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Wire and Wireless Communication Applications Chap. 8
8–18 Using the definition for the available power gain, G a ( f ), as given by (8–18), show that
G a ( f ) depends on the driving source impedance as well as the elements of the device and
that G a ( f ) does not depend on the load impedance. [Hint: Calculate G a ( f ) for a simple
resistive network.]
8–19 Show that the effective input-noise temperature and the noise figure can be evaluated from measurements
that use the Y-factor method. With this method the device under test (DUT) is first
connected to a noise source that has a relatively large output denoted by its source temperature,
T h , where the subscript h denotes “hot,” and then the available noise power at the output of the
DUT, P aoh is measured with a power meter. Next, the DUT is connected to a source that has
relatively low source temperature, T c , where the subscript c denotes “cold,” and noise power at
the output of the DUT is measured, P aoc . Show that
(a) The effective input noise temperature of the DUT is
T e = T h - YT c
Y - 1
where Y = P aoh P aoc is obtained from the measurements.
(b) The noise figure of the DUT is
F = [(T h>T 0 ) - 1] - Y[(T c >T 0 ) - 1]
Y - 1
where T 0 = 290 K.
8–20 If a signal plus noise is fed into a linear device, show that the noise figure of that device is given
by F = (SN) in (SN) out (Hint: Start with the basic definition of noise figure that is given in this
chapter.)
★ 8–21 An antenna is pointed in a direction such that it has a noise temperature of 30 K. It is connected
to a preamplifier that has a noise figure of 1.6 dB and an available gain of 30 dB over an effective
bandwidth of 10 MHz.
(a) Find the effective input noise temperature for the preamplifier.
(b) Find the available noise power out of the preamplifier.
8–22 A 10-MHz SSB-AM signal, which is modulated by an audio signal that is bandlimited to 5 kHz,
is being detected by a receiver that has a noise figure of 10 dB. The signal power at the receiver
input is 10 -10 mW, and the PSD of the input noise, ( f ) = kT2, is 2 × 10 -21 . Evaluate
(a) The IF bandwidth needed.
(b) The SNR at the receiver input.
(c) The SNR at the receiver output, assuming that a product detector is used.
★ 8–23 An FSK signal with R = 110 bs is transmitted over an RF channel that has white Gaussian noise.
The receiver uses a noncoherent detector and has a noise figure of 6 dB. The impedance of the
antenna input of the receiver is 50 Ω. The signal level at the receiver input is 0.05 mV, and the
noise level is N 0 = kT 0 , where T 0 = 290 K and k is Boltzmann’s constant. Find the P e for the
digital signal at the output of the receiver.
8–24 Work Prob. 8–23 for the case of DPSK signaling.
8–25 Prove that the overall effective input-noise temperature for cascaded linear devices is given by
Eq. (8–37).