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engineer23
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Homework Statement
We are using Raman spectroscopy to detect the presence of chemicals from emitted light.
We have a light transistor that behaves as a photo-resistor of 50k-ohm resistance. The light signal generates 2 microvolts of 2 kHz signal at normal Raman levels. We want at least a 20 to 1 SNR (Signal to noise ratio).
Cool the circuit to 77 K. What is the SNR?
What two things can be done to improve SNR without changing the sensor?
Homework Equations
noise for a resistor = sqrt(4KTRf), where K is the Boltzmann constant, T is the temperature, R is the resistance, and f is the bandwidth
The Attempt at a Solution
Substituting directly into the equation for noise with T = 77 K, R = 50000 ohms, and f = 2000 Hz, I get sqrt (4*1.38*10E-23*77*50000*2000) = .651 microvolts.
The SNR is then signal/noise = 2 microvolts/.651 microvolts = 3 This is much less than the 20 SNR we need.
But shouldn't the resistance of the photoresistor change with temperature as well? Intuitively, it seems that resistance would increase with decreasing temperature? Is there an equation I should be aware of which governs this behavior?
Also, I suppose that we could cool the circuit more to meet spec? But is there something else that can be done without changing the device itself?