Understanding Quantization Effects

[X1088LoD]

I am obtaining data with a sample rate of 6250 samples/second on a digital oscilloscope. Ideally, I am obtaining a sinusoid output through a system from a sinusoid input. My expected results through the system are lower in amplitude than I am actually recording. I have some reasons for why this is occurring pertaining to the system itself, but I have been asked to also describe how the 8-bit quantization of the data can be affecting the outcome. I don't really know why this is. I would appreciate any advice or information anyone can give on the matter.

Thanks

Brent

[waht]

Scopes have input impedance 1 to 10 Mega Ohms so they affect the measurment so little they can't even measure that.

The problem might be the load impedance of your circuit. Could be low enough to lower the voltage.

[vsage]

How much lower is the amplitude than what you expect? For 8 bits it shouldn't be by much. I think the key here is how bit rate affects the signal to noise ratio. Pulling up an equation from my old communications book, this error ratio that is *inherent to A/D conversion* can be expressed in terms of bits as 10*log(3*2^(2*bits)*Sx) where Sx is the original signal power (just set Sx equal to 1 if it disturbs you). This equation isn't all-encompassing and actually makes some assumptions like your quantization levels are equally spaced and that there is an equal probability that the signal gets rounded down by the same amount as up somewhere else in the sample, but the general concept is there.

Quantization error causes some power of the original signal to be moved to other garbage frequencies, and therefore your sinusoidal signal's output would appear slightly smaller than expected on the o-scope.