Signal to noise ratio for thermal and shot noise

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Homework Help Overview

The discussion revolves around calculating the signal to noise ratio (SNR) for a sensor output connected to a parallel RC circuit, with specific values for resistance and capacitance. The context includes considerations of thermal and shot noise at a given temperature.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the calculation of voltage from charge and capacitance, and the power of the signal. There are questions about the correct interpretation of the number of electrons and the implications for noise calculations. Some participants suggest checking equations and clarify the relationship between the RC filter and noise bandwidth.

Discussion Status

The discussion is ongoing, with participants providing hints and questioning assumptions about the equations used. There is no explicit consensus on the calculations, but guidance regarding the noise bandwidth and voltage equations has been offered.

Contextual Notes

Participants note the lack of information regarding the frequency bandwidth and the ambiguity in the interpretation of "10,000 electrons." There is also a mention of needing to consider both thermal and shot noise in the calculations.

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Homework Statement


The output of a sensor which produces 10000 electrons is connected to parallel RC circuit with Resistance= 50 ohm, and the capacitance=10pF.
Calculate the signal to noise ratio at temperature 300K.


Homework Equations


SNR= 10 log (power of signal/ power of noise)
Or SNR = 20log ( voltage signal / voltage noise)



The Attempt at a Solution


Voltage=C/Q=624.15V
Power of signal= voltage square / resistance= 7791.2 J
But how to calculate power of noise? The thermal noise = 4kTf, where k is Boltzmann constant, f is frequency bandwidth. Yet not given , but I can only think of these formula for thermal noise and 10000 electron need to include shot noise?

Please help
 
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Check your equation for the voltage on a capacitor--it's not quite right. Then use this hint: the noise bandwidth is determined by the RC filter.
 
Is that 10,000 electrons or 10,000 electrons per second?
 
marcusl said:
Check your equation for the voltage on a capacitor--it's not quite right. Then use this hint: the noise bandwidth is determined by the RC filter.

Yup, V =Q/C , and f=1/(2∏RC)
But why is this the Bandwidth? The impedance of capacitor is same as resistance so we get maximum power for?
And 10000 electrons need to consider shot noise? If I consider, so I just add thermal noise voltage and shot noise together to get the total voltage noise?
 
rude man said:
Is that 10,000 electrons or 10,000 electrons per second?
10000 electrons without telling time, but even telling time, I still can calculate the thermal and shot noise.
 

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