A coastal monitoring buoy transmits its sea-temperature reading on 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 coastal monitoring buoy transmits its sea-temperature reading on a frequency-modulated carrier at

f_{\rm car} = 150\,\mathrm{MHz}

to a shore receiver a distance

d = 40\,\mathrm{km}

away. The 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 = 250

; one stage at an 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 in decibels. The receiver must reject the image by at least

55\,\mathrm{dB}

. The buoy transmits

P_t = +23\,\mathrm{dBm}

from an antenna of gain

G_t = +2\,\mathrm{dBi}

; the shore antenna has gain

G_r = +13\,\mathrm{dBi}

, and

1.5\,\mathrm{dB}

of cable and connector loss sits between the antenna and the receiver input. Free space with no other loss is assumed between the two antennas. The frequency modulation carries the temperature signal with peak deviation

f_{\rm dev} = 4\,\mathrm{kHz}

and highest modulating frequency

f_m = 3\,\mathrm{kHz}

. The receiver's noise figure is

\mathrm{NF} = 7\,\mathrm{dB}

, its noise-equivalent bandwidth is taken equal to the transmitted (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

55\,\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 the received power 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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