# How to create a noise budget and what to do with it afterwards?

While reading some questions/answers on this site, I came across this answer from Scott Seidman and I found it interesting.

So, work out your noise budget, figure out how many bits you need, and do what you need to get them. Try to remember that an engineer who consistently exceeds specs instead of meeting them is wasting time and money.

How do you create a noise budget, and when you have one or are given one, how do you use that to determine what components you would need (opamps, adcs etc..) ?

For instance, if you are given a noise budget, how would you determine how many bits you need for an ADC ?

• Can you link the question this quoted answer is from? A budget of any form is just a type of project constraint. How it is used is determined by the type of project in question. A noise budget is really just the expected margin of error in your signal that can be tolerated. It can be used to determine how precise your components need to be. May 10, 2013 at 7:03
• @KurtE.Clothier posted original link. May 10, 2013 at 7:18
• Isn't the ADC bits determined by the required dynamic range and resolution? Perhaps the noise budget is reference to the effective resolution in the presence of noise. Jun 12, 2013 at 5:15
• Im not sure but I think the noise budget comes before you even start picking parts. The budget should help you decide which parts are good etc.. but since I asked the question, that means I really dont know. Jun 12, 2013 at 5:22
• @efox29 Then I think my link addresses your question doesn't it? You have to figure your effective resolution to know what parts to pick. Jun 19, 2013 at 19:28

A noise budget in this context seems to be the minimum resolution you need in order to obtain the information you want.

For the ADC example - if you want to be able to resolve 0.25v out of a 5v signal then your signal-to-noise ratio is 5v/0.25v = 20. To achieve this signal-to-noise ratio you'll need an ADC with at least 5 bits of resolution - 2^5 is 32. 4 bits will not work because 2^4 is 16 which is less than 20.

To summarize - to pick your noise budget, figure out what is the minimum signal you need to resolve. Then calculate the lowest bit rate you'll need in order to resolve that signal.

Of course when working with analog circuits you have to take the non-linearity of the circuits into account. The Wikipedia entry on ADCs has a great summary of things to consider: http://en.wikipedia.org/wiki/Analog-to-digital_converter

Bottom line: You generally should pick an ADC with slightly higher sampling than the minimum you require.

For completeness I'll also mention circuit noise. Circuit noise is the noise generated by the components within a circuit. Examples include thermal noise, shot noise, and 1/f noise. These place a minimum level at which you can resolve a signal and increasing the resolution of the ADC in a circuit will not help with this. More information on the Wikipedia page: http://en.wikipedia.org/wiki/Noise_(electronics)

• You probably need at least 6 bits to get an effect five bits. You lose a certain amount of resolution just because of quantization error-- and that's in the ideal case. There a more effective bits to be lost for non-idealities. Jul 1, 2013 at 16:40

I've got a great ref at work I'll dig up on Monday. The error budget can involve making sure your signal is big enough to cover enough bits and might involve such things as tolerances on resistors controlling your gain. I'll flesh this out better at my desk.

UPDATE:

Found it: http://www.maximintegrated.com/app-notes/index.mvp/id/4300. Another good synposes is at this other maxim App Note.

As I was saying above,noise is just one part of this, but it can bubble through in suprising places.

What to do with it when you're done? Well, like many other engineering practices, its best to treat error budgeting as a SPECIFICATION-- that is, by the time you're actually designing you should already know how much error you can tolerate and what sort of resolution you need. That way, you know what you're shooting for, and you're not constantly moving your own goalposts. Once you know, then you could use a budget procedure to help you in your design. After that, it's all bench verification, followed by tweaking out of your design if you need to.

A noise "budget" is really a spec for maximum allowable noise at each step thru a system. Usually you start with what the end result needs to be, then work backwards to find what that means each previous step. Since the steps add noise, the noise budget gets tighter and tighter (higher signal to noise ratio is required) as you go further back.