Appendix 3C. I and Q Imbalance and Image-Rejection Formula

The I and Q signal imbalances limit the image rejection and the dynamic range of a receiver or a transmitter. The image-rejection formula (3.3.4) can derived based a simplified quadrature conversion system model as shown in Fig. 3C.1. The received RF desired signal has a frequency ? _RF an angle modulation ?( t) and an amplitude of normalized to one. Assuming that all the imbalances in the I and Q channels are concentrated on the imbalances of the quadrature LO signals, the amplitude normalized I and Q LO signals are expressed as cos( ? _LOt) and (1 + ?) sin( ? _RFt + ?) , respectively, where ? is the amplitude imbalance and ? is the phase imbalance.

Figure 3C.1: Simplified quadrature conversion system model

If the gain of the converter is unity, the I and Q signals at the downconverter outputs have expressions as

and

where ? _IF is the low IF frequency.

After low-pass filtering, if not considering the channel gain or loss, we obtain two low IF signals having forms,

(3C.1)

and

(3C.2)

The desired low IF signal S _d can be obtained from the I _IF signal subtracting 90 phase shifted Q _IF signal. It is expressed as

(3C.3)

where

(3C.4)

For the image signal it possesses a frequency ? _img = ? _RF - 2 ?