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Immaculate Reception

When designing a wireless product or system, don’t discount the importance of receiver sensitivity.

What does receiver sensitivity really have to do with wireless system performance? Along with transmit power and antenna gains, it is a key indicator not only of the range of the signal but also the data rate and the bit error rate (BER). Here’s the real truth about receiver sensitivity.

A major goal in designing a wireless product or system is maximizing the range between transmitter and receiver. All short-range wireless technologies used for IoT and other applications operate on frequencies in the VHF, UHF, and microwave spectrum. Signals in this range travel in a straight line from transmitter to receiver. This is what we call line of sight (LOS). During the flight from antenna to antenna, the signal undergoes significant attenuation. This is called free space path loss (FSPL). The range is strictly limited by the physics of the system. The Friis formula shows the factors involved:

Pr = PtGtGrλ2/16π2d2

Distance (d), or the range between the Tx and Rx, is given in meters. Wavelength (λ) is also in meters. Wavelength (λ) = 300/fMHz . Other factors are transmitted power (Pt), received power (Pr), transmitter antenna gain (Gt), and receiver antenna gain (Gr).The power is expressed in watts and the antenna gains are power ratios. If you assume a dipole or its equivalent, the power ratio is 1.64. Both antennas are assumed to have the same polarization.

The obvious way of looking at this is that as the distance increases, the received power is less. The attenuation is proportional to the square of the distance (d) and the frequency of operation (f). An important take-away is that the range for a given transmit power and antenna gains is less at the higher frequencies. A 915 MHz signal will naturally travel farther than a 2.4 GHz signal for the same power and antenna gains.

To see this more clearly, here is a way to calculate the FSPL directly: 

FSPL (dB) = 32.45 + 20log(f) + 20log(d)

The frequency (f) is in MHz and distance (d) is in kilometers.

For instance, what is the FSPL for a 5.8 GHz signal at 50 meters?

FSPL(dB) = 32.45 + 20log(5800) + 20log(0.05) = 32.45 + 75.3 – 26 = 81.75 dB

Keep in mind that this is the loss of the best possible link where there is a clear path between transmitter and receiver antennas. It assumes no obstacles like trees, walls, or terrain features. In the real world there will be obstacles that will add an extra 10 to 20 dB or more of loss. Therefore you should estimate an additional loss factor and add it in, plus a safety factor of 10 or more dB.

To keep all our gains, loses, and power levels in the same units of measurement, let’s express transmitter power (Pt) in decibels or dBm (milliwatt reference). Assume a transmit power of 100 mW.

dBm = 10log (Pt/1mW) = 10log(100) = 20 dBm

We need to factor in the antenna gains. A dipole or its equivalent has some gain—specifically, a 1.64 power ratio or 2.15 dB. Assume that both transmitter and receiver use a dipole. The real transmit power then is:

Pt = 20 + 2.15 = 22.15 dBm

Now we can factor in the FSPL to get the actual received power:

Pr = Pt + Gt + Gr – FSPL = 20 + 2.15 + 2.15 – 81.75 = −57.45 dBm

In terms of power this is about 1.8 µW. This is a very small signal. The big question—and the point to this blog—is whether the receiver can handle it.

An often-overlooked factor in all this is receiver sensitivity (R). This is the smallest signal the receiver can reliably demodulate the signal. R is usually stated in –dBm and is determined by receiver gain. Typical ranges for R are approximately –70 to –150 dBm. For this example, assume a receiver sensitivity of –90 dBm. The received power as calculated above is –57.45 dBm. That is a greater power level than –90 dBm, so the receiver has more than enough power to recover the signal.

Now, just for fun, you can compute the maximum path loss and range for this combination given the transmit power, receiver sensitivity, and antenna gains.

 FSPL (max) = Pt + Gt + Gr – R = 20 + 2.15 + 2.15 – (–90) = 114.3 dB

Next, rearrange the FSPL formula and calculate the maximum possible range (d) for this example. In this case, the maximum range is 2.13 km.

Remember, this is the maximum theoretical range with clear LOS. If the receiver gain and sensitivity are insufficient, the signal may not be recoverable. Data rate may decline in some systems as it may adjust to cope with the environment. Or the BER will increase.

In all cases, try to clearly define the maximum potential range needs for your application. Then factor in some additional attenuation for obstacles, fading, or reflected signals if the application environment calls for it. With this approach, you will know what you can expect in designing your system and determining what it can do.

Finally, note that the effect of noise in the system is also a factor. But that’s another story. More later.

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