NOTES FROM THE TEST BENCH
By Bruce Hofer
Several months ago I wrote about non-linearity in resistors. This month I would like to comment about resistors being noise generators. Almost any good electronics textbook will either contain or derive the formula:
where” Vn” is the rms noise voltage measured over the bandwidth “BW”, “k” is Boltzmann’s constant, “T” is absolute temperature, and “R” is the value of the resistor. There are several important insights revealed by this formula.
First, noise voltage is proportional to .
An alternative way to look at this is that noise “power” is proportional to BW, or the noise power density is constant per Hertz of bandwidth. In the world of audio design, there is usually very little than can be done with this portion of the equation.
Second, noise voltage is proportional to .
Room temperature is normally taken to be about +23C which is 296K in the absolute scale. However, the temperature that really matters is the temperature of the resistive element inside the resistor. This can be significantly higher than room ambient depending upon power dissipation and temperature rises inside the product. A 30C rise roughly causes about 5% or 0.4 dB higher noise voltage, all other factors being equal.
Finally, noise voltage is proportional to .
Larger valued resistors simply produce larger amounts of noise. Now, to be honest, one needs to calculate the transfer function from a given resistor to the circuit output node to make a fair assessment. However, the lesson here is that one should design with lowest value of resistors that a circuit will tolerate. Unfortunately way too many audio engineers seem to overlook this fact.
The design of extremely low-noise, high performance analog continues to be a challenge that no number of advances in the digital realm can fully address, as everything audio starts and ends as analog data. The pursuit of as much perfection as physics will allow remains my goal here at Audio Precision, and I welcome your feedback about how our equipment can help you along this shared path.
Audio Precision co-founder and Chief Analog Engineer