JEE Physics Communication System Notes Set 01

Communication System and Modulation

A communication system has a transmitter, a transmission channel and a receiver. The transmitter converts the information (sound, picture or data) into an electrical signal and sends it into the channel (wire, optical fibre, free space), where noise is added. The receiver recovers the information and delivers it to the destination.
Analog signals vary continuously, digital signals take only two levels (0 and 1) and are more reliable and easy to store and process. An audio signal has frequency 20 Hz to 20 kHz and a TV signal needs a bandwidth of about 6 MHz.
A baseband signal cannot be sent directly over a long distance because (1) an efficient antenna must have a length comparable to the wavelength, which is impractically large at low frequency, (2) signals from many sources would mix, and (3) low-frequency radiation is poorly radiated. We therefore modulate: the signal is superimposed on a high-frequency carrier. Modulation reduces antenna size, allows many stations at different carrier frequencies (selectivity) and reduces the fractional bandwidth. It does not make the signal travel faster.

Amplitude Modulation

In amplitude modulation (AM) the amplitude of the carrier \( c(t)=A_c\sin\omega_ct \) is varied in proportion to the signal \( m(t)=A_m\sin\omega_mt \):
\[ c_m(t)=A_c\sin\omega_ct+\frac{mA_c}{2}\cos(\omega_c-\omega_m)t-\frac{mA_c}{2}\cos(\omega_c+\omega_m)t \]
The modulation index is \( m=\frac{A_m}{A_c}=\frac{V_{max}-V_{min}}{V_{max}+V_{min}} \), and it should not exceed 1 (100%), otherwise the envelope is distorted. The wave contains three frequencies: \( f_c \), \( f_c+f_m \) (upper sideband) and \( f_c-f_m \) (lower sideband). The bandwidth is \( 2f_m \) and the carrier frequency must be much larger than \( f_m \).
Power: \( P_c=\frac{A_c^2}{2R} \), total power \( P_T=P_c\left(1+\frac{m^2}{2}\right) \), and the fraction in the sidebands is \( \frac{m^2}{2+m^2} \). The information is carried only by the sidebands, so AM is wasteful of power. Its limitations are noise, low efficiency and small operating range.
A demodulator (detector) recovers the signal: a diode rectifies the AM wave and an RC filter removes the carrier.

Frequency and Phase Modulation

In frequency modulation (FM) the frequency of the carrier varies with the signal amplitude, while the carrier amplitude stays constant; in phase modulation the phase varies. FM is almost immune to amplitude noise, gives better sound quality and is used in VHF broadcasting (88 to 108 MHz), at the cost of a larger bandwidth. Commercial AM radio uses the medium-wave band, and TV uses VHF/UHF.
Pulse modulation (PAM, PWM, PPM) and pulse code modulation (PCM) are used for digital transmission.

Propagation of Electromagnetic Waves

Ground (surface) wave: travels along the earth's surface, used for frequencies up to about 1.5 MHz (medium and long waves). The range depends on the frequency (higher frequencies are absorbed more) and on the transmitter power.
Sky wave: reflected back by the ionosphere, used from 1.5 MHz to about 30 MHz for long-distance (short-wave) communication. The highest frequency reflected for vertical incidence is the critical frequency \( f_c=9\sqrt{N_{max}} \) (N in m⁻³). Sky wave signals are less stable than ground wave signals because the ionosphere varies with time of day and season (fading).
Space wave (line of sight): used above about 30 MHz (VHF, UHF, microwaves) for TV, FM, mobile and satellite links. The range of a transmitting antenna of height h is \( d=\sqrt{2Rh} \); when both transmitter and receiver have antennas, \( d=\sqrt{2Rh_T}+\sqrt{2Rh_R} \). The area covered is \( A=\pi d^2 \). A geostationary satellite orbits at a height of about 36,000 km (about 6 Re) with a period of 24 hours and is used to relay signals over large distances.
Frequency bands: HF 3 to 30 MHz, VHF 30 to 300 MHz, UHF 300 to 3000 MHz, SHF 3 to 30 GHz.

Optical Fibre Communication

An optical fibre guides light by total internal reflection at the boundary between a core of refractive index \( \mu_1 \) and a cladding of lower index \( \mu_2 \). It carries information as modulated light with very large bandwidth and little loss, and is free from electrical interference. The speed of electromagnetic waves in a medium is \( v=\frac{c}{\sqrt{\varepsilon_r\mu_r}} \).

Worked Examples

Worked Example 1. A carrier of amplitude 10 V is modulated by a signal of amplitude 4 V. Find the modulation index and the maximum and minimum amplitudes of the AM wave.
Answer:
\( m=\frac{4}{10}=0.4 \). \( V_{max}=10+4=14\ \text{V} \), \( V_{min}=10-4=6\ \text{V} \).

Worked Example 2. A 1 MHz carrier is amplitude modulated by a 5 kHz signal. Find the sideband frequencies and the bandwidth.
Answer:
Sidebands: \( 1000-5=995\ \text{kHz} \) and \( 1000+5=1005\ \text{kHz} \). Bandwidth \( =2\times5=10\ \text{kHz} \).

Worked Example 3. A TV tower is 100 m tall. Find the range of the broadcast and the area covered (R = 6400 km).
Answer:
\( d=\sqrt{2\times6.4\times10^6\times100}=\sqrt{1.28\times10^9}=3.58\times10^4\ \text{m}\approx35.8\ \text{km} \).
Area \( =\pi d^2=3.14\times(35.8)^2\approx4000\ \text{km}^2 \).

Worked Example 4. For 100% modulation, what fraction of the total power is carried by the carrier?
Answer:
\( P_T=P_c\left(1+\frac12\right)=1.5P_c \), so the carrier carries \( \frac{1}{1.5}=\frac23 \) of the total power; the sidebands carry one-third.