Radio Frequency Integrated Circuit Design - Webs

38 Radio Frequency Integrated Circuit Design
Figure 2.16 Translation of the RF signal to an IF in a superheterodyne receiver.
‘‘on top’’ of the desired frequency. Thus, before mixing can take place, this
unwanted image frequency must be removed. Typically, this is done with a
filter that attenuates the image.
Thus, another important specification in a receiver is how much image
rejection it has. Image rejection is defined as the ratio of the gain of the desired
signal through the receiver Gsig to the gain of the image signal through the
receiver Gim.
IR = 10 log� Gsig
Gim�
(2.80)
The amount of filtering provided can be calculated by knowing the undesired
frequency with respect to the filter center frequency, the filter bandwidth,
and filter order. The following equation can be used for this calculation:
A dB = n
2 � 20 log� f ud − f c n
�f
= � 20
f be − f c� log�2 (2.81)
2 f BW�
where A dB is the attenuation in decibels, n is the filter order (and thus n/2 is
the effective order on each edge), f ud is the frequency of the undesired signal,
f c is the filter center frequency, f be is the filter band edge, �f is f ud − f c , and
f BW is 2( f be − f c ).
Example 2.9 Image Reject Filtering
A system has an RF band from 902 to 928 MHz and a 200-kHz channel
bandwidth and channel spacing. The first IF is at 70 MHz. With a 26-MHz