428

Quantisationprinciple

Quantisation errors can bemore simply shown as a saw tooth function, for which, in an

interval of

s2

q

⋅

−

to

s2

q

⋅

:

ts )t(e

⋅ =

The root-mean square value of the quantisation noiseQof aperfect ADC is thus

12

q dt )ts(

q

s

s

q

dt )t(e

Q

s2

q

s2

q

2

s2

q

s2

q

2

= ⋅

=

=

∫

∫

⋅

⋅

−

⋅

⋅

−

in the range from 0Hz to half the sampling frequency f

S

) for a DC input

signal. Without any further derivation, this gives a signal to noise ratio (SNR) for a

sinusoidal signal of:

dB)76.1n02.6(

SNR

+ ⋅

=

In a real ADC, parasitic effects lower the SNR value, which produces a lower effective

resolution of the signal in n-bit. This actual resolution is known as "effective number of

bits" (ENOB), and:

dB02.6

dB76.1 SNR

ENOB

−

=

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