19

DDC101

®

Basic Integration Frequency Response

The sin(x)/x basic integration characteristic is controlled by

the digital filter’s measurement time (T

ment frequency, f

sponse of the DDC101 is down –3dB at f

null at f

Subsequent nulls are at harmonics 2f

3f

below. This characteristic is often used to eliminate known

interference by setting f

frequency of the interference. Table VI illustrates the fre-

quency characteristics of the DDC101 integration function

for various measurement times. As an example, for N =

2272, K = 16, and M = 256: T

256-16)/2MHz = 1ms and f

= 1.14ms; f

MEASUREMENT TIME

–3dB FREQUENCY

f

MEAS

100

µs

4.42kHz

10kHz

1ms

442Hz

1kHz

10ms

44.2Hz

100Hz

16.66ms

26.5Hz

60Hz

20ms

22.1Hz

50Hz

TABLE VI. Basic Integration Frequency Response Examples.

FIGURE 16. Basic Integration Frequency Response.

0.1f

MEAS

f

MEAS

10f

MEAS

Frequency

0

–10

–20

–30

–40

–50

–20dB/decade

Slope

Nyquist

(f

f

CONV

Oversampling Frequency Response

The M oversamples of the initial and the final data points

create an oversampling sin(x)/x type of low pass filter

response. The oversampling function reduces broadband

noise of the input signal and the DDC101. Broadband noise

is reduced approximately in proportion to the square root of

the number of oversamples, M. As an example, a conversion

with 128 oversamples will have approximately 1/2 the noise

of a conversion with 32 oversamples (

√32/128 = √1/4 =

1/2) The oversampling low pass filter response creates a null

at f

256 and f

quent nulls are at harmonics 2f

point is at f

Table VII illustrates the DDC101

oversampling frequency characteristics with approximate

values for f

frequency response graph is shown below in Figure 17. This

figure shows the frequency response for M = 256 oversamples

with an f

decreases at approximately 20dB/decade.

OVERSAMPLES (M)

–3dB FREQUENCY

f

OS

256

3.5kHz

7.8kHz

128

6.9kHz

15.6kHz

64

13.9kHz

31.2kHz

16

55kHz

125kHz

TABLE VII. Oversample Frequency Response Examples.

Normalized DDC101 Frequency Response

The normalized frequency response, H(f), of the DDC101 that is applied to the input signal consists of the product of the three

frequency response components:

Where:

f

is the signal frequency

f

CLK

is the system clock frequency, typically 2MHz

N

is the total number of clock periods in each integration time, T

integration time

M

is the number of oversamples in one oversampled data point

K

is the number of clocks used in the acquisition time

(N-M-K)/f

CLK

is the digital filters measurement time, T

M/f

CLK

is the oversample time, T

OS

LN/f

CLK

is the total conversion time for multiple integrations, T

CONV

The DDC101's transfer response has a linear phase characteristic as indicated by the exponential term.

Hf

sin

πfN − M − K

CLK

(

()

πfN − M − K

CLK

•

sin

πfM/f

CLK

()

Msin

πf/f

CLK

()

•

sin

πfLN/f

CLK

()

Lsin

πfN/f

CLK

()

CLK

Basic Integration

Oversampling

Multiple Integrations

Linear Phase