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

Question

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.

Accepted Answer

First we transfer the reference of [latex]IP_{3}[/latex] for the mixer from its input to its output:

[latex]OIP^{′′}_{3} =(IIP^{′′}_{3})G_{2} = 13 dBm − 6 dB = 7 dBm.[/latex]

Converting the necessary dB values to numerical values yields:

[latex]OIP^{′}_{3}[/latex] = 22 dBm = 158 mW (for amplifier),
[latex]OIP^{′′}_{ 3}[/latex] = 7 dBm = 5 mW (for mixer),
[latex]G_{2}[/latex] = −6 dB = 0.25 (for mixer).

Assuming coherence, equation (10.53) gives the intercept point of the cascade as

[latex]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,[/latex]

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

[latex]OIP_{3}=(\frac{1}{G_{2}^{2}(OIP_{3}^{'})^{2}} + \frac{1}{(OIP_{3}^{''})^{2}} )^{-1/2}=(\frac{1}{(0.25)^{2}(158)^{2}} ) + \frac{1}{(5)^{2}} )^{-1/2} = 4.96 mW = 6.9 dBm[/latex]

As expected, the noncoherent case results in a slightly higher intercept point.

Question 10.4: A low-noise amplifier and mixer are shown in Figure 10.19. T...

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