Marković Applied Electromagnetics Laboratory page 8 (a) Voltage as a function of angle in radians. (b) Voltage as a function of angle in degrees. (c) Voltage as a function of angle in radians. (d) Voltage as a function of angle in degrees. (e) Voltage as a function of angle in degrees. Figure 5: Displaying signals as a function of angle in radians.

9 Dr. Milica Marković Applied Electromagnetics Laboratory page 9 (a) Voltage as a function of angle in radians. (b) Voltage as a function of angle in degrees. Figure 6: Displaying signals as a function of angle in radians and degrees.

10 Dr. Milica Marković Applied Electromagnetics Laboratory page 10 5 Simulation Analysis Q Answer the following questions: 1. Read the magnitude, phase and time delay of the source voltage from the diagrams above. Use Markers to read graphs precisely. Compare with your hand calculations in Section 2. How do they compare? Name all the graphs that you can use to read magnitude, phase and time-delay? 2. Answer the questions above for the voltage on the resistor. 3. Answer the questions above for the voltage on the capacitor. 4. On the phasor diagram, what is the angle between the vector of voltage on the capacitor and resistor? Explain how can you confirm this by reading the graph voltage as a function of angle in degrees. Compare these values with yoru calculations. Do they match? 5. Explain why the voltage magnitudes on capacitor and resistor do not add up. Compare with your calculations. Do they match? 6. Sketch the voltage on the capacitor and resistor as a function of time. What is the total voltage equal to at any time instance? For example, look at the time instance t=0, t=0.5 ns, then calculate the voltages on resistor, capacitor and input voltage. What can you conclude? Compare these values with your calculations. Do they match? 6 Series RL Circuit In this section, you will check whether you are able to repeat the simulations above for a different circuit. Simulate in ADS the currents and voltages in a series RL circuit, R=1kΩ, L=200 nh. Q Using markers measure the magnitude of the voltage on the resistor and inductor. Add them up. Do they add up to the voltage of the source? Why or why not? When do the voltages add up? 7 Design a Parallel RL Circuit Simulate the currents and voltages in a parallel RL circuit. Pick R and L values in such a way that all currents have the magnitudes of about 0.5 of the source current. Q Simulate and record the magnitude of the current through the resistor and inductor. Add them up. Do they add up to the current of the source? Why or why not. When do you see that the currents add up to the source current? 8 Hand Calculations Solve the problems 6 and 7 on paper using phasors. Look at the KVL equation for the voltage.

11 Dr. Milica Marković Applied Electromagnetics Laboratory page 11 Q The voltage on the resistor and inductor (or capacitor) should add up to the voltage of the source. What is the issue in addition of these two voltages/currents? Assuming you measured 1V for the voltage across the capacitor and 2V for the voltage across the resistor, is the source voltage then 3V? Why or why not. Draw a vector diagram for the voltage or current to prove your point. Discuss time and frequency domains. 9 What is a linear circuit? Assume that a sinusoidal source is driving the linear circuit. Q Without knowing the topology of the circuit, what can you state about all currents and voltages in this linear circuit? Explain what is a definition of a linear circuit?

RC, RL, and LCR Circuits

RC, RL, and LCR Circuits EK307 Lab Note: This is a two week lab. Most students complete part A in week one and part B in week two. Introduction: Inductors and capacitors are energy storage devices. They