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How Does Noise Affect Circuits? - Understanding Noise Part I

I am back from a little hiatus. I've been meaning to write something about noise in the circuits, because I know it's one of the least understood topics in electronics. It's something that one can easily attribute to when something goes odd in the circuit, yet so few have the courage to delve into it.

In audio applications, it's easy to describe what noise is. We know if the music is clear and pure, it is free of noise. Anything that is unwanted we can call noise, well, in a broad sense of the word.

Noise comes in different forms and from different sources, but in the hope of making some order out of chaos we can attempt to categorize them in the following:

1. Device Noise - noise coming from active and passive devices
2. Emitted Noise - those coming from power lines, motors, radio trasmission, etc.
3. Conducted Noise - those that are already in the circuit, either from the device or transmitted into

Electronics components are indeed sources of noise in the circuit. The most prominent is the noise coming from the resistor and operational amplifiers. The noise from the resistor is called thermal or Johnson noise. It can also be called white noise, because it is present in all frequencies. If you make a frequency plot of the noise power, it will look something like this.

Johnson Noise


Resistor Noise
When you put your resistor in a circuit, it becomes like an unwanted voltage source, sourcing noise. Even if you take a resistor, let it lie on a table and get an RMS voltmeter, you can expect to measure a voltage equivalent to the noise that the resistor produces. This noise is inherent in the device and is due to the particles in the resistor, whether you apply power or not. The noise in rms is given by:



We don't really have to always use the formula, just keep in mind that a 1KOhm resistor produces 4nV per root Hz of noise. Stating that in mathematical form,

This representation is called noise spectral density. Intuitively, it simply states that there is 4nV of rms noise in 1 Hz step for a given range of frequency. So in order to determine the total noise of in a system due to a 1KOhm resistor, you multiply that with the square root of your bandwidth and you come up with the noise in RMS. A 2KOhm resistor will not double the noise value, but rather will have 5.65nV/(root Hz). This is because we add the noise by RSS (Root of the Sum of Squares), that is, square the value of the individual noise due to particular resistance, add them, and get the square root.

In the next parts of this series we will be discussing the meaning of the terms spectral noise density, noise power, noise rms, and noise peak-to-peak.

References:
1. Tackle Noise From Three Perspectives, Bonnie Baker - EDN
2. Chapter 8, Noise: The Three Categories by B. Baker- Analog Circuits: World Class Designs, Robert A. Pease



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