6. Noise of the resistor
The resistance of the resistor comes from the inductance in the resistor, the capacitive effect, and the thermal noise of the resistor itself. For example, a solid core resistor with a resistance value of R can be equivalent to a series-parallel connection of the resistor R, the parasitic capacitor C, and the parasitic inductance L. Generally, the parasitic capacitance is 0.1 to 0.5 pF, and the parasitic inductance is 5 to 8 nH. These parasitic inductances and capacitances cannot be ignored at frequencies above 1MHz.
All types of resistors generate thermal noise. When a resistance of R (or the body resistance of BJT or the channel resistance of the FET) is not connected to the circuit, the thermal noise voltage generated in the bandwidth B is:
Where: k is the Boltzmann constant; T is the absolute temperature (unit: K). The thermal noise voltage itself is a function of the time of a non-periodic change, so its frequency range is very broad. Therefore, the wideband amplifying circuit is affected by noise more than the narrow band.
In addition, the resistor also generates contact noise, and its contact noise voltage is:
Where: I is the mean square value of the current flowing through the resistor; f is the center frequency; k is a constant related to the geometry of the material. Since Vc plays an important role in the low frequency band, it is the main noise source of the low frequency sensor circuit.
Post time: Aug-23-2021