Many delta-sigma converters have a programmable data rate. The
decimation ratio (DR) of a delta-sigma converter equals the number
modulator samples per data output, or DR = Fs/Fd. Decimation ratio
values range anywhere from four or eight (ADS1605) to 32,768 (ADS1256).
The relationship between the output data rate and the sampling rate
directly impacts the effective-number-of-bits (ENOB) at the converter’s
output.

Consider the output spectrum of a delta-sigma modulator (Fs) versus the digital / decimation filter (Fd) in **Figure 3**. The modulator sample rate (Fs) shapes the quantization bandwidth. The data rate (Fd) is always smaller than Fs, as in **Figure 3A and 3B**.
The signals from zero to Fd are included in the converter’s output.
Note the noise level in this frequency band. The ENOB describes noise
and distortion in the converter’s output data. The ENOB in Figure **3A** is higher than the ENOB in Figure **3B** _{[4]}.

**Click on image to enlarge.**
**Figure 3. The digital / decimation filter cut-off frequency (Fd) is lower than the modulator’s sampling frequency (Fs). The modulator’s integrator successfully shapes quantization noise toward Fs.**

**Using digital process gain**
Implementation
of the SAR-ADC external, analog-gain stage typically includes at least
one, if not more, operational amplifiers. Designers use these amplifiers
to gain and level-shift the analog signal. The delta-sigma converter
handles these analog functions with an internal digital process gain.
You can use the delta-sigma’s process gain to create a 10-, 12-, or
16-bit system with a 24-bit converter. This eliminates the external gain
and level shift circuits

_{[5]}.

For instance, a
noiseless 24-bit delta-sigma converter has 4096 individual, 12-bit
converters across the converter’s output range. Noiseless, 24-bit
delta-sigma converters are hard to find, but a delta-sigma converter
with an effective resolution of 19.5-bits (rms) is more realistic.

**Figure 4** shows the relationship between output codes and noisy bits of
this realistic 24-bit delta-sigma converter.

**Click on image to enlarge.**
**Figure 4. Capturing the right output codes of the 19.5-bit (rms) delta-sigma converter **

can provide a level shift and process gain.

**Figure 4**
diagrams the technique used to absorb the analog functions of gain and
level-shift into the delta-sigma converter. Ignoring the
most-significant-bits allows you to implement a level-shift function.
Process gain is equivalent to an analog gain by determining the location
of the new MSB at the converter’s output. A gain change is implemented
by shifting the 12-bit window in

**Figure 4** to the right or towards
the converter’s least significant bit (LSB). Each one-bit shift to the
right is equivalent to doubling the process gain. As in the analog
domain, an increase in process gain lessens the input range. In

**Figure 4**, you can increase the process gain to 64 or 128. This is equivalent to an analog gain of 64 V/V or 128 V/V.

With
this technique, you have the full resolution of 224 codes at our
disposal. Select the ADC range portion and focus just on the area where
the signal response is occurring. Note that you are trading off the loss
of your 24-bit converter’s dynamic range with the elimination of the
external analog circuitry.

**Conclusion**
Delta-sigma
converters are available with many additional features that make them
ideal for data acquisition. Many of these types of converters include a
programmable-gain amplifier (PGA) and input buffer that can further
reduce the requirements for external signal conditioning. Some also have
special features for sensor connections, like burnout current sources.

Delta-sigma
converter applications have fewer components as compared to SAR-ADC
circuits. While in operation, the delta-sigma ADC continuously
oversamples an input voltage signal. The ADC then applies a digital
filter on these samples to achieve a multi-bit, low-noise digital
output. The byproduct of this algorithm is a higher dynamic range and
lower output speeds. Many designers focus on the number of output bits
that this type of converter can produce. However, the often overlooked
hidden feature is process gain. This feature allows the designer to
eliminate external analog circuitry in these low-frequency signal
chains.

11111

**References**
**1.** “

Delta-sigma antialiasing filter with a mode rejection circuit,” Bonnie Baker, EDN, September 17, 2012.

**2.** “

Delta-sigma ADCs in a nutshell, part 2: the modulator,” Bonnie Baker, EDN, January 24, 2008.

**3.** “

Delta-sigma ADCs in a nutshell, part 3: the digital/decimator filter,” Bonnie Baker, EDN, February 21, 2008.

**4.**
“

A glossary of analog-to-digital specifications and performancecharacteristics,” Bonnie Baker, Application Report (SBAA147B), Texas
Instruments, October 2011.

**5.** “

Take a risk; throw away those bits!,” Bonnie Baker, EDN, October 22, 2009.

**Related articles**
ADC Basics (Part 1): Does your ADC work in the real world?
ADC Basics, (Part 2): SAR and delta-sigma ADC signal path
ADC Basics (Part 3): Using successive-approximation register ADC in designs