TABLE OF CONTENTS The second fundamental source of noise, thermal noise, was investigated by Johnson and Nyquist in the 1920s. It is present in all resistors at a temperature above absolute zero and is characterized by internal current fluctuations and fluctuations in voltage across their open circuit terminals, even when no external current is flowing. If connected into an external circuit, these will also cause external current fluctuations. Although the warm resistor acts as a little generator, it is not possible to extract power from it. Anything connected to it deposits as much power into the resistor as is extracted from it. Analogous to the treatment of shot noise currents, a resistor of R ? will show a noise power spectral density given in voltage or current by:
where k is Boltzmann's constant (1.381 10 ?23J/K) and T is the absolute temperature in K ( ?300K at room temp.).
Equation 3.7 is the Johnson or Nyquist formula. As with shot noise, this thermal noise power is proportional to the measurement bandwidth. In photoreceiver design it is usually more convenient to calculate and measure voltages and currents rather than powers, so we can rewrite Eq. 3.7 in convenient engineering units, either as a voltage source in series with a (noiseless) resistor R or as a current generator in parallel with R:
A few calculated values will give a feel for the voltage magnitudes (Table 3.2):
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