DT Integrator

Real discrete-time integrator for delta-sigma modulator

Since R2026a

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Libraries:
Mixed-Signal Blockset / ADC / Building Blocks

Description

Use the DT Integrator block to perform true discrete-time integration of the voltage difference between the input ports. It is used for behavioral modeling of switched‑capacitor delta-sigma (ΔΣ) modulators. The block operates in the discrete‑time domain and implements integration using either a Forward Euler (FE) or Lossless‑Direct (LD) solver, closely matching the behavior of practical SC integrators.

The integrator supports 1 to 4 branched inputs, allowing straightforward realization of feedforward and feedback summation paths commonly found in delta-sigma loop filters. Its internal operation is based on charge‑transfer principles, rather than ideal mathematical integration, enabling accurate modeling of real switched‑capacitor architectures.

To support realistic system‑level simulation, the block includes a range of circuit‑level non‑idealities, such as finite op‑amp gain and bandwidth, sampling delay, capacitor mismatch, and clock‑phase timing effects. These non-idealities make the block particularly suitable for evaluating stability, noise‑shaping performance, and robustness of ΔΣ modulators prior to circuit‑level implementation.

Ports

Input

+1 — Non-inverting input signal at branch 1

scalar

Input signal at the non-inverting input port at branch 1, specified as a scalar.

Data Types: double

-1 — Inverting input signal at branch 1

scalar

Input signal at the inverting input port at branch 1, specified as a scalar.

Data Types: double

+2 — Non-inverting input signal at branch 2

scalar

Input signal at the non-inverting input port at branch 2, specified as a scalar.

Dependencies

To enable this port, set Number of branch to 2 or higher.

Data Types: double

-2 — Inverting input signal at branch 2

scalar

Input signal at the inverting input port at branch 2, specified as a scalar.

Dependencies

To enable this port, set Number of branch to 2 or higher.

Data Types: double

+3 — Non-inverting input signal at branch 3

scalar

Input signal at the non-inverting input port at branch 3, specified as a scalar.

Dependencies

To enable this port, set Number of branch to 3 or higher.

Data Types: double

-3 — Inverting input signal at branch 3

scalar

Input signal at the inverting input port at branch 3, specified as a scalar.

Dependencies

To enable this port, set Number of branch to 3 or higher.

Data Types: double

+4 — Non-inverting input signal at branch 4

scalar

Input signal at the non-inverting input port at branch 4, specified as a scalar.

Dependencies

To enable this port, set Number of branch to 4.

Data Types: double

-4 — Inverting input signal at branch 4

scalar

Input signal at the inverting input port at branch 4, specified as a scalar.

Dependencies

To enable this port, set Number of branch to 4.

Data Types: double

Output

out — Output signal

scalar

Integrated output signal, returned as a scalar.

Data Types: double

Parameters

To edit block parameters interactively, use the Property Inspector. From the Simulink^® Toolstrip, on the Simulation tab, in the Prepare gallery, select Property Inspector.

Solver type — Solver type for integrator model

Forward - Euler (default) | Lossless - Direct

Solver type for the integrator model, specified as one of the following:

• Forward - Euler — This method approximates the integral by assuming that the input remains constant at the beginning of the sampling interval. This method finds the solution by stepping forward in small increments. It is easy to implement but can be unstable for stiff equations or large time steps. This method is suitable for simple systems where stability is not a major concern. It is typically used for basic numerical simulations, simple DSP demonstrations, and educational examples.

• Lossless - Direct — This method uses a middle-point integrator that approximates the integral using the input value at the center of the interval. This symmetry makes the method lossless in phase. This method offers excellent frequency-domain accuracy and preserves the sinusoidal waveforms. But the stability is not guaranteed and it is not suitable for standalone robust filter designs. It is usually used for switched‑capacitor filter analysis, signal modeling and theory, and lossless integrator structures.

Programmatic Use

Block parameter: SolverType

Type: character vector

Values: Forward - Euler | Lossless - Direct

Default: Forward - Euler

Number of Branch — Number of integrator branches

2 (default) | 1 | 3 | 4

Number of integrator branches, specified as 1, 2, 3, or 4.

Programmatic Use

Block parameter: NumberOfBranches

Type: character vector

Values: 1 | 2 | 3 | 4

Default: 2

Sample period — Clock period

1/5.12e6 (default) | positive real scalar

Clock period to use to sample the input signal, specified as a positive real scalar.

Programmatic Use

Block parameter: SampleTime

Type: character vector

Values: positive real scalar

Default: 1/5.12e6

Enable settling effect — Option to enable settling error

on (default) | off

Select this parameter to enable nonlinear incomplete settling error. By default, this option is selected.

Programmatic Use

Block parameter: EnableSettling

Type: character vector

Values: off | on

Default: on

Capacitor

Integration capacitor (F) — Capacitance of integration capacitor

24e-12 (default) | nonnegative real scalar

Capacitance of integration capacitor in F, specified as a nonnegative real scalar.

Programmatic Use

Block parameter: Ci

Type: character vector

Values: nonnegative real scalar

Default: 24e-12

Sampling capacitor (Branch 1) (F) — Capacitance of sampling capacitor at branch 1

6e-12 (default) | nonnegative real scalar

Capacitance of sampling capacitor at branch 1 in F, specified as a nonnegative real scalar.

Programmatic Use

Block parameter: Csb1

Type: character vector

Values: nonnegative real scalar

Default: 6e-12

Sampling capacitor (Branch 2) (F) — Capacitance of sampling capacitor at branch 2

6e-12 (default) | nonnegative real scalar

Capacitance of sampling capacitor at branch 2 in F, specified as a nonnegative real scalar.

Dependencies

To enable this parameter, set Number of branch to 2.

Programmatic Use

Block parameter: Csb2

Type: character vector

Values: nonnegative real scalar

Default: 6e-12

Sampling capacitor (Branch 3) (F) — Capacitance of sampling capacitor at branch 3

6e-12 (default) | nonnegative real scalar

Capacitance of sampling capacitor at branch 3 in F, specified as a nonnegative real scalar.

Dependencies

To enable this parameter, set Number of branch to 3.

Programmatic Use

Block parameter: Csb3

Type: character vector

Values: nonnegative real scalar

Default: 6e-12

Sampling capacitor (Branch 4) (F) — Capacitance of sampling capacitor at branch 4

6e-12 (default) | nonnegative real scalar

Capacitance of sampling capacitor at branch 4 in F, specified as a nonnegative real scalar.

Dependencies

To enable this parameter, set Number of branch to 4.

Programmatic Use

Block parameter: Csb4

Type: character vector

Values: nonnegative real scalar

Default: 6e-12

Load capacitor (F) — Capacitance of load capacitor

2.28e-12 (default) | positive real scalar

Capacitance of load capacitor in F, specified as a positive real scalar.

Programmatic Use

Block parameter: Cload

Type: character vector

Values: positive real scalar

Default: 2.28e-12

Enable capacitor non-linearity — Option to enable capacitor nonlinearity effect

off (default) | on

Select this parameter to enable the effects of capacitor nonlinearity. By default, this option is deselected.

Programmatic Use

Block parameter: EnableCapacitorNonlinearity

Type: character vector

Values: off | on

Default: off

Capacitor 1st order non-linear coefficient — First-order coefficient for capacitor nonlinearity

0 (default) | nonnegative real scalar

First-order coefficient for capacitor nonlinearity, specified as a nonnegative real scalar.

Dependencies

To enable this parameter, select Enable capacitor non-linearity in the Capacitor tab.

Programmatic Use

Block parameter: CapacitorFirstOrderNonlinearity

Type: character vector

Values: nonnegative real scalar

Default: 0

Capacitor 2nd order non-linear coefficient — Second-order coefficient for capacitor nonlinearity

0 (default) | nonnegative real scalar

Second-order coefficient for capacitor nonlinearity, specified as a nonnegative real scalar.

Dependencies

To enable this parameter, select Enable capacitor non-linearity in the Capacitor tab.

Programmatic Use

Block parameter: CapacitorSecondOrderNonlinearity

Type: character vector

Values: nonnegative real scalar

Default: 0

Enable capacitor mismatch error — Option to enable capacitor mismatch error

off (default) | on

Select this parameter to enable capacitor mismatch error. By default, this option is deselected.

Programmatic Use

Block parameter: EnableCapacitorMismatch

Type: character vector

Values: off | on

Default: off

Variance of the capacitor mismatch error — Variance of capacitor mismatch error

0 (default) | nonnegative real scalar

Variance of the capacitor mismatch error, specified as a nonnegative real scalar.

Dependencies

To enable this parameter, select Enable capacitor mismatch error in the Capacitor tab.

Programmatic Use

Block parameter: CapacitorMismatch

Type: character vector

Values: nonnegative real scalar

Default: 0

OTA

DC Gain — DC gain of OTA

2.63e3 (default) | positive real scalar

DC gain of the operational transconductance amplifier (OTA), specified as a positive real scalar.

Programmatic Use

Block parameter: OTADCGain

Type: character vector

Values: positive real scalar

Default: 2.63e3

Transconductance — Transconductance of OTA

4.5e-3 (default) | positive real scalar

Transconductance of the operational transconductance amplifier (OTA), specified as a positive real scalar.

Programmatic Use

Block parameter: OTATransconductance

Type: character vector

Values: positive real scalar

Default: 4.5e-3

Maximum output current — Maximum output current of OTA

0.977e-3 (default) | positive real scalar

Maximum output current of the operational transconductance amplifier (OTA), specified as a positive real scalar.

Programmatic Use

Block parameter: OTAMaximumCurrent

Type: character vector

Values: positive real scalar

Default: 0.977e-3

Maximum/minimum output swing limits — Output voltage swing of OTA

2.7 (default) | positive real scalar

Output voltage swing of the OTA, specified as a positive real scalar. The function assigns the +V_ref as the maximum voltage and -V_ref as the minimum voltage.

Programmatic Use

Block parameter: OTAOutputSwing

Type: character vector

Values: positive real scalar

Default: 2.7

Enable non-linearity of OTA DC gain — Option to enable nonlinearity of OTA DC gain

off (default) | on

Select this parameter to enable nonlinearity of the OTA DC gain. Enabling this option degrades the SNR of the integrator. It also generally raises the power density across the entire frequency spectrum.

Programmatic Use

Block parameter: EnableOTAGainNonlinearity

Type: character vector

Values: off | on

Default: off

1st order non-linear coefficient — First-order nonlinear coefficient of OTA DC gain

0 (default) | nonnegative real scalar

First-order nonlinear coefficient of the OTA DC gain, specified as a nonnegative real scalar.

Dependencies

To enable this parameter, select the Enable non-linearity of OTA DC gain parameter in the OTA tab.

Programmatic Use

Block parameter: OTAGainFirstOrderNonlinearity

Type: character vector

Values: nonnegative real scalar

Default: 0

2nd order non-linear coefficient — Second-order nonlinear coefficient of OTA DC gain

0 (default) | nonnegative real scalar

Second-order nonlinear coefficient of the OTA DC gain, specified as a nonnegative real scalar.

Dependencies

To enable this parameter, select the Enable non-linearity of OTA DC gain parameter in the OTA tab.

Programmatic Use

Block parameter: OTAGainSecondOrderNonlinearity

Type: character vector

Values: nonnegative real scalar

Default: 0

3rd order non-linear coefficient — Third-order nonlinear coefficient of OTA DC gain

0 (default) | nonnegative real scalar

Third-order nonlinear coefficient of the OTA DC gain, specified as a nonnegative real scalar.

Dependencies

To enable this parameter, select the Enable non-linearity of OTA DC gain parameter in the OTA tab.

Programmatic Use

Block parameter: OTAGainThirdOrderNonlinearity

Type: character vector

Values: nonnegative real scalar

Default: 0

4th order non-linear coefficient — Fourth-order nonlinear coefficient of OTA DC gain

0 (default) | nonnegative real scalar

Fourth-order nonlinear coefficient of the OTA DC gain, specified as a nonnegative real scalar.

Dependencies

To enable this parameter, select the Enable non-linearity of OTA DC gain parameter in the OTA tab.

Programmatic Use

Block parameter: OTAGainFourthOrderNonlinearity

Type: character vector

Values: nonnegative real scalar

Default: 0

Enable parasitic capacitance — Option to enable parasitic capacitance

off (default) | on

Select this parameter to enable parasitic capacitance before the OTA input or the sampling capacitor.

Programmatic Use

Block parameter: EnableParasiticCapacitance

Type: character vector

Values: off | on

Default: off

Parasitic capacitance before the OTA (F) — Parasitic capacitance at OTA input

0.6e-12 (default) | nonnegative real scalar

Parasitic capacitance at the input of the OTA, specified as a nonnegative real scalar.

Dependencies

To enable this parameter, select the Enable parasitic capacitance parameter in the OTA tab.

Programmatic Use

Block parameter: ParasiticCapacitanceBeforeOTA

Type: character vector

Values: nonnegative real scalar

Default: 0.6e-12

Parasitic capacitance before sampling cap (F) — Parasitic capacitance before sampling capacitor

0.6e-12 (default) | nonnegative real scalar

Parasitic capacitance before the sampling capacitor, specified as a nonnegative real scalar.

Dependencies

To enable this parameter, select the Enable parasitic capacitance parameter in the OTA tab.

Programmatic Use

Block parameter: ParasiticCapacitanceBeforeSamplingCapacitor

Type: character vector

Values: nonnegative real scalar

Default: 0.6e-12

Switch

Switch on-resistance — On-resistance of switch

60 (default) | nonnegative real scalar

On-resistance of the switch, specified as a nonnegative real scalar.

Programmatic Use

Block parameter: SwitchOnResistance

Type: character vector

Values: nonnegative real scalar

Default: 60

Enable thermal noise — Option to enable thermal noise

off (default) | on

Select this parameter to enable thermal noise. Enabling thermal noise increases the overall power across all frequencies.

Programmatic Use

Block parameter: EnableThermalNoise

Type: character vector

Values: off | on

Default: off

Temperature (K) — Noise temperature

175 (default) | nonnegative real scalar

Noise temperature in K, specified as a nonnegative real scalar.

Dependencies

To enable this parameter, select the Enable thermal noise parameter in the Switch tab.

Programmatic Use

Block parameter: Temperature

Type: character vector

Values: nonnegative real scalar

Default: 175

Input equivalent thermal noise (Vrms) — OTA input-referred thermal noise

0 (default) | nonnegative real scalar

Input-referred thermal noise at the OTA, specified as a nonnegative real scalar.

Dependencies

To enable this parameter, select the Enable thermal noise parameter in the Switch tab.

Programmatic Use

Block parameter: InputEquivalentThermalNoise

Type: character vector

Values: nonnegative real scalar

Default: 0

Version History

Introduced in R2026a