[Fwd: LF: LF propagation abstract]
Andre' Kesteloot
akestelo@bellatlantic.net
Tue, 15 Dec 1998 08:25:48 -0500
A very interesting paper on propagation as it applies to LF
Andre'
*******************************************************
Soegiono, Gamal wrote:
> soegiono@nm.hsd.utc.com
>
> LF Propagation
>
> This abstract intends to give an overview to the relevant mechanism of
> propagation of RF waves in the LF range, which according to ITU
> addresses frequencies from 30kHz to 300kHz. As usual a lot of
> simplifications are
> necessary to describe natural effects. This is called modelling. The
> following explanations are based on simplified, but scientifically
> accepted models
> to ease assumptions and predictions on propagation properties.
>
> Some of the basic simplifications are:
> The earth is a sphere.
> The earths surface is smooth and homogen.
> The earths electrical properties are (at least in certain regions)
>
> homogenious and constant.
> The ionosphere consists of tiny layers of distinct height above
> the earths surface having constant reflectivity (at least for
> portions of a day, season, solar cycle).
>
> There are essentially two modes of propagation relevant in the LF range.
> Ground Wave Propagation and Sky Wave Propagation.
>
> Ground Wave Propagation
>
> Ground Wave Propagation concerns electromagnetic fields traveling
> along the earths surface, while inducing and being induced by
> currents flowing on and slightly below the earths surface. Sometimes
> those fields are referred to as the surface wave.
>
> If the electrical properties of the earths soil were ideal, i.e.
> infinite conductivity, unity permittivity, unity permeability, then the
> field strength of the ground wave would strictly follow the "rule of
> inverse distance". If at a distance of 1km the field strength is
> 1mV/m, then at a distance of 10km it is 100uV/m and at 1000km 1uV/m.
> This is not the case, because the conductor "earth" is in no way
> perfect.
> Conducting RF currents in it cause energy from the RF field being
> converted into heat.
>
> For the practical prediction of the ground waves fieldstrength,
> CCIR has issued Recommendation 368-6, which consist of a set
> of diagrams for typical ground properties. Each diagram contains
> graphs showing available fieldstrength for 25 frequencies from
> 10kHz to 30MHz in dependance of the distance. This method was
> compiled from a mathematical model and verified to provide
> accurate data by practical measurements.
>
> For use in our 136kHz band I pick the 150kHz-graph for "average
> ground" (sigma=3mS/m, epsilon=22) and compile the values for
> a standardized ERP = 1 W. To adapt to other values of ERP
> use the equation
> E(ERP) = E(1W) + 10*log(ERP/1W)
>
> 100 km 37 dBuV/m
> 200 km 28 dBuV/m
> 300 km 23 dBuV/m
> 400 km 18 dBuV/m
> 500 km 13 dBuV/m
> 600 km 9 dBuV/m
> 700 km 5 dBuV/m
> 800 km 1 dBuV/m
> 900 km - 2 dBuV/m
> 1000 km - 6 dBuV/m
> 1100 km - 9 dBuV/m
> 1200 km -13 dBuV/m
> 1300 km -17 dBuV/m
> 1400 km -20 dBuV/m
> 1500 km -23 dBuV/m
> 1600 km -27 dBuV/m
> 1700 km -30 dBuV/m
> 1800 km -34 dBuV/m
> 1900 km -37 dBuV/m
> 2000 km -40 dBuV/m
> 2100 km -43 dBuV/m
> 2200 km -47 dBuV/m
>
> The practical ground wave coverage range would depend on the
> lowest fieldstrength discernable from external noise in a given
> receiver IF Bandwidth (signal equals noise). Assuming an
> IF-BW=500Hz an equivalent external noise level expressed as
> vertical field strength of -9dBuV/m would classify a "very quiet
> site" (Recommendation ITU-R PI.372-6) for natural, atmospheric
> as well as artifical, man-made noise.
>
> A radiated power of 1 W then yields a boundary of useful ground
> wave coverage (wanted signal equals external noise) in
> dependece of the ground properties (assumed homogeneous) over
> a depiced ground path as follows:
>
> range ground condition ground parameters
> 1600 km sea water sigma= 5 S/m epsilon=70
> 1600 km marsh land sigma= 30 mS/m epsilon=40
> 1450 km wet ground sigma= 10 mS/m epsilon=30
> 1080 km fresh water sigma= 3 mS/m epsilon=80
> 1100 km average ground sigma= 3 mS/m epsilon=22
> 700 km medium dry ground sigma= 1 mS/m epsilon=15
> 430 km dry ground sigma=300 uS/m epsilon=7
> 290 km very dry ground sigma=100 uS/m epsilon=3
> 200 km fresh w. ice - 1Cels. sigma= 30 uS/m epsilon=3
> 180 km fresh w. ice -10Cels. sigma= 10 uS/m epsilon=3
>
> Sky Wave Propagation
>
> Sky Wave Propagation concerns electromagnetic fields leaving the
> antenna in two ways. One traveling in a straight line which encloses
> a positive angle (take-off angle = TOA) with the ground level, the
> other one in a straight line which encloses a negative angle with
> the ground level. The latter line bounces the ground level at a certain
> distance, to be reflected and finally travelling in parallel (with a
> phase delay) with the former line. Some refer the first skywave portion
> as the direct wave, the second skywave portion as the ground reflected
> wave.
>
> Depending on the ground properties at the TX antenna site, depending on
> the polarization of the antenna (vertical in this sense) and the value of
> the TOA, the combined skywave traveling upwards to the ionosphere has
> differing energy content for the same ERP.
>
> The combined skywave traveling upwards reaches the boundary of
> the ionosphere at a certain ground-distance from the TX site. It's
> direction of travel encloses an angle with the line perpendicular to
> the boundary's area (angle of ionospheric impact = AOI). The skywave
> then penetrates the ionospheric region, exchanges energy with the
> molecules and ions present there, while being continuously refracted.
> Refraction occurs due to the fact that in the conductive ionospheric
> region the speed of propagation increases with the rate of ionization.
> The higher rays of the travelling wave penetrating into the ionospheric
> region become higher speed than the lower rays. This is similar to
> the effect observeable on a light beam traveling through a prisma of
> glas.
>
> Assuming the ionospheric refraction coefficient were high enough to aim
> the direction of travel back towards ground, the refracted skywave then
> will leave the ionospheric region with quite the same AOI and will
> arrive ground level at twice the former mentioned ground-distance with an
>
> angle equal to the former TOA.
>
> Assuming the ionospheric refraction coefficient were too low, the
> incoming skywave would fully pass the first ionospheric region
> under a now modified direction of travel to reach the next ionospheric
> region. While passing the first region, the energy content of the
> skywave would have decreased (inversely proportional to the frequency
> squared).
>
> As the boundaries of the ionosphere constitute shells of spherical shape,
> they tend to focus the arriving skywave (analogy to spherical mirrors).
> Assuming the arriving wave consists of parallel rays, the departing rays
> then become convergent.
>
> CCIR has issued Report 265-7 which provides a simplified model of
> ionospheric refraction and attenuation, incorporating most of the
> former mentioned effects using tailored diagrams derived from
> practical measurements and normalization thereof for frequencies
> from 30 kHz to 500 kHz.
>
> The method is based on reducing the "true" ionosphere into a tiny
> layer of zero thickness, having a constant height of 70km during
> daytime and 90km during night-time. The geometric path of the
> skywave is approximated by straight lines (ray method), the actual,
> continuous refraction is replaced with distinct reflection
> (mirror analogy).
>
> Effects of ground dependent vertical antenna pattern is accounted
> for by introducing a factor "Ft" for the TX antenna, "Fr" for the
> RX antenna in dependence of the ground properties in the
> first fresnel zone arround the antennas site, the actual TOA
> and the actual operating frequency.
>
> Effects of ionospheric focusing is accounted for by a factor
> "D" in dependence of the TX-RX ground distance, actual operating
> frequency and time of day (daytime, night-time).
>
> The energy exchange with the refracting ionosphere is accounted
> for by a factor "RC" (reflection coefficient) in dependence of the
> normalized frequency, time of day, season of year and epoch of
> solar activity. The basic data are for an typical minimum epoch of
> the solar activity, showing three graphs (day-time in winter,
> day-time in summer and night-time). The normalized frequency is
> the product of the cosine of AOI and the actual operation frequency.
>
> It is a time consuming job to combine all the highly empiric diagrams
> for Fr, Ft, D, RC together into the final equation to derive
> skywave fieldstrengths "Es" for a given ERP in Watts, operating
> frequency "f" in kHz, variable TX-RX ground distance "d" in
> km - even for a single time of day, season of year and epoch
> of solar activity.
>
> >From "simple" geometric evaluation, values for ionospheric path
> length (IPL), TOA, AOI can be derived for a given ground distance
> "d" using the following constants:
>
> h: daytime height (hday=70km), or night-time height (hnight=90km)
> U: earths circumference (U=40074 km)
>
> deriving:
>
> great circle angle in between TX and RX site
> c=d*2*pi/U angle in radians
> c=d*360/U angle in degrees
>
> earths radius (km)
> R = U/(2*pi) angle in radians
> R = U/(360) angle in degrees
>
> half the IPL (km)
> i = (R^2+(R+h)^2-2*R*(R+h)*cos(c/2))^0.5
>
> angle of ionospheric incidence
> AOI = asin((R*sin(c/2))/i)
>
> take-off angle
> TOA = pi/2-c/2-AOI angle in radians
> TOA = 90-c/2-AOI angle in degrees
>
> ionospheric path length (km)
> IPL = 2*i
>
> To read the reflection coefficient from the diagram we
> need the effective frequency (kHz)
> feff =f*cos(AOI)
> and obtain "RC" for a season and a time of day during solar minimum.
>
> skywave fieldstrength (result is uV/m)
> when received with a magnetic antenna then becomes:
> Es = 2*10^3*Eu*cos(TOA)*RC*D*Fr*Ft/IPL
>
> when received with a short vertical antenna then becomes:
> Es = 2*10^3*Eu*(cos(TOA))^2*RC*D*Fr*Ft/IPL
>
> where
> Eu = (ERP*90/W)^0.5
> is the "uncorrected" fieldstrength
>
> For those interested in doing yourself,
> the following frequency dependent parameters
> (representative only for 137 kHz) were
> "optically digitized" from the original graphs:
>
> TX-RX ground distance in km
> d:100,200,300,400,500,600,700,800,
> 900,1000,1100,1200,1300,1400,1500,
> 1600,1700,1800,1900,2000,2100,2200
>
> ionospheric focusing factor daytime
> D:1,1.02,1.05,1.07,1.1,1.15,1.18,
> 1.22,1.3,1.35,1.45,1.56,1.7,1.83,
> 1.97,2.1,2.2,2.27,2.3,2.35,2.42,2.5
>
> ionospheric focusing factor night-time
> D:1,1.02,1.05,1.07,1.08,1.1,1.14,
> 1.18,1.22,1.3,1.35,1.4,1.5,1.6,1.72,
> 1.9,2.05,2.2,2.3,2.4,2.42,2.5
>
> ionospher. reflection coefficient summer daytime
> RC:0.00027,0.00045,0.0008,0.0014,0.0024,
> 0.0036,0.005,0.0075,0.01,0.012,0.014,
> 0.0155,0.017,0.019,0.021,0.023,0.0237,
> 0.0242,0.0245,0.0247,0.0249,0.025
>
> ionospher. reflection coefficient winter daytime
> RC:0.012,0.017,0.025,0.035,0.05,0.07,
> 0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,
> 0.165,0.18,0.19,0.20,0.21,0.215,0.218,0.22
>
> ionospher. reflection coefficient night-time
> RC:0.09,0.1,0.12,0.14,0.16,0.18,0.195,
> 0.21,0.225,0.24,0.25,0.26,0.27,0.28,
> 0.29,0.3,0.31,0.318,0.323,0.326,0.328,0.33
>
> RX antenna ground pattern factor
> (sigma=2mS/m, epsilon=15)
> Fr:0.8,0.8,0.79,0.78,0.77,0.76,0.75,0.74,
> 0.73,0.71,0.69,0.67,0.65,0.6,0.55,0.48,
> 0.44,0.4,0.35,0.33,0.31,0.3
>
> TX antenna ground pattern factor
> (sigma=2mS/m, epsilon=15)
> Ft=Fr
>
> For your convenience I post the results from my last
> weekend "calculation marathon" which is only valid for:
>
> solar minimum epoch
> operating frequency = 137 kHz
> ERP=1W
> magnetic receiving antenna
>
> distance summerday winterday night-time
> 100 km -39 dBuV/m -6 dBuV/m 8 dBuV/m
> 200 km -35 dBuV/m -3 dBuV/m 11 dBuV/m
> 300 km -31 dBuV/m -1 dBuV/m 11 dBuV/m
> 400 km -28 dBuV/m 0 dBuV/m 11 dBuV/m
> 500 km -25 dBuV/m 1 dBuV/m 11 dBuV/m
> 600 km -23 dBuV/m 3 dBuV/m 10 dBuV/m
> 700 km -21 dBuV/m 3 dBuV/m 10 dBuV/m
> 800 km -19 dBuV/m 3 dBuV/m 10 dBuV/m
> 900 km -17 dBuV/m 3 dBuV/m 9 dBuV/m
> 1000 km -16 dBuV/m 3 dBuV/m 9 dBuV/m
> 1100 km -16 dBuV/m 3 dBuV/m 9 dBuV/m
> 1200 km -15 dBuV/m 3 dBuV/m 8 dBuV/m
> 1300 km -15 dBuV/m 3 dBuV/m 8 dBuV/m
> 1400 km -16 dBuV/m 2 dBuV/m 7 dBuV/m
> 1500 km -16 dBuV/m 2 dBuV/m 6 dBuV/m
> 1600 km -18 dBuV/m 0 dBuV/m 4 dBuV/m
> 1700 km -19 dBuV/m -1 dBuV/m 3 dBuV/m
> 1800 km -21 dBuV/m -2 dBuV/m 1 dBuV/m
> 1900 km -23 dBuV/m -5 dBuV/m -1 dBuV/m
> 2000 km -25 dBuV/m -6 dBuV/m -2 dBuV/m
> 2100 km -26 dBuV/m -7 dBuV/m -3 dBuV/m
> 2200 km -26 dBuV/m -7 dBuV/m -4 dBuV/m
>
> Assuming external noise fieldstrength of -9dBuV/m
> equals useful signal, the one-hop skywave coverage
> has the following boundaries:
>
> more than 2200 km during night-time
> more than 2200 km during winter daytime
> apparently none during summer daytime
>
> As we are definitely no more in the minimum
> epoch of the solar activity cylce, nor at the
> maximum, the values derived so far may be
> utilized as a raw scale rather than exact
> figures. The original CCIR report provides
> a last diagram (dependent on the effective
> frequency, time of day, season of year) showing
> the "offsets" in between the values for minimum
> and maximum epoch of solar activity.
>
> The differences pertaining the distances 100km
> through 2200km are:
>
> The maximum epoch values for night-time are
> 2-4dB higher than those for the minimum epoch.
> (May be appoximated by a constant 3dB offset
> for all these distances)
>
> The maximum epoch values for winter daytime
> are 2-11dB higher than those for the minimum
> epoch. 2dB for 100km, 11dB for 300km, 5dB for
> 2200km (logarithmic interpolation in between).
>
> The maximum epoch values for summer daytime
> are 3-9dB higher than those for the minimum epoch.
> 3dB for 100km, 9dB for 300km (logarithmic
> interpolation in between), no values for
> greater distances contained in the original graph.
>
> By comparing the skywave values with groundwave values
> we see that both waves are of equal strength (under
> the constrains of ground property etc.)
> at 550 km during night-time
> at 750 km during winter daytime
> at 1250 km during summer daytime
>
> Those distances mark the range center where ground
> wave and sky will vectorially sum to the total field.
> By calculating the travel time from TX to RX via
> ground distance and via ionospheric path length and
> the speed of light, we can derive the phase lag in
> between both waves, relate it to a wavelength and
> can assume the effect of interference, either
> constructively, or destructively.
>
> Every change propagation mode which cause variations
> in direction (virtual height of ionospheric region),
> amplitude (reflection coefficient of the ionospheric
> region, i.e. ionization) of the traveling waves will
> also vary the received total field. This is what is
> called interference fading.
>
> Effect of ionospheric and magnetospheric disturbances
>
> The previous mentioned CCIR report 265-7 exclusively
> relates to sky wave fieldstrengths under a typical,
> average solar (either minimum or maximum) activity
> profile. There are no values or estimates provided
> which are accounting for deviations from the
> average solar activity.
>
> In a forecoming abstract I offer to sample
> facts which are drawn from literature pertaining
> MW DX-ing showing apparent analogies with propagation
> alterations as could be seen by long term measurements
> of DCF39 signal strength.
>
> *************** Acknowledgments ***************
> Grateful appreciation is expressed to
>
> Mr. Buchmann
> AEG Telefunken
> Sendertechnik
> Sickingenstr. 20-18
> D-10553 Berlin/Germany
>
> for valuable information on CCIR report 368-6
>
> Mr. Axel Stark
> Rohde & Schwarz GmbH & CoKG
> Muehldorfstr. 15
> D-81671 Muenchen/Germany
>
> for valuable information on CCIR report 368-6
> and for discussion of details therein
>
> Mr. Reiche
> Thomcast GmbH
> Ohmweg 11
> D-68197 Mannheim/Germany
>
> for valuable information on Recommendations ITU-R PI.372-6,
> ITU-R PN.341-3, on CCIR Recommendation 435-7 and 339-6
> for spending a day in discussing hundred of associated matters
>
> Mr. Peter Hetzel
> Physikalisch-Technische Bundesanstalt
> Labor fuer Zeiteinheit
> Bundesallee 100
> D-38116 Braunschweig/Germany
>
> for valuable information on CCIR Report 265-7
> on DCF77 and his laboratory
>
> Mr. Scholz
> Europaeische Funk-Rundsteuerung GmbH
> Wilhelm von Siemens Str. 2-10
> D-12277 Berlin
>
> for discussing LF propagation associated with
> DCF39 and DCF49
> **********************************************
> ==Stop Abstract==================================================