frequency modulation experiment conclusion

LAB 1: AMPLITUDE MODULATION

Achievements:.

Modeling of an amplitude modulated (AM) signal; method of setting and measuring the depth of modulation; waveforms and spectra; trapezoidal display.

PREREQUISITES:

A knowledge of DSBSC generation . Thus reviewing of the experiment entitled DSBSC generation would be an advantage.

In this lab you will begin to look at the frequency power spectrum of signals. This is traditionally done with a Spectrum Analyzer however we will use the FFT capability of our oscilloscopes here. Read about spectrum analyzers . Read about using the FFT on the Tektronix DPO 2000 series oscilloscopes manual .

Understand the differences between swept frequency, FFT, and real-time spectrum Analyzers, as well as the term resolution bandwidth.

An important characteristic of Spectrum analyzers is the noise floor or signal sensitivity. For an FFT based analyzer this is related to the number of bits per sample for the A/D converter. A modern spectrum analyzer can detect signals below -100 dbm. The noise floor or lower limit for our oscilloscope FFTs is closer to -60 dbm. We can use this feature since it won't be a limit for us in this experiment.

Please review the FFT description in the manual for the Tektronix 2000 series scopes on the lab web site under useful links. The FFT is calculated from 5,000 points (typical) of the source waveform. When the input area contains more than 5,000 points, the area is reduced in resolution . The sampling frequency is therefore determined by the length of the waveform sampled. The width of the waveform used for the FFT can be displayed on the screen and is slightly less than the full screen display. Thus the sampling frequency is determined by the horizontal scale setting. For the FFT process, the horizontal scale determines the FFT bandwidth via the sampling frequency and the resolution bandwidth via the length of the signal that is sampled.

Question for Pre-lab: You will be looking at a carrier near 100 kHz that is modulated with close to 1 kHz signal so you will want to be able to see signals separated by 1 kHz at minimum. Determine the screen width in time that provides 1 kHz frequency spacing in the Discrete Fourier Transform. How many cycles of the 100 kHz carrier will be on the screen given the screen width needed?

Please make certain that you also read about the various windowing techniques: Rectangular, Hamming, Hanning and Blackman-Harris. A brief description is in the Tek manual. This will allow you to choose the best one for your lab use.

PREPARATION

In the early days of wireless, communication was carried out by telegraphy, the radiated signal being an interrupted radio wave. Later, the amplitude of this wave was varied in sympathy with (modulated by) a speech message (rather than on/off by a telegraph key), and the message was recovered from the envelope of the received signal. The radio wave was called a 'carrier', since it was seen to carry the speech information with it. The process and the signal were called amplitude modulation, or 'AM' for short.

In the context of radio communication, near the end of the 2Oth century, few modulated signals contain a significant component at 'carrier' frequency. However, despite the fact that a carrier is not radiated. the need for such a signal at the transmitter (where the modulated signal is generated), and also at the receiver, remains fundamental to the modulation and demodulation process respectively. The use of the term 'carrier' to describe this signal has continued to the present day.

As distinct from radio communications, present day radio broadcasting transmissions do have a carrier. By transmitting this carrier the design of the demodulator, at the receiver, is greatly simplified, and this allows significant cost savings.

The most common method of AM generation uses a 'class C modulated amplifier'; such an amplifier is not available in the BASIC TIMS set of modules. It is well documented in text books. This is a 'high level' method of generation, in that the AM signal is generated at a power level ready for radiation. It is still in use in broadcasting stations around the world, ranging in powers from a few tens of watts to many megawatts.

Unfortunately, text books which describe the operation of the class C modulated amplifier tend to associate properties of this particular method of generation with those of AM, and AM generators, in general. This gives rise to many misconceptions. The worst of these is the belief that it is impossible to generate an AM signal with a depth of modulation exceeding 100% without giving rise to serious RF distortion.

You will see in this experiment, and in others to follow, that there is no problem in generating an AM signal with a depth of modulation exceeding 100%, and without any RF distortion whatsoever.

But we are getting ahead of ourselves, as we have not yet even defined what AM is!

The amplitude modulated signal is defined as:

'E' is the AM signal amplitude from eqn. ( 1 ). For modeling convenience eqn. ( 1 ) has been written into two parts in eqn. ( 2 ), where (A·B) = E .

'm' is a constant, which, as you will soon see, defines the 'depth of modulation'. Typically m < 1 . Depth of modulation, expressed as a percentage, is 100.m. There is no inherent restriction upon the size of 'm' in eqn. (1). This point will be discussed later .

' μ ' and ' ω ' are angular frequencies in rad/s, where μ/(2·π) is a low, or message frequency, say in the range 300 Hz to 3000 Hz; and ω/(2.π) is a radio, or relatively high, 'carrier' frequency. In TIMS the carrier frequency is generally 100 kHz.

Notice that the term a(t) in eqn. (3) contains both a DC component and an AC component. As will be seen, it is the DC component which gives rise to the term at ω - the 'carrier' - in the AM signal. The AC term 'm.cosμt' is generally thought of as the message, and is sometimes written as m(t) . But strictly speaking, to be compatible with other mathematical derivations. the whole of the low frequency term a ( t ) should be considered the message.

a ( t ) = DC + m ( t )     ( 4 )

Figure 1 below illustrates what the oscilloscope will show if displaying the AM signal.

A block diagram representation of eq. ( 2 ) is shown in Figure 2 below.

For the first part of the experiment you will model eq. (2) by the arrangement of Figure 2. The depth of modulation will be set to exactly 100% (m = 1). You will gain an appreciation of the meaning of 'depth of modulation' , and you will learn how to set other values of 'm " including cases where m > 1.

The signals in eq. (2) are expressed as voltages in the time domain. You will model them in two parts, as written in eq. (3).

Depth of Modulation

100% amplitude modulation is defined as the condition when m = 1 . Just what this means will soon become apparent. It requires that the amplitude of the DC (= A) part of a ( t ) is equal to the amplitude of the AC part (= A.m). This means that their ratio is unity at the output of the ADDER, which forces 'm' to a magnitude of exactly unity.

By aiming for a ratio of unity it is thus not necessary to know the absolute magnitude of A at all

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.

Analysis shows that the sidebands of the AM, when derived from a message of frequency μ rad/s, are located either side of the carrier frequency, spaced from it by μ rad/s.

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.

Other Generation Methods

There are many methods of generating AM, and this experiment explores only one of them. Another method, which introduces more variables into the model, is explored in the experiment entitled .Amplitude modulation -method 2, to be found in volume A2- Further & Advanced, Analog Experiments.

It is strongly suggested that you examine your text book for other methods.

Practical circuitry is more likely to use a modulator, rather than the more idealized multiplier. These two terms are introduced in the Chapter of this Volume entitled Introduction to modeling with TIMS, in the section entitled multipliers and modulators.

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·cosμt)     ( 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.cosωt  ( 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

T1  First patch up according to Figure 6, but omit the input X and Y connections to the MULTIPLIER. Connect to the two oscilloscope channels using the SCOPE SELECTOR, as shown.

T2   Use the FREQUENCY COUNTER to set the AUDIO OSCILLATOR to about 1 kHz.

T3   Switch the SCOPE SELECTOR to CH1-B, and look at the message from the AUDIO OSCILLATOR. Adjust the oscilloscope to display two or three periods of the sine wave in the top half of the screen.

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

T4   Turn both g and G fully anti-clockwise. This removes both the DC and the AC parts of the message from the output of the ADDER.

T5   Switch the scope selector to CH1-A. This is the ADDER output. Switch the oscilloscope amplifier to respond to DC if not already so set, and the sensitivity to about 0.5 volt/cm.

T6 Set gain on ADDER to set VDC

VDC = +1Volt

T7 Now set amplitude of AC signal also to 1 Volt

T8 Connect the output of the ADDER to input X of the MULTIPLIER. Make Sure the MULTIPLIER is switched to accept DC.

Now prepare the carrier signal:

c ( t ) = B.cosωt           ( 10 )

T9  Connect a 100 kHz analog signal from the MASTER SIGNALS module to input Y of the MULTIPLIER

T10    Connect the output of the MULTIPLIER to the CH2-A of the SCOPE SELECTOR. Adjust the oscilloscope to display the signal conveniently on the screen.

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.

T11 Display the FFT of the waveform on the screen. Vary the time base and determine how it affects the widths of the signal peaks in the FFT, this determines the minimum resolution bandwidth. Using the FFT measure the ratio of power in the carrier to the side lobe(s). In your lab write up compare this with what is expected for a modulation depth of m = 1.

T12 Measure the peak-to-peak amplitude of the AM signal, with m = 1, and confirm that this magnitude is as predicted, knowing the signal levels into the MULTIPLIER, and its  'k' factor.

The significance of 'm'

First note that the shape of the outline, or envelope. of the AM waveform  (lower trace), is exactly that of the message waveform (upper trace). As mentioned earlier, the message includes a DC component, although this is often ignored or forgotten when making these comparisons.

You can shift the upper trace down so that it matches the envelope of the AM signal on the other trace. Now examine the effect of varying the magnitude of the parameter 'm'. This is done by varying the message amplitude with the ADDER gain control G.

for all values of 'm' less than that already set (m = 1), the envelope of the AM is the same shape as that of the message.

for values of m > 1 the envelope is NOT a copy of the message shape.

It is important to note that, for the condition m > 1:

it should not be considered that there is envelope distortion, since the resulting shape, whilst not that of the message, is the shape the theory predicts.

there need be no AM signal distortion for this method of generation. Distortion of the AM signal itself, if present, will be due to amplitude overload of the hardware. But overload should not occur, with the levels previously recommended, for moderate values of m > 1.

T13   Vary the ADDER gain G, and thus 'm' and confirm that the envelope of the AM behaves as expected, including for values of m > 1. Note both the time-base signal and the FFT on the oscilloscope. Save them for your report for m = .75, m = 1, and m = 1.5 if possible.

TUTORIAL QUESTIONS

Q1   There is no difficulty in relating the formula of eqn. (5) to the waveforms  of Figure 7 for values of 'm' less than unity. But the formula is also valid for m > 1, provided the magnitudes P and Q are interpreted correctly. By varying 'm'  and watching the waveform, can you see how P and Q are defined for m > 1?

Q2    Derive eqn.(5), which relates the magnitude of the parameter 'm' to the peak-to-peak and trough-to-trough amplitudes of the AM signal.

Q3    If the AC/DC switch on the MULTIPLIER front panel is switched to AC what will the output of the model of Figure 6 become?

Q4   An AM signal, depth of modulation 100%.from a single tone message, has a peak-to-peak amplitude of 4 volts. What would an RMS voltmeter read if connected to this signal ? You can check your answer if you have a WIDEBAND TRUE RMS METER module.

Q5    In Task T6, when modeling AM, what difference would there have been to the AM from the MULTIPLIER if the opposite polarity (+ ve) had been taken from the VARIABLE DC module?

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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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Frequency Modulation

Frequency Modulation or FM is a method of encoding information on one carrier wave by changing the wave carrier frequency. Frequency Modulation technology is used in the fields of computing, telecommunications, and signal processing. In frequency modulation, the frequency of the carrier wave is changed according to the frequency of the modulating signal.

In this article, we will discuss the definition of frequency modulation, its advantages and disadvantages, the modulation index, the differences between AM and FM, and the expressions for frequency modulation.

Table of Content

What is Frequency Modulation?

Frequency modulation deviation, frequency modulation demodulation, application of frequency modulation, modulation index, difference between fm and am.

Frequency Modulation is a process of encoding information on one carrier wave by changing its frequency. The frequency of the carrier wave is changed according to the frequency of the modulating signal. Frequency modulation is used for broadcasting and radio communication. Modulation is the process of converting the carrier signal into an electrical signal. Amplitude and phase remain the same in FM.

Frequency Modulation is used in FM radio broadcasting, magnetic tape-recording systems, monitoring newborns for seizures via EEG, radar, seismic prospecting, sound synthesis, telemetry, two-way radio systems, and video-transmission systems.

Frequency Modulation System

A Frequency Modulation system refers to a communication or signal processing system that utilizes frequency modulation to encode and transmit information. Frequency Modulation system consist of input signal, carrier wave, modulation process, transmission, reception, demodulation and output signal.

Frequency Modulation Deviation refers to the extent to which the frequency of a carrier wave is changed or deviated from its center frequency in response to change in the amplitude of the modulating signal. It is a key parameter in frequency Modulation systems and determines the amount by which the carrier frequency shifts during the modulation process.

Frequency Modulation Demodulation is the process of extracting the original information usually an audio signal from a modulated FM carrier wave. Demodulation is an important step in FM receivers to recover the transmitted information accurately. The goal of FM modulation is to reproduce the original information encoded in the FM signal, ensuring high-quality audio output.

Frequency Modulation Waveform

Frequency Modulation generates a modulated waveform by changing the frequency of a carrier signal in response to change in the amplitude of a modulating signal. The result is s waveform that has characteristic distinct from the original carrier wave. The shape of the waveform is highly dependent on the characteristic of the modulating signal and the specific parameters of the FM modulation process.

The wave form of frequency modulation signal is shown in the image added below,

Representation of Frequency Modulation Signal

Frequencies in Frequency Modulation

In Frequency Modulation, the frequency of the carrier signal is varied in accordance with the instantaneous amplitude of the modulating signal. The parameters associated with FM are carrier frequency, Modulating Signal Frequency, Frequency deviation, Modulation index, Sideband Frequencies and Total Bandwidth. The expression for the instantaneous frequency can be expressed mathematically based on the modulation index, the frequency deviation and the modulating signal.

Expression for Frequency Modulated Wave

The expression for a frequency modulated wave can be derived from the basic equation for frequency modulation. The general form of an FM wave can be written as

s(t) = A c cos(2πf c t + 2πk f ∫ t 0 m(τ)dτ where, A c is the Amplitude of the Carrier Signal f c is the Frequency of the Carrier Signal k f is the Frequency Deviation Sensitivity m(t) is the Modulating Signal

Radio Frequency Modulation

Radio frequency Modulation is a technique of encoding the information on a carrier wave by changing its frequency. It is used in field of telecommunication and employed in radio broadcasting, two-way radio communication, television broadcasting and various wireless communication systems. Radio frequency Modulation is a fundamental concept in the world of wireless communication, enabling the transmission of information over the airwaves efficiently and reliably.

Pulse frequency Modulation

Pulse frequency Modulation is a type of modulation where the information is encoded by changing the frequency of a series of pulses. It is used in field of digital communication and control system. Pulse frequency Modulation is commonly used in applications where resistance to noise is important.

Frequency Modulation Synthesis

Frequency Modulation synthesis is a method of sound synthesis that uses the frequency of carrier waveform, to modulate the frequency of modulator waveform. This is particularly associated with the creation of complex and evolving sounds.

Frequency Modulation Receiver

A Frequency Modulation receiver is a device that is used to demodulate and recover the original modulating signal from an FM modulated carrier wave. The receiver is a crucial part of the communication system and it has various applications such as FM radio broadcasting, two-way radio communication, and various wireless communication system.

Frequency Modulation Music

Frequency Modulation is used in electronic music for creating a wide range of sounds, from classic bell tones to complex textures. FM can generate complex waveforms by modulating the frequency of one oscillator with another. Musicians explore vast sonic possibilities of FM synthesis to create sounds that stand out and contribute to the unique character of track.

Frequency Modulation Broadcasting

Frequency Modulation broadcasting is a widely used method for transmitting audio signals over the airways. FM broadcasting offers several advantages, including higher audio quality and resistance to certain types of interference compared to other modulation methods like Amplitude Modulation. It is commonly used for music, talk show, news and other forms of radio programming.

Advantages of Frequency Modulation

Some of the advantages of Frequency modulation are listed below

• The Amplitude of FM wave remains constant over time. This helps in removing noise from received signal.
• FM is resistant to single strength variation.
• It enhances more efficient use of bandwidth.
• FM is used in radio broadcasting because FM is known for its superior quality compared to other methods of modulation.
• It improves and increase the capacity for communication.

Disadvantage of Frequency Modulation

Some of disadvantages of Frequency Modulation are listed below

• Modulation of wave increases the complexity in implementation.
• It requires specialized equipment and knowledge to implement, which makes it less accessible.
• Sometimes modulation leads to loss in quality of signal received, which reduces the clarity of transmitted data.
• FM has a large bandwidth which makes it costlier.

Frequency Modulation has many applications in science and technological field. Some of its real life uses are mentioned below

• FM is used in radio broadcasting.
• It is used by many radio stations to broadcast music over the radio (One must have heard the term FM in radio while listening it).
• FM is used in radar.
• It is used in seismic prospecting.
• It is used in Electroencephalogram (EEG) , which is a test of brain activity.
• Frequency modulation is superior than other modulations. That’s why it has many applications in various fields.

Modulation index is denoted by μ. It is the ratio of the amplitude of modulating signal to that of the carrier signal.

μ = A m / A c 

Frequency Modulation Formula

The mathematical representation of an FM signal can be expressed by using the formula. The instantaneous frequency , of the FM waveform at any given time is given by

F(t) = F c + K f . m(t)

where, f(t) is instantaneous frequency at time t of the modulated signal

F c is the carrier frequency, representing the unmodulated frequency

K f is the frequency sensitivity of the modulator, often referred to as the modulation index

m(t) is the message signal, which contains the information to be encoded into the carrier signal.

Frequency Modulation Width

The frequency modulation index is denoted by Δf or Δf max and is defined as the maximum deviation of the instantaneous frequency from the carrier wave.

It is expressed as

Δf = k f . A m where, Δf is the Frequency Deviation K f is the Frequency Sensitivity of Modulator A m is the Amplitude of Message Signal

Expression For Frequency Modulation

We can represent the expression for frequency-modulated wave by using a sine or cosine work for the vitality of the baseband signal.

We know wave equation as:

m(t) = A m cos(ω m t + ϴ) m(t) is Balancing Signal A m is Amplitude of Balancing Signal ω m is Angular Recurrence of Tweaking Signal ϴ is is Period of the Balancing Signal

when we try to modulate an input signal, we need an expression for carrier wave also

C(t) = A C cos(w c t + ϴ)

From amplitude modulation , we need two sine or cosine waves for modulation

m(t) = A m cos (ω m t) and

c(t) = Ac cos (ω c t)

m(t) = A m cos (2π f m t)

c(t) = A c cos (2πf c t)

Then frequency modulated wave will be:

f m (t) = fc + k A cos (2π f m t )

f m (t) = f c + k m(t) where, f m (t) is Frequency Modulated Wave f c is Frequency of Carrier Wave m(t) is Modulating Signal k is Proportionality Constant

Frequency Modulation Transmitter

A Frequency Modulation transmitter is a device that modulates a carrier wave’s frequency with an input signal, typically an audio or data signal. This device is used in broadcasting, two-way radio communication, and various wireless applications. FM transmitters are regulated, and their use may be subjected to licensing depending on the frequency and power at which they operate.

The differences between FM and AM can easily learnt form the table added below,

Also, Check

• Difference between Frequency Modulation and Phase Modulation
• Radio Waves

Frequency Modulation IIT JEE Questions

Q1: What is the modulation index of an FM signal having a carrier of 100 kHz when the modulating signal has a frequency of 8 kHz ?

Modulation Frequency, f m = 8 kHz Carrier Swing = 2 × Δ f 2 × Δ f = 100 kHz Δ f = 50 kHz Modulation Index = Δ f /f m = 50/8 = 6.25

Q2: Calculate percentage modulation of the signal if it is broadcast in the 88-108 MHz and FM transmission has a frequency deviation of 20 kHz ?

For FM broadcast (Δ f )max = 75 kHz %M = (Δ f )actual/(Δ f )max %M = 20kHz/75kHz %M = 26.67%

Q3: A signal of 5 kHz frequency is amplitude modulated on a carrier wave of frequency 2 MHz. The frequencies of the resultant signal are.

F m = 5 kHz F c = 2 MHz = 2000 kHz Frequencies of Resultant Signal are = F c + F m = ( 2000 + 5)kHz = 2005 kHz F c – F m = (2000 – 5) = 1995 kHz

Q4: Consider telecommunication through optical fibers. Which of the following statements is not true ?

• (a) Optical fibers can be of graded refractive index
• (b) Optical fibers are subject to electromagnetic interference from outside
• (c) Optical fibers have extremely low transmission loss
• (d) Optical fibers may have a homogenous care with a suitable cladding

Option (b) is correct

Frequency Modulation-FAQs

What is full form of fm and am.

Full form of FM and AM is FM: Frequency Modulation AM: Amplitude Modulation

What is Modulation of Signal?

Modulation is process of changing a characteristic of a waveform, such as its amplitude or frequency.

Why Value of Modulation Index is kept less than 1 in General ?

Its value is kept less than 1 to avoid overmodulation which leads to distortions in the modulated signal and makes it very hard to demodulate and extract the modulating signal.

What is Modulation Index ?

Modulation index is the ratio of the amplitude of modulating signal to that of the carrier signal.

What is Demodulator?

Demodulator is the device which is used for extracting the original information from a modulated carrier wave.

Frequency modulation is a way of changing frequency of the carrier signal in accordance to the amplitudes of the signal.

What are the Uses of Modulation?

Various uses of Modulation are, It reduces the height of Antenna It avoids mixing of signal. It increases communication range. It is improves reception quality.

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