518 Chapter 8. Signal Processing
The signal to noise ratio for the system is then
S/N =
[
Vs,out
Vn,out] 2
=
A^2 Vs,in^2
A^2[(
v^2 as+Af)
f+2eIdτRs^2 f+^4 kRBpT f+4kBTRs f]
=
Vs,in^2
(
vas^2 +Af)
f+2eIdτRs^2 f+^4 kRBpT f+4kBTRs f. (8.9.26)
This expression shows that the signal to noise ratio is independent of the amplifier’s
amplification factor. The only frequency dependent component in this expression is
the amplifier’s 1/fnoise. All other factors have bandwidth dependence.
B.2 NoiseinADCs
The most significant ADC noise source is the process of quantization itself. The
corresponding quantization noise is given by
σq=V
√
12
, (8.9.27)
where Vis the change in analog voltage corresponding to one bit. In other words
it is given by the ADC resolution multiplied by its dynamic range. Recall that the
resolution of an-bit ADC is given by
R=V
V
=
1
2 n, (8.9.28)
This implies that the analog voltage increment can be written as
V=V
2 n. (8.9.29)
Substituting this in the above expression for ADC noise gives
σq=V
2 n√
12
(8.9.30)
Example:
Determine the quantization noise corresponding to a 12-bit ADC having an
analog range of 0 to 10 volts.Solution:
The voltage range of the ADC is 10 volts andn= 12. Hence, according to
equation 8.9.30, the quantization noise is given byσq =V
2 n√
12
=
10
212
√
12
=0. 7 mV.