# Fundamentals of ISM-Band and short range device antennas, Part 3

This 4-part report discusses antenna fundamentals and the various types of antennas used for short range devices. Fundamentals are presented along with practical design principles. It is excerpted from the report: ISM-Band and Short Range Device Antennas. This part covers RF Propagation.

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:

_{L}) For Four Short Range Frequency 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.