Radio Frequency Integrated Circuit Design - Webs

26 Radio Frequency Integrated Circuit Design
Table 2.1
Summary of Distortion Components
Frequency Component Amplitude
dc k o + k 2
2 (v 2 1 + v 2 � 1
2 )
k 1v 1 + k 3v 1�3 4 v 2 1 + 3
2 v 2 � 2
2�
k 1v 2 + k 3v 2�3 4 v 2 2 + 3
2 v 2 1�
2� 1
k 2v 2 1
2
2� 2
� 1 ± � 2
� 2 ± � 1
3� 1
3� 2
2� 1 ± � 2
2� 2 ± � 1
k 2 v 2 2
2
k 2v 1v 2
k 2v 1v 2
k 3v 3 1
4
k 3v 3 2
4
3
4 k 3v 2 1 v 2
3
4 k 3v 1v 2 2
Note that in the case of an amplifier, only the terms at the input frequency
are desired. Of all the unwanted terms, the last two at frequencies 2� 1 − � 2
and 2� 2 − � 1 are the most troublesome, since they can fall in the band of the
desired outputs if � 1 is close in frequency to � 2 and therefore cannot be easily
filtered out. These two tones are usually referred to as third-order intermodulation
terms (IM3 products).
Example 2.5 Determination of Frequency Components Generated in a Nonlinear
System
Consider a nonlinear circuit with 7- and 8-MHz tones applied at the input.
Determine all output frequency components, assuming distortion components
up to the third order.
Solution
Table 2.2 and Figure 2.11 show the outputs.
It is apparent that harmonics can be filtered out easily, while the thirdorder
intermodulation terms, being close to the desired tones, may be difficult
to filter.