Page 211 - Fundamentals of Radar Signal Processing

FIGURE 3.19 Relative power of I/Q mismatch-induced signal image as a
function of amount of phase and amplitude mismatch.

It is also useful to consider simplifications of Eq. (3.37) for the cases of
small amplitude mismatch only and small phase mismatch only. First consider
the case of small amplitude mismatch only (ε 1), so that ϕ = 0. Then

(3.38)

Amplitude mismatch is often specified in decibels, as is the relative power of
the image signal component. A mismatch of k dB implies that 20 log (1 + ε) =
10
k. Substituting this relation in Eq. (3.38) and expressing the result in decibels
gives

(3.39)

For example, an amplitude mismatch of 0.1 dB gives rise to an image
component 44.7 dB below the desired component of x(t).

A result similar to Eq. (3.38) holds for the case of small phase mismatch