Finite-Gain Op-Amp

Gain-limited operational amplifier model with optional noise

Libraries:
Simscape / Electrical / Integrated Circuits

Description

The Finite-Gain Op-Amp block models a gain-limited operational amplifier. If the voltages at the positive and negative ports are V_p and V_m, respectively, the output voltage is:

$V_{o u t} = A (V_{p} - V_{m}) - I_{o u t} * R_{o u t}$

where:

A is the gain.
R_out is the output resistance.
I_out is the output current.

The input current is:

$\frac{V_{p} - V_{m}}{R_{i n}}$

where R_in is the input resistance.

The output voltage is limited by the minimum and maximum output values you specify in the block dialog box.

Thermal Noise

The Finite-Gain Op-Amp block can generate thermal noise. If you set the Noise mode parameter to Enabled, then the equivalent circuit for the block includes a noise current source attached to each of the inputs, and a noise voltage source attached to the noninverting input. These three noise sources are independent and uncorrelated.

The block generates noise voltage and current according to:

$v_{n o i s e} = \frac{v_{d e n s i t y}}{\sqrt{2 h}} N (0, 1)$

$i_{n o i s e} = \frac{i_{d e n s i t y}}{\sqrt{2 h}} N (0, 1)$

where:

v_noise is the noise voltage.
v_density is the single-sided, spectral amplitude density of the voltage noise.
i_noise is the noise current at an input.
i_density is the single-sided, spectral amplitude density of the current noise applied to that input.
h is the sampling time.
N is a Gaussian random number with zero mean and standard deviation of one.

The block generates Gaussian noise by using the PS Random Number source in the Simscape™ Foundation library. You can control the random number seed by setting the Repeatability parameter:

Not repeatable — Every time you simulate your model, the block resets the random seed using the MATLAB^® random number generator:
```
seed = randi(2^32-1);
```
Repeatable — The block automatically generates a seed value and stores it inside the block, to always start the simulation with the same random number. This auto-generated seed value is set when you add a Finite-Gain Op-Amp block from the block library to the model. When you make a new copy of the Finite-Gain Op-Amp block from an existing one in a model, a new seed value is generated. The block sets the value using the MATLAB random number generator command shown above.
Specify seed — If you select this option, additional parameters let you directly specify the random number seed values for input voltage, noninverting input current, and inverting input current.

Examples

Digital Potentiometer Parameterized from Datasheet

How to model a digital potentiometer such as is used to control audio amplifiers from a digital circuit or microprocessor-controlled system. The model also shows how you can create your own custom blocks in order to extend the Simscape™ Electrical™ library.

Open Model

Ports

Conserving

expand all

+ — Positive electrical voltage
electrical

Electrical conserving port associated with the op-amp noninverting input.

- — Negative electrical voltage
electrical

Electrical conserving port associated with the op-amp inverting input.

out — Output voltage
electrical

Electrical conserving port associated with the op-amp output. The port name is hidden on the block icon, but you can see it in simulation data logs.

Parameters

expand all

Main

Gain, A — Open-loop gain
1000 (default)

The open-loop gain of the operational amplifier.

Input resistance, Rin — Resistance at block input
1e6 Ohm (default)

The resistance at the input of the operational amplifier that the block uses to calculate the input current.

Output resistance, Rout — Resistance at block output
100 Ohm (default)

The resistance at the output of the operational amplifier that the block uses to calculate the drop in output voltage due to output current.

Minimum output, Vmin — Output voltage lower limit
-15 V (default)

The lower limit on the operational amplifier output voltage.

Maximum output, Vmax — Output voltage upper limit
15 V (default)

The upper limit on the operational amplifier output voltage.

Noise

Noise mode — Select whether op-amp generates thermal noise
`Disabled` (default) | `Enabled`

Select whether to model thermal noise effects:

Disabled — Op-amp does not generate thermal noise.
Enabled — Op-amp generates thermal noise voltage and current, and the associated parameters become visible in the Noise section.

Input noise voltage density — Density of voltage noise
30e-9 V/Hz^0.5 (default)

Single-sided, spectral amplitude density of the voltage noise applied to the noninverting input.

Dependencies

Enabled when the Noise mode parameter is set to Enabled.

Noise current parameterization — Select whether noise current density is different or the same for both inputs
`Apply same density function to both inputs` (default) | `Apply different density function to each input`

Select whether current density values applied to block inputs are different or the same.

Dependencies

Enabled when the Noise mode parameter is set to Enabled.

Input noise current density — Current noise at both inputs
0.5e-12 A/Hz^0.5 (default)

Single-sided, spectral amplitude density of the current noise applied to both inputs. Note that even though the density function is the same for both inputs, the actual noise current also depends on the random number seed. If the seeds used for the random number generation are different, then the actual noise currents at the inputs are also different.

Dependencies

Enabled when the Noise current parameterization parameter is set to Apply same density function to both inputs.

Noninverting input noise current density — Current noise at noninverting input
0.5e-12 A/Hz^0.5 (default)

Single-sided, spectral amplitude density of the current noise applied to noninverting input.

Dependencies

Enabled when the Noise current parameterization parameter is set to Apply different density function to each input.

Inverting input noise current density — Current noise at inverting input
0.5e-12 A/Hz^0.5 (default)

Single-sided, spectral amplitude density of the current noise applied to inverting input.

Dependencies

Enabled when the Noise current parameterization parameter is set to Apply different density function to each input.

Sample time — Rate at which the noise source is sampled
1e-3 s (default)

Defines the rate at which the noise source is sampled. Choose it to reflect the frequencies of interest in your model. Making the sample time too small will unnecessarily slow down your simulation.

Dependencies

Enabled when the Noise mode parameter is set to Enabled.

Repeatability — Select the noise control option
`Not repeatable` (default) | `Repeatable` | `Specify seed`

Select the noise control option:

Not repeatable — The random sequence used for noise generation is not repeatable.
Repeatable — The random sequence used for noise generation is repeatable, with a system-generated seed.
Specify seed — The random sequence used for noise generation is repeatable, and you control the seed by using the seed parameters. You specify seed values separately for input noise voltage, noninverting input noise current, and inverting input noise current.

Dependencies

Enabled when the Noise mode parameter is set to Enabled.

Input noise voltage auto-generated seed used for repeatable option — Auto-generated random number seed for voltage noise
random real number

Random number seed stored inside the block to make the random sequence repeatable. The parameter value is automatically generated using the MATLAB random number generator command. You can modify this parameter value, but it gets overwritten by a new random value if you copy the block to another block in the model. Therefore, if you want to control the seed of the random sequence, use the Specify seed option for the Repeatability parameter and specify the desired seed value using the Input noise voltage seed parameter.

Dependencies

Enabled when the Repeatability parameter is set to Repeatable.

Noninverting input noise current auto-generated seed used for repeatable option — Auto-generated random number seed for current noise at noninverting input
random real number

Dependencies

Enabled when the Repeatability parameter is set to Repeatable.

Inverting input noise current auto-generated seed used for repeatable option — Auto-generated random number seed for current noise at inverting input
random real number

Dependencies

Enabled when the Repeatability parameter is set to Repeatable.

Input noise voltage seed — Random number seed for voltage noise
0 (default)

Seed used by the noise random number generator.

Dependencies

Enabled when the Repeatability parameter is set to Specify seed.

Noninverting input noise current seed — Random number seed for current noise at noninverting input
0 (default)

Seed used by the noise random number generator.

Dependencies

Enabled when the Repeatability parameter is set to Specify seed.

Inverting input noise current seed — Random number seed for current noise at inverting input
0 (default)

Seed used by the noise random number generator.

Dependencies

Enabled when the Repeatability parameter is set to Specify seed.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2008b

Finite-Gain Op-Amp

Description

Thermal Noise

Examples

Digital Potentiometer Parameterized from Datasheet

Ports

Conserving

+ — Positive electrical voltage electrical

- — Negative electrical voltage electrical

out — Output voltage electrical

Parameters

Main

Gain, A — Open-loop gain 1000 (default)

Input resistance, Rin — Resistance at block input 1e6 Ohm (default)

Output resistance, Rout — Resistance at block output 100 Ohm (default)

Minimum output, Vmin — Output voltage lower limit -15 V (default)

Maximum output, Vmax — Output voltage upper limit 15 V (default)

Noise

Noise mode — Select whether op-amp generates thermal noise Disabled (default) | Enabled

Input noise voltage density — Density of voltage noise 30e-9 V/Hz^0.5 (default)

Dependencies

Noise current parameterization — Select whether noise current density is different or the same for both inputs Apply same density function to both inputs (default) | Apply different density function to each input

Dependencies

Input noise current density — Current noise at both inputs 0.5e-12 A/Hz^0.5 (default)

Dependencies

Noninverting input noise current density — Current noise at noninverting input 0.5e-12 A/Hz^0.5 (default)

Dependencies

Inverting input noise current density — Current noise at inverting input 0.5e-12 A/Hz^0.5 (default)

Dependencies

Sample time — Rate at which the noise source is sampled 1e-3 s (default)

Dependencies

Repeatability — Select the noise control option Not repeatable (default) | Repeatable | Specify seed

Dependencies

Input noise voltage auto-generated seed used for repeatable option — Auto-generated random number seed for voltage noise random real number

Dependencies

Noninverting input noise current auto-generated seed used for repeatable option — Auto-generated random number seed for current noise at noninverting input random real number

Dependencies

Inverting input noise current auto-generated seed used for repeatable option — Auto-generated random number seed for current noise at inverting input random real number

Dependencies

Input noise voltage seed — Random number seed for voltage noise 0 (default)

Dependencies

Noninverting input noise current seed — Random number seed for current noise at noninverting input 0 (default)

Dependencies

Inverting input noise current seed — Random number seed for current noise at inverting input 0 (default)

Dependencies

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using Simulink® Coder™.

Version History

See Also

+ — Positive electrical voltage
electrical

- — Negative electrical voltage
electrical

out — Output voltage
electrical

Gain, A — Open-loop gain
1000 (default)

Input resistance, Rin — Resistance at block input
1e6 Ohm (default)

Output resistance, Rout — Resistance at block output
100 Ohm (default)

Minimum output, Vmin — Output voltage lower limit
-15 V (default)

Maximum output, Vmax — Output voltage upper limit
15 V (default)

Noise mode — Select whether op-amp generates thermal noise
`Disabled` (default) | `Enabled`

Input noise voltage density — Density of voltage noise
30e-9 V/Hz^0.5 (default)

Noise current parameterization — Select whether noise current density is different or the same for both inputs
`Apply same density function to both inputs` (default) | `Apply different density function to each input`

Input noise current density — Current noise at both inputs
0.5e-12 A/Hz^0.5 (default)

Noninverting input noise current density — Current noise at noninverting input
0.5e-12 A/Hz^0.5 (default)

Inverting input noise current density — Current noise at inverting input
0.5e-12 A/Hz^0.5 (default)

Sample time — Rate at which the noise source is sampled
1e-3 s (default)

Repeatability — Select the noise control option
`Not repeatable` (default) | `Repeatable` | `Specify seed`

Input noise voltage auto-generated seed used for repeatable option — Auto-generated random number seed for voltage noise
random real number

Noninverting input noise current auto-generated seed used for repeatable option — Auto-generated random number seed for current noise at noninverting input
random real number

Inverting input noise current auto-generated seed used for repeatable option — Auto-generated random number seed for current noise at inverting input
random real number

Input noise voltage seed — Random number seed for voltage noise
0 (default)

Noninverting input noise current seed — Random number seed for current noise at noninverting input
0 (default)

Inverting input noise current seed — Random number seed for current noise at inverting input
0 (default)

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.