Radio Frequency Integrated Circuit Design - Webs

224 Radio Frequency Integrated Circuit Design
inputs can be applied at nodes ‘‘a’’ and ‘‘c.’’ With the simple differential inputs,
the other nodes, ‘‘b’’ and ‘‘d,’’ can be connected to ‘‘a’’ and ‘‘c,’’ left open, or
grounded.
The polyphase filter is designed such that at a particular frequency (nominally
at � = 1/RC ), all outputs are 90° out of phase with each other. The filter
also has the property that with each additional stage, phase shifts become more
precisely 90°, even with a certain amount of tolerance on the parts. Thus, when
they are used in an image reject mixer, if more image rejection is required, then
polyphase filters with more stages can be employed. The drawback is that with
each additional stage there is an additional loss of about 3 dB through the filter.
This puts a practical upper limit on the number of stages that can be used.
7.10.3 Image Rejection with Amplitude and Phase Mismatch
The ideal requirements are that a phase shift of exactly 90° is generated in the
signal path and that the LO has perfect quadrature output signals. In a perfect
system, there is also no gain mismatch in the signal paths. In a real circuit
implementation, there will be imperfections as shown in Figure 7.27. Therefore,
an analysis of how much image rejection can be achieved for a given phase and
amplitude mismatch is now performed.
The analysis proceeds as follows:
1. The input signal is mixed with the quadrature LO signal through the
I and Q mixers to produce signals V1 and V 2 after filtering. V 1 and
V2 are given by
V1 = 1
2 sin (� LO − � 1
RF )t −
2 sin (� IM − � LO )t (7.26)
Figure 7.27 Block diagram of an image reject mixer, including phase and gain errors.