Radio Frequency Integrated Circuit Design - Webs

Issues in RFIC Design, Noise, Linearity, and Filtering
k 1v 1dB + 3
4 k 3v 3 1dB
k 1v 1dB
31
= 0.89125 (2.65)
Note that for a nonlinearity that causes compression, rather than one that
causes expansion, k 3 has to be negative. Solving (2.65) for v1dB gives
v 1dB = 0.38 √ k 1
k 3
(2.66)
If more than one tone is applied, the 1-dB compression point will occur
for a lower input voltage. In the case of two equal amplitude tones applied to
the system, the actual output power for one frequency is
vo = k 1vi + 9
4 k 3v 3 i
The ideal output voltage is still given by (2.64). So now the ratio is
(2.67)
k 1v 1dB + 9
4 k 3v 3 1dB
= 0.89125 (2.68)
k 1v1dB Therefore, the 1-dB compression voltage is now
v 1dB = 0.22 √ k 1
k 3
(2.69)
Thus, as more tones are added, this voltage will continue to get lower.
2.3.5 Relationships Between 1-dB Compression and IP3 Points
In the last two sections, formulas for the IP3 and the 1-dB compression point
have been derived. Since we now have expressions for both these values, we
can find a relationship between these two points. Taking the ratio of (2.53)
and (2.66) gives
vIP3 =
v1dB 2 √ k 1
3k 3
0.38 √ k 1
k 3
= 3.04 (2.70)