Consider the two (equivalent) formulas for the noise power spectra of a ohmic resistor:
$$W_u(f)=4kT\cdot R~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(1)$$
and
$$W_i(f)=4kT\cdot G~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(2)$$
with the Boltzmann constant \$k\$, the temperature \$T\$, the resistance \$R\$ and the conductance \$G\$ each representing a equivalent circuit source.
General saying is that the noise increases with increasing value of resistance. E.g. in the datasheet for the AD745 it says that the noise contribution decreases with increasing resistance, which holds true for current noise considering formula (2), but is a contradiction considering formula (1).
Now, current noise produces a voltage noise when applied to a resistor with ohms law, but decreasing current noise and increasing resistance still yields a different result than just increasing voltage noise.
The equivalence of the circuits can be shown easily:
$$W_u(f)=W_i(f)\cdot\frac{1}{|G|^2}=\frac{4kT\cdot G}{G^2}=\frac{4kT}{G}=4kT\cdot R. ~~~~~~(3)$$
Please clarify the result in terms of noise of increasing the value of an ohmic resistor and explain the formulas (1) and (2) in the context of the stated contradiction?!
Best Answer
I think you're comparing two different physical situations. (1) is for voltage across an open-circuit resistor, (2) is for current through a shorted resistor.