Arrange the following modulation systems in decreasing order of the bandwidth requirements. A. Single Side Band B. Double Side Band C. Vestigial Side Band D. Frequency Modulation Choose the correct answer from the options given below
D, B, C, A
Understanding Modulation System Bandwidth Requirements
Modulation is a crucial process in communication systems where a characteristic of a carrier wave is varied in accordance with a message signal. Different modulation techniques have different bandwidth requirements, which is the range of frequencies needed to transmit the modulated signal effectively. The bandwidth directly impacts how much data can be transmitted and the efficiency of spectrum usage.
Let's analyze the bandwidth requirements for each of the given modulation systems, assuming the maximum frequency of the message signal is \(f_m\).
Bandwidth Analysis of Modulation Types
- Double Side Band Suppressed Carrier (DSB-SC) or just DSB: In DSB modulation, both the upper sideband and the lower sideband of the modulated signal are transmitted. The bandwidth required is twice the maximum frequency of the message signal.
Bandwidth (\(BW_{DSB}\)) \( = 2 \times f_m \) - Single Side Band (SSB): In SSB modulation, only one sideband (either upper or lower) is transmitted. This makes SSB the most bandwidth-efficient amplitude modulation technique.
Bandwidth (\(BW_{SSB}\)) \( = f_m \) - Vestigial Side Band (VSB): VSB modulation is a compromise between DSB and SSB. It transmits one full sideband and a portion (vestige) of the other sideband, along with the carrier (though carrier can be suppressed in VSB-SC). This technique is commonly used in television broadcasting. Its bandwidth is greater than SSB but less than DSB.
Bandwidth (\(BW_{VSB}\)) \( = f_m + f_v \), where \(f_v\) is the bandwidth of the vestigial sideband (\(0 < f_v < f_m\)).
Typically, \(BW_{VSB}\) is slightly greater than \(f_m\). - Frequency Modulation (FM): FM is a type of angle modulation where the frequency of the carrier wave is varied in proportion to the message signal. The bandwidth of an FM signal depends on both the maximum frequency deviation (\(\Delta f\)) and the maximum message frequency (\(f_m\)). According to Carson's Rule (for wideband FM), the bandwidth is approximately:
Bandwidth (\(BW_{FM}\)) \( \approx 2 (\Delta f + f_m) \)
For narrowband FM, \(BW_{FM} \approx 2 f_m\), similar to DSB. However, standard FM used in broadcasting is wideband FM, which has a significantly larger bandwidth compared to AM techniques like DSB, SSB, and VSB.
Comparing Bandwidth Requirements
Based on the analysis, we can compare the typical bandwidth requirements:
\(BW_{SSB} = f_m\)
\(BW_{VSB} \approx f_m + f_v\)
\(BW_{DSB} = 2 f_m\)
\(BW_{FM} \approx 2 (\Delta f + f_m)\)
In typical scenarios, especially for wideband FM, \(\Delta f\) is much larger than \(f_m\), making \(BW_{FM}\) significantly larger than \(2f_m\). Thus, the bandwidth order from largest to smallest is generally:
FM > DSB > VSB > SSB
This corresponds to the order of the given options:
- D. Frequency Modulation (FM)
- B. Double Side Band (DSB)
- C. Vestigial Side Band (VSB)
- A. Single Side Band (SSB)
The decreasing order of bandwidth requirements is D, B, C, A.
| Modulation Type | Abbreviation | Typical Bandwidth |
|---|---|---|
| Single Side Band | SSB | \(f_m\) |
| Vestigial Side Band | VSB | \(f_m + f_v\) (\(f_m < BW_{VSB} < 2f_m\)) |
| Double Side Band | DSB | \(2f_m\) |
| Frequency Modulation | FM | \(\approx 2(\Delta f + f_m)\) (usually \(BW_{FM} > 2f_m\)) |
Arranging these in decreasing order of bandwidth:
- Frequency Modulation (FM) - Largest bandwidth
- Double Side Band (DSB)
- Vestigial Side Band (VSB)
- Single Side Band (SSB) - Smallest bandwidth
Conclusion on Modulation Bandwidth Order
The decreasing order of bandwidth requirements for the given modulation systems is Frequency Modulation (D), Double Side Band (B), Vestigial Side Band (C), and Single Side Band (A).
Revision Table: Modulation Bandwidth Summary
| Modulation System | Relative Bandwidth | Efficiency | Common Applications |
|---|---|---|---|
| SSB (Single Side Band) | \(f_m\) (Most efficient AM) | High | Voice communication (e.g., amateur radio, point-to-point) |
| VSB (Vestigial Side Band) | \(f_m + f_v\) (Compromise) | Moderate | TV broadcasting |
| DSB (Double Side Band) | \(2f_m\) (Least efficient AM) | Low | Analog TV sound, early radio systems, laboratory use |
| FM (Frequency Modulation) | Typically \( >> 2f_m \) (using Carson's Rule) | Low spectral efficiency per channel, but good noise immunity | FM radio broadcasting, television audio, mobile radio |
Additional Information: Factors Affecting Bandwidth
While \(f_m\) is a primary factor for AM techniques, other aspects influence the required bandwidth:
- Nature of the Message Signal: The frequency content of the original signal (voice, music, data) determines \(f_m\).
- Modulation Index (for FM/PM): For angle modulation like FM, the modulation index (\(\beta = \Delta f / f_m\)) significantly impacts the bandwidth as per Carson's Rule. Higher deviation or higher message frequency increases bandwidth.
- Filtering: Practical implementations often involve filtering the modulated signal, which affects the occupied bandwidth.
- Transmission Standards: Specific communication standards (like those for radio or TV broadcasting) define channel bandwidths allocated for different modulation types.
Understanding the bandwidth is crucial for efficient spectrum utilization and designing communication systems that meet performance requirements.
Important Questions from Amplitude Modulation
The highest modulation frequency typically used in AM broadcast is
Which of the following is NOT the advantage of amplitude modulation?
The frequency range of AM radio is:
In an amplitude modulated system, a sinusoidal carrier signal of 1 MHz is modulated by a 10 kHz sinusoidal signal. If the lower sideband and the carrier are suppressed and if the amplitude modulated signal is sampled for further processing, what should be the minimum sampling frequency for baseband sampling?
A 10kW carrier is simultaneously modulated by two modulating signals corresponding to a modulation index of 40% and 30%, respectively. The total radiated power will be:
