Photoresistor and noise

[engineer23]

1. The problem statement, all variables and given/known data

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?

2. Relevant 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


3. 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?

[mgb_phys]

You are assuming that all the noise is thermal.
There is also power supply ripple, 1/f noise and shot noise.

If you can find a copy "Building electro optical systems" - Philip Hobbs, is excellent for this sort of thing