Click here for Part 1: Antenna Basics
Click here for Part 2: Types of antennas used for short range devices
Click here for Part 4: Examples

Path Loss
The basis for an estimation of the achievable distance in a communication link is the link budget. The link budget describes the relationship between the received power P_r and the transmitted power P_t as:

G_t and G_r are the gains of the transmitter and receiver antennas respectively. λ is the wavelength and d the distance between transmitter and receiver. Identical units must be used for λ and d. As we can see, the received power increases with the square of the wavelength (or decreases with the square of the frequency). This comes from the fact that an antenna with the same gain is larger at lower frequencies and therefore catches more power from the radiated field.

The path loss exponent describes the influence of the transmission medium. In free space, the path loss exponent is theoretically two, which describes the equal power distribution from an isotropic radiator on the surface of a sphere. N < 2 means that the medium bundles the wave, giving a path loss smaller than in free space. An attenuating medium gives a path loss exponent n > 2.

The path loss is the ratio of the powers between the transmitter and receiver antennas in logarithmic units:

For convenience, we can use the formula:

In outdoor applications, we often have a direct line of sight between the transmitter and the receiver. In this case, we can use a path loss coefficient of two, if there are no obstacles in the first order Fresnel zone. The Fresnel zone is an ellipsoid, which has the transmitter and receiver antennas at its foci as shown in Figure 19.

In the middle between the transmitter and the receiver, the first Fresnel zone has the diameter

Often it is assumed that a path loss coefficient of two still can be used, if at least 60% of this zone is free from obstacles.

Figure 20 shows the free space path loss (n = 2) for four frequently used short range bands:

If we have no line of sight conditions, there will be additional losses due to absorption, diffraction and refraction. These losses are described empirically by the path loss coefficient n. Table 3 has some measured values of the path loss coefficient together with the associated standard deviations /5/, /6/. It is assumed that the transmitter and the receiver are on the same floor.

If the transmitter and the receiver are not on the same floor, a floor attenuation factor L(N_f) with N_f as the number of penetrated floors, must be added. Table 4 has some typical floor attenuation factors according to /5/.

We can see that the standard deviations are extremely large; there will be a lot of uncertainty in the path loss prediction. An improvement is possible if we track the path from the transmitter to the receiver. This method is called ray tracing and accounts for all the individual partition losses at walls, doors, windows, etc. The estimated path loss is then:

Table 5 has some typical partition losses according to /5/.

The partition loss values depend on the individual construction of the particular obstacle and also on the frequency.

Multipath Propagation Effects
In a practical transmission system, the receiver does not only get the signal via the direct path, but also from reflections, diffracted, and scattered rays.

Multipath propagation can cause two kinds of problems: fading and inter symbol interferences (ISI).Fading occurs if the time difference between the arrival of the direct and the delayed (reflected) wave is in the order of magnitude of the RF period time.

If the time difference is an integer multiple of the period time, both waves interfere constructively; the received signal is stronger than without fading.

If the time difference is an odd multiple of the half-period time, the direct and the indirect component subtract from each other, in the worst case they totally cancel out.

If a receiver is moved into an environment with multipath transmission, there will be an alternating stronger and weaker signal. The damage from the mutual cancellation is much more significant than the advantage from the constructive interference at other locations. If the time difference, τ, is on the order of magnitude of the bit duration, multipath transmission leads to inter-symbol interference. This principle is shown in Figure 22.

Even with a strong RF signal at the receiver input, the transmission is disturbed by ISI. The influence of the ISI is particularly important for higher bit rates, because then a time difference in the order of magnitude of the bit duration can occur in smaller rooms.

To avoid fading problems, antenna diversity on the transmitter or the receiver side can be used. In the simplest realization, two or more antennas are combined by a passive divider. The probability that both antennas are in a deep fade is much smaller than for one antenna only. This simple structure can give a substantial improvement in the line reliability.

For better performance, an RF switch is used which connects either one or the other antenna to the IC device. During the preamble of the protocol, the RSSI signal can give information on which of both antennas performs better. This antenna is then used during the data package.

In some cases where the link reliability is important, true diversity can be implemented. This means that two complete receivers with separated antennas are used. Depending on the signal quality at the receiver outputs, one or the other is used.

In most simple applications, antenna or time diversity are cost-prohibited and seldom used. If neither the transmitter nor the receiver is mobile, antennas with a high directivity can suppress the unwanted reflections.

Part 4 will cover examples and measurements.

References

1. L.J.Chu, Physical limitations of Omni-Directional Antennas, J. Appl. Phys., Vol19, Dec. 1948, pp. 1163 -1175

2. H.A.Wheeler, Fundamental Limitations of Small Antennas, Proc. IRE, Vol. 35, Dec. 1947, pp. 1479 " 1484

3. H. Johnson, M. Graham, High Speed Digital Design, Prentice Hall, 1993, ISBN 0133957241

4. C.A. Balanis, Antenna theory, Analysis and Design, Wiley, 1996, ISBN 0471 592684

5. T.S. Rappaport, Wireless Communication, Principles and Practice, Prentice Hall, 2002, ISBN 0-13-042232-0

6. Recommendation ITU-R P.1238-2 - Propagation data and prediction methods for the planning of indoor radio communication systems and radio local area networks in the frequency range 900 MHz to 100 GHz.