ECE 3300 ANT Lecture Notes #7: Link Budgets

Objectives:

• Write a “link budget” for a wireless network (compare the power supplied to a transmitting antenna and the power delivered to the receiver) • Compare the link budget to the Friis Transmission Formula • Consider additional propagation losses that may occur between the transmitter and receiver • Consider sources of noise

Corresponding Book Section(s):

• Section 9-6 (Friis Transmission Formula) • Section 10-3 (Communication-Link Power Budget) • (Optional) Wireless Networking the Developing World, 3rd edition, 2013, http://wndw.net • (Optional) www.piscespacific.org/livesite/files/Link_Budget_Calculation.pdf

Notes:

1. Link Budgets

A link budget predicts how much power is received from a known transmitter. It accounts for the directivity, losses, etc. of the transmitter and receiver, as well as the losses and reflections/scattering over the propagation path between the transmitter and receiver. A general link budget equation has the following form:

Received power (dB) = Transmitted Power (dB) + Gains (dB) – Losses (dB)

2. Link Budget Example

Let’s say we have an optical fiber carrying internet connectivity to a main island, but now we want to distribute that internet to the inhabitants of the island. Further, we want to connect smaller, neighboring islands to the internet. Although optical fiber can be used by a large number of people at high data rates, there aren’t enough funds initially to lay optical fiber throughout the islands. Instead, let’s build an inexpensive wireless network throughout the islands operating at a frequency of 2.4 GHz.

It’s a good idea to calculate a link budget between each client and the internet access point before setting up antennas, etc. The resulting link margin must be positive. In this case, for a reliable link we want the client to receive a signal at least 10 dB higher than the minimum (minimum sensitivity of the receiver in both directions).

In the case of our example, the internet access point is connected to an antenna with 10 dBi gain, with a transmitting power of 20 dBm and a receive sensitivity of -89 dBm.

The client is connected to an antenna with 14 dBi gain with a transmitting power of 15 dBm and a receive sensitivity of -82 dBm.

The cables in both systems are short, with a loss of 2 dB.

Let’s estimate the feasibility of a 5-km link between two mountain tops (for now, with no trees or obstacles between the two paths). Calculate the link margin for the client as well as for the internet access point.

Solution:

Let’s start by considering the link from the access point to the client. If the transmitting antenna is an isotropic, lossless radiator, the power density at the client receiver would be (where R is 5 km):

t Slossless, isotropic = = (the power at the input terminals of the transmitting antenna divided by surface area of sphere for radius R)

But the transmitting antenna is not isotropic and not lossless. It has a gain of 10 dBi. Gain takes into account directionality as well as the losses of the transmitter. From the definition of gain,

direction of interest (or max value) direction of interest (or max value) � = = (calculated using supplied to a lossless, isotropic antenna) t/() or t/( )

Since we’ll have both of our antennas directed towards each other, we can solve the above equation for Smax. Then, transmitter t Smax, at receiver at distance R = � � = lossless, isotropic transmitter

The receiver “sees” Smax at receiver at distance R over its effective area. The total power intercepted by the receiving antenna is then: �receiver, intercepted = �max, at receiver at distance ∗ �, receiver

So, we need to calculate the effective area of the receiving antenna: intercepted receivier �, receiver = = incident

Then, the power intercepted by the receiving antenna is: � = � ∗ � = transmitter receiver receiver, intercepted max, at receiver at distance , receiver Since there may be losses in the receive antenna, the intercepted power is scaled by the efficiency of the receiving antenna to yield the actual received power: � = � � = transmitter receiverreceiver received receiver, intercepted receiver

Now we want solve for the total path loss. So we should rearrange our equation to solve for the following ratio: �received �transmitter � �receiver�receiver � �receiver�transmitter = = � 4�� 4� (4��) Where we used �� = �.

Compare the equation we just developed to the Friis Transmission formula: rec ,, = = �� Equation 9.69, Equation 12 on Equation Sheet In other words, the Friis Transmission Formula calculates the total power loss between a transmitter and receiver while accounting for directivity, the effective area of the antennas, and also the radial spreading of the propagating wave.

Let’s use the Friis Transmission Formula now to calculate the link budget for our example. First, � = = 0.125 m. We also need to convert the gain values to linear values in order . to plug them into our Friis Transmission formula: 10 dBi à 10(10/10)=10 and 14 dBi à10(14/10)=25.1. received receivertransmitter . ()(.) Then, = = = 9.9 × 10 or -90 dB () (∗)

The total link budget for the access point to the client is: +20 dBm (transmitting power) -2 dB cable loss (transmitter cables) -90 transmitter to receiver antenna and propagation gains and losses -2 dB cable loss (receiver cables) ______-74 dBm (expected received signal)

Compare this to the client receiver sensitivity of -82 dBm. Thus, the link margin is −82 dBm − (−74 dBm) = 8 dB. This link budget is shown graphically in Fig. 1.

Fig. 1 Access point to client link [Courtesy of wndw.net].

Everything is the same for the (reverse direction) client to access point link budget except for the transmitting power (it is weaker) and receiver sensitivity (it is more sensitive):

+15 dBm (transmitting power) -2 dB cable loss (transmitter cables) -90 transmitter to receiver antenna and propagation gains and losses -2 dB cable loss (receiver cables) ______-79 dBm (expected received signal)

Compare this to the access point receiver sensitivity of -89 dBm. Thus, the link margin is −89 dBm − (−79 dBm) = 10 dB. This link budget is shown graphically in Fig. 2.

Fig. 2 Client to access point link (opposite direction as that shown in Fig. 1) [Courtesy of wndw.net].

3. Real-World Example

The following real-world example is of a wireless link set up in 2012 between two islands in Micronesia as part of the Pacific Island Schools Connectivity, Education, and Solar (PISCES) Project. First, a computer program called Radio Mobile (free online) was used to calculate the link budget and required height of the antennas (we’ll talk more about how to calculate the required height of the antennas in Notes 8) for a link between the Udot School on the island of Udot and the main island, Weno, 15 km away as shown in Fig. 3. Based on the calculations, the antenna on the main island, Weno, was mounted on the 3rd story roof of the Truk Stop Hotel. On the island of Udot, the antenna was mounted on a 40-foot (12 m) pole mast next to the single-level Udot School shown in Fig. 4. This wireless link represents the first connection to the Internet for the inhabitants of Udot. From the antenna on Udot, the network was routed through a local DSL Internet connection to provide Internet connectivity to the school and surrounding local community.

Fig. 3 Wireless link path between the Udot School on Udot Island and the main island, Weno, 15 km away [Courtesy of wndw.net].

Fig. 4 The antenna on Udot is mounted on a 40-foot (12 m) pole mast next to the single- level school [Courtesy of wndw.net].

4. Other Considerations

The Friis Transmission Formula introduced in Section 2 assumes free space between the transmitter and receiver. If we have a signal traveling in a lossy or more complex medium, then we need to account for the effects that material will have on the propagating electromagnetic wave. For example, for an electromagnetic wave traveling from a ground station to a satellite, we might need to add in losses due to:

• Clouds and rain in the Earth’s atmosphere (when present) • Certain atmospheric gases (primarily oxygen and water vapor)

As another example, consider your ECE 3300 labs. The electromagnetic wave propagates through the person’s chest. You have been assuming a homogeneous, lossy body material which will attenuate the wave by a factor of � . You’ll also see a reflection at the body- air interface. If you were to improve your calculation, you might model the propagation of the waves through a more realistic chest structure using a computational electromagnetics solver, such as Remcom’s XFDTD. Fig. 5 shows an example patch antenna simulated in a human body at 2 mm resolution using XFDTD. Fig. 6 shows a snapshot of the outward propagating electromagnetic waves from the patch antenna.

Fig. 5 (a) Human model with patch antenna; (b) electromagnetic waves propagating from the patch antenna calculated using XFDTD [www.recom.com].