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By Jain J., Narayan A., Fujita M.

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Base stations for mobile communications can provide coverage up to a few tens of kilometres in rural areas but, in urban areas, the coverage range is restricted to a kilometre or so, particularly if communication to mobile terminals located indoors is to be provided. When it is required to predict the coverage from a broadcasting transmitter, it must be acknowledged that the terrain will vary with direction of transmission. If it can be assumed that the broadcasting antenna is placed well above any surrounding ‘clutter’ (such as nearby buildings) then it is possible to use a ‘path-general’ prediction model (‘path-general’ models do not consider every nuance of the path profile between the transmitter and receiver) to obtain a rapid prediction of the 28 p o i n t - t o - a r e a t ra n sm i s si o n power density produced at points in the surrounding area.

When considering radio waves, the magnetic field gets little mention. When wire p o w er de n s i t y a n d e l ec t r i c f i e l d s t r e n g t h 29 antennas are used as receivers, the picture we imagine is of the electric field inducing currents in the antenna. In free space (and, as far as we are concerned, in air) the ratio of the electric and magnetic fields in an electromagnetic wave is constant (the ratio E/H in free space is called the ‘intrinsic impedance’ of free space). In free space, E ¼ 120pH ð2:2Þ and hence the power density can be determined in terms of the electric field strength alone: Pd ¼ E2 : 120p ð2:3Þ Electric field strength is often preferred to power density in performing calculations with broadcast transmitters.

Similarly, distances are more commonly measured in kilometres. 64 as a ratio). Thus a standard value of PtGt is 1640. In this way pffiffiffiffiffiffiffiffiffiffi 1640 222 000 : ð2:6Þ E ðlV=mÞ ¼ 5480 ¼ d d 30 p o i n t - t o - a r e a t ra n sm i s si o n As always, as a final manoeuvre, we usually express this in logarithmic units (dB relative to 1 microvolt/m, or dBlV/m):   222 000 ¼ 106:9 À 20 log d: ð2:7Þ EdBlV=m ¼ 20 log d Notice that this equation, unlike the equation for free-space loss, has no frequency term, making it easier to use in certain circumstances, particularly when the sensitivity of a receiving system is expressed in dBlV/m (as is often the case with receivers of broadcast signals) rather than dBm.

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A survey of techniques for formal verification of combinational circuits by Jain J., Narayan A., Fujita M.

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