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Peter the Great Saint Petersburg Polytechnic University
Institute of Physics, Nanotechnology and Telecommunications
Higher School of Applied Physics and Space Technologies
A laboratory report on
“Delta-sigma modulation and demodulation”
Written by ___________________ A. A. Assim
Assistant professor ___________________ M. M. Pilipko
Saint Petersburg
2020
Page 2 of 8
Topic overview:
Delta-sigma modulation is a type of pulse modulation scheme that can be thought
of as a simple variation of delta modulation, it is also denoted as ΔΣ.
In simplest words, this modulation type is a method for encoding analog signals
into digital signals as found in an analog-to-digital converter (ADC). It is also used
to convert high bit, low-frequency signals to lower bit, higher-frequency digital
signals as part of the process to convert digital signals into analog as part of a
digital-to-analog converter (DAC).
It's structure can be described with block diagrams as shown below:
Figure A. (Delta sigma modulator scheme)
Importantly, where delta modulation quantises the difference between the
message and the integral of the delta signal, delta-sigma modulation quantises the
integral of the difference between the message and the delta-sigma signal. So,
although the two modulation schemes look similar they're quite different
mathematically. The result is a spectral composition that better suites low-pass
filtering for demodulation because the quantisation noise occurs at higher
frequencies.
Delta-sigma modulation is one of the most effective forms of data conversion in
the digital world. It has many applications including communication systems,
professional audio, and precision measurements.
Page 3 of 8
Screenshots from the experiment:
Fig. 1 (Delta sigma modulation circuit)
Fig. 2 (in, rc and delta signals)
Signal “in” is the input message signal and signal delta are the digitized version of
it, which will be transmitted. Rc signal is also shown (in pink) this is the integrated
version of the error (difference) signal thus has such strange form.
Page 4 of 8
Fig. 3 (Parametric analysis, cond)
First three signals are captured when the capacitor values are at (50 nF), next
three at (200 nF), and the last three are at (100 nF).
Figure 3 investigates the effect of change of capacitance on delta and rc signals.
Fig. 4 (Parametric analysis, takt)
First three signals are at (50 nF), next three at (100 nF), and the last three at (200
nF).
The figure above demonstrates the effect of over sampling, oversampling improves
signal-to-noise ratio (SNR). When noise power is reduced, an increase in SNR is
expected so it is desired to use it as in the case of delta modulation.
Page 5 of 8
Fig. 5 (Delta and out signals in time domain)
Fig. 6 (Delta and out signals in time domain)
Page 6 of 8
Fig. 7 (spectrum of output (out) signal)
Signal-to-noise and distortion ratio (SINAD) value is 27.9 dB.
Fig. 8 (spectrum of delta signal)
Signal-to-noise and distortion ratio (SINAD) value is 57.001 dB.
Page 7 of 8
CONCLUSION
In this experiment sigma delta modulation was taken into consideration, it is one
of the widely used analog to digital conversion scheme due to its convenience and
availability in form of integrated circuit, for instance Texas instruments’
ADS1255IDBT:
In addition to the modulator itself, it is necessary to become familiar with a few
concepts that play a significant role in its operation, these are: quantization noise
and oversampling.
The quantized signal is the input signal along with the quantization noise:
ε
In general, the signals can be sampled with a frequency that is much greater than
the Nyquist frequency. The ratio of sampling frequency (fs) to Nyquist frequency
(2fO) is called an oversampling ratio (OSR), where fO is the frequency of the input
signal. So, OSR can be written as:
In addition to the model mentioned in this laboratory work, higher order
modulators exist as well, using higher-order modules, delta-sigma will further
improve SNR. A second-order modulator improves SNR by 15 dB for each doubling
of oversampling ratio.
Figure B. second-order ΔΣ modulator