What is the primary purpose of amplitude modulation (AM) in communication systems?
To increase the power of the transmitted signal
To reduce the bandwidth of the signal
To enable transmission of baseband signals over long distances
To improve the signal-to-noise ratio
Correct Answer: To enable transmission of baseband signals over long distances
Amplitude modulation allows low-frequency information signals (like audio) to be efficiently transmitted over long distances by embedding them in high-frequency carrier waves. Baseband signals attenuate rapidly and can't propagate far through space, so modulation shifts the signal to a higher frequency band suitable for radio transmission.
2
What is the mathematical expression for a standard AM wave?
s(t) = Ac cos(2πfct) + Am cos(2πfmt)
s(t) = Ac [1 + μ m(t)] cos(2πfct)
s(t) = Ac cos(2πfct) × m(t)
s(t) = Ac cos(2π(fc + fm)t)
Correct Answer: s(t) = Ac [1 + μ m(t)] cos(2πfct)
The standard AM equation is:
sAM(t) = Ac [1 + μ · m(t)] cos(2πfct)
Where:
Ac = Carrier amplitude
μ = Modulation index (0 < μ ≤ 1)
m(t) = Normalized message signal (|m(t)| ≤ 1)
fc = Carrier frequency
The term [1 + μ m(t)] represents the time-varying amplitude of the carrier wave.
3
An AM wave has a maximum amplitude of 18V and a minimum amplitude of 6V. What is the modulation index?
0.25
0.4
0.5
0.6
Correct Answer: 0.5
The modulation index (μ) is calculated as:
μ = (Amax - Amin) / (Amax + Amin)
Plugging in the values:
μ = (18 - 6) / (18 + 6) = 12 / 24 = 0.5
This indicates under-modulation (μ < 1), which is distortion-free and suitable for envelope detection.
4
What occurs when an AM signal is over-modulated (μ > 1)?
The signal becomes more power efficient
The bandwidth is reduced by half
The carrier frequency shifts
Distortion occurs and envelope detection fails
Correct Answer: Distortion occurs and envelope detection fails
When μ > 1 (over-modulation):
The minimum amplitude of the AM wave becomes negative (Amin < 0)
Envelope detectors cannot track these reversals, causing clipping and distortion
Synchronous detection must be used instead for proper demodulation
The signal becomes more susceptible to noise interference
Over-modulation violates the condition |m(t)| ≤ 1, leading to non-linear distortion in the output signal.
5
A 1.5 MHz carrier is modulated by a 8 kHz audio signal. What is the bandwidth of the AM signal?
8 kHz
16 kHz
1.5 MHz
3 MHz
Correct Answer: 16 kHz
The bandwidth of an AM signal is given by:
BW = 2 × fm(max)
Where fm(max) is the highest frequency in the modulating signal.
In this case:
BW = 2 × 8 kHz = 16 kHz
This bandwidth contains the carrier frequency and both sidebands (USB and LSB). Note that the carrier frequency itself does not affect the bandwidth calculation.
6
What is the maximum theoretical power efficiency of standard AM?
25%
33.3%
50%
66.7%
Correct Answer: 33.3%
The efficiency of AM is calculated as:
η = [μ² / (2 + μ²)] × 100%
Efficiency is maximized when μ = 1 (critical modulation):
This efficiency limit is due to the carrier component, which contains two-thirds of the total power but carries no information. The sidebands contain the actual information but only use one-third of the power at maximum modulation.
7
Which components are essential in an envelope detector circuit for AM demodulation?
Operational amplifier and feedback resistor
Diode and RC network
Frequency mixer and local oscillator
Phase-locked loop and voltage-controlled oscillator
Correct Answer: Diode and RC network
An envelope detector consists of:
Diode: Rectifies the AM wave by allowing current flow in only one direction
RC network: The capacitor charges to the peak voltage during positive cycles and discharges through the resistor during negative cycles, tracking the envelope of the AM wave
This simple circuit is used in AM radios because it's low-cost and effective for signals with μ ≤ 1. The time constant of the RC network must be carefully chosen to follow the message signal variations without excessive ripple.
8
What occurs during critical modulation (μ = 1) in AM?
Carrier amplitude becomes zero
Bandwidth is minimized
Minimum amplitude touches zero
Signal becomes frequency modulated
Correct Answer: Minimum amplitude touches zero
At critical modulation (μ = 1):
The minimum amplitude of the AM wave touches zero: Amin = 0
Efficiency reaches its maximum (33.3%)
Envelope detectors can still demodulate the signal but become more sensitive to noise
The carrier envelope just reaches zero at its minimum points
The relationship between carrier and message amplitudes is: Am = Ac
This is the boundary between under-modulation and over-modulation. While theoretically optimal for efficiency, practical systems avoid μ = 1 due to its sensitivity to noise and potential for distortion.
9
Why is AM more susceptible to noise compared to frequency modulation (FM)?
Because AM uses higher frequencies
Because information is encoded in amplitude variations
Because AM receivers are less sophisticated
Because AM has lower bandwidth efficiency
Correct Answer: Because information is encoded in amplitude variations
AM is susceptible to noise because:
Noise primarily affects the amplitude of signals in communication channels
Since AM encodes information in amplitude variations, noise directly corrupts the message
In contrast, FM encodes information in frequency variations, which are less affected by amplitude noise
AM receivers have no effective way to distinguish between desired amplitude variations and noise-induced variations
Noise can cause envelope distortion, making it difficult to recover the original signal
This fundamental vulnerability is why FM is preferred for high-fidelity audio transmission despite its greater bandwidth requirements.
10
In commercial AM broadcasting, why is the modulation index typically kept below 1 (μ < 1)?
To reduce bandwidth requirements
To allow envelope detection and prevent distortion
To increase carrier power
To enable digital transmission
Correct Answer: To allow envelope detection and prevent distortion
In AM broadcasting, μ is typically kept between 0.3-0.8 because:
It allows simple envelope detectors to be used in receivers
It prevents distortion that occurs when μ > 1
It provides a margin of safety against noise that might cause over-modulation
It ensures compatibility with millions of existing AM radios
It maintains a reasonable balance between power efficiency and signal quality
Although critical modulation (μ = 1) is more efficient, practical systems trade some efficiency for reliability and compatibility with simple receiver designs.