AD7705_06 datasheet(24/44 Pages) AD

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AD7705/AD7706

Rev. C | Page 24 of 44

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

)

(

−

and in the frequency domain by

()

sin

)

(

where N is the ratio of the modulator rate to the output rate.

The phase response is defined by the following equation:

(

)

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.

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.

FREQUENCY (Hz)

–140

–240

120

180

240

300

360

–20

–160

–180

–60

–100

–40

–80

–200

–220

–120

Figure 15. Frequency Response of AD7705 Filter

Postfiltering

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.

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.

AD7705 Datasheet(PDF) 24 Page - Analog Devices

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