In order to get numbers out, we need a value for the effective aperture. It is not trivial to derive what this area should be, but it is plausible (and correct) to guess that the effective aperture of an antenna around a half-wavelength long might correspond to a square around a half wavelength on a side. The actual answer for an isotropic antenna (which a tag isn't quite) is:
With a value for the aperture, we can now obtain an estimate of the path loss for our proposed isotropic link. At a distance of 1 m, the spherical surface has an area of 12.6 m2, so for 1 watt of transmit power, we get about 1(86)/(126,000) = 7 - 10'4 = 0.7 mW (-1.6 dBm). Since we started with a watt or 30 dBm, the path loss is about 32 dB.
Since the area scales with the square of the radius, we can very easily scale path loss, especially in dB: a factor of 10 in distance adds 20 dB to the path loss (20 dB/decade). A factor of
3 is worth just a bit less than half of this (about 9.5 dB). So at 3 m, the path loss is about (32+9.5) ≈ 41 dB, and at 10 m it is about 52 dB.
Tag Power Requirement
The tag antenna needs to deliver enough power to turn the tag IC on. We will consider this problem in some detail in Chapter 5; for the present, it suffices to give the results. Modern tag
ICs actually consume around 10"30 μW to operate when being read (much more power is required to write new data to the tag memory). This power must be supplied by a rectifying circuit, which is about 30% efficient, due primarily to the substantial turn-on voltage required to make current flow through the diodes (see Chapter 5).
As a consequence, tags require about 30 to 100 μW of power to be delivered from the antenna to provide the required 10 to 30 μW of power to the chip. For simplicity, let us for the moment use a rather conservative 100 μW (-10 dBm) as the required threshold power. If we started at the transmitter with 1 watt (30 dBm), and we need to end up with -10 dBm, we have room for a path loss of (30-(-10)) = 40 dB. By reference to the previous paragraph, this corresponds to a distance of just less than 3 m. Thus, we expect the forward-link-limited range of a 1-watt reader connected to an isotropic antenna to be no more than about 3 m, for a tag that requires 100 μW to power up.
Most RFID readers use modulation depths (the extent to which the power is reduced in the low-power state of e.g., Figure 3.6 or Figure 3.8) of nearly 100%, so it is reasonable to guess that any time the tag has enough power to turn the IC on, it also receives more than enough signal power to interpret the data being sent by the reader.
The calculation is depicted graphically in Figure 3.22. We construct a line of slope -20
dB/decade (-6 dB/octave) and adjust the height of the line to give -1.5 dBm at 1 m. We can
then immediately obtain the range as the intersection of this line with the required power for
the IC, here taken as -10 dBm.
3.22. Forward Link Budget Calculation For Passive Tag, United States Operation. (Note, Simple Scaling is Not Valid When the Tag is Within a Wavelength of the Antenna, Here Shown as a Dotted Line.)