Effective gain of one bit quantizer for sigma delta modulator

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Mauder

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Dear all,
If I use an one-bit quantizer in sigma delta system, we all know there is an effective gain of quantizer should be considered in NTF.

But I cannot figure out why we need this effective gain?

I think the basic definition of quantization noise is quantizer's output subtract it's input so the linear model of quantizer can be just an additional noise.

Why we need to model an effective gain in one-bit quantizer?

What is the benifit when considering this effective gain?

Thanks for answering.
 

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