ECE 321 - Amplitude Modulation Laboratory Exercise

Carrier: 38 kHz, Modulating Signal: 1 kHz, Modulation Index: 0 to 1

Pre-Lab: Theoretical Background

Learning Objectives

After completing this lab exercise, students will be able to:

Theory of Amplitude Modulation

Amplitude Modulation (AM) is a modulation technique used in electronic communication, most commonly for transmitting information via a radio carrier wave. In AM, the amplitude of the carrier wave is varied in proportion to the instantaneous amplitude of the modulating signal.

Mathematical Representation of AM:

\[ s(t) = A_c[1 + m \cdot \cos(2\pi f_m t)] \cdot \cos(2\pi f_c t) \]

Where:

\( A_c \) = Carrier amplitude

\( f_c \) = Carrier frequency (38 kHz in this lab)

\( f_m \) = Modulating frequency (1 kHz in this lab)

\( m \) = Modulation index (0 ≤ m ≤ 1)

Modulation Index

The modulation index (m) is a measure of the extent of amplitude variation about the unmodulated carrier level. It is defined as:

\[ m = \frac{A_{max} - A_{min}}{A_{max} + A_{min}} \]

Where \( A_{max} \) and \( A_{min} \) are the maximum and minimum amplitudes of the modulated waveform.

Important: For distortion-free AM, the modulation index must be between 0 and 1. If m > 1, overmodulation occurs, causing distortion in the demodulated signal.

Frequency Domain Representation

In the frequency domain, an AM signal consists of three components:

  1. Carrier frequency (fc): At 38 kHz with amplitude proportional to Ac
  2. Upper sideband (fc + fm): At 39 kHz with amplitude proportional to m·Ac/2
  3. Lower sideband (fc - fm): At 37 kHz with amplitude proportional to m·Ac/2

\[ S(f) = \frac{A_c}{2}[\delta(f - f_c) + \delta(f + f_c)] + \frac{mA_c}{4}[\delta(f - f_c - f_m) + \delta(f - f_c + f_m) + \delta(f + f_c - f_m) + \delta(f + f_c + f_m)] \]

Required Equipment

Function Generator 1

For 38 kHz carrier signal

Function Generator 2

For 1 kHz modulating signal

Analog Multiplier

Or AM modulator circuit

Oscilloscope

For time domain analysis

Spectrum Analyzer

For frequency domain analysis

Pre-Lab Questions

1. For an AM signal with carrier amplitude of 10V and modulation index of 0.8, what are the maximum and minimum amplitudes of the modulated wave?

A. Max = 18V, Min = 2V
B. Max = 10V, Min = 2V
C. Max = 18V, Min = -2V
D. Max = 20V, Min = 0V

Answer: A. Max = 18V, Min = 2V

Explanation: Using the formula: Amax = Ac(1 + m) = 10(1 + 0.8) = 18V, Amin = Ac(1 - m) = 10(1 - 0.8) = 2V.

2. What happens to the sideband amplitudes when the modulation index increases from 0 to 1?

A. They remain constant
B. They decrease linearly
C. They increase linearly
D. They become zero

Answer: C. They increase linearly

Explanation: The sideband amplitudes are proportional to m·Ac/2, so as m increases from 0 to 1, the sideband amplitudes increase linearly from 0 to Ac/2.

Laboratory Procedure

Part 1: Setting Up the Experiment

  1. Connect Function Generator 1 to produce a 38 kHz sine wave with amplitude of 5V peak-to-peak.
  2. Connect Function Generator 2 to produce a 1 kHz sine wave with adjustable amplitude.
  3. Connect both signals to the analog multiplier (AM modulator circuit).
  4. Connect the output of the modulator to the oscilloscope (Channel 1) and spectrum analyzer.
  5. Set the oscilloscope to display both the modulating signal (Channel 2) and the modulated signal (Channel 1).

Part 2: Time Domain Analysis

  1. Adjust the amplitude of the 1 kHz signal to achieve a modulation index of 0.3.
  2. Observe the AM waveform on the oscilloscope. Sketch the waveform.
  3. Measure the maximum and minimum amplitudes of the modulated wave.
  4. Calculate the modulation index using the measured values: m = (Amax - Amin) / (Amax + Amin).
  5. Repeat steps 1-4 for modulation indices of 0.5, 0.8, and 1.0.

Part 3: Frequency Domain Analysis

  1. Connect the spectrum analyzer to the output of the modulator.
  2. Set the spectrum analyzer center frequency to 38 kHz with a span of 10 kHz.
  3. Observe the frequency spectrum for m = 0.3. Note the amplitudes of the carrier and sidebands.
  4. Repeat for m = 0.5, 0.8, and 1.0.
  5. Verify that sideband amplitudes increase linearly with modulation index.

Interactive AM Simulation

Use the controls below to simulate AM with different modulation indices. Observe the changes in both time and frequency domains.

Time Domain: AM Waveform

Carrier: 38 kHz, Modulating: 1 kHz, m = 0.5

Frequency Domain: AM Spectrum

Carrier at 38 kHz, Sidebands at 37 kHz & 39 kHz

Modulating Signal (1 kHz)

Carrier Signal (38 kHz)

Expected Observations

Post-Lab Quiz

Test your understanding of amplitude modulation concepts covered in this lab exercise.

1. In an AM system with carrier frequency of 38 kHz and modulating frequency of 1 kHz, what are the frequencies of the sidebands?

A. 37 kHz and 39 kHz
B. 36 kHz and 40 kHz
C. 1 kHz and 38 kHz
D. 37.5 kHz and 38.5 kHz

2. An AM signal has a maximum amplitude of 12V and minimum amplitude of 4V. What is the modulation index?

A. 0.25
B. 0.33
C. 0.5
D. 0.67

3. What percentage of total power is in the sidebands when modulation index is 1?

A. 25%
B. 33%
C. 50%
D. 67%

4. What happens if the modulation index exceeds 1?

A. Sideband amplitudes decrease
B. Carrier amplitude increases
C. Overmodulation occurs causing distortion
D. The frequency of sidebands changes

5. For an AM signal with carrier power of 100W and modulation index of 0.8, what is the total transmitted power?

A. 100W
B. 132W
C. 164W
D. 180W

Amplitude Modulation Laboratory Exercise | For Undergraduate Electrical Engineering Students

This interactive lab exercise demonstrates amplitude modulation principles with carrier frequency of 38 kHz and modulating frequency of 1 kHz.