A biosensor's input capacitance is

PHYSICS · Multi-part · Fermi University Physics · Electronics, Instrumentation & Communication · Feedback, operational amplifiers and analogue signal processing · Feedback, operational amplifiers and analogue signal processing

Inside the Instrument, Ch Noise sources and amplifier noise

Problem

C = 4.7\,\mathrm{pF}

, in series with the sensor's leakage resistance

R

, at body temperature

T = 310\,\mathrm{K}

. ((a)) Starting from the Johnson-noise density

4k_BTR

of the leakage resistance and the transfer function of the

RC

low-pass it forms with

C

, integrate

4k_BTR|H(f)|^2

over all frequencies to show that the mean-square voltage across the capacitor is

k_BT/C

, independent of

R

. ((b)) Recover the same result from equipartition alone, without any reference to

R

. ((c)) Evaluate the rms voltage across the capacitor at

310\,\mathrm{K}

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