4.1 Introduction

This chapter considers transmission between radar and target in an unbounded vacuum. In this hypothetical free space, environmental effects are ignored; there is no atmosphere, weather, Earth surface or other tiresome practicality. We shall derive basic forms of equations, the radar range equations, describing the energy reaching the target on the transmit leg and echoing back to the radar on the receive leg of its journey, on which later chapters will build when examining practical conditions including the environment. Application of free space equations directly to the real world without allowance for environmental effects often leads to gross errors, especially when range is long so rays traverse a lot of atmosphere. Throughout this chapter we assume the target remains of constant electrical size and is physically small enough to behave like a geometrical point.

In free space, energy radiated from a source such as a lamp or radar transmitter propagates in straight lines at the speed of light without loss; as explained in Chapter 2, Section 2.7. Doubling range, R, doubles the height and width of the beam and reduces the energy density to one quarter its original value, so energy density ? 1/ R ². This inverse square law, which applies to light and sound as well as radar waves, is the reason why distant targets are illuminated weakly. Echoes from ordinary passive objects again suffer the inverse square law, making...