1. Signal Transmission and Channel Bandwidth
Contents
Modulation
Channel bandwidth
Vestigial side band transmission
Transmission efficiency
Complete channel bandwidth

2. Necessity of modulation
Need for modulation: There are three basic reasons of modulation:
To reduce antenna height
To increase radiation efficiency
To separate out the individual signal from the mutiplexed signal.
The greatest difficulty in the use of unmodulated wave is the need for long antennas for efficient radiation and reception. For example, a quarter-wavelength antenna for the transmitting frequency of 15 kHz would be 5000 meters long. A vertical antenna
of this size is unthinkable and in fact impracticable.
Signal radiation efficiency is proportional to frequency.
When same bandwidth signals are multiplexed, it is difficult to separate out them by filtering process.

3. Amplitude modulation
In amplitude modulation the intelligence to be conveyed is used to vary the amplitude of the carrier wave. An amplitude modulated signal is shown below

4. Amplitude modulation
The above equation may be expanded by the use of trigonometrical identities and expressed as :
This result shows that if a carrier wave having frequency equal to fc is amplitude modulated with a single frequency fm, the resultant wave consists of the carrier (fc) and the sum and difference components (fc± fm) of the carrier frequency and the modulating frequency.
The region between fc and (fc+ fm) is called the upper sideband (USB) and that between fc and (fc– fm) the lower sideband (LSB). Therefore if the modulated wave is to be transmitted without distortion by this method, the transmission channel must be at least of width 2fm centred on fc.

5. Channel bandwidth
Total channel bandwidth using double sideband picture signal. P is picture carrier and S is sound carrier.

6. Vestigial Side band
In the video signal very low frequency modulating components exist along with the rest of the signal. These components give rise to sidebands very close to the carrier frequency which are difficult to remove by physically realizable filters. Thus it is not possible to fully suppress one complete sideband. Any effort to completely suppress the lower sideband would result in objectionable phase distortion at these frequencies. This distortion will be seen by the eye as ‘smear’ in the reproduced picture. Therefore, as a compromise, only a part of the lower sideband, is suppressed, and the radiated signal then consists of a full upper sideband together with the carrier, and the vestige (remaining part) of the partially suppressed lower sideband. This pattern of transmission of the modulated signal is known as vestigial sideband.

7. Transmission efficiency
The total power Pt in the modulated wave is the sum of the carrier power Pc and the power in the two sidebands. This can be expressed as
Where is the r.m.s. value of the sinusoidal carrier wave, and R is the resistance in which the power is dissipated.
Eeps
At 100% modulation (m= 1) the transmitted power attains its maximum possible value. Pt (max) = 1.5 Pc, where the power contained in the two sidebands has a maximum value of 50% of the carrier power.

8. Complete Channel Bandwidth
TV channel sideband spectrum. C is color subcarriers
UK TV channel standard with vestigial sideband

9. Complete Channel Bandwidth
American TV channel standard with vestigial sideband
Sideband spectrum of two adjacent channels of the lower VHF
band of television station allocations

10. Demerits of Vestigial Sideband Transmission
A small portion of the transmitter power is wasted in the vestigial sideband filters which remove the remaining lower sideband.
Signal to noise voltage ratio decreases about 6 db relative to what be available if double sideband transmission is used.
Some phase and amplitude distortion of the picture signal occurs.
More critical tuning at the receiver is necessary because degeneration of picture quality is less with wider lower sideband than with narrow lower sideband.
Despite these demerits of vestigial sideband transmission it is used in all television systems because of the large saving it effects in the bandwidth required for each channel.

11. Frequency modulation
The sound signal is frequency modulated because of its inherent merits of interference-free reception. Here the amplitude of the modulated carrier remains constant, whereas its frequency is varied in accordance with variations in the modulating signal. The variation in carrier frequency is made proportional to the instantaneous value of the modulating voltage. The rate
at which this frequency variation takes place is equal to the modulating frequency.

12. Analysis of FM Wave
In order to understand clearly the meaning of instantaneous frequency fi and the associated instantaneous angular velocity ωi = 2πfωi, the equation of an ac wave in the generalized form may first be written as:
The instantaneous frequency
A frequency modulated wave with sinusoidal modulation can now be expressed as

13. Analysis of FM wave
The above equation can be commonly written in the form

14. FM channel bandwidth FM channel bandwidth
where fm is the frequency of the modulating wave and n is the number of the significant side frequency components. The value of n is determined from the modulation index
The maximum frequency deviation of commercial FM is limited to 75 kHz, and the modulating frequencies typically cover 25 Hz to 15 kHz.
The 625 line television standard specify that the maximum deviation (∆f) should not exceed ± 50 kHz for the highest modulating frequency of 15 KHz. Thus the modulation index
The resultant deviation of ± 75 kHz around the sound carrier is very much within the guard-band edge and reasonably away from any significant video sideband components.

15. How to calculate the value of n

16. Merits of FM modulation
Frequency modulation has the following advantages over amplitude modulation.
(a) Noise Reduction:
The greatest advantage of FM is its ability to eliminate noise interference and thus increase the signal to noise ratio. In FM, amplitude variations of the modulating signal cause frequency deviations and not a change in the amplitude of the carrier. Noise interference results in amplitude variations of the carrier and thus can be easily removed by the use of amplitude limiters.
(b) Transmitter Efficiency:
The amplitude of the FM wave is independent of the depth of modulation, whereas in AM it is dependent on this parameter. This means that low level modulation can be used in FM and all succeeding amplifiers can be class ‘C’ which are more efficient.
(c) Adjacent Channel Interference:
Because of the provision of a guard band in between any two TV channels, there is less interference than in conventional AM broadcasts.
(d) Co-channel Interference:
The amplitude limiter in the FM section of the receiver works on the principle of passing the stronger signal and eliminating the weaker. In this manner, a relatively weak interfering signal or any pick-up from a co-channel station (a station operating at the same carrier frequency) gets eliminated in a FM system.

17. Determine the transmitted signal power for SSB and DSB transmission after AM modulation with a carrier wave fc(t)= 75cos5000t. If the modulating signal varies fm(t)=40cos 500t. Assume any missing data.
Calculate the FM channel bandwidth for 625 line television standard that specify the maximum frequency deviation (∆f) should not exceed ± 50 kHz for the highest modulating frequency of 15 KHz.
Calculate the FM channel bandwidth for the maximum frequency deviation of ± 75 kHz. Assume that the highest modulating frequency cover 20Hz to 20kHz.