Continuous Time Delta Sigma Modulator

ADC based on continuous-time delta-sigma modulator

Since R2024b

• 

Libraries:
Mixed-Signal Blockset / ADC / Building Blocks

Description

The Continuous Time Delta Sigma Modulator block models an ADC based on continuous-time delta-sigma modulator using two different sets of architectures.

• Cascade of integrators with feedback (CIFB)

• Cascade of integrators with feed-forward (CIFF)

You can model a continuous-time DSM of orders from one to four. You can also use the block to design cascaded structures such as multistage noise shaping (MASH) and sturdy MASH (S-MASH).

Examples

Model Continuous Time Delta Sigma Modulator based ADC

This example shows how to model a Continuous Time Delta Sigma Modulator (CT DSM) based ADC using the Continuous Time Delta Sigma Modulator block from Mixed-Signal Blockset™.

CT DSMs are well suited for high bandwidth applications since they employ continuous time integrators. CT DSMs also possess inherent anti-aliasing property which can reduce system cost since such a system can do away with an anti-aliasing filter or use a less complicated anti-aliasing filter. Open the model thirdOrderCTDSM which consists of the CT DSM block, FIR filter and the ADC AC Measurement block. The input sinusoid source is set to a frequency of 1 kHz.

open_system('thirdOrderCTDSM.slx')

The CT DSM block is configured as a third order Cascade of Integrators with FeedBack (CIFB) DSM. The system bandwidth is set to 10 kHz with an OSR of 64 and the number of quantizer levels is set to 16. In the "Impairment" tab, you can set a finite gain for the integrator opamp and enable noise impairment. "Advanced" tab has parameters to set optimization settings for NTF synthesis as per Schreier's Delta-Sigma Toolbox, passband options i.e., lowpass and bandpass. There is also an option to set infinity norm H_inf which is set to 1.9. Run simulation and verify that the SNR is 116 dB with Effective Number Of Bits (ENOB) of 19 bits. You can increase infinity norm H_inf to increase SNR and ENOB.

The simulation result below shows the input signal (Sine Wave) and the ADC output (FIR Decimation). The ADC output has the same amplitude as the input and is delayed due to the presence of Decimation filter.

Ports

Input

input — Analog input signal

scalar

Analog input signal, specified as a scalar.

Data Types: double

reset — Reset delta-sigma modulator

scalar

Reset signal for Delta Sigma Modulator block, specified as a scalar.

Data Types: double

feedback — Output from next stage

scalar

Output from the next stage. Use this port to feed the output back into the block when modeling a multistage DSM. If there is no feedback from the next stage, connect this port to the ground.

Use this port to build cascaded DSM structures such as MASH and S-MASH.

Data Types: double

Output

dsmOut — Digital output signal

scalar

Digital output signal, returned as a scalar.

Data Types: fixed point | single | double | int8 | int16 | int32 | uint8 | uint16 | uint32 | Boolean

filterOut — Output of loop filter

scalar

The output of the loop filter inside the delta-sigma modulator, returned as a scalar.

Data Types: fixed point | single | double | int8 | int16 | int32 | uint8 | uint16 | uint32 | Boolean

quantOut — Output of quantizer

scalar

The output of the quantizer inside the delta-sigma modulator, returned as a scalar. If you do not use this port, connect it to a terminator.

If you do not use the feedback port, quantOut and dsmOut ports have the same values.

Use this port to build cascaded DSM structures such as MASH and S-MASH.

Data Types: fixed point | single | double | int8 | int16 | int32 | uint8 | uint16 | uint32 | Boolean

Parameters

Delta Sigma Modulator architecture — Architecture of delta-sigma modulator

CIFB (default) | CIFF

Architecture of the delta-sigma modulator, specified as:

• CIFB — Cascade of feedback integrators

• CIFF — Cascade of feed-forward integrators

Programmatic Use

Block parameter: dsmArchitecture

Type: character vector

Values: CIFB | CIFF

Default: CIFB

Delta Sigma Modulator order — Order of delta-sigma modulator

2nd order (default) | 1st order | 3rd order | 4th order

Order of the delta-sigma modulator. You can choose between orders one to four.

Programmatic Use

Block parameter: dsmOrder

Type: character vector

Values: 1st order | 2nd order | 3rd order | 4th order

Default: 2nd order

Input Parameters

System bandwidth (Hz) — Bandwidth of delta-sigma modulator system

1000 (default) | nonnegative real scalar

Bandwidth of the delta-sigma modulator system, specified as a nonnegative real scalar.

Programmatic Use

Block parameter: BandWidth

Type: character vector

Values: nonnegative real scalar

Default: 1000

OSR — Ratio of delta-sigma modulator sampling rate to Nyquist rate

64 (default) | nonnegative real scalar

Ratio of the delta-sigma modulator sampling rate to the Nyquist rate, specified as a nonnegative real scalar. A high oversampling ratio results in a relaxed anti-aliasing filter and reduced in-band quantization noise.

Programmatic Use

Block parameter: OSR

Type: character vector

Values: nonnegative real scalar

Default: 64

Sampling frequency (Hz) — Sampling frequency of delta-sigma modulator

128e3 (default) | positive real scalar

Sampling frequency of the delta-sigma modulator. This read-only parameter is calculated from the System bandwidth and OSR parameters.

Programmatic Use

Block parameter: SamplingFrequency

Type: character vector

Values: positive real scalar

Default: 128e3

Quantizer levels — Number of quantizer levels in delta-sigma modulator

2 (default) | positive real integer

Number of quantizer levels in the delta-sigma modulator, specified as a positive real integer.

Programmatic Use

Block parameter: NumberLevels

Type: character vector

Values: positive real scalar

Default: 2

Quantizer output — Range of quantizer output

[-1,1] (default) | real-valued vector

Range of the quantizer output in the delta-sigma modulator architecture, returned as a vector with real elements. This parameter is read-only.

Programmatic Use

Block parameter: QuantizerOutput

Type: character vector

Values: real valued vector

Default: [-1;1]

Use custom coefficient values — Option to use custom values for coefficients 'a', 'g', 'b', and 'c'

off (default) | on

Use custom values for coefficients 'a', 'g', 'b', and 'c'.

Coefficient 'a' — Feedback/feed-forward coefficients from/to the quantizer

[0.5714 0.1601] (default) | real-valued vector

Feedback coefficients from the quantizer or feed-forward coefficients to the quantizer, specified as a vector with real elements.

Dependencies

To enable this parameter, select the Use custom coefficient values parameter.

Programmatic Use

Block parameter: a

Type: character vector

Values: real valued vector

Default: [0.5714 0.1601]

Coefficient 'g' — Resonator coefficients

[0.0000] (default) | real-valued vector

Resonator coefficients, specified as a vector with real elements.

Dependencies

To enable this parameter, select the Use custom coefficient values parameter.

Programmatic Use

Block parameter: g

Type: character vector

Values: real valued vector

Default: [0.0000]

Coefficient 'b' — Feed-in coefficients from the modulator input to each integrator

[1.000 0.5714 0.1601] (default) | real-valued vector

Feed-in coefficients from the modulator input to each integrator, specified as a vector with real elements.

Dependencies

To enable this parameter, select the Use custom coefficient values parameter.

Programmatic Use

Block parameter: b

Type: character vector

Values: real valued vector

Default: [1.000 0.5714 0.1601]

Coefficient 'c' — Integrator inter-stage coefficients

[1.0000 1.0000] (default) | real-valued vector

Integrator inter-stage coefficients, specified as a vector with real elements.

Dependencies

To enable this parameter, select the Use custom coefficient values parameter.

Programmatic Use

Block parameter: c

Type: character vector

Values: real valued vector

Default: [1.0000 1.0000]

Impairment

Integrator opamp gain — Open loop gain of op-amp

Inf (default) | positive real scalar

Open loop gain of the internal op-amp, specified as a positive real scalar. This parameter is used in the analysis of the noise transfer function (NTF). Ideal NTF assumes that the op-amp gain is infinite.

Programmatic Use

Block parameter: OLgain

Type: character vector

Values: positive real scalar

Default: Inf

Enable Noise Impairment — Enable noise calculations in delta-sigma modulator ADC

off (default) | on

Enable noise calculations in the delta-sigma modulator ADC.

Thermal noise value — Thermal noise density

200e-6 (default) | real scalar

Thermal noise density, specified in units of V_rms or dB/Hz.

When you specify the thermal noise in units of V_rms, the value of this parameter must be a nonnegative real scalar.

Dependencies

To enable this parameter, select the Enable Noise Impairment parameter.

Programmatic Use

Block parameter: thermalNoiseValue

Type: character vector

Values: real scalar

Default: 0.125

Reference resistance (ohm) — Reference resistance for power calculation

50 (default) | positive real scalar

Reference noise to use for power calculations, specified as a positive real scalar in ohms.

Dependencies

To enable this parameter, select the Enable Noise Impairment parameter.

Programmatic Use

Block parameter: refResistance

Type: character vector

Values: positive real scalar

Default: 50

1/f corner frequency (Hz) — Corner frequency for flicker noise

1000 (default) | positive real scalar

Corner frequency for flicker (1/f) noise, specified as a positive real scalar in Hz. At this frequency, the 1/f noise approximately equals the thermal noise.

Dependencies

To enable this parameter, select the Enable Noise Impairment parameter.

Programmatic Use

Block parameter: fcorner

Type: character vector

Values: positive real scalar

Default: 1000

Advanced

NTF zeros opitimization flag — Method to optimize zeros in NTF

2 (default) | 0 | 1

Method that the block uses to optimize the zeros in the NTF:

• 0 — Not optimized

• 1 — Optimized

• 2 — Optimized with at least one zero at the center of the band

Programmatic Use

Block parameter: ntfOptim

Type: character vector

Values: 0 | 1 | 2

Default: 2

Modulator passband — Type of modulator passband

Lowpass (default) | Bandpass

Type of passband of the delta-sigma modulator.

Programmatic Use

Block parameter: passbandType

Type: character vector

Values: Lowpass | Bandpass

Default: Lowpass

Center frequency — Center frequency of modulator

0 (default) | scalar in the range [0 0.5]

Center frequency of the modulator, specified as a scalar in the range [0 0.5]. For a lowpass filter, the center frequency is zero.

Dependencies

To enable this parameter, set the Modulator passband parameter to Bandpass.

Programmatic Use

Block parameter: centerFrequency

Type: character vector

Values: scalar in the range [0 0.5]

Default: 0

Use custom value of H_inf — Option to use custom value of H_inf

off (default) | on

Select this parameter to use custom values for H_inf. By default, this option is cleared.

Maximum out-of-band H_inf — Maximum out-of-band gain of NTF

1.4 (default) | positive real scalar

Maximum out-of-band gain of the NTF.

Lee’s rule states that H_inf < 2 yields a stable modulator with a binary quantizer. Reducing H_inf increases the likelihood of success, but reduces the magnitude of the attenuation provided by the NTF and the theoretical resolution of the modulator.

Dependencies

To enable this parameter, select the Use custom value of H_inf parameter.

Programmatic Use

Block parameter: Hinf

Type: character vector

Values: positive real scalar

Default: 1.4

Note

You need a Control System Toolbox™ license to use the parameters in the Advanced tab.

More About

NTF

The block calculates the noise transfer function using the equation:

$$NTF=\frac{1}{1+L_1},$$

where L₁ is the feedback path of the internal loop filter inside the DSM.

Ideal NTF assumes an infinite gain of the internal op-amp. Finite gain affects the NTF.

To synthesize continuous-time NTF, the block first synthesizes discrete-time NTF using [1]. It then calculates the continuous-time filter coefficients using the impulse invariance transformation of the loop filter.

STF

The block calculates the signal transfer function using the equation:

$$STF=\frac{L_0}{1+L_1},$$

where:

• L₀ is the feed forward path of the internal loop filter inside the DSM.

• L₁ is the feedback path of the internal loop filter inside the DSM.

References

[1] Delta Sigma Toolbox, Richard Schreier.

[2] Shanthi Pavan; Richard Schreier; Gabor C. Temes, Understanding Delta-Sigma Data Converters, second edition, IEEE Press, 2017.

Version History

Introduced in R2024b