
Differential Input Circuit
(Continued)
The differential input impedance is a function of the value of
the input capacitor array and the sampling frequency. The
capacitor C
BIAS
is used to generate a bias voltage across
the Differential Input impedance (Z
DIFF
). This bias voltage is
similar to the Lambda Sensor output voltage at the stoichio-
metric air-fuel mixture (
l
e
1). The bias voltage is set by the
ratio of C
IN
and C
BIAS
, and the value of V
CC
.
The resulting bias voltage across the Differential Input is
defined as:
V
CC
#
C
BIAS
(C
IN
a
C
BIAS
)
With C
BIAS
e
0.7286 pF, C
IN
e
7.421 pF, F
CLOCK
e
100 kHz, and V
CC
e
5V:
5
#
7.286E-13
(7.4213E-12
a
7.286E-13)
V
BIAS
e
447 mV
In effect, the result is the same as forcing a bias current
through the Differential Input impedance.
V
BIAS
e
V
BIAS
e
The bias current is defined as:
I
BIAS
e
V
CC
#
C
BIAS
#
F
CLOCK
I
BIAS
e
364.3 nA
The Differential Input impedance is defined as:
Z
DIFF
e
1
(C
IN
a
C
BIAS
)
#
F
CLOCK
Z
DIFF
e
1.227 M
X
This bias voltage will be developed across the Differential
Input impedance (Z
DIFF
) if there is no other path available
from the non-inverting input pin for I
BIAS
, and the inverting
input has a current path to ground. See Figure 5. During
normal operating conditions I
BIAS
will have a negligible ef-
fect on accuracy
TL/H/12372–15
FIGURE 5. Equivalent Input Bias Circuit
Differential Input Filtering
Since each input is sampled independently, an anti-aliasing
filter is required at the amplifier inputs to ensure that the
input signal does not exceed the Nyquist frequency.
This external low-pass filter is implemented by adding a ca-
pacitor (C
DIFF
) across the differential input. See Figure 6.
This forms an RC network across the differential inputs in
conjunction with the required external 4 k
X
resistors and
the differential input impedance (Z
DIFF
). The capacitor se-
lected should be small enough to have minimal effect on
gain accuracy in the application, yet large enough to filter
out unwanted noise. Given that the F
C
of the LM9040 is
typically 500 Hz, the use of a 0.01
m
F capacitor will general-
ly provide adequate filtering, with less than
b
0.4 dB of input
attenuation at 500 Hz and approximately
b
28 dB at 50 kHz.
A larger value capacitor can be used if needed, but a value
larger than typically 0.02
m
F will begin to dominate the cut-
off frequency of the application. This capacitor must be a
low leakage and low ESR type so that circuit performance is
not degraded.
TL/H/12372–16
FIGURE 6. Differential and Common Mode Filtering
Common Mode Filtering
The differential input sampling of the LM9040 actually re-
duces the effects of common mode input noise at low fre-
quencies. The time interval between the sampling of the
inverting input and the non-inverting input is one half of a
clock period. A change in the common mode voltage during
this short time interval can cause an error in the charge
stored on C
IN
. This will result in an error seen on the output
voltage. For a sine-wave common mode voltage the mini-
mum common mode rejection is:
CMRR
e
2
#
q
#
F
CMR
#
(0.5/F
CLOCK
)
#
4.53
Where F
CMR
is the frequency of the common mode signal,
and F
CLOCK
is the clock frequency.
5