Datasheet
19
DDC101
®
Basic Integration Frequency Response
The sin(x)/x basic integration characteristic is controlled by
the digital filter’s measurement time (T
MEAS
). The measure-
ment frequency, f
MEAS
is l/T
MEAS
. The input frequency re-
sponse of the DDC101 is down –3dB at f
MEAS
/2.26 with a
null at f
MEAS
. Subsequent nulls are at harmonics 2f
MEAS
,
3f
MEAS
, 4f
MEAS
, etc. as shown in the frequency response curve
below. This characteristic is often used to eliminate known
interference by setting f
MEAS
or a harmonic to exactly the
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
MEAS
= (N-M-K)/f
CLK
= (2272-
256-16)/2MHz = 1ms and f
MEAS
= 1kHz. T
INT
= 2272/2MHz
= 1.14ms; f
CONV
= l/T
INT
= 880Hz.
MEASUREMENT TIME –3dB FREQUENCY f
MEAS
100µs 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
Gain (dB)
0
–10
–20
–30
–40
–50
–20dB/decade
Slope
Nyquist
(f
CONV
/2)
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
OS
= 1/T
OS
. The oversample time, T
OS
, is M/f
CLK
. For M =
256 and f
CLK
= 2MHz, f
OS
is approximately 7.8kHz. Subse-
quent nulls are at harmonics 2f
OS
, 3f
OS
, 4f
OS
, etc. The –3dB
point is at f
OS
/2.26. Table VII illustrates the DDC101
oversampling frequency characteristics with approximate
values for f
OS
and the –3dB frequency. An oversampling
frequency response graph is shown below in Figure 17. This
figure shows the frequency response for M = 256 oversamples
with an f
CLK
of 2MHz . The slope of the attenuation curve
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
INT
= N/f
CLK
, T
INT
is the DDC101 CDAC's
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
MEAS
, (T
MEAS
= T
INT
–(M+K)/f
CLK
)
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
π
fN−M−K
)
/f
CLK
(
()
π
fN−M−K
()
/f
CLK
•
sin
π
fM/f
CLK
()
Msin
π
f/f
CLK
()
•
sin
π
fLN/f
CLK
()
Lsin
π
fN/f
CLK
()
•
e
−j
π
fLN−K−1
()
/f
CLK
Basic Integration
Oversampling
Multiple Integrations
Linear Phase