## Engineering Question #1767

Mark McDonald, a 42 year old male from Morgan Hill asks on December 29, 2003,

I am interested in the transmission of RF through different materials (especially water). I am trying to understand for instance, how much an RF signal will be antenuated traveling through water relative to the frequency (say 100MHz - 10 GHz).

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### Rodney Vaughan, Professor of electrical engineering, Simon Fraser University answered on January 26, 2004

Mostly, radiowaves are used in the context of free space (i.e., vacuum, or air). When radiowaves travel through some medium which is not free space then a couple of things change. Firstly, the wavelength gets smaller, and associated with this, the wave travels slower. Secondly, the wave peters out more quickly, or in engineering jargon, attenuates more quickly. This is particularly so for a water medium. How much these changes occur depends on the material properties of the media through which the radiowave is propagating. In metals, the electric field part of the radiowave (there is also a magnetic field part) gets effectively short-circuited, and the radiowave travels a very small distance before dying out. In dielectrics (plastics, wood, water, etc), the radiowave also peters out, but normally over a longer distance than in metal. In fresh water, there some electrical conduction, so fresh water behaves as a both a dielectric and a metal. Salt water is quite conductive, and a radiowave attenuates very quickly when travelling through it, but not as quickly as in metal.

The physical mechanisms of the losses of the radiowave power are very complicated, with more than one physical factor, including molecular goings-on, influencing things. The easiest way to view it is just to accept that some materials are “lossy”, which means they conduct electricity to some extent, and have an electrical resistance. The material’s resistance is “seen” by electric currents caused by the radiowave as it travels through it. So the power loss turns up as a heating of the media (like a microwave oven). Only ideal dielectrics conduct no electricity through having a zero resistance. Some materials, such as pure teflon, are nearly ideal dielectrics, even at microwave frequencies.

Mathematically, a radiowave, when propagating through water, attenuates proportional to the exponential of the distance. The power is the amplitude squared, and changes as a function of distance.

Because of the large range of values of the fields and powers in radiowaves (and many other physical signals), electrical engineers often use decibels (dBs) as the units. A huge range of numbers representing physical values can be replaced by a manageable numerical range of dBs. Mathematically we cannot take a log of a number with units so we have to express it relative to the power at some reference point. The way logs work, 3 dB represents a power difference of 0.5. This means that 6dB (2 times 3 dB) represents two times a halving of the power, or a physical value of one quarter.

So 12 dB means one sixteenth and so on. This scale gets really useful for really big numbers, for example a power loss of one million (this physical value is getting awkward as a numerical value) is a mere 60, in decibel units. 600dB is a modest and manageable numerical value, but represents {zero point {60 zeros, then 1}} of the power, a difficult number to imagine, or manage in some calculations. I have written a program which plots (below) the reducing power of a radiowave travelling through water and ocean salt water (3.5% salt). The graph has a lot of information on it, so I include some explanation here. The x-axis is distance in mm. This sounds like very short distances for propagation, but you will see the reason for this short distance as we proceed. The y-axis represents the relative power lost as our radiowave travels from one point to another point at distance x mm away. The y-scale is in dB for the reasons above. At the top of the graph, the blue solid lines are the power loss with distance in free space. The four lines are for the four frequencies, 100MHz, 1GHz, 5GHz, and 10GHz. As the frequency goes up, the loss increases for a given distance. So this is the normal radiowave situation. For example, at a distance of 500mm, a frequency of 10GHz drops its power by about 50dB on this scale. Remember the dB power is a ratio, and so it is relative to a reference rather than having an absolute value, in say, Watts; see below. The term “power loss” is a bit misleading here, there is no power lost in electrically resistive mechanisms (free space is lossless), it is just because of the spherical spreading of the wave as it propagates. The power is lost because it travels elsewhere, not because it is expended as heat in the medium. This is also known as the inverse square law. The inverse square law states that the power loss is proportional to the inverse of the distance (in wavelengths - not metres or feet, etc.) squared. Each time the distance is doubled, the inverse square power law shows that we lose another 6dB of power (=10*log(0.5 2)). For example, when we go from x=250mm to x=500mm, we lose 6 dB of power, and when we go from 500mm to 1000mm, we lose another 6dB of power. This will apply to all the free space curves. (Right-click on the graphic to open in a new window. It is a jpeg file and can be enlarged to read the text and axis units.)

For the radiowave in fresh water, the power loss is shown with green dotted lines. The fresh water is lossy, and the resistive loss behaviour is a complicated function of frequency, which I have not described here. Here we see two “loss” mechanisms at work. There are resistive losses in the water, and the inverse square law, which appears much more strongly than in the free space case because for a given distance, there are many more wavelengths that the wave propagates. (For both fresh water and salt water, the wavelength is about a ninth the length of the wavelength in free space.) For example, at 5 GHz (the third green dotted curve down the graph), at a separation distance of 350mm, the amount of radiowave power attenuation is about 300dB. This is a hopelessly large attenuation for everyday communications, so this choice of frequency is not suitable for radio communications through water. For 10GHz, the lowest green dotted curve, note we are losing over 300dB per doubling of distance! For the radiowave in salt water, we have red circles and joining line. The fourth curve (10GHz) is off the scale because the attenuation is too much for this graph to show. The salt water has high conduction losses which really finish off the radiowave in a very, very short distance. You can see there is little point in plotting a longer distance on the graph! Note that lower frequencies, even lower than 100MHz, are much more suitable for radio communications through water, than microwave frequencies, such as those plotted here. On the other hand, salt water looks very useful for stopping radiowaves!

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