Total Distance to Target in Radians

The total distance (D) traveled by the wave is 2r

The number of wavelengths (l) in the total distance (D) is equal to 2r/l

We can also express D in terms of radians:

since 1 l = 2p radians, then,

radians

if:

f₀ = phase of pulse sent out by radar

f = phase of returning signal then,

(1)

differentiating (1) yields:

(2)

Simple Example:

r = 10 cm then D = 2r = 20cm

number of wavelengths in the total distance (D) is equal to 2r/l = 20cm/10cm = 2 wavelengths

so, in terms of radians,

= 2(2p) = 4p radians

so phase of returned signal is:

if f₀ = 0, then f = 4p