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Virtual Lab Program: Chapter 3

FM Waveforms PathWave System Design (SystemVue)

Introduction Keysight Technologies’ virtual laboratory program (VLP) utilizes PathWave design software to help students develop an understanding of:

o the operation of test and measurement (T&M) equipment; o the measurement and analysis of different electrical quantities; and o the selection of T&M equipment

Note to Instructors Keysight Technologies’ VLPs are provided as a set of resources to support instructors. Each VLP is comprised of three essential components:

o laboratory script(s); o SystemVue workbench(es); and, where needed o configuration file(s) for virtual instruments

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The first component of the VLP, the script (such as this), is self-contained, thus allowing instructors to use it fully (as it stands) or partially (together with other material). Each script is tagged with a set of identifiers that include references to the: level of difficulty; experiment number; stimulus number; objective; and virtual instrument to be used. A summary of these identifiers with cross-references to the scripts and workbenches is given in the instructors’ overview at the end of this section.

The second component of the VLP is a SystemVue workbench. This can be thought of as a signal generator and is arranged in such a way that the student can select predefined signal characteristics using a simple top-level interface. Beneath this, SystemVue code blocks interpret the students’ input selection and correspondingly configure the parameters of schematic components. Upon execution of the simulation, SystemVue generates the required signal which can then analyzed and visualized in the third component of the VLP, the virtual instrument, and/or in SystemVue. In addition to the pre-configured settings, the instructor may adapt the parameter settings in order to provide alternative configurations. The instructor may also choose to adapt the supplied SystemVue workbenches according to their specific requirements and teaching objectives.

Software Versions The workspaces included in this VLP were developed in Keysight PathWave System Design (SystemVue) 2021 and were tested using Keysight PathWave Vector Signal Analysis (89600 VSA) Version 2020. These software packages are recommended as the basis for the VLP.

Instructors’ Overview The SystemVue workspace “FM waveforms.wsv”—summarized in the table below—has been designed to provide the instructor with a total of 4 x 2 x 8 x 4 x 4 = 1024 experiments.

Parameter Index #1 Index #2 Index #3 Index #4 Index #5 Index #6 Index #7 Index #8

Modulating waveforms sinewave triangular square DC - - - -

Modulating inversions 0 1 - - - - - -

Modulation index 0 0.1 0.5 1 5 10 50 100

Modulating signal frequencies [Hz] 10 50 100 200 - - - -

Modulating signal amplitudes [V] 0.0 0.1 1.0 10 - - - -

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Downloading VLP Packages There are several different VLP packages available for download. To download the various packages, go to www.Keysight.com/find/PathWave-System-Design-Virtual-Labs. This landing page contains links to the PDF lab scripts, workspaces, and configuration files.

Technical and Sales Support PathWave System Design (SystemVue) Technical Support

PathWave System Design (SystemVue) Sales Support

Background for Students In this set of exercises, you will create a variety of signals and visualize them in both the time and frequency domain using Keysight PathWave System Design (SystemVue). A common SystemVue workspace is used for all of the exercises. This is conceptually similar to a laboratory workbench comprised of a signal generator (the source) and signal analyzers (the sinks). The latter includes a time domain data sink which can be thought of as an oscilloscope and a frequency domain sink which is similar to a spectrum analyzer.

To begin with the exercises, it is assumed that you have a PC or laptop on which the suitable software has been installed and that you have access to the relevant workspace which forms part of the VLP.

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Prerequisites In order to work through Keysight Technologies’ VLP (either fully or partly), a basic level of competence with SystemVue is required. This should include the ability to:

o open a workspace; o navigate through the workspace tree and view its components; o execute simulations; o adjust workspace parameter settings (mainly by using pre-configured sliders); and

visualize simulation results.

Students who are unfamiliar with any of the above aspects of SystemVue should take advantage of the on-line resources provided in Table 1—a Keysight account might be required.

Table 1. An overview of on-line training resources.

Resource Description On-line link

SystemVue video library available

A collection of SystemVue instructional videos presented by Keysight Technologies

https://bit.ly/3cck4vW

Learn SystemVue in 5 mins

A collection of SystemVue instructional videos presented by Anurag Bhargava Tutorial-1: What is Pathwave System Design (SystemVue) Tutorial-2: Understanding SystemVue Design Environment Tutorial-3: Getting Started with Data Flow Simulation in SystemVue Tutorial-4: Working with Graphs in SystemVue Tutorial-8: Vector Modulation Analysis using VSA in SystemVue

Blog: http://abhargava.wordpress.com T1: https://youtu.be/UHh_0RVGI58 T2: https://youtu.be/oRy9suFdB7c T3: https://youtu.be/ZWtJ84oLhF0 T4: https://youtu.be/S0MhwflXM3A T5: https://youtu.be/5cDdl9ohJnM

SystemVue Essentials & Intro to Phased Array Beam Forming and 5GNR Library

This workshop is intended to get you up to speed on SystemVue essentials. After learning the basics, this workshop covers Phased Array, Beamforming, and 5G NR integration. Data analysis in PathWave VSA is also covered.

Keysight Knowledge Center

Vector Signal Analysis Basics

This application note serves as a primer on performing vector signal analysis using the 89600 VSA software to measure and manipulate complex data.

Keysight website (5990-7451)

Digital Modulation in Communication Systems

Understand concepts of digital modulation and learn new digital modulation techniques in communication systems to make informed decisions to optimize your systems.

Keysight website (5965-7160)

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Spectrum Analysis Basics (App Note 150)

Spectrum Analysis Basics teaches the fundamentals of spectrum analyzers and spectrum analysis including the latest advances in spectrum analyzer capabilities.

Keysight website (5952-0292)

Signal Analyzer Fundamentals (What the RF)

This course covers when and how to use different applications and capabilities of signal/spectrum analyzers to make various RF measurements.

Keysight website

Topics Covered In this VLP, you will experiment with fundamental signal properties including: amplitude; offset; inversion; and frequency. You will investigate sinewaves, square waves and triangular waves in both the time domain and the frequency domain.

Wireless communication and modulation In simple terms, it could be said that radio frequency, microwave, millimeter-wave and sub-millimeter-wave communication systems all rely on the following fundamental principles:

• an electromagnetic (EM) carrier wave—in essence a sinewave—can transfer energy from a transmitter to a receiver without using wires (hence the term “wireless”); and

• a modulated carrier can be used to transfer information. In other words, by continually altering or modulating the characteristics of a sinusoid, we can use it to transfer information wirelessly.

The purpose of a wireless communication system is, however, not to transfer high frequency energy from a transmitter to a receiver: it is instead to transfer information; the carrier provides the means to do so using high frequency EM waves. These waves (unlike the relatively low frequency information signals) have the ability to travel or propagate through space without cables or wires. All that is needed to form a wireless communication link is an RF transmitter and an RF receiver, each connected to a suitable antenna. The transmitter is an electronic device that places information onto a carrier using a technique called modulation and the receiver is an electronic device that retrieves information form a carrier using demodulation. As the invention of wireless communication dates back to the late nineteenth century, it should be no surprise that many different types of modulation have been developed during this time and indeed continue to be developed to this day.

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Frequency modulation In this VL, we shall investigate frequency modulation. This form of analog modulation has, amongst other things, been used for broadcasting radio services for more than a century and is still in use today on the very high frequency (VHF) band of your radio. In contrast to AM radio stations that are broadcast on the medium wave bands, FM stations provide superior greater audio quality (typically in stereo) due to their relatively greater bandwidth. They are also less affected by the ionospheric propagation effects that can use medium wave (AM) stations to slowly wow and flutter, especially in the evening and at a night.

The process of varying the frequency of a carrier wave in proportion to a modulating signal, is known as frequency modulation (FM). The carrier amplitude of an FM wave is kept constant during modulation and so the power associated with an FM wave is constant. During modulation, the carrier frequency increases when the modulating voltage increases positively and it decreases, when the modulating voltage becomes negative. This is illustrated in Figures, Figure 1 - Figure 3.

Figure 1. The carrier with amplitude cA

Figure 2. The modulating signal with amplitude mA

Vc

0

V

t

0

VVm

t

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Figure 3. The instantaneous frequency of modulated signal (shown in red) is a function of the modulating signal (shown in blue).

To obtain an expression for an FM wave, let the instantaneous carrier wave be represented by

sin sin 2c c i c iv V t V f tω π= =

(1)

where if is the instantaneous frequency. For a positive increase in frequency, we have

sini c c mf f f tω= + ∆ (2)

where cf is the carrier frequency and cf∆ is the frequency deviation of the carrier wave, due to the

modulating signal of frequency mf .

If the instantaneous carrier phase is iϕ then:

1 sin

2i

i c c md f f f tdtϕ ω

π= = + ∆ (3)

Or, rearranging for the rate of change of phase:

2 2 sinii c c m

d f f tdtϕ π ω π ω= = + ∆

(4)

The instantaneous phase is obtained by integration and the correct choice of phase angle:

cosci c m

m

ft tf

ϕ ω ω∆= −

(5)

cosi c f mt m tϕ ω ω= −

(6)

Where /f c mm f f= ∆ is called the modulation factor or modulation index.

Since sinc c iv V ϕ= we obtain

sin cosc c c f mv V t m tω ω = − (7)

Vc

0

V

t

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FM spectrum

Expanding eqn. (7) cv yields

( ) ( )sin cos cos cos sin cosc c c f m c f mv V t m t t m tω ω ω ω = ⋅ − ⋅ (8)

Now

( ) ( ) ( ) ( )0 2 4cos cos 2 cos 2 2 cos 4f m f f m f mm t J m J m t J m tω ω ω= − +

(9)

Thus

( ) ( ) ( )1 3sin cos 2 cos 2 cos3f m f m f mm t J m t J m tω ω ω= − +

(10)

The coefficients ( )n fJ m are Bessel functions of the first kind and order n . They are generally tabulated

and a typical plot is shown in Figure 4.

Figure 3. Bessel functions of the first kind for mf in [0, 2].

Substituting into cv yields the results

( ) ( ) ( ) ( ){ }( ) ( ) ( ){ }

0 1

2

sin cos cos

sin 2 sin 2

f c f c m c m

c

f c m c m

J m t J m tv Vc

J m t t

ω ω ω ω ω

ω ω ω ω

− + + − = − + + − +

(11)

0 2 4 6 8 10 12m

f

-0.5

0

0.5

1

Jn

(mf)

J0

J1

J2

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Which reveals an infinite set of sidebands whose amplitudes are determined by the Bessel function

( ) ( )0 1,f fJ m J m etcetera. Typical plots for 0.2fm = and 5.0fm = are shown in the FIGURE.

Figure 4. An example of an FM spectrum in which the modulation factor is set to a value of 0.2.

Figure 5. An example of an FM spectrum in which the modulation is set to a value of 5.0.

Figures Figure 5 and Figure 6 show that when fm is small, there are few sideband frequencies of large

amplitude and when fm is large, there are many sideband frequencies but with smaller amplitudes.

Hence, in practice, it is only necessary to consider a finite number of significant sideband components whose amplitudes are greater than about 4% of the unmodulated carrier.

mf = 0.2

fc f-f

Ampl

itude

mf = 5.0

fc f-f

Ampl

itude

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Phasor representation

A carrier wave of constant frequency cf can be represented as a rotating phasor OA with constant

angular velocity we as shown in Figure 7. If its frequency is slightly increased or decreased, the phasor

would rotate slightly faster or slower than cω . Hence, relative to cω , the phasor OA would advance to

position OB or be retarded to position OC . This amounts to varying the angle θ and so FM is a form of angle modulation and the phasor OA traces out the arc BAC .

Figure 7. Phasor representation

Overview Level 2 Experiment reference number 03 Stimulus reference number 001-1024 Objective number 2 (FM waveforms, simulation and analysis) Instrument SystemVue

CB

ωc

A

θ

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Learning Objective In this Virtual Laboratory (VL), students will use Keysight PathWave System Design (SystemVue) electronic system-level design software to explore and measure signals. This VL will assist students in their understanding of signal analysis with the following learning objective(s):

o Observe a signal in the time domain and identify its: amplitude; peak voltage; peak-to-peak voltage; DC offset voltage; and period. Calculate the frequency from the signal’s period.

o Observe a signal in the frequency domain and identify its amplitude and frequency and its DC offset if present.

o Observe a signal in the frequency domain and identify its carrier and its sidebands and their relative amplitudes.

Student Outcomes Upon successful completion of this VL exercise, students will:

o Be familiar with the principle of the VLP. o Understand how to execute a SystemVue simulation, change parameter settings and

collect data. o Analyze and measure signals in the time and frequency domains using SystemVue. o Interpret spectral plots. o Understand the basics of frequency modulation and identify how signal and modulation

parameters affect the resulting waveforms in both the time and frequency domains.

Procedure The following steps will help you through the procedure needed to complete a successful simulation and to then visualize and analyze the resulting simulation data. In this VL, you will create simple waveforms, adjust the values of certain parameters that describe the waveforms and produce graphs or plots of the waveforms in both the time and frequency domains.

Step 1: Starting SytemVue and opening the workspace 1. Start SystemVue on your computer using any of the following methods:

a. From the Windows start menu navigate to SystemVue 2021 SystemVue 2021.

b. Tap the Windows key and then start typing “Syst…” until SystemVue appears. Select it with the mouse or cursor and press enter; or

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c. Double click on the desktop icon which was placed there during the installation of SystemVue (see Figure 8)

Figure 8. The SystemVue 2021 icon is normally placed on the desktop when the software is installed.

2. After SystemVue has loaded, you will probably be greeted with a “Getting Started with SystemVue” screen, similar to that shown in Figure 9.

Figure 9. The "Getting Started with SystemVue" screen normally appears just after the program is started.

3. In the top panel, click on More Workspaces and using the file explorer, navigate your way to the workspace “FM waveforms.wsv”. This workspace (and perhaps others too) might have already been installed on the machine you are using or on a network drive to which you have access. It is recommended that you save a local copy of the workspace and use that version to work with. This will allow you to revert to the original version with its default settings should the need arise.

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Step 2: Understanding the SystemVue window 1. After you have successfully opened the workspace, your screen should be similar to that shown in

Figure 10.

Figure 10. The default view of the “FM Waveforms” workspace in SystemVue.

2. The default view of the FM Waveforms workspace comprises a number of panels or windows. These are listed below together with links to the relevant parts of the user manual:

a) The workspace tree – see: Home > Users Guide > Environment > Design Environment > Workspace Tree SystemVue 2021: qthelp://systemvue.2021/doc/users/Workspace_Tree.html

b) The design – see: Home > Users Guide > Using PathWave System Design > Designs SystemVue 2021: qthelp://systemvue.2021/doc/users/Designs.html

c) A graph (for time domain analysis) – see: Home > Users Guide > Using PathWave System Design (SystemVue) > Graphs SystemVue 2021: qthelp://systemvue.2021/doc/users/Graphs.html

d) A graph (for frequency domain analysis) – see: Home > Users Guide > Using PathWave System Design (SystemVue) > Graphs SystemVue 2021: qthelp://systemvue.2021/doc/users/Graphs.html

e) The tune window – see: Home > Users Guide > Environment > Design Environment > Tune Window SystemVue 2021: qthelp://systemvue.2021/doc/users/Tune_Window.html

b

a

d

e

c

f g h

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f) The autorecalc window– see: Home > Users Guide > Environment > Design Environment > Tune Window SystemVue 2021: qthelp://systemvue.2021/doc/users/Tune_Window.html

g) The error, messages and status window – see: Home > Users Guide > Environment > Design Environment > Error Log SystemVue 2021: qthelp://systemvue.2021/doc/users/Error_Log.html

h) The command prompt – see: Home > Users Guide > Environment > Design Environment > Command Prompt SystemVue 2021: qthelp://systemvue.2021/doc/users/Command_Prompt.html

3. Referring to list item ‘b’ above, the design window of the Basic Waveforms looks like that shown in Figure 11.

Figure 11. The “FM waveforms” design window showing source, sink and waveform settings.

a b

c

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4. The design window shows an apparently very simple schematic diagram which has been arranged into three main areas:

a) A signal source which is configured using predefined parameter values selectable thru the use of sliders. In this step and the next, it is recommended to leave the sliders set to their default positions. The source parameters are grouped into five sets:

i. Waveform_Selection – this slider allows the student to select one of the following waveforms: sinewave (1); triangular wave (2); square wave (3); and DC (4).

ii. Inversion_Selection – this slider allows the student to leave the waveforms non-inverted (0) or inverted (1).

iii. ModulationFrequency_Selection – the student can set the frequency of the modulating signal from four defined values.

iv. ModulationIndex_Selection – the student can set the modulation index from eight defined values.

v. ModulationAmplitude_Selection – this allows the student to select the amplitude of the modulating signal. Four settings are predefined.

b) An area showing three different sinks. These are used in SystemVue to collect data during a data flow simulation. In this step and the next, it is recommended to leave the sliders set to their default positions. The sinks shown are:

i. TimeSink, this is used to visualize and analyze the signal in the time domain. By default, the sink is activated (1). It can be controlled using the slider useTimeSink – see: Home > Part Catalog > Algorithm Design Library > Sinks Category > Sink Part > Sink (Data Sink) SystemVue 2021: qthelp://systemvue.2021/doc/algorithm/Sink.html

ii. SpectrumSink, this is used to visualize and analyze the signal in the frequency domain. By default, the sink is activated (1). It can be controlled using the slider useSpectrumSink – see: Home > Part Catalog > Algorithm Design Library > Sinks Category > SpectrumAnalyzer Part SystemVue 2021: qthelp://systemvue.2021/doc/algorithm/SpectrumAnalyzer_Part.html

c) An area that presents a textual summary of the parameter settings used for: the modulating signal showing the type of waveform, whether or not it is inverted, its frequency and its amplitude; the modulation index; and the amplitude of the carrier.

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Step 3: Executing the simulation with default parameter settings 1. Using the default settings for both the source parameter values and the sink activation controls (see

Figure 11), execute the simulation by using anyone of the following methods:

a) Click on the green Run Analyses arrow shown below:

Figure 12. A closeup view of the menu bar and main toolbar showing the green Run Analyses button.

b) On the menu bar, go to Action -> Run All Out-of-Date Analyses and Sweeps; or

c) Press F5 on your keyboard.

2. A status display window similar to that shown below will appear very briefly on your screen. This tells you that the data flow simulation is running. Due to the speed with which SystemVue completes the simulation, this may only be visible for a couple of seconds.

Figure 13. The SystemVue data flow simulation status window appears during the execution of a simulation.

3. A successful simulation will result in a status display window which is free of errors and warnings as shown in Figure 14.

Figure 6. A successful SystemVue simulation results in an error- and warning-free status window.

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Step 4: Visualize and analyze the results 1. The Basic Waveforms workspace includes two graph windows. These were shown as ‘c’ and ‘d’ in

Figure 10 before the simulation was executed and were thus labelled “No Data”.

2. Now that the system has simulated successfully, the two graph windows should resemble Figure 15 for the time domain and Figure 16 for the frequency domain. In the time domain, carefully zoom in and observe that the period of the modulated signal changes due to the frequency modulation and in accordance with the modulating signal.

Figure 15. A SystemVue graph window showing the instantaneous signal voltage plotted against time [ms]. The left Y-axis shows the modulating signal while the right Y-axis shows the modulated carrier.

Figure 16. A SystemVue graph window showing the signal waveform in the frequency domain in which the signal power (developed in a 50 ohm resistor) [dBm] is plotted against frequency [kHz].

Frequency (KHz)

Mod

ulat

ed c

arrie

r (dB

m)

-80-70

-60-50-40

-30-20-10

010

20

Frequency (KHz)0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Power Spectrum

Modulated carrier

Time (s)

Mod

ulat

ing

sign

al [V

]

-1-0.8-0.6-0.4-0.2

00.2

0.40.60.8

1

Modulated signal [V

]

-1-0.8-0.6-0.4-0.200.2

0.40.60.81

Time (s)0 0.025 0.05 0.075 0.1 0.125 0.15 0.175 0.2 0.225 0.25

Waveform

Modulated signal Modulating signal

0.051 s, -0.19

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3. SystemVue graphs enable you to explore and examine your data in many different ways. The user manual provides detailed instructions that include:

a) An overview – see: Home > Users Guide > Using PathWave System Design (SystemVue) > Graphs SystemVue 2021: qthelp://systemvue.2021/doc/users/Graphs.html

b) Zooming a graph – see: Home > Users Guide > Using PathWave System Design (SystemVue) > Graphs > Zooming Graphs SystemVue 2021: qthelp://systemvue.2021/doc/users/Zooming_Graphs.html

c) Using markers on graphs – see: Home > Users Guide > Using PathWave System Design (SystemVue) > Graphs > Using Markers on Graphs SystemVue 2021: qthelp://systemvue.2021/doc/users/Using_Markers_on_Graphs.html

d) Annotate a graph – see: Home > Users Guide > Using PathWave System Design (SystemVue) > Graphs > Annotating Graphs SystemVue 2021: qthelp://systemvue.2021/doc/users/Annotating_Graphs.html

e) Copying and saving a graph – see: Home > Users Guide > Using PathWave System Design (SystemVue) > Graphs > Copying and Saving Graphs SystemVue 2021: qthelp://systemvue.2021/doc/users/Creating_Graphs.html#CreatingGraphs-CopyingandSavingGraphs

f) Creating a graph – see: Home > Users Guide > Using PathWave System Design (SystemVue) > Graphs > Creating Graphs SystemVue 2021: qthelp://systemvue.2021/doc/users/Creating_Graphs.html

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Step 5: Explore parameter settings 1. Now that you have completed your first simulation and have viewed and analyzed the results

obtained, you should be ready to investigate what happens when other modulation parameter settings are used.

2. Your instructor might provide you with a list of configuration settings to explore. If not, you are encouraged to make small changes to the settings, re-simulate and observe the changes. For example, now that you have analyzed the default settings, you might like to visualize what happens to the carrier when you:

a) Change the modulation index; b) Change the frequency of the modulating signal; c) Change the type of modulating waveform; d) Turn inversion on and off; and e) Adjust the amplitude of the carrier.

3. Referring to the section “Topics covered”, you should make sure that you understand the relationship of ‘a’ to ‘e’ above and their effect on the modulated carrier. In addition, you should also be familiar with:

a) Measuring signal quantities from plots and calculating the frequency of a periodic signal from an estimation of its period in the time domain.

b) Using graph markers. c) The relationship between signal amplitude and signal power. d) Decibels and the unit dBm. e) The fundamentals of frequency modulation. f) The terms modulation index and frequency deviation. g) A basic understanding of the pros and cons of FM when compared to AM.

Review Congratulations, you have now completed your first virtual laboratory and have:

o Observed a signal in the time domain and identified its: amplitude; peak voltage; peak-to-peak voltage; period and from this, calculated its frequency.

o Observed a signal in the frequency domain and studied the amplitude and frequency of an amplitude modulated signal.

o Become familiar with the principle of the VLP; o Understood how to execute a SystemVue simulation, change parameter settings and

collect data; o Analyzed and measured signals in the time and frequency domains using SystemVue; o Understood the principles of amplitude modulation and become familiar with the

modulation index and how it affects the modulated carrier.

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Learn more at: www.keysight.com For more information on Keysight Technologies’ products, applications or services, please contact your local Keysight office. The complete list is available at: www.keysight.com/find/contactus

Suggested Exercises In addition to the tasks assigned to you by your instructor, here are some exercises that you might like to try:

1. Using a sinusoidal waveform, set the modulation index to 0 and any modulation amplitude setting:

a) observe the signal in the frequency domain and explain the results;

b) change the modulation frequency setting and explain the results;

c) change the waveform setting and explain the results;

d) change the modulation amplitude setting and explain the results;

2. Using a sinusoidal waveform, increase the modulation index to 0.5:

a) repeat 1a (remember to explain the results);

b) repeat 1b (remember to explain the results);

c) repeat 1c (remember to explain the results);

d) repeat 1d (remember to explain the results);

3. Using a sinusoidal waveform, experiment with the setting of the modulation index according to 2a – 2b and understand explain the relationship between the different parameters.

4. Using any non-sinusoidal AC waveform, repeat exercises 1 – 3 and describe your observations.

5. Using a DC waveform, determine the relationship between the modulation frequency, the modulation amplitude and the modulation index (refer to the introductory notes).

Acknowledgement Keysight would like to thank Dr. Paul Leather at Technische Hochschule Rosenheim for his help in developing these lab guides.