Communication Systems — JEE Mains Physics

Formulas (2)

• Elements of a communication system and the number of channels · Number of channels
  $$N = \frac{\text{available bandwidth}}{\text{bandwidth of one channel}}, \qquad f = \frac{c}{\lambda}$$
• Antenna length and why a high-frequency carrier is needed · Antenna length and radiated power
  $$l_{\min} = \frac{\lambda}{4} = \frac{c}{4f}, \qquad P \propto \left(\frac{l}{\lambda}\right)^{2}$$

Reference tables (1)

Watch out for (10)

• Find the frequency before taking the percentage
  → Elements of a communication system and the number of channels
• A repeater is a receiver and a transmitter
  → Elements of a communication system and the number of channels
• Attenuation and demodulation are easy to swap
  → Elements of a communication system and the number of channels
• kHz for AM, MHz for FM
  → Frequency bands, propagation modes and atmosphere layers
• Uplink is the higher frequency
  → Frequency bands, propagation modes and atmosphere layers
• Use NCERT's layer labels
  → Frequency bands, propagation modes and atmosphere layers
• A quarter, not a half
  → Antenna length and why a high-frequency carrier is needed
• Size the antenna for the carrier
  → Antenna length and why a high-frequency carrier is needed
• Divide c by the refractive index in a medium
  → Antenna length and why a high-frequency carrier is needed
• Largest antenna, lowest frequency
  → Antenna length and why a high-frequency carrier is needed

Formulas (2)

• Range of one antenna on a round earth · Line-of-sight range of one antenna
  $$d = \sqrt{2Rh}, \qquad A = \pi d^{2} = 2\pi R h$$
• Range between a transmitting and a receiving antenna · Line-of-sight range of two antennas
  $$d_M = \sqrt{2Rh_T} + \sqrt{2Rh_R}$$

Watch out for (6)

• Increased by, or increased to
  → Range of one antenna on a round earth
• Keep one unit inside the root
  → Range of one antenna on a round earth
• The range grows as the square root
  → Range of one antenna on a round earth
• Add the ranges, not the heights
  → Range between a transmitting and a receiving antenna
• Do not forget the second antenna
  → Range between a transmitting and a receiving antenna
• Identical towers divide by 8R
  → Range between a transmitting and a receiving antenna

Formulas (3)

• Amplitude modulation and the modulation index · Modulation index
  $$\mu = \frac{A_m}{A_c}, \qquad \mu \le 1$$
• Maximum and minimum amplitude of an AM wave · Modulation index from the envelope
  $$\mu = \frac{A_{\max} - A_{\min}}{A_{\max} + A_{\min}}, \qquad A_{\text{side band}} = \frac{\mu A_c}{2} = \frac{A_m}{2}$$
• Side-band frequencies and the bandwidth of an AM wave · Side bands and bandwidth
  $$f_{\text{LSB}} = f_c - f_m, \quad f_{\text{USB}} = f_c + f_m, \qquad \text{BW} = 2f_m$$

Watch out for (10)

• Message over carrier, not the other way
  → Amplitude modulation and the modulation index
• Read the amplitude, not the swing
  → Amplitude modulation and the modulation index
• It is the carrier whose amplitude changes
  → Amplitude modulation and the modulation index
• μ is not the ratio of the largest to the smallest
  → Maximum and minimum amplitude of an AM wave
• A side band carries half the message amplitude
  → Maximum and minimum amplitude of an AM wave
• Check which ratio is asked
  → Maximum and minimum amplitude of an AM wave
• Convert ω to f first
  → Side-band frequencies and the bandwidth of an AM wave
• The message frequency is not in the AM wave
  → Side-band frequencies and the bandwidth of an AM wave
• Bandwidth is twice the message frequency
  → Side-band frequencies and the bandwidth of an AM wave
• Each station needs 2fₘ, not fₘ
  → Side-band frequencies and the bandwidth of an AM wave