friis: Friis power gain between two antennas.

In jbrzusto/sensorgnome-R-package: Tools for the sensorgnome project.

Description

Given the position and orientation of two antennas, calculate the one-way free space power gain between them, taking into account distance, antenna patterns, and polarization, but not atmospheric effects.

Usage

friis(ant1, ant2, waveLength = 3e+08/166380000)

Arguments

ant1	first antenna (a 'proto' object of class 'antenna')
ant2	second antenna (a 'proto' object of class 'antenna')
waveLength	in metres. Defaults to the wavelength of the telemetry band frequency 166.38 MHz

Author(s)

John Brzustowski jbrzusto@REMOVE_THIS_PART_fastmail.fm

References

http://en.wikipedia.org/wiki/Dipole_antenna#Half-wave_dipole

Examples

##
##
## simple test: 4 omnis set up at corners of 1000 metre square
## bird flies past on random path at random speed
##

## receivers: 4 vertical omni antennas at corners of 1000 metre square
## centred at (0, 0, 0)

rx = list (
   makeOmni(c( -500, -500, 0), "vertical"),
   makeOmni(c( -500,  500, 0), "vertical"),
   makeOmni(c(  500, -500, 0), "vertical"),
   makeOmni(c(  500,  500, 0), "vertical")
   )

## random uniform bird path (parallel to ground at random height)

## uniform velocity (x, y) each component in range [-10, 10] m/s
## and component 0 in z direction

velocity = c(runif(2, -10, 10), 0)

## constant height

height = runif(1, 0, 2000)

## random (x, y) location at time zero, in 2000 x 2000 metre square
## centred at (0, 0, 0)

loc0 = c(runif(2, -1000, 1000), height)

## path time interval is [-100, 100] seconds; tag bursts every 5 seconds

t = seq(from = -300, to = 300, by = 5)
n = length(t)
## path: n x 3 matrix giving x, y, z at each location

path =  t(t(outer(t, velocity, `*`)) + loc0)

## bird's transmitter antenna

tx = makeOmni(pos=path[1,], axis=velocity)

dB = function(x) 10*log10(x)

## calculate relative signal strength at each receiver at each point in time

tx$pos = path

rss = lapply(rx, function(x, y) dB(friis(x, y)), tx)

plot(t, rss[[1]], ylim=range(unlist(rss)))
for(i in 2:length(rx))
   points(t, rss[[i]], col=i)
plot(path[,1:2], xlim=c(-2000,2000), ylim=c(-2000,2000), type="l")
arrows(path[1,1], path[1,2], path[n,1], path[n,2])
for (i in seq(along=rx))
   points((t(rx[[i]]$pos[1:2])), pch=as.character(i), col=i)


## another test: each antenna oriented horizontally and perpendicular
## to displacement from origin

rx = list (
   makeOmni(c( -500, -500, 0), c(1, -1, 0)),
   makeOmni(c( -500,  500, 0), c(1, 1, 0)),
   makeOmni(c(  500, -500, 0), c(1, 1, 0)),
   makeOmni(c(  500,  500, 0), c(1, -1, 0))
   )

rss = lapply(rx, function(x, y) dB(friis(x, y)), tx)

plot(t, rss[[1]], ylim=range(unlist(rss)))
for(i in 2:length(rx))
   points(t, rss[[i]], col=i)
plot(path[,1:2], xlim=c(-2000,2000), ylim=c(-2000,2000), type="l")
arrows(path[1,1], path[1,2], path[n,1], path[n,2])
for (i in seq(along=rx))
   points((t(rx[[i]]$pos[1:2])), pch=as.character(i), col=i)



## now a Yagi antenna pointing NE at 45 degrees upward

a = makeYagi(n=9, axis1=c(45, 45), axis2="horizontal", pos=c(0, 0, 0))

## verify that the antenna pattern in the plane containing the antenna
## matches that of the antenna in standard position.

th=rad(0:360)

## a circle in the antenna's plane, starting in the antenna's major
## direction and going counter-clockwise (the antenna's axis matrix
## has the major axis on the second row; the cross-piece axis on the
## first row)
pl = cbind(cos(th), sin(th)) %*% a$axis[2:1,]

g = a$gain(pl)

scaled.g = 30 + pmax(-30, 10*log10(g))

plot(cos(th) * scaled.g, sin(th) * scaled.g)

jbrzusto/sensorgnome-R-package documentation built on May 18, 2019, 9:19 p.m.