Friis Transmission Equation

Friis Transmission Equation Friis Transmission Equation Friis Transmission Formula can be used to study RF communication links. The formula can be used in situations where the distance between two antennas are known and a suitable antenna needs to be found. Using Friis transmission equation, one can solve for the antenna gains needed at either the transmitter or receiver in order to meet certain design specifications. Where Preceiver is the recieved power in Watts (W), Ptransmitter is the transmitted power, Gt is the transmitting antenna's gain, Gr is the receiving antenna's gain, is the wavelength of the transmitted and received signal in meters, and R is the distance between the antennas in meters. The gain of the antennas is not in decibels. To convert to the gain back to a power ratio use: . Example 1 An engineer is designing a communications link at 3 GHz where the receiver sensitivity is such that of power is needed to overcome receiver noise. The receiving antenna gain is 8dB, the transmitter antenna gain is 10dB, the transmitting power level is 25 Watts, and the distance between the two antennas is 1km. Will the communications link work? Solution The problem is solved by first converting the frequency of 3 GHz to a wavelength , and converting the antenna gains from decibels to a power ratio. where c is the speed of light in meters per second, and f is the frequency in Hz. We will use a c of 300 million m/s. This means that lambda is 0.1 meters. Using the conversion formula given above, the transmitter antenna gain Gt is 10, and the receiver antenna gain is 6.3. Using Friis Equation we have the following relation where the transmitted power is 25 Watts, and the distance R is 1000 meters. Using the given values Preceiver is or 99.7 nanowatts (nW) which is much less than the needed 1 microwatts needed to overcome receiver noise. Answer The communication link will not work unless the antenna gains or the transmitter power levels are dramatically increased. Example 2 If an engineer is designing a communications link with a receiver antenna gain of 10dB and transmitter antenna gain of 12dB at a frequency of 10GHz, how much power will be received at the receiver if the transmitter is transmitting with a power of 25 watts across a distance of 1 kilometer. Figuring out wireless transmission distance When planning or updating a wireless LAN installation, it's often necessary to determine if your wireless equipment can achieve a certain transmission distance. However, this information is not printed in the specs for wireless devices and antennas. The reason is simple – there are too many factors that affect the transmission distance, particularly the combination of transmission power and antenna gain. In this article, you can learn how to use your wireless device and antenna specifications to quickly determine the theoretical transmission distance. First, the basics The theoretical transmission distance that can be achieved between two wireless devices can be calculated from just a few key specifications. Tx power = transmission power of device This is the wireless device's transmission power and is typically measured in dBm. With greater Tx power, greater transmission distances can be achieved. Data rate The data rate is the number of bits that are conveyed or processed per unit of time. Since higher data rates require greater transmission power, a wireless device may offer different Tx power specifications for different data rates. Rx sensitivity = receiver sensitivity of device This is the wireless device's receiver sensitivity and is typically measured in dBm. With greater Rx sensitivity, the device is able to receive weaker signals, which means greater transmission distances can be supported Don't forget that wireless communication occurs between two devices. If two devices have different Tx power and Rx sensitivity specifications, the theoretical transmission distance may be different depending on which direction the data is being transmitted. You will need to consider the Tx power and Rx sensitivity in both directions. In most cases, it is simpler to make sure that every wireless device in your network adheres to the same specifications for Tx power and Rx sensitivity. Antenna gain The gain for an antenna is typically measured in dBi and basically indicates how much the signal is boosted by the antenna. Although high gain antennas mean greater transmission distances, they are usually highly directional. Frequency The frequency is typically measured in MHz or GHz and indicates which electromagnetic band is used for wireless communication. The frequency is determined by the IEEE 802.11 standard that you have selected for your network. All IEEE 802.11b and IEEE 802.11g devices use the 2.4 Ghz band, while IEEE 802.11a devices use the 5 Ghz band. The selection of IEEE 802.11 standard (and therefore frequency) is usually determined by factors such as national restrictions and existing device support. If you have the information above for your wireless devices, you can easily determine the theoretical transmission distance between two wireless devices. The formula explained The formula for calculating the theoretical transmission distance is based on the Friis Transmission Equation for free space loss: In this equation, R is the range and is the wavelength. We can take a look at the following figure to see how this corresponds with the specifications of our devices and antennas. The Friis Transmission Equation requires a bit of modification to suit our needs. What we want is an equation that tells us the transmission distance directly. Also, it's easier for us to work with communication frequency rather than wavelength. We can modify the Friis Transmission Equation to fit our needs more closely, as follows: Let's try an example With this equation, we can quickly determine whether we will need new wireless equipment to reach a particularly remote site. Suppose you need to connect wirelessly to a node that is 4 km away. You are running an IEEE 802.11b network and you are currently using wireless devices with the following specifications: Tx power: 18 dBm @ 11 Mbps Rx sensitivity: -90 dBm @ 11 Mbps Antenna gain: 2 dBi With our formula, you have all the information you need to determine the theoretical transmission range that is possible with this set of equipment. Frequency Tx power Tx antenna gain Rx antenna gain Rx sensitivity 2442 MHz (all IEEE 802.11b devices ) 18 dBm 2 dBi 2 dBi -81 dBm When you plug these numbers into our formula, you get a value of 1.38 km. This is the theoretical transmission distance that can be achieved by your wireless equipment. We could use the same formula to see how much further wireless signals would travel using 9-dBi antennas instead of 2-dBi antennas. (The theoretical transmission distance goes up to 6.92 km). Another way to increase the transmission distance would be to employ wireless devices that offer higher Tx power and/or lower Rx sensitivity. Now for the fine print Of course, there can be a big difference between the theoretical transmission distance and the actual results in the field. These calculations are based on an unobstructed line-of-sight signal with no electronic interference. However, the real world presents many variables that result in less-than-perfect wireless performance, such as mismatched impedance, electronic noise, building obstructions, reflected signals, etc. This is why it is so important to conduct a thorough site survey in order to determine what is actually happening to your wireless signals in the field. Before you conduct that site survey, however, you still need some way to evaluate the different options you have for wireless hardware. This formula provides a straightforward way to perform that evaluation. With this formula, you can now easily estimate whether you will be able to achieve your desired transmission distance with a given set of hardware. Using this formula, you can make an informed decision when selecting antennas and devices for different wireless applications. On this page, we introduce one of the most fundamental equations in antenna theory, the Friis Transmission Equation. The Friis Transmission Equation is used to calculate the power received from one antenna (with gain G1), when transmitted from another antenna (with gain G2), separated by a distance R, and operating at frequency f or wavelength lambda. This page is worth reading a couple times and should be fully understood. Derivation of Friis Transmission Formula To begin the derivation of the Friis Equation, consider two antennas in free space (no obstructions nearby) separated by a distance R: Figure 1. Transmit (Tx) and Receive (Rx) Antennas separated by R. Assume that Watts of total power are delivered to the transmit antenna. For the moment, assume that the transmit antenna is omnidirectional, lossless, and that the receive antenna is in the far field of the transmit antenna. Then the power density p (in Watts per square meter) of the plane wave incident on the receive antenna a distance R from the transmit antenna is given by: If the transmit antenna has an antenna gain in the direction of the receive antenna given by , then the power density equation above becomes: The gain term factors in the directionality and losses of a real antenna. Assume now that the receive antenna has an effective aperture given by . Then the power received by this antenna ( ) is given by: Since the effective aperture for any antenna can also be expressed as: The resulting received power can be written as: [Equation 1] This is known as the Friis Transmission Formula. It relates the free space path loss, antenna gains and wavelength to the received and transmit powers. This is one of the fundamental equations in antenna theory, and should be remembered (as well as the derivation above). Another useful form of the Friis Transmission Equation is given in Equation [2]. Since wavelength and frequency f are related by the speed of light c, we have the Friis Transmission Formula in terms of frequency: [Equation 2] Equation [2] shows that more power is lost at higher frequencies. This is a fundamental result of the Friis Transmission Equation. This means that for antennas with specified gains, the energy transfer will be highest at lower frequencies. The difference between the power received and the power transmitted is known as path loss. Said in a different way, Friis Transmission Equation says that the path loss is higher for higher frequencies. The importance of this result from the Friis Transmission Formula cannot be overstated. This is why mobile phones generally operate at less than 2 GHz. There may be more frequency spectrum available at higher frequencies, but the associated path loss will not enable quality reception. As a further consequence of Friss Transmission Equation, suppose you are asked about 60 GHz antennas. Noting that this frequency is very high, you might state that the path loss will be too high for long range communication - and you are absolutely correct. At very high frequencies (60 GHz is sometimes referred to as the mm (millimeter wave) region), the path loss is very high, so only point-to-point communication is possible. This occurs when the receiver and transmitter are in the same room, and facing each other. As a further corrollary of Friis Transmission Formula, do you think the mobile phone operators are happy about the new LTE (4G) band, that operates at 700MHz? The answer is yes: this is a lower frequency than antennas traditionally operate at, but from Equation [2], we note that the path loss will therefore be lower as well. Hence, they can "cover more ground" with this frequency spectrum, and a Verizon Wireless executive recently called this "high quality spectrum", precisely for this reason. Side Note: On the other hand, the cell phone makers will have to fit an antenna with a larger wavelength in a compact device (lower frequency = larger wavelength), so the antenna designer's job got a little more complicated! Finally, if the antennas are not polarization matched, the above received power could be multiplied by the Polarization Loss Factor (PLF) to properly account for this mismatch. Equation [2] above can be altered to produce a generalized Friis Transmission Formula, which includes polarization mismatch: [Equation 3]