Question

Question # B.5 signal power-level at the coresponding change in is signal power-level at the input is kept constant? Is C a linear function of temperature? Justify (a) In a communication system, suppose the associated operating temperature is doubled. Then, what is the corresponding change in the system capacity (C), if the (b) A mixer-stage in a radio receiver has a NF-20 dB and this mixer-stage is preceded by a preamplifier with a NF 9 dB. The available power-gain ratio of the amplifier is equal to A. The overall noise figure (NF) of the system with reference to the input is 10.44 dB. A signal of power level equal to 5 dBm is applied at the input of the preamplifier. Determine the power gain of the| preamplifier Hint: Refer to formula sheet Answer hints: Ai 15 dB

Answer 1

Question # B.5 (а) The expression for the signal-to-noise ratio is, SNR=Signal Power Noise Power Generally, the noise will be thermal noise. Thus, Noise Power = KTB Thus SNR= Signal Power KTB Here, k is Boltzmann's constant, T is temperature and B is bandwidth This means that SNR decreases when temperature increases. Since, the signal power-level is kept constant Assume that the signal-to-noise ratio for a temperature T is (SNR). Thus, the signal-to-noise ratio for a temperature 2T is (SNR) The expression for the Channel Capacity or System Capacity for a temperature T is CT Blog21(SNR For (SNR), >>>1 CT Blog2 ((SNR) And for a temperature 2T is 1 Cr Blog2 (SNR) Here, B is kept constant because the bandwidth of the channel B is same Thus (SNR),- Blog (SNR),) Ст — С — Blog,

1 (SNR 2 - Blog2SNR), 1 - Blog2 Therefore, the corresponding change in the system capacity (C), if the signal power-level at the input is kept constant is -B. The Channel Capacity C cannot be a linear function of temperature but logarithmic function of temperature from the expression (b) Consider the following block diagram of radio receiver: NF 20 dB (SNR) NF 9 dB (SNR), Preamplifier Mіxer Calculate the noise factor of the preamplifier 10log F 9 F 1009 7.943 = Calculate the noise factor of the mixer 10log F 20 F 102 100 The overall noise figure of the system is, 10log F 10.44 F, 101.044 11.066

Apply the Friis formula. F 1 Fr= F + 100-1 11.066 7.943 A 31.7 _ Thus, the power gain factor of the preamplifier is 31.7 In decibels 10log10 A10log.0 31.7 = 15 dB