Conceptual Noise Question

[Evan.Cornell]

This may be basic analog that I learned in school, but can't quite remember the correct answer.

Say one requires a 1kOhm resistor in op-amp feedback path, is it lower noise to just use a 1kOhm resistor, or instead to use some parallel combination of resistors to get to 1kOhm (2x 2kOhm, 3x 3kOhm, etc.)?

[magic]

Same thing.

2kΩ has sqrt(2) more noise than 1kΩ. Two equal noise sources mixed equally average out and end up sqrt(2) less than each of them.
1kΩ is about 4nV/rtHz at room temperature, by the way.

For unequal resistors, you treat the circuit as two noise voltage sources mixed by noiseless resistors. Attenuate each noise source by its corresponding resistive division ratio and RMS sum them (calculate sqrt(N₁²+N₂²)). The result should be the same as the noise of a single resistor equivalent to their parallel combination.

Bottom line: you can't escape Johnson by cheating.

[RoGeorge]

This may be basic analog that I learned in school, but can't quite remember the correct answer.

Say one requires a 1kOhm resistor in op-amp feedback path, is it lower noise to just use a 1kOhm resistor, or instead to use some parallel combination of resistors to get to 1kOhm (2x 2kOhm, 3x 3kOhm, etc.)?

For resistors there is no benefit, but for amplifiers it is.

When two identical amplifiers are connected in parallel, the internal noise of the resulting amplifier is with 3dB smaller than the noise of a single amplifier.  You get 3 dB less internal noise each time you double the number of parallel amplifiers.  This is valid for internal uncorrelated (random) noise only, for example it will not reduce the mains hum noises.

[TimFox]

Parallel devices (not resistors) is a common technique for reducing noise from low-impedance sources.  If you parallel N BJTs, the noise voltage density decreases and the noise current density increases (both by N^1/2).  In a resistor, the noise current or voltage is the same noise power source, but at audio the two noise densities in a BJT are (almost) uncorrelated.

[ejeffrey]

Available noise power density from any passive circuit is just kT or -174 dBm/Hz.  Doesn't matter if it is a micro-ohm or megaohm, whether it is a single resistor or a complex RLC network.  The actual magnitude of current and voltage noise depend on the impedance, but two networks with the same impedance will have the same noise.