AD7705/AD7706
0
–20
Filter Characteristics
The AD7705/AD7706 digital filter is a low-pass filter with a
(sinx/x)3 response (also called sinc3). The transfer function for
the filter is described in the z-domain by
–40
–60
–80
–100
–120
–140
–160
–180
–200
–220
–240
3
1 − Z−N
1
N
H (z)
×
1 − Z−1
and in the frequency domain by
3
sin
(
N × π × f / fS
)
1
N
H ( f ) =
×
sin π × f / fS
(
)
0
60
120
180
240
300
360
FREQUENCY (Hz)
Figure 15. Frequency Response of AD7705 Filter
where N is the ratio of the modulator rate to the output rate.
Postfiltering
The phase response is defined by the following equation:
The on-chip modulator provides samples at a 19.2 kHz output rate
with fCLKIN at 2.4576 MHz. The on-chip digital filter decimates
these samples to provide data at an output rate that corresponds
to the programmed output rate of the filter. Because the output
data rate is higher than the Nyquist criterion, the output rate for
a given bandwidth satisfies most application requirements. Some
applications, however, might require a higher data rate for a
given bandwidth and noise performance. Applications that need
this higher data rate will require postfiltering following the digital
filtering performed by the AD7705/AD7706.
∠ H = − 3π
N − 2 × f fS Rad
Figure 15 shows the filter frequency response for a cutoff
frequency of 15.72 Hz, which corresponds to a first filter notch
frequency of 60 Hz. The plot is shown from dc to 390 Hz. This
response is repeated at either side of the digital filter’s sample
frequency and at either side of multiples of the filter’s sample
frequency.
The response of the filter is similar to that of an averaging filter,
but with a sharper roll-off. The output rate for the digital filter
corresponds with the positioning of the first notch of the filter’s
frequency response. Thus, for Figure 15, where the output rate
is 60 Hz, the first notch of the filter is at 60 Hz. The notches of
this (sinx/x)3 filter are repeated at multiples of the first notch.
The filter provides attenuation of better than 100 dB at these
notches.
For example, if the required bandwidth is 7.86 Hz, but the
required update rate is 100 Hz, data can be taken from the
AD7705/AD7706 at the 100 Hz rate, giving a −3 dB bandwidth
of 26.2 Hz. Postfiltering can then be applied to reduce the
bandwidth and output noise to the 7.86 Hz bandwidth level
while maintaining an output rate of 100 Hz.
Postfiltering can also be used to reduce the output noise from
the devices for bandwidths below 13.1 Hz. At a gain of 128 and
a bandwidth of 13.1 Hz, the output rms noise is 450 nV. This is
essentially device noise, or white noise. Because the input is
chopped, the noise has a primarily flat frequency response. By
reducing the bandwidth below 13.1 Hz, the noise in the resultant
pass band is reduced. A reduction in bandwidth by a factor of 2
results in a reduction of approximately 1.25 in the output rms
noise. This additional filtering results in a longer settling time.
The cutoff frequency of the digital filter is determined by the value
loaded to Bit FS0 and Bit FS1 in the clock register. Programming a
different cutoff frequency via Bit FS0 and Bit FS1 does not alter
the profile of the filter response, but changes the frequency of
the notches. The output update of the part and the frequency of
the first notch correspond.
Because the AD7705/AD7706 contain this on-chip, low-pass
filtering, a settling time is associated with step function inputs,
and data on the output is invalid after a step change until the
settling time has elapsed. The settling time depends on the output
rate chosen for the filter. The settling time of the filter to a full-
scale step input can be up to four times the output data period.
For a synchronized step input using the FSYNC function, the
settling time is three times the output data period.
Rev. C | Page 24 of 44
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