Analog and electronic circuits
When a voltage is sampled onto a capacitor C through a switch, what is the RMS thermal noise voltage left on the capacitor? (k: Boltzmann constant, T: absolute temperature)
- AIt grows as the capacitance C increases
- B√(kT/C), independent of the switch resistance
- CIt grows as the switch resistance increases
Show answer and explanation
Answer: B. √(kT/C), independent of the switch resistance
The thermal noise from the switch resistance grows with resistance, but the bandwidth narrows at the same time, and the two effects cancel, leaving an RMS noise voltage of √(kT/C) on the capacitor. This is called kT/C noise; reducing it requires a larger capacitance.
- A. A larger capacitance gives a smaller noise voltage.
- B. Correct. It is √(kT/C) and does not depend on the resistance.
- C. A larger resistance raises the noise density but narrows the bandwidth, so the result is independent of resistance.