Subhash Janakiraman from Icon Systems Inc. has submitted this month’s question:

Dear Harlan,

I am trying to test a RF communication link inside an enclosed chamber which is free from RF leakage. I want to emulate a test in the same set up in such a way that the receiver and transmitter are 30 metres apart. I thought calculating the signal strength at this distance and attenuating the transmit power accordingly will justify my testing. Is that true? Am I justified to introduce that attenuation to account for the distance despite the fact that there is no free space loss? Can you point me to a link to calculate the attenuation in the transmit power due to varying distances?

**From:** Melanie Barclay, Scientific Research Corp.

Dear Subhash,

If I name these variables as follows: Received Power = Pr Transmitter Power = Pt Transmitting Antenna Gain = Gta Spreading Loss = Ls Atmospheric Loss = La Receiving Antenna Gain = Gra then the following equation is true: Pr = Pt + Gta - Ls - La + Gra. Notice that there are two losses in the equation above: Spreading Loss and Atmospheric Loss. Spreading Loss is defined as being related to distance, as: Ls(dB) = 32.4 + 20log(base 10)(distance in km) + 20 log(base 10)(frequency in MHz). It appears that you will want to consider this in determining the total losses related to distance. That leaves atmospheric loss (attenuation). The best way to determine the atmospheric loss is to refer to a chart, rather than an equation. I referred to page 14 of a book from Artech House by David Adamy called "EW 101: A First Course in Electronic Warfare." Figure 2.3 in this book is a graph of atmospheric attenuation (in dB) per kilometer of transmission path. This graph has frequency (GHz) on the X-axis, and Atmospheric Loss (dB per km) on the Y-axis. You will have to look at the graph and find where the line is at the frequency you are transmitting.

**From:** Andy Knitt, Caterpillar Inc.

Dear Subhash,

You are on the right track. Your first step should be to calculate your expected link budget, which will tell you how much power your receiver will see at the desired separation distance. The link budget must include things like antenna gain of the transmitter and receiver, cable losses, etc. A sample link budget calculation will look something like this: ReceivedPower(dBm) = TransmittedPower(dBm) + TxAntGain(dBi) + RxAntGain(dBi) - Rxcableloss(dB) - Txcableloss - Pathloss(dB). Free space path loss can be calculated using the formula PathLoss(dB) = 20*log10(4*pi*d/lambda), where d is distance and lambda is wavelength, both in meters. Note that this does not take terrain or obstructions into account (it is a theoretical formula), and it is not valid if the distance between the transmitter and receiver is less than a few wavelengths. Once you have calculated the theoretical received power, you can add attenuation between your transmitter and receiver until the power at the receiver's antenna terminal is equal to what you calculated. It should be noted that this is a "best case" scenario since there is no external interference present, which could raise your noise floor and affect your communications link significantly in the real world. A full communication link analysis should include your expected and required receiver signal-to-noise ratios (SNR) in addition to just receiver sensitivity.

**From:** Daniel Amor, RBZ Robot Design

Dear Subhash,

By using an attenuator you will be degrading S/N ratio, degradating the signal in a way different from free space loss. The presence of obstacles that may introduce reflection in the signal path should also be taken into account. Depending on the conditions of the problem such as distance and frequency there are several different models that may be applied. A couple of links that may be useful: http://en.wikipedia.org/wiki/Free-space_loss and http://people.deas.harvard.edu/~jones/es151/prop_models/propagation.html.

**From:** Trevor Haydu-Jones, Microdynamics Ltd.

Dear Subhash,

The best way to do this is to place the transmitting end inside the screened room, and pass the full power through a high power fixed attenuator rated for the Tx power and of about 20 to 30 dB value, then through good coaxial cable through the choked transit to a variable attenuator, then to the receiver. In order to decide what setting to adjust for the variable attenuator you need to understand there are two different zones around an antenna: the near field and the far field. This depends on the frequency of the transmission and the gain of the antenna. The rough estimate for the grey cross-over range where you go from one to the other is 2*D^2/wavelength, where D is the major dimension of the Tx antenna in meters (wavelength is also in meters). For simplicity, assume the 30 meters puts your receive antenna in the far field (it may not be so, in which case it is far more complicated). Then the formula for path loss is approximately 32.45+20*LOG10(0.03*frequencyMHz) in decibels. The 0.03 is because the distance is normally in kilometers. From this figure you subtract the high power attenuator setting, and an allowance for the length of connecting coaxial cable. The closest simulation, to allow for any transit time delay, is to use a coaxial cable 30 meters long, then look up in manufacturer's datasheets or measure on a VNA what the loss is, including connectors.

**From:** Kathi Vamsi Krishna, RF Arrays Systems Pvt. Ltd.

Dear Subhash,

You said 'emulate a test' - if you are using some other equipment in the place of an actual transmitter for the emulation purpose and the signal power at the receiver is more in this case compared to the one in which the actual transmitter is used, then your thought of 'attenuating the transmit power accordingly' is correct. Signal strength in free space is inversely proportional to the square of the distance, i.e. signal strength is proportional to (1/d)*(1/d). The formula for free space propogation is Pr = ( ë/4ðd)2 GrPtGt Pr : Power at the terminals of the receiving antenna. ë : c/f d : Distance between transmitter and receiver. Pt : Transmitted power. Gt : Gain of transmitting antenna. Gr : Gain of receiving antenna. As the distance increases the signal strength decreases though there is no free space loss.

**From:** Andreas Schwarz, Austrian Aerospace

Dear Subhash,

Under the assumptions listed below, the received power level versus distance follows a 20 dB/Decade law. If you change the antenna distance from 30 to 3 m, the received power level would increase by 20 dB. To compensate you would have to decrease the transmitter power level for exactly 20 dB. Assumptions: 1) no athmospheric losses (frequency sufficiently low); 2) anechoic chamber (no significant reflections inside the chamber); 3) measurment distance inside chamber large compared to antenna dimensions (antenna far field assumption). Ref: Free Space Loss Calculator: http://www.comsearch.com/microwave/tools_fsl.jsp. "Free Space Loss (FSL) is the transmission loss between two isotropic antennas, separated by a distance D, assumed to be in a vacuum. FSL is the propagation loss due solely to spreading of the wave front and assumes no blockage of line of sight or the first Fresnel zone." [Comsearch]

**From:** Arun Kumar, Sameer Kolkata Centre

Dear Subhash,

I think you can use the well known Friss transmission formula to calculate the attenuation of power transmitted by the transmitter at a distance. You can get this formula in any standard antenna text book. You can calculate the attenuation corresponding to 30 meters and with that attenuation you can introduce the transmitting antenna by attenuator pads. I think this should work.