Signal to noise ratio for thermal and shot noise

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SUMMARY

The discussion focuses on calculating the signal-to-noise ratio (SNR) for a sensor output connected to a parallel RC circuit with a resistance of 50 ohms and a capacitance of 10 pF at a temperature of 300K. The SNR is defined using the formula SNR = 10 log (power of signal / power of noise) or SNR = 20 log (voltage signal / voltage noise). Key calculations include determining the voltage across the capacitor and the power of the signal, while also addressing the contributions of thermal noise and shot noise to the overall noise power.

PREREQUISITES
  • Understanding of RC circuit behavior and calculations
  • Knowledge of thermal noise and shot noise concepts
  • Familiarity with Boltzmann constant and its application in noise calculations
  • Ability to perform logarithmic calculations for SNR
NEXT STEPS
  • Learn about calculating thermal noise using the formula 4kTf
  • Study shot noise and its impact on electronic circuits
  • Explore the relationship between bandwidth and RC filters in noise analysis
  • Investigate advanced SNR calculations in sensor applications
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Electrical engineers, physicists, and students involved in sensor design and noise analysis in electronic circuits.

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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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