Understanding White Noise Behaviour in an Ideal Mixer - SNR Unchanged"

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In summary, the question posed is regarding the behavior of white noise when passed through an ideal mixer in a system with filtered high frequency contents. The textbooks suggest that the signal-to-noise ratio remains unchanged from input to output, but the individual asking the question is confused as to why this is the case. They question whether the assumption that the in-phase and quadrature components have equal power spectral densities is reasonable, and if the phase of white noise being white would affect this. The response suggests that the SNR should not be changed significantly, as each baseband component would be mixed up to a corresponding product component with the same relationship to each other.
  • #1
diemilio
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Hello everyone,

I have a question regarding the way white noise behaves when passed through an ideal mixer.

Picture the system shown in the attached image. Assume the mixer is ideal and that the high frequency contents of the multiplication are filtered out. Therefore the output of the system will be A*B/2. My question is, how does wide-band white noise behave when passed through the mixer?

In several textbooks, I've seen that in this system the signal-to-noise ratio remains unchanged from input to output. However, I am confused because I would think that in the case of white noise, it would be possible to express the signal as a composition of in-phase and quadrature components with equal power spectral densities, thus part of the noise should be, phase-filtered.

Is this an unreasonable assumption? Isn't the phase of white noise also white, thus 0º and 90º components are equally probable?

What am I missing here? Why is the SNR unchanged?

Regards,

diemilio
 

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  • #2
I don't understand "in-phase and quadrature components with equal power spectral densities". Why do you think they would be equal? (asking, not testing you). I don't think the in-phase and quadrature components are in any way correlated. (I'm not an expert)

Are you thinking that when you mix to zero the resulting pos and neg frequencies add and might cancel? That would only happen to the extent they are correlated.
 
  • #3
diemilio said:
What am I missing here? Why is the SNR unchanged?

Regards,

diemilio

Why would you expect the SNR to be changed at all (apart from a finite amount of added noise from the mixer)? Every baseband component (signal and noise) will find itself mixed up to a corresponding 'product' component and they should all have the same relationship to each other. Are you looking for something more than that?
 

1. What is noise in an ideal mixer?

Noise in an ideal mixer refers to the unwanted random fluctuations or disturbances in the output signal of a mixer. It can be caused by various factors such as thermal noise, shot noise, and flicker noise.

2. How does noise affect the performance of an ideal mixer?

Noise can significantly degrade the performance of an ideal mixer by reducing its sensitivity and signal-to-noise ratio. This can result in inaccurate measurements and lower quality output signals.

3. Can the noise in an ideal mixer be reduced?

Yes, the noise in an ideal mixer can be reduced by implementing various techniques such as using low-noise components, shielding the mixer from external sources of interference, and optimizing the mixer's circuit design.

4. How is noise measured in an ideal mixer?

Noise in an ideal mixer is measured using a metric called noise figure, which represents the ratio of the output signal-to-noise ratio to the input signal-to-noise ratio. The lower the noise figure, the better the performance of the mixer.

5. What are the consequences of excessive noise in an ideal mixer?

Excessive noise in an ideal mixer can lead to poor signal quality, reduced sensitivity, and inaccurate measurements. It can also affect the overall performance of the system or device in which the mixer is used.

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