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Third Order Delta Sigma ADC

This example shows how to model a 3rd order Delta Sigma ADC and measure its performance using the ADC AC Measurement block. This ADC model consists of a behavioral model of a delta sigma ADC that uses a 3rd order feedforward modulator. The ADC input sample rate is 64 MHz and after decimating filters, the output sample rate is 1 MHz.

model = 'MSADCThirdOrderDeltaSigma';

The modulator block implements a discrete-time behavioral 3rd order feedforward modulator based on the paper in the references. The individual 1st order modulators include gain, pole position, and comparator impairments. The impairment settings are in the mask of the modulator block.

The modulator sampling frequency is defined by the MATLAB® variable Fs defined in the model initialization callback:

Fs = 64e6;     % sampling frequency (Hz)

The circuit-level switched capacitor implementation of the modulator uses Simscape. The parameters for the implementation are defined in the model initialization callback:

Ci=4.0e-12;    % integrating capacitor (F)
Cs=2.0e-12;    % sampling capacitor (F) 
Ron=200;       % switch on resistance (Ohm)
Fb1=5e8;       % op-amp break freq (Hz)
Avol=1e4;      % op amp gain 
Vcc = 4;       % supply voltage (V)

The modulator output drives a multi-rate discrete-time low pass filter that uses a Cascade Integrator Comb (CIC) Filter for a data rate reduction by 16. The following FIR filter further reduces the rate by a factor of 4 and is designed to have an inverse sinc roll-up in the passband to compensate for the droop in the CIC stage. This can be seen by clicking on 'View Filter Response'.

The CIC filter must be implemented in fixed-point. The polyphase filter is implemented in 16-bit fixed-point precision.

A single-tone sine wave is used to test the ADC, where the input frequency is set via a continuous-time voltage controlled oscillator (VCO). You can visualize the ADC output in both the time- and frequency-domains. You can activate the measurements capability of the spectrum analyzer block to compute distortion metrics such as THD, SNR, and SFDR.

Simulate the model using the command shown below. If you are interested only the behavioral model, you can speed up simulations by commenting out the switched capacitor model. Right click on "Switched Capacitor 3rd Order Modulator" and select "Comment out".


Required Products

This example requires:


  • Simulink

  • Signal Processing Toolbox

  • DSP System Toolbox

  • Simscape

  • Simscape Electrical


  1. M. Rebeschini, N. van Bavel, P. Rakers, R. Greene, J. Caldwell, J. Haug, "A high-resolution CMOS sigma-delta A/D converter with 320 kHz output rate", IEEE International Symposium on Circuits and Systems, 1989, pages 246-249.


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