A low-orbit weather satellite transmits a frequency-modulated image downlink at to a…

PHYSICS · Multi-part · Fermi University Physics · Electronics, Instrumentation & Communication · Communication systems and RF engineering · Communication systems and RF engineering

Electronics for Measurement, Ch Modulation, receivers and the link that carries the measurement

Problem

A low-orbit weather satellite transmits a frequency-modulated image downlink at

f_{\rm car} = 137\,\mathrm{MHz}

to a ground station a slant distance

d = 1000\,\mathrm{km}

away. The ground receiver is a superheterodyne with intermediate frequency

f_{\rm IF} = 10.7\,\mathrm{MHz}

and a local oscillator tuned below the carrier. Its preselector is built from identical tuned resonator stages of loaded quality factor

Q = 300

; one stage at offset

\Delta f

from its centre frequency

f_0

gives a rejection of

20\log_{10}(2Q\Delta f/f_0)\,\mathrm{dB}

, and

n

identical stages in cascade give

n

times that figure. The receiver must reject the image by at least

45\,\mathrm{dB}

. The satellite transmits

P_t = +33\,\mathrm{dBm}

from an antenna of gain

G_t = +3\,\mathrm{dBi}

; the ground antenna has gain

G_r = +15\,\mathrm{dBi}

, and

2.0\,\mathrm{dB}

of cable and connector loss sits before the receiver input. Free space with no other loss is assumed along the path. The link carries

f_{\rm dev} = 20\,\mathrm{kHz}

peak deviation and highest modulating frequency

f_m = 5\,\mathrm{kHz}

. The receiver's noise figure is

\mathrm{NF} = 3\,\mathrm{dB}

, its noise-equivalent bandwidth is taken equal to the Carson bandwidth, and the reference temperature is

T_0 = 290\,\mathrm{K}

. Frequency modulation is usable down to a carrier-to-noise ratio of about

10\,\mathrm{dB}

. ((a)) Find the image frequency and the ratio of the wanted frequency to the image frequency. ((b)) Find the smallest number of resonator stages meeting the

45\,\mathrm{dB}

image-rejection requirement, and the rejection they actually give. ((c)) Lay out the link budget in two steps: the received power between isotropic antennas with free-space path loss only, then with the stated antenna gains and cable loss included. ((d)) Find the receiver's noise floor and the carrier-to-noise ratio. ((e)) Find the frequency-modulation improvement above threshold and the output signal-to-noise ratio, and state the margin in carrier-to-noise ratio over the usability threshold.

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