Penetration of materials

The amount by which a radio wave penetrates a material depends on the electrical properties of that material. Good insulators tend to allow the wave to propagate through them with only low loss. Glass is an example of a good insulator. If it were not a good insulator, light would not pass through it. Good conductors tend to reflect the radio wave at its surface and very little signal passes through. A thin sheet of aluminium foil will effectively block most radio waves. When it is required to communicate between two transceivers, one of which is inside a building and one outside (a common requirement with mobile telephony systems), the

penetration loss of building materials becomes very important, as does the internal structure of the building. A building with an open-plan structure whose walls contain large glass windows will introduce little extra path loss (less than 5 dB), whereas a building with thick stone walls and small windows and an internal structure consisting of many solid walls can introduce extra path loss amounting to several tens of dB.

The process by which an electromagnetic wave travels from one side of a sheet of material to the other involves propagation (typically through a lossy medium) and multiple reflections.

The recommendation ITU-R P. 1238 publishes information that facilitates the calculation of typical values for the losses introduced by building materials. This information is published in the form of a material’s ‘complex permittivity’. The imaginary part of the complex permittivity can be converted into an effective resistivity that repre- sents the lossy nature of the material. The loss depends upon the fre- quency: the higher the frequency the greater the loss. As an example, the permittivity of concrete is quoted as 7− j0.85 at a frequency of 1 GHz. This will allow us to estimate both the amount of energy in an incident wave that gets reflected at the surface and the amount that will be lost on passing through the concrete. A full treatment of this problem involves a detailed analysis of electromagnetic waves and boundary conditions that is beyond the scope of this book. However, it is possible to make deductions and approximations that provide a useful practical insight into the problem.

Firstly we introduce a little bit of arithmetic to make the problem simpler. We have stated that the reflection coefficient is given by

q ¼Z
120p

Z þ 120p: ð4:15Þ

Now if, as is usual, the material is non-ferrous (lr¼ 1), it is possible to

re-write the equation as

q ¼120p= ffiffi e p
120p 120p=pffiffie þ 120p¼ 1
pffiffie 1þp :ffiffie ð4:16Þ p e n e t r a t i o n o f m a t e r i a l s 107

Thus, for concrete, the reflection coefficient would be 1
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi7
j0:85

1þpffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi7
j0:85¼
0:449 þ j0:064 ¼ 0:454h172



: ð4:17Þ

Thus the incident wave would be expected to undergo a near phase reversal on reflection and the amplitude of the reflected wave would be approximately 45% that of the incident wave. That means that the power density of the reflected wave would be only 20% that of the incident wave. By the law of conservation of energy the wave entering the concrete would have a power density 80% that of the incident wave. Once inside the concrete, the wave would propagate through but would dissipate energy as it travelled. The loss is determined by knowing the frequency and the imaginary part of the permittivity. The higher the frequency and the bigger the imaginary part of the permittivity, the greater the loss. For concrete with the electrical characteristics specified, the loss would be about 29 dB per metre at a frequency of 1 GHz. The loss is roughly proportional to frequency. So at 500 MHz the loss would be 14.5 dB per metre and at 2 GHz the loss would be 58 dB per metre.

4.9 Summary

We have seen that standing wave patterns form when two or more coherent waves interact. Where the two waves are in phase, a maximum disturbance will occur, whereas, where they are in anti-phase, a minimum or ‘null’ will occur. If the reflecting surfaces that cause the multipath situation do not move, the locations of the maxima and minima will not move, hence the name ‘standing wave’. The depth of the null in a standing wave pattern is dependent upon the magnitude of the reflection coefficient of any reflecting surface. If the reflected wave is almost as strong as the direct wave then the difference between the signal strengths at maxima and minima will be great. The magnitude of the reflection coefficient can be determined if the electrical characteristics of the reflecting surface are known. Good, smooth, conductors will provide near-perfect reflection.

The effect of reflections is shown to be very noticeable when con- sidering propagation over a flat plane. At near-grazing incidence the

reflection coefficient, even of poor conductors, is very high and leads to strong peaks and nulls. Although the variation in signal strength with distance can be very high in this circumstance, the general trend is for the signal strength to reduce with distance. At a certain distance, the ‘break point’, the oscillation between peaks and nulls ceases and the signal strength reduces more rapidly with distance. The distance of the break point from the transmitter is seen to be dependent upon the heights of the transmitting and receiving antennas and the frequency of operation.

Microwave links propagating over water provide another example where the effect of reflections can be dramatic. Water forms a good smooth reflecting surface, particularly at near-grazing incidence. If the direct signal and that reflected from the water arrive at the receiving antenna in anti-phase, a null will occur and the link will fail. The best way of mitigating against this effect is to establish a second receiving antenna such that they will not both be in a null simultaneously. The most suitable separation distance between the two antennas has been derived and found to depend upon the transmitting antenna height, the path length and the frequency of operation.

Multipath environments have been characterised according to whether or not a single signal dominates. In a Rayleigh environment, all signals will be of about the same strength. This produces a very chaotic standing wave pattern with sharp nulls and peaks. If one of the con- tributing signals dominates then the environment is said to be Rician in nature. In this situation, the strength at any one point is dominated by the strongest signal, with the effect of the other signals resembling the effect of noise on a signal. The variation of signal strength with distance is not so great in a Rician environment as it is in a Rayleigh environment. The Cornu spiral has been used to demonstrate the effect of increasing the roughness of a surface. It is seen that the reflected signal strength, even from good conductors, is very small if the phase of the reflected signal varies randomly by 3 radians or more. The final section examines the way in which radio waves can penetrate obstacles. Good conductors will form a near-total block to radio waves, but electrical insulators can be lossy at high frequencies. Concrete was chosen as a typical example and the insertion loss was derived from its electrical characteristics.