Propagation of Radio Waves via Line-of-Site and Ionospheric Paths

Author: R.J.Edwards G4FGQ © 5th May 2006

This program is intended to introduce newcomers to signal strengths expected from transmitters of given output power, over various radio path distances and under average propagation conditions. It should be borne in mind that ionospheric conditions can cause path loss to vary by 20 dB about so-called average values which may not exist at some hours of the day or time of the year. Much depends on operating frequency and transmitting and receiving antennas. However, average or typical antenna directional power gains can be estimated.

The program averages out the great variety of antennas by assuming transmitting and receiving antennas to be isotropes which radiate and receive equally in all directions. Computed received signal strength in particular maximum directions can then be mentally adjusted according to transmitting and receiving antenna gains in those directions.

It is assumed the efficiency of the transmit and receive antennas is 100% and that the receiving antennas is Z-matched to the receiver input impedance. Path loss between transmitting and receiving input is computed in decibels. Radio paths are extended attenuators and receiver S-meters are power meters. So its better not to think in terms of amps or volts. S9 corresponds to 50 picowatts.

The received signal strength as displayed on the receiver's S-meter is computed in terms of S-units. Signal strengths exceeding S9 are displayed as dB above S9.

The noise level at the receiver, in terms of S-units, is input to the program. The received signal-to-noise ratio is computed in decibels.

The S-meter is assumed to be perfectly calibrated, S9 corresponding to 50 picowatts receiver input power, with one S-unit corresponding to a change in input power of 4 times, or a doubling/halving of receiver input volts.

With a standard 50-ohm receiver S9 corresponds to a signal level of 50 microvolts.

The noise power level at S = -2 corresponds roughly to an internal thermal agitation noise from a resistor at room temperature in a 2.5 KHz, SSB, bandwidth.

Loss in the ionosphere is greatest when the whole path is in sunlight. Nearly all of the loss occurs in passage through the D-region at a height of 70 to 90 kM. But only frequencies below 5 MHz are affected. In sunlight the 160m band is almost entire absorbed in the D-region, no refraction or reflection from the E or F-layers occurs and propagation is restricted to groundwave. When the sun sets on the D-region the 160m band comes to life. The 80m band is less affected and signals vary according to yearly seasons and the 11-year sun-spot cycle.

Received signal strength is computed over unobstructed direct line-of-sight radio paths, or multi-hop propagation via the ionosphere. The first is chosen by selecting zero hops. The second is chosen by selecting one or more hops.

In the case of multi-hop propagation additional losses due to passage through through the ionosphere and due to reflections from the ground are taken into account. These additional losses are average expected values when a path is open and depends on frequency, time of day, heights of reflecting layers and ionospheric conditions. This program is not intended for accurate predictions, but is intended to familiarise users with signal strengths and S-meters.

An average length of path for one hop is taken as 2000 kM which corresponds to an elevation angle of about 15 degrees with the height of the F-layer being an average of 350 kM. The F-layer can vary between heights of 280 and 450 kM and can differ from one hop to the next. The E-layer at a constant height of 115 kM is present only when radiated by sunlight. It is neglected by this program.

The program also neglects the fact that frequencies above the Maximum Usable Frequency, the MUF, pass right through both the E and F-layers and never return to Earth. For the F-layer, MUF's are lower when the path is in darkness than when in sunlight. MUF's are also lower in winter than in summer. DX MUF's range between 7 MHz and 50 MHz, being highest only at a sun-spot maximum.

The efficiency of most antennas exceeds 90 percent, which for the purpose of estimating received signal strength can be ignored.

In this program, predictions are most accurate with line-of-sight radio paths (See also Propagation Over "Line-of-Sight" Radio Paths) and single hops of ionospheric paths. Multiple hop paths, when ionospheric conditions allow, can vary by plus or minus 2.5 S-units or about 15 decibels.

Line-of-sight propagation assumes a smooth Earth, without obstructions, high antennas at both ends of the path, and over distances not much greater than to the radio horizon. Earth curvature is a limitation. Antennas should be at a minimum of several wavelengths above ground level.

The radio horizon is notionally at a distance of 80/CubeRoot(F) kilometres, between points at low heights above ground, where F is the frequency in MHz.

To ensure high efficiency antennas the dimensions are required to be of the order of half-wavelength or greater. Combined with height requirements, this makes line-of-sight operation at frequencies below 30 MHz impractical. Propagation beyond the radio horizon is quite possible, there is no sudden cut-off, but communication becomes progressively more unreliable.

At great distances through the ionosphere the number of hops involved will be very uncertain but computed signal strengths will provide a fair idea of what can be expected. Ground path distances will be roughly 15% shorter than skywave paths - a 2000 kM radio hop via the F-Layer corresponding to a 1000 mile ground path. It should be remembered if only one hop in a string of hops is in sunlight then propagation below about 5 MHz will be seriously affected.

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