Author: Zhao Shengyun

- Decibels relative to a square meter - dBsm

In later chapters, we will be examining how a target scatters energy. When we work out the radar equation, there is a term that represents the radar "size" of the target. We call this the radar cross section, or RCS, and typically represent it by the Greek letter s. Note that it gives an equivalent area that represents how much reflection is returned to the radar. It does not correspond to physical size.

The units of radar cross section are the equivalent area, usually expressed in square meters m2. We know from previous problems that dB is always a power ratio. Since RCS is in units of area, how can a term like dB relative to a square meter (dBsm) be meaningful?

The trick is to realize that when we talk about dBsm, we are really still talking about power, but the power aspect is hidden. The power that we are actually concerned with is the power received by the radar, which is represented by the radar equation you will cover soon. If we hold constant all other terms in the received radar power, we find the received power is directly proportional to the RCS. This can be written as

Preceive = k·s

Consider the received power for two targets that differ only in their RCS. We then have

P1 = k·s1
P2 = k·s2

Now we can take the power ratio needed to use dB as

dB = 10·log10(P1/P2) = 10·log10(k·s1/k·s2) = 10·log10(s1/s2)

Note that the only terms left are RCS, which is in area units. This gives the equation for getting the difference in dB between two targets of different RCS. We can now take the final step in this derivation. If we pick a reference RCS of s2 = 1 m2, we call the results from this formula the decibels relative to a square meter, or dBsm.

RCS (dBsm) = 10·log10(s/1 m2)

Questions

  1. The RCS (radar cross section) of a warship,a fighter aircraft and a stealthy fighter aircraft are 1000 m2, 3 m2, and 0.001 m2 respectively. Express the RCS in terms of dBsm.
  2. The largest targets that we typically see with radars are 1000000 m2. How many dBsm is this?
  3. The radar cross section of some large birds is reported as up to 1 m2. How many dBsm is this?
  4. If an insect is -30 dBsm, how many square meters is the radar cross section?
  5. If you double the RCS of a target (multiply the number of square meters by two), what happens to the dBsm equivalent?
  6. If you halve the RCS of a target (divide the number of square meters by two), what happens to the dBsm equivalent?