Amplitude Modulation and Demodulation



ECE1201- Electronic Measurements and Circuits Laboratory

Experiment #10-Amplitude Modulation and Demodulation

In this experiment, you will generate and display amplitude modulation signals, and investigate a simple AM receiver circuit.

Introduction:

1. Communication and Modulation.

Communication is the process of transmitting a message from one location to another though some medium. In wireless communication, such as radio, broadcast television, or cellular telephone, the medium is air. Modulation is the process of encoding the information in a message (voice, music, video, or data) onto a carrier signal whose frequency is much higher than that of the message. There are two practical reasons why modulation is necessary for efficient wireless communication:

• The minimum length of the antenna required for a practical transmitter or receiver is one-tenth of the signal wavelength, given by [pic], where f is the frequency and c is the speed of light. This means that the antenna needed to transmit a 10 kHz signal (e.g. music) would be 3 km in length!

• By using different carrier frequencies, many different radio stations, television stations, and cell phone users can each transmit and receive their signals simultaneously through the same medium.

2. Amplitude Modulation.

The AM in AM radio stands for amplitude modulation.  The idea is simple: take a sinusoidal signal called the carrier, and vary its amplitude according to the message one wishes to communicate.  Let [pic] be the message and let the carrier signal be [pic], where [pic] and [pic] is the carrier frequency.  For example WJAS AM 1320 has a carrier frequency of 1320 kHz or 1.32 MHz.  Then the AM signal that is broadcast by WJAS is given by

[pic].

The figures on the next page show this waveform. The underlying sinusoid is at the carrier frequency fc.

[pic]

Note that if there is no message, [pic], and [pic] is just a sine wave with a constant amplitude of [pic].  This signal is easy to visualize, but carries no message.

The constants A and B are set at the transmitter, and it is assumed that [pic] is normalized so that its maximum and minimum values are +1 and –1, respectively. Then B determines how much the amplitude of [pic] changes with [pic], and A is used to set the peak amplitude of the AM signal.

Next, let's assume that [pic] is also a sine wave, [pic], where [pic], and [pic] is typically much less than [pic].  In fact, for commercial AM radio, the FCC stipulates that [pic] must be less than 10 kHz, or roughly 130 times smaller than the carrier frequency for WJAS. Real messages are complicated signals containing many frequencies, but all frequencies must be less than 10 kHz. The transmitter for WJAS takes the message to be broadcast and generates the AM signal [pic]. An AM radio receiver takes [pic] (plus other interference) as input and must reproduce the message as accurately as possible.

3. Envelope and Modulation Percentage

The term that forms the amplitude of [pic] is called the envelope, and is denoted by [pic]. For Amplitude Modulation, the envelope is

[pic].

For a sinusoidal message, we have

[pic].

The percent modulation is a number that indicates the relative amplitudes of the message and carrier in an AM signal.  This is calculated as follows,

[pic].

For any message that satisfies [pic], this becomes

[pic].

Note that it is possible to have greater than 100% modulation if B > 1.

Part I: Pre-lab

1. In order to help you visualize AM, follow these steps to sketch an AM signal. For simplicity, assume [pic] and [pic].

(a) Sketch  [pic]versus t.  What are the max/min values?

(b) Sketch [pic]versus t on the same set of axes with [pic].

The space between the two sketches you have just drawn forms the envelope of [pic].  That is, the high frequency carrier [pic] varies between these upper

and lower limits.

c) Roughly sketch a high-frequency signal inside the envelope. This is the AM signal. 

d) Sketch additional AM waveforms for B = 0, 1/2, and 6/5 and 3/2. Determine the modulation percentage for each waveform and write it next to the appropriate sketch.

2. The goal of an AM receiver is to recover the message [pic]. An ideal envelope detector takes the AM signal [pic] as input and produces the absolute value of the envelope as output. You will design and build an approximation to such a circuit later in this lab.

For each of the AM waveforms you sketched in the last part, sketch the corresponding output of an ideal envelope detector. For what modulation percentages is it possible to recover the message [pic] from [pic]?

You should also generate (in the prelab) a PSPICE simulation for the operation of envelope detector shown in Part III of this lab. The PSPICE manual written by Prof. Jan Van der Spiegel from the University of Pennsylvania (accessible here) will be useful in doing this simulation.

Part II: AM signal

Reference: page 2-27 to 2-28 of online signal generator manual. Available here.

We will first use one function generator (CH1) and internally modulate it. Secondly we will modulate one generator (CH1) by the second generator (CH2) Modulation depths up to 120% (1.2) are available for internal modulation but only 60% for external modulation.

1. Internal modulation.

a) Turn on a function generator (CH1) and set it to produce a sine wave. Set the frequency to that of one of the commercial AM radio stations in Pittsburgh, and set the amplitude to 1 V. Connect this signal to the oscilloscope, and set the controls so that you see several periods of the waveform. This signal is the carrier signal.

b) Modulation Signal. Select modulation (Mod). Choose AMFreq (the modulation frequency). Set the frequency somewhere between 500 Hz and 5 kHz. Set the modulation depth (Depth) and investigate modulation depths of 0, 50%, 100% and 120%. Take a picture of each of these waveforms.

2. External modulation.

a) Set the carrier frequency to the frequency of a Pittsburgh AM radio station. Use CH1 for the carrier frequency. (Avoid frequencies with 25 kHz or 1 MHz).

b) Set the modulation frequency to be between 500Hz to 5kHz. Use CH2 to generate this frequency. Connect the output from CH2 to the rear of the function generator (Modulation In).

c) Press mod, SrcInt to choose SrcExt (external modulation)

d) Trigger on the modulation signal, and set the controls so that a few periods of this signal are visible. Obtain scope images for modulation depths 10%, 50% and the maximum possible (60%). Please note: an external modulation signal of 5V peak (10 V peak to peak) will produce 100% modulation depth. Modulation depth is proportional to the amplitude of the external modulating signal.

3. Experiment with different modulating waveforms other than a sine wave, and vary the carrier frequency, modulating frequency, and modulation percentage. Obtain scope images of a few interesting examples.

4. Explain how the amplitudes and frequencies of the two function generators correspond to the parameters in the equation for the AM signal[pic].

Part III: Envelope Detector

1. Construct the circuit shown below. The goal is to provide the AM signal [pic] at the input, and produce the message [pic] as accurately as possible at the output. Design the RC time constant of the circuit to achieve this goal. Simulate this circuit using PSPICE. (How can you use PSPICE to generate an AM signal?) Clarification (added November 21, 2006): Record the output of the envelope detector for two different values of modulation index B. For each value of modulation index do a corresponding PSPICE simulation. When you do the simulation, be sure to use the actual values of A, B, modulation frequency and carrier frequency that you use in the circuit. It may help to include the output impedance of the generator (50() in your simulations. If the output form the envelope detector is not a perfect sine wave, explain the discrepancy.

[pic]

2. Connect the message [pic] to the input of your envelope detector, and obtain a scope image showing the input and output signals. Repeat using the unmodulated carrier signal as the input. Explain the appearance of both images. How should these images appear if you have chosen your RC time constant correctly?

3. Connect the AM signal [pic] to the input of your envelope detector, and obtain a scope image showing the input and output signals. Comment on the performance of the detector in recovering the message, using scope images as necessary. If the amplitude of s(t), A is small (1 V??) then the message g(t) may not be reproduced accurately. Why?

Note: In the following steps, you are asked to change various parameters. In each case, reset the parameters to the original values before proceeding to the next step.

4. Vary the modulation percentage of the AM waveform and determine the effect on the output of the envelope detector. For what modulation percentage does the detector accurately reproduce the message [pic]? Does the fidelity of reproduction depend on the amplitude (A) of s(t) or only on the modulation percentage?

5. Using a decade box, vary the time constant of your envelope detector. For what range of values does it work well? Change the message [pic] to other waveforms: square, triangle, etc. Does this affect the range of RC values that yield good performance?

Clarification-parts 3-5 (added November 21, 2006): Record the output of the envelope detector for at least two different values of modulation index B. For each value of modulation index do a corresponding PSPICE simulation. For each modulation index choose at least two values of the amplitude of the carrier signal. When you do the simulations, be sure to use the actual values of A, B, modulation frequency and carrier frequency that you use in the circuit. It may help to include the output impedance of the generator (50() in your simulations. If the output form the envelope detector is not a perfect sine wave, explain the discrepancy.

6. In a real AM receiver, the incoming signal is very weak and must be amplified before the message can be recovered. To investigate this, decrease the amplitude of the AM signal [pic] until it is very small. What effect does this have on the recovered message?

7. Change the message signal to a 50 kHz sine wave. (External modulation must be used. The maximum frequency for internal modulation is 20 kHz.) Vary the time constant of your envelope detector again until optimum performance is achieved. Why is it more difficult to obtain acceptable performance in this case? Design an additional circuit that could be used to improve the quality of the recovered message produced by your envelope detector.

Updated: November 11, 2004, minor change October 21, 2005. Update November 22, 2005

Reviewed March 22, 2006, Change to last part April 3, 2006. Change to Pre-lab requirements November 8, 2006.

Two clarifications added November 21, 2006. Lab reviewed November 6, 2007

One clarification added March 25, 2008.

Minor change November 19, 2008

Update for Rigol, July 27-28, 2011

Update November 16, 2011 and March 26, 2012

Prelab Revised August 21, 2017

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