Biomedical Engineering Reference
In-Depth Information
where
RZ
RZ
lCl
ZR
(17.16)
l
s
l
l
Z
Cl
1/s
C
l,
l
(
R
s
//
R
l
)·
C
l
,
2
R
f
·
C
f
, and
3
R
l
·
C
l
.
Note that uncorrelated noise contributions must be added as sums of squares.
Therefore, SNR can be written as
ET
VV V V
S
N
ph
(17.17)
2
2
2
212
(
)
in
en
iph
Rm
17.4.1.3 Noise Measurement
To investigate noise contribution, the responses of a bR photoreceptor under the condi-
tions of complete darkness and constant illumination are compared with the open-input
noise of the front-end circuit. Figure 17.11 gives time-domain responses that have been
recorded under each of the three test cases. The figures show that there are no obvious dif-
ferences among them. The Matlab quantile-quantile plot is used to determine whether
these datasets are normally distributed. As shown in Figure 17.12, the nearly straight line
relationship indicates that a normal distribution can be assumed for the three samples. The
normal distribution can be parameterized by a mean value and standard deviation. Slight
variations are found when comparing the three standard deviation values. The noise
recorded by the bR photoreceptor in darkness has a higher standard deviation value than
that of the open-input circuit noise. This may be caused by the thermal noise of bR in the
darkness. In addition, the open-input circuit configuration may decrease contributions
from amplifier voltage noise. As
R
m
in Eq. (17.14) is equal to infinity for an open input,
Z
m
increases, resulting in the reduction in amplifier voltage noise in Eq. (17.13). The photore-
ceptor response under steady illumination demonstrates the highest standard deviation,
indicating that photon-induced fluctuation still occur while bR photoreaction is at the
steady state. Since the standard deviation is equivalent to the root-mean-square (RMS)
value for a signal with a zero mean, the standard deviation can be used to quantify the
noise as an RMS voltage. The RMS noise voltages for open-input circuit, no light, and con-
stant light are 3.1, 3.6, and 4.2 mV, respectively.
Signal analysis in the frequency domain provides advantages over those in the time
domain. Time-domain signals are likely to be obscured by noises that normally have wide
bandwidth. Using the fast Fourier transform (FFT) to obtain a power spectrum is a com-
mon method to represent a signal in the frequency domain. The power spectra of noises
generated by the open-input circuit configuration and constant illumination configuration
are plotted as shown in Figure 17.13. Both plots illustrate that a wave pattern with
decreased amplitude superimposes on a nearly flat noise floor. Both shot noise and ther-
mal noise can be well approximated by white noise, implying that the noise power spec-
trum is constant at all frequencies. The observed patterns are actually caused by the
switching noise of the front-end amplifier. The switched integrator greatly reduces input
noise by averaging the noise present in the incident light, photoreceptor, and amplifier.
However, it introduces switching noise at the output as a consequence of high gain and
discrete design. This type of noise is caused by the injection of charges across the parasitic
gate-to-source, gate-to-drain, and source-to-drain capacitances of the FET switches (82). It
can be eliminated by using correlated double sampling technique.
