Link issues in practical EW applications.
Power Out in the Ether Waves
The link equation formulas presented here in "EW 101" (and used by most people who practice system-level EW magic for a living) contain a serious logical flaw. But they make our lives so much simpler that we are ready to fight to defend them against those to whom rigorousness is a theological issue. The flaw is that we state the power of signals "out in the ether waves"--that is, between a transmitting antenna and a receiving antenna--in dBm. The problem is that dBm is just the logarithmic representation of milliwatts. Signal strength in dBm is "power," and electrical power is only defined inside a wire or a circuit. While propagating from a transmitting to a receiving antenna, signals must be accurately described in terms of their "electric intensity," which is most commonly quantified in microvolts per meter ([micro]V/m).
So how do we come up with dBm values for propagating waves that produce correct answers when applied to the analysis of links? We use an artifice [n. 1. An ingenious stratagem; maneuver. 2. Subtle or deceptive craft; trickery]. The artifice creates an imaginary, ideal unity-gain antenna located at the point in space where we want to assign a signal strength to the signal of interest. That signal strength (in dBm) would be present in the output of the imaginary antenna. Thus, the effective radiated power (ERP) would be output by the imaginary antenna if it were located on a line from the transmitting antenna to the receiving antenna and almost touching the transmitting antenna (ignoring near field effects, of course). Likewise, in a representation of the power arriving at the receiving antenna (often called [P.sub.A]), the imaginary antenna would be on the same line, but almost touching the receiving antenna.
[Figures 1 to 2 ILLUSTRATION OMITTED]
Sensitivity in [micro]V/m
Receiver sensitivity is sometimes stated in [micro]V/m rather than in dBm. This is particularly true for devices in which an intimate and complex relationship between the antenna(s) and the receiver exists. The best example is probably a direction-finding system with a space-diverse antenna array. Fortunately, a pair of simple dB-type formulas (based on that imaginary unity-gain antenna) translate between [micro]V/m and dBm. In all of the equations in this column, "log" means log to the base 10. To convert from [micro]V/m to dBm:
P = -77 + 20 log(E) - 20 log(F)
Where: P = signal strength in dBm E = electric intensity in [micro] v/m F = frequency in MHz.
To convert from dBm to [micro] V/m:
E = [10.sup.(P+77 2010g [F])/20]
These formulas are based on the equations:
P = ([E.sup.2]A)/[Z.sub.0] and A = (G [c.sup.2])/(4[Pi][F.sup.2])
Where: P = signal strength in W E = electric intensity in V/m A = antenna area in [m.sup.2] [Z.sub.0] = impedance of free space (120[Pi] ohms) G = antenna gain (= 1 for isotropic antenna) c = speed of light (3 x [10.sup.8] m/sec) F = frequency in Hz.
You are welcome to derive these, if that's your idea of a good time. (It's really quite straightforward if you remember the unit conversion factors and then convert the whole, combined equation to dB form.)
"Links" in Radar Operation
Many textbooks present the radar range equation in the form most useful to radar people, since the equation focuses on how well the radar is doing its job. However, for EW people it is more useful to consider the radar range equation in terms of its component "links," as shown in Figure 3, and to handle everything in terms of dB and dBm. This allows us to deal with the radar power arriving at a target; the power we must generate with a jammer if we are to equal (or exceed by some fixed factor) the power returned by that target to the radar receiver; and many other useful values.
[Figure 3 ILLUSTRATION OMITTED]
You will recognize the expression for spreading loss presented in the July 1995 "EW 101" [32.4 + 20 log(D) + 20 log(F)], but for convenience the 32.4 factor is normally rounded to 32. There is also a handy expression for the signal reflection factor caused by the radar cross section of the target [-39 + 10 log([Sigma]) + 20 log(F)]. This expression will be derived and treated in much more detail when we talk about decoy theory in a few months.
[P.sub.T] is the radar's transmitter power into its antenna (dBm)
G is the main beam gain of the radar antenna (dB)
[P.sub.1] is the signal power arriving at the target (dBm)
[P.sub.2] is the signal power reflected from the target back toward the radar (dBm)
[P.sub.A] is the signal power arriving at the radar's antenna (dBm)
[P.sub.R] is the received power (into the radar receiver) (dBm).
In dB form:
ERP = [P.sub.T] + G
[P.sub.1] = ERP - 32 -20 log(D) - 20 log(F) = [P.sub.T] + G - 32 -20 log(D) - 20 log(F)
D = the distance to the target (km)
F = frequency (MHz).
[P.sub.2] = [P.sub.1] - 39 + 10 log([Sigma]) + 20 log(F)
[Sigma] = the target's radar cross section ([m.sup.2]).
[P.sub.A] = [P.sub.2] - 32 -20 log(D) - 20 log(F)
[P.sub.R] = [P.sub.A] + G
[P.sub.R] = [P.sub.T] + 2G - 103 -40 log(D) - 20 log(F) + 10 log ([Sigma])
If two signals at the same frequency arrive at a single antenna, one is usually considered the desired signal and the second is an interfering signal. The same equations apply whether the interfering signal is unintentional or intentional jamming. The dB expression for the difference in power between the two signals, assuming that the receiver antenna presents the same gain to both signals, is:
[P.sub.S] - [P.sub.1] = [ERP.sub.S] - [ERP.sub.1] - 20 log([D.sub.S] + 20 log([D.sub.1])
[P.sub.S] is the received power (i.e., at the receiver input) from the desired signal
[P.sub.1] is the received power from the interfering signal
[ERP.sub.S] is the effective radiated power of the desired signal
[ERP.sub.1] is the effective radiated power of the interfering signal
[D.sub.S] is the path distance to the desired signal transmitter
[D.sub.1] is the path distance to the interfering signal transmitter.
This is the simplest form of the interference equation. In later "EW 101" columns, we will deal with directional receiving antennas (which cause different antenna-gain factors to be applied to the two signals) and non-cochannel interference (in which there are different frequency terms for the two signals). Also, we will, of course, deal with the situation in which an interfering signal (i.e., from a jammer) is accepted by a radar receiver along with the desired radar return signal. All of these expressions will build on the simple dB form expressions described above.
Next month, as promised, we will deal with specific kinds of receivers and their typical operating characteristics.
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|Title Annotation:||EW 101; electronic warfare|
|Publication:||Journal of Electronic Defense|
|Date:||Sep 1, 1995|
|Previous Article:||A sampling of signal intelligence systems.|
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