# Communications EW, part 4--additional factors in communications signal propagation.

We will cover two subjects this month: the proper units for signals out in the propagation medium and external noise.

Signals in the Propagation Medium

When describing the communications link, we define the signal leaving the transmit antenna as effective radiated power in dBm. This is not literally true, since dBm is only defined inside a circuit. Out in the propagation medium (atmosphere or space), the signal is accurately defined in terms of field strength, and the proper units are microvolts per meter. However, it is extremely convenient to describe signal levels in dBm through the whole link, so we use an artifice to make it work. The artifice is an ideal isotropic (omni-directional) antenna, as shown in Figure 1. If this ideal antenna receives the signal anywhere in the signal transmission path, the antenna output is properly in dBm.

[FIGURE 1 OMITTED]

Since receiver sensitivity and some other important items can be specified in [micro]v/m, we are sometimes required to convert back and forth between field strength and equivalent signal strength to conveniently work propagation problems. The conversion is done by squaring the field-strength value, multiplying by the equivalent area of the isotropic antenna, then dividing by the impedance of free space.

The equivalent area of an antenna is given by the following formula:

A = G([[lambda].sup.2]/2[pi]

Where: A = the antenna area in square meters G = the antenna gain (not in dB) [lambda] = the signal wavelength in meters

For an isotropic antenna, the gain is unity, so the effective area is simply [[lambda].sup.2]/2[pi]. The dB form equation for the antenna area is as follows:

A = 39 + G -20 log(F)

Where: A = the effective area in dBsm, G = the gain in dB, and F = the frequency in MHz

The number 39 is a constant (in dB) that includes the square of the speed of light, 2[pi], and unit-conversion factors. For an isotropic antenna, the gain is unity (0 dB), so the effective area in dBsm is just 39-20 log (F). The impedance of free space is 120[pi]. Multiplying the square of the field strength by the antenna area and dividing by the impedance of free space yields the following formula:

P = [E.sup.2][[lambda].sup.2]/240[[pi].sup.2]

Where: P = signal strength in watts E = field strength in v/m [lambda] = wavelength in meters

Note that the free-space impedance (with units of ohms) is part of the denominator. The dB form of this equation is as follows:

P = -77 + 20 log (E) -20 Log (F)

Where: P = the power in the Antenna output in dBm E = the field strength in [micro]v/m F = the frequency in MHz

The term -77 (dB) includes [c.sup.2], [[pi].sup.2] and unit-conversion factors.

To convert from signal strength in dBm to field strength in [micro]v/m, use the following formula:

E = sqrt(240 [[pi].sup.2]P/[[lambda].sup.2])

Where: E is the field strength in [micro]v/m P = signal strength in watts [lambda] = wavelength in meters

Note that ohms units are in the numerator.

The dB form of this equation is as follows:

E = Antilog{[P + 77 + 20 log (F)]/20}

Where: E = field strength in [micro]v/m P = signal strength in dBm F = operating frequency in MHz.

Table 1 shows the signal strength in dBm for various field strengths at various frequencies.

Background Noise

The chart in Figure 2 shows the background noise in various environments as a function of frequency. External noise is not literally noise (kTB is true noise). It is actually the combined emissions from many low-power interfering signals, such as engine spark plugs, trolley cars, electric motors, etc.

[FIGURE 2 OMITTED]

The data in Figure 2 is from measurements made in a 10-kHz bandwidth with an omni-directional antenna. If the received "noise" power is stated in [micro]v/m, it must be adjusted for the receiver bandwidth. Since this chart is in dBm above kTB (which includes a bandwidth term), it is valid for all bandwidths.

External noise enters the receiver through the receiving antenna, as shown in Figure 3. (Note that kTB is generated inside the receiver.) If the receiving antenna is a whip, dipole, or similar antenna with 360[degrees] angular coverage, Table 2 is applicable; with narrow beam antennas, much lower levels are usually appropriate. The external noise is added to the internal kTB noise when determining the signal-to-noise ratio achievable when a signal is received.

[FIGURE 3 OMITTED]

What's Next

For the next three months, we'll discuss digital communications. For your comments and suggestions, Dave Adamy can be reached at dave@lynxpub.com
```Table 1: Signal strength in dBm for various values of field
strength and frequency.

Field            Signal      Signal       Signal
Strength         strength    strength     strength
([micro]v/m)     @10 MHz     @50 MHz      @100 MHz

1 [micro]v/m     -97 dBm     -111 dBm     -117 dBm
3 [micro]v/m     -87.5 dBm   -101.4 dBm   -107.5 dBm
5 [micro]v/m     -83 dBm     -97 dBm      -103 dBm
10 [micro]v/m    -77 dBm     -91 dBm      -97 dBm
50 [micro]v/m    -63 dBm     -77 dBm      -83 dBm
100 [micro]v/m   -57 dBm     -71 dBm      -77 dBm

Field            Signal       Signal
Strength         strength     strength
([micro]v/m)     @250 MHz     @500 MHz

1 [micro]v/m     -125 dBm     -131 dBm
3 [micro]v/m     -115.4 dBm   -121.4 dBm
5 [micro]v/m     -111 dBm     -117 dBm
10 [micro]v/m    -105 dBm     -111 dBm
50 [micro]v/m    -91 dBm      -97 dBm
100 [micro]v/m   -85 dBm      -91 dBm
```
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