Question 10.4: A low-noise amplifier and mixer are shown in Figure 10.19. T...
A low-noise amplifier and mixer are shown in Figure 10.19. The amplifier has a gain of 20 dB and a third-order intercept point of 22 dBm (referenced at output), and the mixer has a conversion loss of 6 dB and a third-order intercept point of 13 dBm (referenced at input). Find the intercept points of the cascade network for both a phase coherence assumption and a random-phase (noncoherence) assump-tion.
First we transfer the reference of IP_{3} for the mixer from its input to its output:
OIP^{′′}_{3} =(IIP^{′′}_{3})G_{2} = 13 dBm − 6 dB = 7 dBm.Converting the necessary dB values to numerical values yields:
OIP^{′}_{3} = 22 dBm = 158 mW (for amplifier),
OIP^{′′}_{ 3} = 7 dBm = 5 mW (for mixer),
G_{2} = −6 dB = 0.25 (for mixer).
Assuming coherence, equation (10.53) gives the intercept point of the cascade as
OIP_{3}=(\frac{1}{G_{2}(OIP^{'}_{3})} + \frac{1}{OIP^{"}_{3}} )^{-1}=(\frac{1}{(0.25)(158) + \frac{1}{5} })^{-1} = 4.4 mW = 6.4 dBm,which is seen to be lower than the minimum IP3 of the individual components.
Equation (10.54) gives the results for the noncoherent case as
As expected, the noncoherent case results in a slightly higher intercept point.