experiment on amplitude modulation

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Lab 5: Amplitude Modulation and Demodulation

This lab introduces students to communications theory with amplitude modulation and demodulation. Students will explore the mathematical theory behind amplitude modulation and use the Analog Discovery Studio to visualize the effects of amplitude modulation in the time and frequency domains. Then, students will use LabVIEW to program an AM demodulator and use it to explore and visualize the effects of the modulation coefficient on the quality of the demodulated signal and the effects of different parameters (such as windowing and averaging) on the Fast Fourier Transform (FFT). Advanced students can challenge themselves to build a system to send data between two Analog Discovery Studios or to build an analog AM demodulator.

Introduction

In an amplitude modulation (AM) communications system, a device is used to convert data into an electrical signal, for example, a microphone is used to convert audio into an electrical signal. This signal, known as the message or baseband signal, is then used to modify (modulate) the amplitude of another signal, known as the carrier signal.

Learning Objectives

In this section, students will:

• Investigate classical amplitude modulation theory in time and frequency domains.
• Learn about the basic properties of FFTs.
• See how modulation index affects AM signals in time and frequency domains.
• Use LabVIEW to acquire and demodulate an AM signal.
• See how modulation index affects am signals in time and frequency domains.

The following equipment is required for this experiment:

• LabVIEW Community
• Digilent WaveForms VIs

Amplitude Modulation

Amplitude modulation theory.

The image to the right shows how the message modulates the carrier signal to produce the AM signal. Notice that the AM signal’s amplitude increases or decreases as the message signal increases or decreases – this is where the term amplitude modulation comes from. Even though we only need the amplitude to change, looking at the AM signal we can see that by modulating the amplitude, we have added frequency components to the carrier signal. In order to analyze these components, we will use the Fast Fourier Transform or FFT for short.

As the name suggests, the FFT allows us to apply a Fourier transform on the signal and convert the signal from its time-domain representation to its frequency domain representation. By converting to the frequency domain, we can see what frequencies have been added to the signal due to the modulation.

In this lab, we will explore amplitude modulation in the time and frequency domain, and see how the amplitudes of the message and carrier signals affect the modulated signal.

In telecommunications theory, amplitude modulation in its simplest form can be represented as a few signals. The first signal is the carrier signal, $c(t)$. This signal can be represented by the equation: $c(t)=Asin(2{\pi}f_ct)$, where $f_c$ is the frequency and $A$ is the amplitude of the carrier signal. For this lab, we will let $A=1$.

The second signal is the message signal, $m(t)$. This is represented by the equation: $m(t)=Mcos(2{\pi}f_mt+{\phi})$, where $f_m$ is the frequency and $M$ is the amplitude of the message signal. The message signal can also be referred to as the modulation signal. For this lab, we will assume that $M≤1$. This allows us to ensure that $(1+m(t))$ is always positive and prevents overmodulation of the signal.

From these two signals, an amplitude modulated signal, $y(t)$, can be defined as follows: $y(t)=[1+m(t)]c(t)=[1+Mcos(2{\pi}f_mt+{\phi})]Asin(2{\pi}f_ct)$.

Using trigonometric identities, $y(t)$ can be expanded in a sum of three sine waves: $y(t)=Asin(2{\pi}f_ct)+\frac{1}{2}Amsin[2{\pi}(f_c+f_m)t+{\phi}]+\frac{1}{2}Amsin[2{\pi}(f_c-f_m)t+{\phi}]$

The frequencies of the additional sine waves produced by amplitude modulation are called the upper (for the higher frequency) and lower (for the lower frequency) sidebands. The difference between the upper sideband and the lower sideband is referred to as the bandwidth of the AM signal.

• How do the frequencies of the three sine waves compare to the original message and carrier signal frequencies?
• If we took an FFT of this signal, what would we ideally expect to see?
• Given $f_c=100kHz$ and $f_m=1kHz$, find the upper sideband, the lower sideband, and the bandwidth of the AM signal.

Analysis with WaveForms

Now that we have an idea of what to expect given our theoretical signals, we will go ahead and experiment with amplitude modulation using the Analog Discovery Studio. Follow the steps below to output and read back an analog modulated signal in WaveForms.

Connect the function generator's W1 channel (yellow wire) to the oscilloscope's Channel 1+ (orange wire) and the function generator's W2 channel (yellow-white wire) to the Channel 2+ of the oscilloscope (blue wire). Connect together the 1- (orange-white wire) and 2- channels (blue-white wire) of the scope, and the grounds of the function generator channels.

Don't forget to turn the Scope Channel 1 and Scope Channel 2 switches towards the MTE headers.

You can download the wiring diagram here: wiring_diagram_scope.zip

Measurements in the Time Domain

Follow the instructions below to set up your instruments in WaveForms and acquire data for this experiment. We will first generate an amplitude modulated signal using the Wavegen and then read this waveform back in with the Scope . For comparison, we will also generate an unmodulated signal and read the waveform back in on the second channel of the Scope .

Launch WaveForms. Open the Scope instrument, enable both channels, and set the trigger to Channel 2. Start the instrument.

Open the Wavegen instrument, enable both channels and set synchronization mode to Synchronized . On the first channel set Modulation mode and uncheck the FM column. For the carrier signal set a sinusoidal signal with a frequency of 100kHz and an amplitude of 1V. For the modulating signal (AM) set a sinusoidal signal with a frequency of 1kHz and a modulation index of 10%.

On Channel 2 set the same parameters as for the modulating signal. Run the instrument. Adjust the Scope Time and Channel settings so that you can see 3–4 periods of the input waveform on Channel 2.

The envelope of an oscillating signal is the smooth curve outlining the signal peaks.

When discussing amplitude modulation, it can be important to talk about the modulation index ($m$) of a signal. The modulation index describes the extent to which a signal is modulated about the carrier and can be expressed with the equation: $m=\frac{M}{A}$, where $M$ is the amplitude of the message signal and $A$ is the amplitude of the carrier signal.

While we can compute the modulation index directly from a known carrier and message signal, it is more common to compute the modulation index from measurements taken from using the Scope . Using this method, the modulation index can be defined as: $m=\frac{V_{max}-V_{min}}{V_{max}+V_{min}}$, where $V_{max}$ is the maximum peak to peak value of the modulated signal and $V_{min}$ is the minimum peak to peak value of the modulated signal.

• The amplitude of the AM signal is given as a percentage of the carrier. What is the amplitude in volts of the AM signal as configured?
• Describe the upper envelope of the AM signal. How do the upper envelope’s shape and amplitude compare to the message signal? The message signal can be seen as the AM signal in the Wavegen display window.
• What is the theoretical modulation index of the modulated signal as configured?
• Find $V_{max}$, $V_{min}$, and the observed value of $m$. How does the observed value compare to the theoretical value calculated before?
• Go to the Wavegen instrument panel. Slowly increase the AM index value while observing changes on the Scope . How does the modulated signal change as the index approaches 100%? As it goes over 100%?

Measurements in the Frequency Domain

Now that we have looked at the modulated signal in the time domain, we will explore how different characteristics of the message and carrier signal can affect the modulated signal in the frequency domain. Follow the steps below to perform an FFT analysis using the Spectrum Analyzer (Spectrum).

In WaveForms, disable the second channel of the Wavegen instrument and close the Scope . Set the modulation index of the AM signal to 50% and the synchronization mode of the instrument to No Synchronization . Start generating the signal. Open and run the Spectrum instrument. You can disable the second channel.

Remember, the FFT allows us to transform a signal from its time-domain representation (where the independent variable represents time) to its frequency-domain representation (where the independent variable represents frequency).

Looking at the FFT, we can notice a few things. First, we notice that 1MHz is much higher than what we need to show for our modulated signal. Zoom into the Spectrum by making the following changes to the Spectrum configuration: set the start frequency to 70kHz and the stop frequency to 130kHz.

Now that we have zoomed into our signal area of interest, we can stabilize the image by changing the Trace configurations. Currently, Trace 1 is showing an FFT trace every time we take a sample. This results in an image that bounces a lot on the screen. In order to minimize the bounce, we can instead use an average to eliminate some of the noise. With an average trace, the trace is averaged across several samples, giving us a more stable picture. Set the Trace Type to use Exponential dB Average . Now that we have a better picture of what is going on, let us more closely examine the FFT.

As mentioned earlier, an FFT allows us to apply the Fourier transform. Another way of saying this is that the FFT is a digital implementation of the Fourier transform. Thus, the FFT does not yield a continuous spectrum of frequencies. Instead, the FFT returns a discrete spectrum, in which the frequency content of the signal is separated into a finite number of frequency lines, or bins. The number of bins in the FFT is half the number of samples acquired. $bins=\frac{N}{2}$, where $N$ is the number of samples acquired. Aside from the number of bins, the size of each bin is also important when considering FFTs. The bin size, also called the resolution of the FFT, gives us the smallest detectable change in frequency. For example, if our FFT resolution is 1.5kHz, we would not be able to detect the difference between a frequency component that is 1.1kHz and one that is 1.2kHz. Similarly, we would not be able to detect the difference between a frequency component that is 112.1kHz and one that is 113kHz. We define the FFT resolution using the expression below: $df=\frac{1}{T}$, where $df$ is the FFT resolution and $T$ is the total acquisition time for one period of data. $T$ can be defined as follows: $T=\frac{N}{f_s}$, where $N$ is the number of samples acquired and $f_s$ is the sampling rate on the FFT. From there it follows that: $df=\frac{f_s}{N}$.

Lastly, if we multiply the number of bins by the resolution, we can find the bandwidth of the FFT. The bandwidth of the FFT gives us the maximum frequency we can resolve. Using the equation for $df$ and $bins$ the formula for the bandwidth can be given as: $BW=df*bins=\frac{f_s}{N}\frac{N}{2}=\frac{f_s}{2}$.

Look back at the Spectrum display window. Click on the green arrow to see the advanced configuration options for the Spectrum .

Looking at the advanced configuration options, we see that the maximum number of bins we can have is 4097. We can also see that the number of samples acquired (given by Samples) is set and there is no way to change that. Thus, to increase our frequency resolution, we need to lower the sampling rate. Unfortunately, the Spectrum does not expose the sampling rate used to take the FFT. Instead, the sampling rate is automatically chosen based on the range specified by Freq. Range .

Aside from showing the frequency content of a signal, the FFT also gives us a glimpse into the relative power in each frequency. In this case, we can say that the carrier signal contains most of the power in an AM signal while the sidebands contain relatively equal amounts of power.

• Using the cursors, find the frequency where the largest spike occurs. What frequency does this correspond to in our modulated signal? How does the FFT compare to what we expected to see? Is it possible to identify the upper and lower sidebands?
• Observing this equation for $df$, what are two ways we can increase the resolution of the FFT?
• Observing the equation for $BW$, how can you increase the bandwidth of the FFT?
• The BINs value gives us the number of bins in our FFT. Change the BINs value to 4097. What is the resolution of the FFT as configured? What is the bandwidth of the FFT?
• How will the resolution of the FFT change if we lowered the number of bins?
• Lower the frequency range to 94kHz-106kHz. What is the resolution of the FFT now? What is the new bandwidth of the FFT?
• Using the cursors, what is the value of the lower and upper sidebands? How do they compare in amplitude to the carrier frequency?
• Go back to the Wavegen and slowly increase the AM Index value while observing the Spectrum display. How does the modulation index affect the relative power of the sidebands and the carrier frequencies? What happens when the modulation index reaches 200%?

Amplitude Demodulation

Amplitude demodulation theory.

In the first section of this lab, we used a 1kHz sine wave to amplitude modulate a 100kHz carrier. Going through the lab, we saw a key characteristic of an AM signal – the upper envelope of an AM signal is the same shape as the message as long as the modulation index is less than or equal to 1. Therefore, one way to recover the message signal from the modulated carrier (a process called demodulation), is to isolate just the envelope from the rest of the modulated signal.

This form of AM demodulation is called envelope detection and at its simplest involves two steps. The first step rectifies the modulated signal so that only the positive half remains. The second step filters out the high-frequency components of the carrier and leaves us the recovered message.

Traditionally, envelope detection was accomplished using analog components to perform each step. For example, the full-wave rectifier built in Lab 4: Full-Wave Rectifiers and the low-pass filters built in Lab 2: Active and Passive Filters would be used to rectify and filter the signal respectively. With the advent of better software, we can now accomplish the same thing digitally. In this section of the lab, we will use LabVIEW to acquire an AM signal and then demodulate it using envelope detection. We will also analyze the demodulated signal in both the time and frequency domain.

Analysis with LabVIEW

As mentioned earlier, in this section of the lab, we will be using LabVIEW to digitally demodulate an AM signal by implementing envelope detection. By taking advantage of LabVIEW’s ability to visualize data, we can see how each step in the envelope detection process changes the AM signal into the final demodulated signal.

In order to demodulate the signal, we will first acquire the signal using the Analog Discovery Studio, we will then use software to rectify the signal to receive only the positive half of the signal, finally, we will implement a digital filter to remove any of the high-frequency components and recover the original message. Along the way, we will look at the FFT of the rectified signal and the demodulated signal and compare them against what we saw in the first section of this lab.

This section of the lab will assume a working knowledge of the LabVIEW environment and basic programming conventions. For help with getting started in LabVIEW, including installation of the Digilent WaveForms VIs, please view the resources available here: Getting Started with LabVIEW and a Digilent Discovery Device .

Note: Before testing or running your LabVIEW code, make sure that you exit WaveForms. The Digilent WaveForms VIs will throw an error if Digilent WaveForms is still open when you run your code.

Note: If you don't know what a VI does, you can check the Context Help by pressing Ctrl+H, then highlighting the respective VI.

Design a VI in LabVIEW that will demodulate an AM signal using envelope detection. You can build your own VI, following the steps below, or you can download the VI used in this guide from here: am.zip

The Front Panel shows eight graphs. The first two show the carrier and the modulating signals. Three of the remaining graphs are in the time domain and show the modulated signal, the signal after rectification, and finally the recovered signal. The other three graphs are in the frequency domain and show the frequency content of the modulated signal, the signal after rectification, and the frequency content of the recovered signal. The Front Panel also contains controls that we can use to control the parameters of the carrier and of the modulating signals as well as the cut-off frequency of the low-pass filter and the range of the frequency domain graphs.

The Block Diagram contains, except the control and indicator elements, the blocks needed for signal generation, controlling the Wavegen , controlling the Scope , and data processing.

General Operation

This VI should generate the carrier and modulating signals required by the user, then output the modulated signal on the selected Wavegen channel. The selected Scope channel will be used to acquire the modulated signal. The received signal should be displayed, then rectified. The rectified signal should be displayed as well, then filtered with a low-pass filter. After the low-pass filter, the DC component of the resulting signal should be removed before displaying it. The FFT of the received, the rectified, and the resulting signal should be displayed on the required frequency range.

The image to the right presents the general program flow of this VI.

Hardware Setup

For testing the VI, use the same hardware setup as for the Analysis with WaveForms section.

Software Setup

Setup and instrument configuration.

As a first step, the control and indicator elements should be placed by right-clicking on the Front Panel and selecting the required element. In this VI we need three Combo Boxes: one which sets the device type, with the elements “Analog Discovery Studio”, “Analog Discovery 2” and “Analog Discovery”, one which selects the used Scope channel, with the elements “mso/1” and “mso/2” and one which sets the used Wavegen channel, with the elements “fgen/1” and “fgen/2”. A Stop Button should also be placed on the Front Panel, to interrupt the program if needed.

Two Graphs and four Knobs are needed to set the amplitude and the frequency of the carrier, the frequency of the modulating signal and the modulation index, and to display the resulting signals.

The other three Knobs and six Graphs are used to set the frequency range on which the FFTs are displayed, to select the cut-off frequency of the low-pass filter in the demodulator, and to display the modulated signal, the rectified signal, the demodulated signal, and the spectrum of these.

Arrange everything on the Front Panel, then right-click on the y-axis of the time-domain graphs and deselect Autoscale. Set the range of these axes to make the signals visible. Rename the placed elements by double-clicking on their name. Rename the axes of the graphs by double-clicking on them and also set the multiplier of each axis to match with the labeled unit of measurement (for example: set the multiplier to 1e+06 if the labeled unit of measurement is μs).

In the Block diagram, initialize the Scope instrument (MSO), then configure the selected analog channel (mso/1 or mso/2) in DC mode, with 1X probe attenuation, set the vertical offset to 0 and the vertical range to 5V. Enable the channel with a True constant.

Configure the timing of the Scope to sampling mode, with a sampling rate of 12 times of the carrier frequency, the acquisition time of $\frac{1}{message frequency}$ and pretrigger time of 0s.

Initialize the Wavegen instrument (FGEN) and select the desired channel.

In a loop, generate two sinusoidal signals (the carrier and the modulating signal), with the required parameters, then create the modulated signal using the formula presented in the Amplitude Modulation Theory section. You can use the same sampling rate as for the Scope instrument and the number of samples should be equal with the sampling rate multiplied by the acquisition time of the Scope .

The resulting (modulated) signal should be outputted on the selected Wavegen channel.

Measure with the Scope , then extract the data coming from the selected Scope channel from the result. This will be the modulated signal. You can rectify this signal by taking the absolute value of the whole signal. In this case, the absolute value function behaves like an ideal full-wave rectifier. Filter the rectified signal with a low-pass filter. You can even remove the DC component of the filtered signal to eliminate its offset.

To filter the rectified signal, use the Filter express VI. An Express VI is a VI that allows you to configure the parameters of the VI using a dialog box that pops up after the VI is placed. Express VIs are useful for providing multiple configuration options that abstract the required programming from the user.

In this VI, using a third-order, IIR (infinite impulse response) low-pass Butterworth filter is recommended. IIR filters allow us to implement digital filters that resemble traditional analog filters. The Butterworth filter topology maximizes passband flatness. By increasing the filter's order, the attenuation of the stopband increases, but the delay of the output increases as well.

FFT and Exiting the Program

Create property nodes for the x-axis range property of all frequency-domain graphs and change the minimum and maximum values to the ones required by the user.

Use the Spectral Measurement express VI to compute the FFT of the signals.

In this VI, configure the Spectral Measurements to display the magnitude of the output, and average the results (like previously in WaveForms).

From our initial exploration with FFTs, we are familiar with most of these terms. One thing that might be new is the idea of windows in the FFT. To understand windowing, we must first restate that the FFT is a computer implementation of the Discrete Fourier Transform (DFT). The DFT is the sampled implementation of the continuous-time Fourier Transform. As such, the DFT (and by extension, the FFT) always assumes that any signal acquired in one sample frame is periodic. When the two ends of the frame don’t line up, we introduce artificial discontinuities that affect the spectral content of the signal. Windowing helps us to reduce the effects of these artificial discontinuities.

Averaging should be restarted when one of the input signal (carrier or message) parameters changes. Use shift registers to compare the controls with their value from the previous iteration.

Exit the loop when the Stop button is pressed, or when an error appears. After exiting the loop, the used instruments must be stopped and closed, to make them available to other software, then errors should be handled.

• Set the message frequency to 1kHz, the modulation coefficient to 10%, the carrier frequency to 100kHz, and the carrier amplitude to 1V. Set the cut-off frequency of the low-pass filter to 20kHz. Compare the demodulated signal to the original message signal. What is similar between the two signals? What is different between the two signals?
• Compare the demodulated signal to the rectified signal in the time-domain. What is similar between the two signals? What is different between the two signals?
• Compare the demodulated signal to the rectified signal in the frequency-domain. What is similar between the two signals? What is different between the two signals? Use the cursors to find the peak frequencies in the FFT. Modify the axis ranges if necessary.
• With the VI still running, change the cut-off frequency while observing the Demodulated Signal and the Demodulated Signal FFT. How does increasing the cut-off frequency of the low-pass filter affect the demodulated signal? How does decreasing the cut-off frequency of the low-pass filter affect the demodulated signal? What is the lowest cut-off frequency we can use to receive a clean signal? The highest?
• Increase the Modulation Coefficient to 15% in steps of 1%. Observe the graphs as you do this. How does the modulation coefficient affect the demodulated signal? What happens to the demodulated signal as the modulation coefficient increases past 1?
• The maximum buffer size for the Analog Discovery Studio is 8192 samples. This means that the largest number of samples we can acquire during a single read is 8192 samples. Since the number of samples has a set maximum, how else can we increase the resolution of the FFT? Recall the formula for $df$ discussed in the Measurements in the Frequency Domain section of this lab. What is the practical limitation of using this other method to increase the FFT resolution?

Further Exploration

The topics below go over two ways you can continue exploring after finishing this lab. The first topic looks into using multiple instruments to transmit and receive and the second topic goes into transmitting and receiving messages vs single tones.

Two Device Transmitter and Receiver

In this lab, we had both our transmitter and receiver on the same device. However, the vast majority of communications applications do not only involve one device. Partner with another group to use two Analog Discovery Studios. Designate one group as the receiver and the other group as the transmitter. Using jumper wires, connect the two Analog Discovery Studios together such that the transmitter group modulates and sends out the signal and the receiver group gets the signal and demodulates it to recover the original message.

Hint: If you are running the two Analog Discovery Studios from the same computer, make sure to give each device a unique identifier in WaveForms. This will let you call both devices without getting a conflicting resource error.

Analog AM Demodulation

In this lab, we decided to demodulate by implementing a method known as envelope detection in software. However, the steps in envelope detection (rectifying and filtering) can also be done using hardware. In our previous labs we have talked about both rectification ( Lab 4: Full-Wave Rectifiers ) and low-pass filtering ( Lab 2: Active and Passive Filters ). Use the knowledge and circuits you’ve built from these labs to put together a circuit that performs the same function as our software demodulator.

Compare the results of your hardware demodulator to the ones from our software demodulator. What are some considerations and trade-offs between using a hardware system and a software system?

For more complementary laboratories, return to the Complementary Labs for Electrical Engineering page of this wiki.

For technical support, please visit the Test and Measurement section of the Digilent Forums.

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ECE Undergraduate Laboratories

Ece 489 communications systems laboratory.

Lab 1: Amplitude Modulator and Demodulator

• To understand the theoretical foundations of Analog Communications as well as of Double-Side-Band Amplitude Modulation and Demodulation (DSB-AM)
• To design the Simulink model of the DSB-AM to analyze each signal in time and frequency domains using time scope and spectrum analyzer
• To examine the effects of the Additive Gaussian Channel (AWGN) in the Simulink Model of DSB-AM
• To observe the real-time music transmission for DSB-AM modulated signal via USRP trans-receiver

Theoretical Background

• Review of Signals & Systems, Probability and Noise and Starters’ Guide

In order to understand the theory along with the experiments behind this course, the review sections were prepared. It is highly recommended that the Review and the Starters’ Guide are understood. Please see the instructor for any further information.

As a reminder, Review of Signals & Systems, Probability and Noise is valid for all experiments.

• Fundamentals of Analog Communications

Analog Communication is an information transmitting mechanism, i.e. music, voice, and video using broadcast radio, walkie-talkies, or cellular radio, and broadcast television. The significant invention made by Marconi in 1895 was a radio. Later, the foundation of Trans-Atlantic Communication Systems had been taken place. Although digital communications systems are much more efficient, cost-saving, more reliable, some communication systems are still analog.

Analog communication techniques can be summarized as

Advantages of modulation:

• Size of the antenna reduces when a signal is modulated by a larger frequency of a carrier.
• Using modulation to transmit the signal through space to long distances. Therefore, Wireless Communication techniques has raised our standards considerably.
• Modulation allows us to transmit multiple signals in the same medium (i.e. Frequency Division Multiplexing, FDMA)  
• Amplitude Modulation and Demodulation

Let $ω_c = 2πf_c$ be the carrier frequency in radians per second where where $fc >> W$. Then the amplitude modulated signal $s(t)$ can be expressed [1] (H. Taub, 2008, p. section 3.3) as

, where $u$  is the modulation index defined in  $-1<μ<1$

As an example, the following figure shows the Amplitude Modulation with $m(t)=sin(2πt),\:A_C=1,\:μ=0.9, \:and \:f_c=10 Hz$,

In general, the AM modulation is summarized as:

In case of carrier, which could be used sine or cosine wave. Practically, there is no difference except -90-degree phase shift.

Any signal is summed by a constant value means that this signal is raised by the same constant value with respect to the vertical axis in time domain. In frequency domain, the constant value is represented by an impulse at $f=0\: Hz$.

Demodulation

For AM demodulation, we will examine the Square-Law and Envelope Detector techniques.

Demodulation by Squaring

The high frequency is removed after filtering,

Synchronous Demodulator

The block diagram of synchronous demodulator is as shown

In order for the low-pass to detect the information envelope, the frequency of the carrier must be as high as possible. However, as you can imagine the noise from the nature (i.e. white noise) cannot be filtered/removed perfectly in such analog transmissions (AM, or FM).

After the multiplication of $s(t)×sin(2πf_c t)$

Then, the low-pass filter removes the higher frequency components, so we can recover m(t).

2. Building Simulink Model of Amplitude Modulator and Demodulator

The Simulink design of an Amplitude modulator is in the following [2] (M. Boulmalf, 2010)

Parameters:

• Double click on the signal generator, and then set the frequency as 1 kHz with a waveform of sine
• Adjust the carrier sine wave’s frequency as 20 kHz
• Set the simulation time such as 0.01 to observe the signals clearly
• Run your simulation
• In order to observe the spectrum analyzer, please increase the simulation time to 1 or 2 seconds.

As it is clearly seen that the AM model is exactly based upon the mathematical foundation provided in the theoretical section. The message signal is multiplied by the modulation index, then it is added a DC carrier, finally is multiplied with a sinusoidal carrier signal in order to transmit the AM modulated signal.

Demodulation (Square-Law Demodulator)

Apply the similar procedure. You will have the demodulation structure as shown in the following figure:

• Specify the band edge frequency as 2*pi*X

Connect your modulation and demodulation models as shown.

Run your model, you will then observe the following

Simulation time is chosen to be 2 secs for the spectrum analyzers.

3. Building Simulink Model of the Music Transmission Using DSB-AM Modulator and Demodulator (Baseband)

Here, we will implement the DSB-AM baseband modulator and demodulator using a music file as a source. In this case, since the source is a multimedia file rather than a pure sine wave, we need the DSP process, which is the resampling and filtering. You will not be kept responsible for DSP processes. However, you can find them very useful when comprehending sampling rate, rate conversion, Finite Impulse Response (FIR), decimation and interpolation etc. You can also check the following resource:

Chapter 3, Multiresolution Signal Decomposition, Ali N Akansu, Haddat.

The model is shown below.

Transmitting and Receiving a Multimedia File using DSB-AM via USRP

Now, we will go one further step to transmit a music file, and then receive it via USRP hardware. In this case the transmission is real time, therefore unlike the simulations, you will observe the noise through the air.

The model is expressed as

Transmitter (TX)

Receiver (RX)

5. Prelab Instructions

• Starters Guide and Signals and Systems Review Manuals

There are two additional supplements, Simulink and USRP Starters Guide and Review of Signals and Systems, were prepared and added to the course web site. You will find them very useful while answering prelab questions and comprehending lab tasks.

• Answer the following questions:
• $1 + sin(4πt)$
• $A_C[1 + sin(4πt)] cos(80πt)$, where $A_c$ is a positive number
• Plot $|M(f)|$ by hand
• If this message is DSB-AM modulated on a carrier $cos(80πt)$, find the corresponding passband modulated signal $s_c (t)$ and plot $|S_c (F)|$ by hand
• The received signal $s_c (t)$ is the input of the demodulator as described below:

The passband received signal after the demodulation is converted to baseband. This process is simply:

The LPF has the following specifications:

• Find the $y(t)$, and then compare it with $m(t)$. Did you recover the signal? Comment your result.

6. Lab Tasks

• [Synchronous Detector]

Build the model given below [3], and then set up the block parameters as

• m(t) with frequency of 1kHz and sample time:1/100kHz
• carrier: 10kHz, phase:$π/2$  and sample time: 1/100kHz
• Local Oscillator (LO): same as carrier.
• Filter: LowPass, Fs:100kHz, Fpass:6 and Fstop:12
• Set up the simulation time as 50k/100k
• Run your model
• Observe the 3 spectrum analyzers, then explain the waveforms from the frequency point of view (Hint: remember modulation property). Comment your result.
• Change the simulation time to 500/100k (to clearly see the sine wave). Compare signals in the time scope? Did you recover m(t)? Is there any delay between two signals? If yes, explain, why?

• Build the Simulink model of AM modulator and demodulator (Figure-7) explained in this manual. You must determine the analog filter’s passband edge frequency. Then, explain the theoretical side of the blocks. Use the notation as μ:modulation index, $m(t), h(t)$, etc.
• As the nature of transmission, the message can be distorted in different levels by the noise, which may occupy between specific frequencies, i.e. colored noise, or all frequencies, i.e. White Gaussian Noise (WGN). The following block is called “Additive White Gaussian Noise”.

Connect the AWGN channel. Set the variance from mask as 0.01, 0.05, 0.1 and 0.5 respectively. What do you observe in each case? Comment your result

• What happens to the modulated signal’s waveform for each case?
• In which values, the demodulation can be performed correctly? Why?
• Find the AM_Music_Simulation.slx file on your computer, then run the model. Similarly, answer the questions in task-2 based on this model.
• Steps: USRP
• Ask your instructor to open, and then run the TX_AM_Music.slx file. Check the block diagrams for the transmitter (You will find no difference than the music simulation, but the transmitter). Take note the transmitter central frequency.
• Open the RX_AM_Music.slx file in your computer. Set the central frequency same as the transmitter, and then run the file. Observe the real-time transmission through the air.
• Self-Study: Type the following code in the command window [4]: >> dspenvdet

This code will open the Simulink Model of DSB-AM modulator and demodulator techniques based on Envelope Detector by Squaring and Hilbert Transform.

• Run your simulation to observe the waveform in time domain
• Click on dspEnvelopeDetector.m, then run the m-file. Observe the Matlab figures in both envelope detection techniques

7. Lab Report Instructions

Check out the template in the course web site.

8. References

[1] H. Taub, D. L. (2008 ). Principles of Communication Systems (3rd ed.). McGraw Hill.

[2] M. Boulmalf, Y. S. (2010) . Tearching Digital and Anolog Modulation to Undergraduate Information and Technologhy Students Using Matlab and Simulink . IEEE.

[3] Simulink model of Perfect Modulation and Demodulation, Software Defined Radio using MATLAB & Simulink and the RTL-SDR, Strathclyde Academic Media, 2015

[4] The Mathworks Inc ®, Envelope Detection ,

ECE 489 Communications Systems Laboratory

Experiment 5 : Amplitude Modulation

PREPARATION

Measurement of "m' The magnitude of ' m ' can be measured directly from the AM display itself. Thus   ( 5 )   where p and Q are as defined in Figure 3.  

  Spectrum Analysis shows that the sidebands of the AM, when derived from a message of frequency m rad/s, are located either side of the carrier frequency, spaced from it by m rad/s.   Figure 4: AM spectrum   You can see this by expanding eq. (2). The spectrum of an AM signal is illustrated in Figure 4 (for the case m = 0.75 ). The spectrum of the DSBSC alone was confirmed in the experiment entitled DSBSC  generation. You can repeat this measurement for the AM signal. As the analysis predicts. even when m > 1, there is no widening of the spectrum. This assumes linear operation: that is, that there is no hardware overload.   Other message shapes . Provided m � 1 the envelope of the AM will always be a faithful copy of the message. For the generation method of Figure 2 the requirement is that: The peak amplitude of the AC component must not exceed the magnitude of the DC, measured at the ADDER output As an example of an AM signal derived from speech. Figure 5 shows a snap-shot of an AM signal, and separately the speech signal. There are no amplitude scales shown, but you should be able to deduce the depth of modulation (the peak depth) by inspection.  

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Aligning the Model

The low frequency term a ( t ) To generate a voltage defined by eq. (2) you need first to generate the term  a ( t ) .  a ( t )  = A.(1 + m.cos m t)       ( 6 ) Note that this is the addition of two parts, a DC term and an AC term. Each part may be of any convenient amplitude at the input to an ADDER . The DC term comes from the VARIABLE DC module, and will be adjusted to the amplitude 'A' at the output of the ADDER . The AC term m ( t ) will come from an AUDIO OSCILLATOR, and will be adjusted to the amplitude  'A�m'   at the output of the ADDER .   The carrier supply c ( t ) The 100 kHz carrier c ( t ) comes from the MASTER SIGNALS module  c ( t ) = B.cos w t      ( 7 ) The block diagram of  Figure 2 , which models the AM equation, is shown modeled by TIMS in Figure 6 below.  

To build the model

Now start adjustments by setting up a ( t ) , as defined by eqn. (4) , and with m = 1

You have now set the magnitude of the DC part of the message to a known amount. This is about 1 volt, but exactly 2 cm, on the oscilloscope screen. You must now make the AC part of the message equal to this, so that the ratio  Am/A   will be unity. This is easy:

The sine wave will be centered exactly A volts above the previously-chosen zero reference, and so its amplitude is A . Now the DC and AC, each at the ADDER output, are of exactly the same amplitude A. Thus:

You have now modeled A.(1 + m.cos m t) , with m = 1 . This is connected to one input of the MULTIPLIER , as required by eqn. (2) .

Now prepare the carrier signal:

Since each of the previous steps has been completed successfully, then at the MULTIPLIER output will be the 100% modulated AM signal. It will be displayed on CH2-A . It will look like Figure 1 . Notice the systematic manner in which the required outcome was achieved. Failure to achieve the last step could only indicate a faulty MULTIPLIER ?   Agreement with theory It is now possible to check some theory

TUTORIAL QUESTIONS

Amplitude modulation

AM was the earliest modulation method used for transmitting audio in radio broadcasting. Amplitude modulation, Wikipedia .

To transmit an audio signal wireless it must be modulated by a high-frequency carrier so that antennas of practical size can be used.

The amplitude modulator generates a signal

s ^ carrier amplitude

m ( t ) MathType@MTEF@5@5@+=faaagCart1ev2aaaKnaaaaWenf2ys9wBH5garuavP1wzZbqedmvETj2BSbqefm0B1jxALjharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8FesqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9Gqpi0dc9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyBaiaacIcacaWG0bGaaiykaaaa@315D@ modulating signal

k M MathType@MTEF@5@5@+=faaagCart1ev2aaaKnaaaaWenf2ys9wBH5garuavP1wzZbqedmvETj2BSbqefm0B1jxALjharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8FesqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9Gqpi0dc9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4AamaaBaaaleaacaWGnbaabeaaaaa@3007@ sensitivity of the AM modulator - a constant amplification factor

On the 24th of December 1906 Reginald Fessenden, a Canadian inventor, performed the worlds first amplitude modulated transmission. After a few years of research he sent a voice message, which was received by radio equipped ships over hundred miles away. Due to the very simple hardware amplitude modulation became very popular and was used for communication during the first world war. Though there are some disadvantages. AM is very prone to interferences and its need for bandwidth is relatively high.

The amplitude modulated signal is shown in the oscilloscope and spectrum analyzer:

Maximum and minimum amplitudes of the transmission signal's envelope determine the modulation depth:

The modulation index or modulation depth is defined as m = m max ⋅ k m s ^ .

Note that in this setup m has the same value as k m as both the message signal and carrier amplitude are set to 1V.

Compare the AM modulated signal in the time and frequency domain for different modulation indexes.

Switch off the carrier and create a double sideband modulated signal without carrier.

Change source and carrier signal parameters such as amplitude, frequency and waveform. Watch the effect on the modulated signal and spectrum.

• Engineering & Technology
• Electrical Engineering

Experiment 02: Amplitude Modulation

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• IIT JEE Study Material

Amplitude Modulation

Amplitude modulation is a process by which the wave signal is transmitted by modulating the amplitude of the signal. It is often called AM and is commonly used in transmitting a piece of information through a radio carrier wave. Amplitude modulation is mostly used in the form of electronic communication.

Download Complete Chapter Notes of Communication System Download Now

Currently, this technique is used in many areas of communication, such as in portable two-way radios, citizens band radios, VHF aircraft radios and in modems for computers. Amplitude modulation is also used to refer to mediumwave AM radio broadcasting.

Table of Contents

What is amplitude modulation.

• Types of Amplitude Modulation

Communication Systems and Modulation

What is modulation, amplitude phase.

• Need for Modulation

Common Terms

Expression for amplitude modulated wave, frequencies of amplitude modulated wave, advantages and disadvantages of amplitude modulation, solved problems, ncert questions on amplitude modulation.

Amplitude modulation, or just AM, is one of the earliest modulation methods that is used in transmitting information over the radio. This technique was devised in the 20th century at a time when  Landell de Moura and Reginald Fessenden were conducting experiments using a radiotelephone in the 1900s. After successful attempts, the modulation technique was established and used in electronic communication.

In general, amplitude modulation definition is given as a type of modulation where the amplitude of the carrier wave varies in some proportion with respect to the modulating data or the signal.

As for the mechanism, when amplitude modulation is used, there is a variation in the amplitude of the carrier. Here, the voltage or the power level of the information signal changes the amplitude of the carrier. In AM, the carrier does not vary in amplitude. However, the modulating data is in the form of signal components consisting of frequencies either higher or lower than that of the carrier. The signal components are known as sidebands, and the sideband power is responsible for the variations in the overall amplitude of the signal.

The AM technique is totally different from frequency modulation and phase modulation, where the frequency of the carrier signal is varied in the first case and in the second one, the phase is varied.

Types of Amplitude Modulation

There are three main types of amplitude modulation. They are

• Double Sideband-suppressed Carrier Modulation (DSB-SC)
• Single Sideband Modulation (SSB)
• Vestigial Sideband Modulation (VSB)

Also Read:   Amplitude Modulation Derivation 

Designations by  ITU

The International Telecommunication Union (ITU) designated different types of amplitude modulation in 1982. They are as follows:

We are studying modulation under communication systems. They are used to transmit and receive messages (information) from one place to another place in the form of electronic signals, and they are carried out in two different ways.

(i) Analog signal transmission

(ii) Digital signal transmission

So, we can represent an analogue electronic signal (information) as follows:

We can represent the analogue electronic signal either as a sine (or) cosine wave. Every wave will have an amplitude and phase.

Where m(t) = Modulating signal (input signal) or baseband signal

A m = Amplitude of the modulating signal

(ω m t + Ɵ) = Phase of the signal phase contains both frequency (ω m t) ad angle (Ɵ) term

Basically, it is a process in a communication system. For communication, we need some fundamental elements. One is the high-frequency carrier wave, and the other is the information that has to be transmitted (modulating signal) or input signal. These are essential for communication which is done using a device from one place to another. All in all, we need the help of the communication system.

An electronic communication system converts our message (information) into an electronic signal, and the electronic signal is carried out by carrier waves to the destination.

Message (information)

Modulating signal

The superposition of modulating signal onto a carrier wave is known as modulation.

Modulation is defined as,

Varying any one of the fundamental parameters of a carrier wave in accordance with the modulating signal. A carrier wave can be represented as a sine or cosine.

C(t) = A c sin (ω c t + Ɵ)

Also Read: Frequency Modulation vs Amplitude Modulation

If we vary the amplitude of the carrier wave in accordance with the modulating signal (input signal), it is known as amplitude modulation.

Similarly, it can be frequency modulation and phase modulation, too. In other words, modulation is the phenomenon of “superimposition of the modulating signal (input signal) into the carrier wave”.

Why Do We Need Modulation?

Practically speaking, modulation is required for

• High range transmission
• Quality of transmission
• To avoid the overlapping of signals

High Range Transmission: (Effective Length of Antenna)

For effective communication, the length of the antenna should be λ/4 times the modulating signal.

H min = λ/4

λ – Wavelength of the modulating signal or transmitting signal H> λ/4

For example, if I need to transmit a signal of a frequency of f = 20 kHz

As we know, c = f λ

3 × 10 8 = 20 × 10 3 (λ)

H min = 3750 m

H min = 3750 m is practically impossible; for that, we can transmit our modulating signal onto a carrier wave of frequency 1MHz. What we did here is we raised our transmission frequency from 20kHz to 1mHz.

Now, let us find out what the H min is needed for good transmission.

3 × 10 8 = 1×10 6 (λ)

If we increase the transmitting frequency, wavelengths

This is practically possible, so we need modulation to increase the transmission frequency to transmit a low-frequency signal.

Quality of Transmission: (Power of Transmission by Antenna)

Since, from the Q-factor, we know sharpness or quality is maximum when power is maximum.

Sharpness or quality α power

Power radiated by a linear antenna is

Where l =  Length of the antenna

λ = Wavelength of the transmitting signal

Avoiding the Overlapping of Signals

Two different transmitting stations transmit signals of the same frequency. They will get mixed up or overlap one another. To avoid this, we need to modulate these signals by different carrier waves.

When we talk about amplitude modulation, it is a technique that is used to vary the amplitude of the high-frequency carrier wave in accordance with the amplitude of the modulating signal. But the frequency of the carrier wave remains constant. Now, let us see what carrier waves and modulating signals are.

Carrier Wave (High Frequency)

The amplitude and frequency of a carrier wave remain constant. Generally, it will be high frequency, and it will be a sine or cosine wave of electronic signal; it can be represented as

C(t) = A c sin w c t ……………. 1

Modulating Signal

The modulating signal is nothing but the input signal (electronic signal), which has to be transmitted. It is also a sine or cosine wave; it can be represented as

m(t) = A m sin w m t

A c and A m = Amplitude of the carrier wave and the modulating signal

sin w c t = Phase of the carrier wave

sin w m t = Phase of the modulating signal

We have carrier wave and modulating signals,

m(t) = Modulating signal

c(t) = Carrier wave

A m and Ac are the amplitude of modulating signal and carrier wave, respectively, in amplitude modulation. We are superimposing modulating signal into a carrier wave and also varying the amplitude of the carrier wave in accordance with the amplitude of the modulating signal, and the amplitude-modulated wave C m (t) will be

C m (t) = (A c + A m sin ω m t) sin ω c t ……………….. 2

This is the general form of an amplitude-modulated wave.

C m (t) is the amplitude-modulated wave

A = A c + A m sin ω m t = Amplitude of the modulated wave

sin w c t = Phase of modulated wave

C m (t) = A c sin ω c t + A c μ sin ω m t sinω c t

We can rewrite the above equation as

From equation 3, we can see amplitude modulated wave is the sum of three sine or cosine waves.

There are three frequencies in amplitude modulated wave – f 1 , f 2 and f 3 – corresponding to ω c , ω c + ω m and ω c – ω m, respectively.

ω 1 = ω c → it is corresponding f 1 = f c

ω 2 = ω c + ω m → it is corresponding f 2 = f c + f m

ω 3 = ω c – ω m → it is corresponding f 3 = f c – f m

Where f c → Carrier wave frequency

f c + f m → Upper side band frequency

f c – f m → Lower side band frequency

f m → Modulating signal frequency

In general, f c > > f m

Bandwidth: (BW) It is the difference between the highest and lowest frequencies of the signal.

BW = Upper sideband frequency – Lower sideband frequency (f c – f m )

B W = f max − f min

BW = f c + f m – f c + f m = 2 f m

BW = 2f m = Twice the frequency of the modulating signal

Modulation Index

It is the ratio of the amplitude of the modulating signal to the amplitude of the carrier wave.

Amplitude Modulated Waveform

The waveform representation of amplitude modulated wave is given below.

1. Carrier wave

2. Modulating signal

3. Superposition of the carrier wave and modulating signal

4. Amplitude modulated wave

Carrier wave, c(t) = A c sin w c t

Modulating single m(t) = A m sin w m t

Amplitude modulate wave (m(t) = (A c + A m sin ω m t) sin ω c t

Frequencies of modulated wave → f c , f c + f m , f c – f m

Bandwidth (w) = f c + f m – (f c – f m ) = 2f m

Applications of Amplitude Modulation

While amplitude modulation use has decreased over the years, it is still present and has several applications in certain transmission areas. We will look at them below.

• Broadcast Transmissions:  AM is used in broadcasting transmission over the short, medium and long wavebands. Since AM is easy to demodulate, radio receivers for amplitude modulation are, therefore, easier and cheaper to manufacture.
• Air-band Radio: AM is used in VHF transmissions for many airborne applications, such as ground-to-air radio communications or two-way radio links, for ground staff personnel.
• Single Sideband: Amplitude modulation in this form is used for HF radio links or point-to-point HF links. AM uses a lower bandwidth and provides more effective use of the transmitted power.
• Quadrature Amplitude Modulation: AM is used extensively in transmitting data in several ways, including short-range wireless links, such as Wi-Fi to cellular telecommunications and others.

These are some of the important applications of amplitude modulation.

Demodulation Methods

The most simple AM demodulator is made up of a diode that acts as an envelope detector. The product detector, which is another type of demodulator, can offer better-quality demodulation but with a complex additional circuit.

Question 1:

A carrier wave of frequency f = 1mHz with a pack voltage of 20V is used to modulate a signal of frequency 1kHz with a pack voltage of 10v. Find out the following:

(ii) Frequencies of the modulated wave

(iii) Bandwidth

(ii) Frequencies of modulated wave

f → f c , f c + f m and f c – f m

f c = 1mHz, f m = 1kHz

f c + f m = 1×10 6 + 1×10 3 = 1001 ×10 3 = 1001 kHz

f c – f m = 1×10 6 – 1×10 3 = 999 × 10 3 = 999 kHz

(iii) Bandwidth: (W)

(W) = Upper side band frequency – Lower side band frequency

= f c + f m – (fc – fm)

= 2f m = 1001 kHz – 999 kHz = 2 kHz

Question 2:

y = 10 cos (1800 πt) + 20 cos 2000 πt + 10 cos 2200 πt. Find the modulation index (μ) of the given wave.

As we know, the expression for amplitude modulated wave is

C m (t) = (A c + A m cos ω m t) cos ω c t ……………… 1

So, we have to bring the given wave equation into the known form

y = 10 [cos(1800 πt) + cos (2200πt)] + 20 cos 2000 πt

cos(2000 πt) + cos (1800 πt) = 2 cos 2000 πt cos 200 πt

Compare equations 1 and 2.

Then, the modulation index (μ)

We can also find the frequencies of the modulated wave and B and width

(ii) Frequencies off the modulated wave

We know frequencies are fc, fc + fm and fc – fm from the modulated wave expression.

y = (A c + A m cos ω m t) cos ω c t ……………….. 4

Comparing equations 3 and 4, we get

cos ω m t = cos (200 πt)

ω m = 200 π

2 πf m = 200 π

f m = 100 Hz

cos ω c t = cos 2000 πt

ω c = 2000 π

2πf c = 2000 π

f c = 1000 Hz

f c , f c + f m and f c – f m , respectively, 1000 Hz, 1100 Hz and 900 Hz.

(iii) Bandwidth (W)

W = f c + f m – (f c – f m ) = 2f m

1. Why are carrier waves of higher frequency compared to modulating signals?

(i) High-frequency carrier waves effectively reduce the size of the antenna, which increases transmission range.

(ii) They convert wideband signal into a narrowband signal which can easily be recovered at the receiving end.

2. Define modulation index.

The modulation index is defined as the ratio of the amplitude of the modulating signal to the amplitude of the carrier wave (μ).

3. What happens if μ > 1?

As we know, the range of modulation index (μ) should be 0 < μ < 1 if μ > 1. It is said to be over-modulated, and distortion will take place in the modulated signal.

4. Why do we need modulation?

• To transmit the low-frequency signal to a longer distance.
• To reduce the length of the antenna.
• Power radiated by the antenna will be high for high frequency (small wavelength).
• To avoid the overlapping of modulating signals.

5. Why is the amplitude of the modulating signal kept less than the amplitude of the carrier wave?

To avoid overmodulation. Typically, in overmodulation, the negative half cycle of the modulating signal will be distorted.

Frequently Asked Questions on Amplitude Modulation

Explain amplitude modulation..

The amplitude of the wave is altered in proportion to the message signal, such as an audio signal, in amplitude modulation. Amplitude modulation is a modulation technique extensively used in electronic communication to send messages through radio waves.

What is the difference between amplitude modulation and frequency modulation?

The distinction is in the modulation or alteration of the carrier wave. To add sound information into amplitude modulation radio, the broadcast’s amplitude, or overall strength, is changed. The carrier signal’s frequency (the number of times per second that the current changes direction) is altered with frequency modulation.

Which one is preferable: amplitude modulation or frequency modulation?

Because of the increased bandwidth, FM has better sound quality and is the preferable one.

Put your understanding of this concept to test by answering a few MCQs. Click ‘Start Quiz’ to begin!

Select the correct answer and click on the “Finish” button Check your score and answers at the end of the quiz

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