Package Modelica.​Electrical.​Analog.​Examples
Examples that demonstrate the usage of the Analog electrical components

Information

This package contains examples that demonstrate the usage of the components of the Electrical.Analog library.

The examples are simple to understand. They will show a typical behavior of the components, and they will give hints to users.

Extends from Modelica.​Icons.​ExamplesPackage (Icon for packages containing runnable examples).

Package Contents

NameDescription
AD_DA_conversionConversion circuit
AmplifierWithOpAmpDetailedSimple Amplifier circuit which uses OpAmpDetailed
CauerLowPassAnalogCauer low pass filter with analog components
CauerLowPassOPVCauer low pass filter with operational amplifiers
CauerLowPassSCCauer low-pass filter with operational amplifiers and switched capacitors
CharacteristicIdealDiodesCharacteristic of ideal diodes
CharacteristicThyristorsCharacteristic of ideal thyristors
ChuaCircuitChua's circuit, ns, V, A
CompareTransformersTransformer circuit to show the magnetization facilities
ControlledSwitchWithArcComparison of controlled switch models both with and without arc
DifferenceAmplifierSimple NPN transistor amplifier circuit
GenerationOfFMUsExample to demonstrate variants to generate FMUs (Functional Mock-up Units)
HeatingMOSInverterHeating MOS Inverter
HeatingNPN_OrGateHeating NPN Or Gate
HeatingPNP_NORGateHeating PNP NOR Gate
HeatingRectifierHeating rectifier
HeatingResistorHeating resistor
IdealTriacCircuitIdeal triac test circuit
InvertingAmpInverting amplifier
NandGateCMOS NAND Gate (see Tietze/Schenk, page 157)
OpAmpsExamples with operational amplifiers
OvervoltageProtectionExample for Zener diodes
RectifierB6 diode bridge
ResonanceCircuitsResonance circuits: example to demonstrate generation of FMUs (Functional Mock-up Units)
ShowSaturatingInductorSimple demo to show behaviour of SaturatingInductor component
ShowVariableResistorSimple demo of a VariableResistor model
SimpleTriacCircuitSimple triac test circuit
SwitchWithArcComparison of switch models both with and without arc
ThyristorBehaviourTestThyristor demonstration example
UtilitiesUtility components used by package Examples

Model Modelica.​Electrical.​Analog.​Examples.​CauerLowPassAnalog
Cauer low pass filter with analog components

Information

The example Cauer Filter is a low-pass-filter of the fifth order. It is realized using an analog network. The voltage source V is the input voltage (step), and the R2.p.v is the filter output voltage. The pulse response is calculated.

The simulation end time should be 60. Please plot both V.p.v (input voltage) and R2.p.v (output voltage).

Extends from Modelica.​Icons.​Example (Icon for runnable examples).

Parameters

TypeNameDefaultDescription
Inductancel11.304filter coefficient I1
Inductancel20.8586filter coefficient I2
Capacitancec11.072filter coefficient c1
Capacitancec2(2.906997720064 * l1) ^ (-1)filter coefficient c2
Capacitancec31.682filter coefficient c3
Capacitancec4(1.392270203025 * l2) ^ (-1)filter coefficient c4
Capacitancec50.7262filter coefficient c5

Model Modelica.​Electrical.​Analog.​Examples.​CauerLowPassOPV
Cauer low pass filter with operational amplifiers

Information

The example Cauer Filter is a low-pass-filter of the fifth order. It is realized using an analog network with operational amplifiers. The voltage source V is the input voltage (step), and the OP5.out.v is the filter output voltage. The pulse response is calculated.

This model is identical to the CauerLowPassAnalog example, but inverting. To get the same response as that of the CauerLowPassAnalog example, a negative voltage step is used as input.

The simulation end time should be 60. Please plot both V.v (which is the inverted input voltage) and OP5.p.v (output voltage). Compare this result with the CauerLowPassAnalog result.

During translation some warnings are issued concerning resistor values (Value=-1 not in range [0,1e100]). Do not worry about it. The negative values are o.k.

Extends from Modelica.​Icons.​Example (Icon for runnable examples).

Parameters

TypeNameDefaultDescription
Capacitancel11.304filter coefficient i1
Capacitancel20.8586filter coefficient i2
Capacitancec11.072filter coefficient c1
Capacitancec2(2.906997720064 * l1) ^ (-1)filter coefficient c2
Capacitancec31.682filter coefficient c3
Capacitancec4(1.392270203025 * l2) ^ (-1)filter coefficient c4
Capacitancec50.7262filter coefficient c5

Model Modelica.​Electrical.​Analog.​Examples.​CauerLowPassSC
Cauer low-pass filter with operational amplifiers and switched capacitors

Information

The example CauerLowPassSC is a low-pass-filter of the fifth order. It is realized using an switched-capacitor network with operational amplifiers. The voltage source V is the input voltage (step), and the OP5.out.v is the filter output voltage. The pulse response is calculated.

This model is identical to the CauerLowPassAnalog example, but inverting. To get the same response as that of the CauerLowPassAnalog example, a negative voltage step is used as input.

This model is identical to the CauerLowPassOPV example. But the resistors are realized by switched capacitors (see SwitchedCapacitor). There are two different types of instances, one with a value of R=1 and one with a value of R=-1.

The simulation end time should be 60. Please plot both V.v (which is the inverted input voltage) and OP5.out.v (output voltage). Compare this result with the CauerLowPassAnalog result.

Due to the recharging of the capacitances after switching the performance of simulation is not as good as in the CauerLowPassOPV example.

Extends from Modelica.​Icons.​Example (Icon for runnable examples).

Parameters

TypeNameDefaultDescription
Capacitancel11.304filter coefficient i1
Capacitancel20.8586filter coefficient i2
Capacitancec11.072filter coefficient c1
Capacitancec2(2.906997720064 * l1) ^ (-1)filter coefficient c2
Capacitancec31.682filter coefficient c3
Capacitancec4(1.392270203025 * l2) ^ (-1)filter coefficient c4
Capacitancec50.7262filter coefficient c5

Model Modelica.​Electrical.​Analog.​Examples.​CharacteristicIdealDiodes
Characteristic of ideal diodes

Information

Three examples of ideal diodes are shown:
the totally ideal diode (Ideal) with all parameters to be zero, the nearly ideal diode with Ron=0.1 and Goff=0.1 and the nearly ideal but displaced diode with Vknee=5 and Ron=0.1 and Goff=0.1. The resistance and conductance are chosen untypically high since the slopes should be seen in the graphics.

Simulate until T=1 s. Plot in separate windows: Ideal.i versus Ideal.v, With_Ron_Goff.i versus With_Ron_Goff.v, With_Ron_Goff_Vknee.i versus With_Ron_Goff_Vknee.v

Extends from Modelica.​Icons.​Example (Icon for runnable examples).


Model Modelica.​Electrical.​Analog.​Examples.​CharacteristicThyristors
Characteristic of ideal thyristors

Information

This example compares the behavior of the ideal thyristor and the ideal GTO thyristor with Vknee=1 both. The thyristors IdealThyristor1 and IdealGTOThyristor1 are controlled by an unregular Boolean fire signal. The aim is to show several cases for the fire signal in combination with the state (s<0 or s>0)of the thyristors. Please simulate until 6 seconds and compare IdealThyristor1.v with IdealGTOThyristor1.v, the same with IdealThyristor1.s and IdealGTOThyristor1.s (attention: s is a protected variable in each thyristor). Also compare IdealThyristor1.off and IdealGTOThyristor1.off and have a look at the fire signal (e.g. IdealThyristor1.fire). It can be seen that the IdealGTOThyristor1 reacts on switching off the fire signal whereas the IdealThyristor1 does not show this behavior.

The other thyristors IdealThyristor2 and IdealGTOThyristor2 are controlled by an periodic Boolean fire signal to show a typical use case. Please compare IdealThyristor2.v with IdealGTOThyristor2.v

Extends from Modelica.​Icons.​Example (Icon for runnable examples).


Model Modelica.​Electrical.​Analog.​Examples.​ChuaCircuit
Chua's circuit, ns, V, A

Information

Chua's circuit is the most simple nonlinear circuit which shows chaotic behaviour. The circuit consists of linear basic elements (capacitors, resistor, conductor, inductor), and one nonlinear element, which is called Chua's diode. The chaotic behaviour is simulated.

The simulation end time should be set to 5e4. To get the chaotic behaviour please plot C1.v. Choose C2.v as the independent variable .

Reference:

Kennedy, M.P.: Three Steps to Chaos - Part I: Evolution. IEEE Transactions on CAS I 40 (1993)10, 640-656

Extends from Modelica.​Icons.​Example (Icon for runnable examples).


Model Modelica.​Electrical.​Analog.​Examples.​DifferenceAmplifier
Simple NPN transistor amplifier circuit

Information

It is a simple NPN transistor amplifier circuit. The voltage difference between R1.p and R3.n is amplified. The output signal is the voltage between R2.n and R4.n. In this example the voltage at V1 is amplified because R3.n is grounded.

The simulation end time should be set to 1e- 8. Please plot the input voltage V1.v, and the output voltages R2.n.v, and R4.n.v.

Reference:

Tietze, U.; Schenk, Ch.: Halbleiter-Schaltungstechnik. Springer-Verlag Berlin Heidelberg NewYork 1980, p. 59

Extends from Modelica.​Icons.​Example (Icon for runnable examples).


Model Modelica.​Electrical.​Analog.​Examples.​HeatingMOSInverter
Heating MOS Inverter

Information

The heating MOS inverter shows a heat flow always if a transistor is leading.

Simulate until T=5 s. Plot in separate windows:
Sin.p.v and Capacitor1.p.v
HeatCapacitor1.port.T and H_PMOS.heatPort.T and H_NMOS.heatPort.T
H_PMOS.heatPort.Q_flow and H_NMOS.heatPort.Q_flow

Extends from Modelica.​Icons.​Example (Icon for runnable examples).


Model Modelica.​Electrical.​Analog.​Examples.​HeatingNPN_OrGate
Heating NPN Or Gate

Information

The heating "NPN or" gate shows a heat flow always if a transistor is leading.

Simulate until T=200 s. Plot in separate windows:
V1.v and V2.v and C2.v
HeatCapacitor1.port.T and T1.heatPort.T and T2.heatPort.T
T1.heatPort.Q_flow and T2.heatPort.Q_flow

Extends from Modelica.​Icons.​Example (Icon for runnable examples).

Parameters

TypeNameDefaultDescription
CapacitanceCapVal0 
TimetauVal0 

Model Modelica.​Electrical.​Analog.​Examples.​HeatingPNP_NORGate
Heating PNP NOR Gate

Information

The heating "PNP NOR" gate shows a heat flow always if a transistor is conducting.

Simulate until T=200 s. Plot V1.v and V2.v and C2.v to see the NOR-functionality. High potential is -6V which means logic "true". Low potential is 0V which means logic "false".

To see which transistor is conducting one can have a look at the temperatures T1.heatPort.T and T2.heatPort.T and the heat flows T1.heatPort.Q_flow and T2.heatPort.Q_flow of the heatports of the transistors T1 and T2.

They are different from zero if the transistor is conducting.

Extends from Modelica.​Icons.​Example (Icon for runnable examples).

Parameters

TypeNameDefaultDescription
CapacitanceCapVal0 
TimetauVal0 

Model Modelica.​Electrical.​Analog.​Examples.​HeatingResistor
Heating resistor

Information

This is a very simple circuit consisting of a voltage source and a resistor. The loss power in the resistor is transported to the environment via its heatPort.

Extends from Modelica.​Icons.​Example (Icon for runnable examples).


Model Modelica.​Electrical.​Analog.​Examples.​HeatingRectifier
Heating rectifier

Information

The heating rectifier shows a heat flow always if the electrical capacitor is loaded.

Simulate until T=5 s.Plot in separate windows:
SineVoltage1.v and Capacitor1.p.v
HeatCapacitor1.port.T and HeatingDiode1.heatPort.T
HeatingDiode1.heatPort.Q_flow

Extends from Modelica.​Icons.​Example (Icon for runnable examples).


Model Modelica.​Electrical.​Analog.​Examples.​NandGate
CMOS NAND Gate (see Tietze/Schenk, page 157)

Information

The nand gate is a basic CMOS building block. It consists of four CMOS transistors. The output voltage Nand.y.v is low if and only if the two input voltages at Nand.x1.v and Nand.x2.v are both high. In this way the nand functionality is realized.

The simulation end time should be set to 1e-7. Please plot the input voltages Nand.x1.v, d Nand.x2.v, and the output voltage Nand.y.v.

Reference:

Tietze, U.; Schenk, Ch.: Halbleiter-Schaltungstechnik. Springer-Verlag Berlin Heidelberg NewYork 1980, p. 157

Extends from Modelica.​Icons.​Example (Icon for runnable examples).


Model Modelica.​Electrical.​Analog.​Examples.​OvervoltageProtection
Example for Zener diodes

Information

This example is a simple circuit for overvoltage protection. If the voltage zDiode_1.n.v is too high, the Diode zDiode_2 breaks through and the voltage gets down.

The simulation end time should be set to 0.4. To get the typical behaviour please plot sineVoltage.p.v, RL.p.v, zDiode_2.n.v and zDiode_1.n.i.

Extends from Modelica.​Icons.​Example (Icon for runnable examples).


Model Modelica.​Electrical.​Analog.​Examples.​Rectifier
B6 diode bridge

Information

The rectifier example shows a B6 diode bridge fed by a three phase sinusoidal voltage, loaded by a DC current. DC capacitors start at ideal no-load voltage, thus making easier initial transient.

Simulate until T=0.1 s. Plot in separate windows:
uDC ... DC-voltage
iAC ... AC-currents 1..3
uAC ... AC-voltages 1..3 (distorted)
Try different load currents iDC = 0..approximately 500 A. You may watch losses (of the whole diode bridge) trying different diode parameters.

Extends from Modelica.​Icons.​Example (Icon for runnable examples).

Parameters

TypeNameDefaultDescription
VoltageVAC400RMS line-to-line
Frequencyf50line frequency
InductanceLAC6e-5line inductor
ResistanceRon0.001diode forward resistance
ConductanceGoff0.001diode backward conductance
VoltageVknee2diode threshold voltage
CapacitanceCDC0.015DC capacitance
CurrentIDC500load current

Model Modelica.​Electrical.​Analog.​Examples.​ShowSaturatingInductor
Simple demo to show behaviour of SaturatingInductor component

Information

This simple circuit uses the saturating inductor which has a changing inductivity.

This circuit should be simulated until 1 s. Compare SaturatingInductance1.p.i with Inductance1.p.i to see the difference between saturating and ideal inductor.

Extends from Modelica.​Icons.​Example (Icon for runnable examples).

Parameters

TypeNameDefaultDescription
InductanceLzer2Inductance near current=0
InductanceLnom1Nominal inductance at Nominal current
CurrentInom1Nominal current
InductanceLinf0.5Inductance at large currents
VoltageU1.25Source voltage (peak)
Frequencyf(2 * Modelica.Constants.pi) ^ (-1)Source frequency
Anglephase0.5 * Modelica.Constants.piSource voltage phase shift

Model Modelica.​Electrical.​Analog.​Examples.​ShowVariableResistor
Simple demo of a VariableResistor model

Information

It is a simple test circuit for the VariableResistor. The VariableResistor should be compared with R2.

Simulate until T=1 s.

Extends from Modelica.​Icons.​Example (Icon for runnable examples).


Model Modelica.​Electrical.​Analog.​Examples.​SwitchWithArc
Comparison of switch models both with and without arc

Information

This example is to compare the behaviour of switch models with and without an electric arc taking into consideration.

The difference in the closing area shows that the simple arc model avoids the suddenly switching.

Extends from Modelica.​Icons.​Example (Icon for runnable examples).


Model Modelica.​Electrical.​Analog.​Examples.​ThyristorBehaviourTest
Thyristor demonstration example

Information

This is a simple test circuit, to test the behavior of the thyristor model.

Interesting values to plot are Cathode.v, Gate.v and sineVoltage.p.v. and in another plot window pulseCurrent.p.i

The simulation time should be from 0 seconds to 2e-4 seconds.

Extends from Modelica.​Icons.​Example (Icon for runnable examples).


Model Modelica.​Electrical.​Analog.​Examples.​AmplifierWithOpAmpDetailed
Simple Amplifier circuit which uses OpAmpDetailed

Information

With the test circuit AmplifierWithOpAmpDetailed a time domain analysis of the example arrangement with a sinusoidal input voltage (12 V amplitude, frequency 1 kHz) using the operational amplifier model OpAmpDetailed is carried out. The working voltages are 15 V and -15 V.

Extends from Modelica.​Icons.​Example (Icon for runnable examples).


Model Modelica.​Electrical.​Analog.​Examples.​CompareTransformers
Transformer circuit to show the magnetization facilities

Information

This example is to demonstrate the behaviour of transformer models. The Basic.Transformer, which consists of mutual coupled inductors, is compared with the ideal transformer model. If the ideal model is used with considerMagnetization=true leakage inductances are taken into account, otherwise not. The example is constructed in such a way that the ideal transformer circuit with considerMagnetization=true shows the same behaviour as the basic transformer.

Simulate until T=50 s with both considerMagnetization=false and considerMagnetization=true of the ideal transformer. Plot in separate windows for comparison:
basicTransformer.p1.v and idealTransformer.p1.v
basicTransformer.p1.i and idealTransformer.p1.i
basicTransformer.p2.v and idealTransformer.p2.v basicTransformer.p2.i and idealTransformer.p2.i

Extends from Modelica.​Icons.​Example (Icon for runnable examples).

Parameters

TypeNameDefaultDescription
VoltageVdc0.1DC offset of voltage source
VoltageVpeak0.1Peak voltage of voltage source
Frequencyf10Frequency of voltage source
Anglephi00.5 * piPhase of voltage source
Realn2Turns ratio primary:secondary voltage
ResistanceR10.01Primary resistance w.r.t. primary side
InductanceL1sigma0.05 / (2 * pi * f)Primary leakage inductance w.r.t. primary side
InductanceLm110 / (2 * pi * f)Magnetizing inductance w.r.t. primary side
InductanceL2sigma0.05 / (2 * pi * f) / n ^ 2Secondary leakage inductance w.r.t. secondary side
ResistanceR20.01 / n ^ 2Secondary resistance w.r.t. secondary side
ResistanceRL(n ^ 2) ^ (-1)Load resistance
final InductanceL1L1sigma + M * nPrimary no-load inductance
final InductanceL2L2sigma + M / nSecondary no-load inductance
final InductanceMLm1 / nMutual inductance

Model Modelica.​Electrical.​Analog.​Examples.​ControlledSwitchWithArc
Comparison of controlled switch models both with and without arc

Information

This example is to compare the behaviour of switch models with and without an electric arc taking into consideration.

The difference in the closing area shows that the simple arc model avoids the suddenly switching.

Extends from Modelica.​Icons.​Example (Icon for runnable examples).


Model Modelica.​Electrical.​Analog.​Examples.​SimpleTriacCircuit
Simple triac test circuit

Information

The simple TRIAC example shows how the SimpleTriac is used within an alternating current circuit.

The TRIAC is not conducting until the Gate input g becomes positive. Then it becomes "conducting". If the TRIAC voltage changes its direction, the TRIAC becomes blocking. Due to the antiparallel connection of the internal two thyristors the same behavior is repeated in the negative half-wave.

Simulate until 0.001 seconds. Display V.p.v (input voltage), simpleTriac.g.i (gate input), and both simplelTriac.n.v and simpleTriac.n.i, which demonstrate the TRIAC behavior.

Extends from Modelica.​Icons.​Example (Icon for runnable examples).


Model Modelica.​Electrical.​Analog.​Examples.​IdealTriacCircuit
Ideal triac test circuit

Information

The simple ideal TRIAC example shows how a triac is used within an alternating current circuit.

The TRIAC is not conducting until the Boolean input becomes true (internally coded by 1, therefore the input is called fire1). Then it becomes "conducting", the knee voltage is reached. If the TRIAC voltage falls below the knee voltage, the TRIAC becomes blocking. Due to the antiparallel connection of the internal two thyristors the same behavior is repeated in the negative half-wave.

Simulate until 2 seconds. Display V.p.v (input voltage), booleanPulse.y (fire1 input), and both idealTriac.n.v and idealTriac.n.i, which demonstrate the TRIAC behavior.

Extends from Modelica.​Icons.​Example (Icon for runnable examples).


Model Modelica.​Electrical.​Analog.​Examples.​AD_DA_conversion
Conversion circuit

Information

The simple converter circuit converts an analog sine signal into a N-bit (by default a 4 bit) logic signal, which is converted backward into an analog signal.

Compare the input voltage (aD_Converter.p.v) with the output voltage (dA_Converter.p.v). By changing N the influence of the digital signal width can be studied. Otherwise the trigger frequency pulse.period can be changed to see its influence.

Extends from Modelica.​Icons.​Example (Icon for runnable examples).

Parameters

TypeNameDefaultDescription
IntegerN7Digital signal width

Model Modelica.​Electrical.​Analog.​Examples.​GenerationOfFMUs
Example to demonstrate variants to generate FMUs (Functional Mock-up Units)

Information

This example demonstrates how to generate an input/output block (e.g. in form of an FMU - Functional Mock-up Unit) from various Electrical components. The goal is to export such an input/output block from Modelica and import it in another modeling environment. The essential issue is that before exporting it must be known in which way the component is utilized in the target environment. Depending on the target usage, different connector variables need to be in the interface with either input or output causality. Note, this example model can be used to test the FMU export/import of a Modelica tool. Just export the components marked in the icons as "toFMU" as FMUs and import them back. The models should then still work and give the same results as a pure Modelica model.

Connecting two capacitors
The first part (DirectCapacitor, InverseCapacitor) demonstrates how to export two capacitors and connect them together in a target system. This requires that one of the capacitors (here: DirectCapacitor) is defined to have states and the voltage and derivative of voltage are provided in the interface. The other capacitor (here: InverseCapacitor) requires current according to the provided input voltage and derivative of voltage.

Connecting a resistance element between two capacitors
The second part (Resistor2) demonstrates how to export a resistance element that needs only voltages for its resistance law and connect this resistance law in a target system between two capacitors.

Connecting two inductors
The third part (DirectInductor, InverseInductor) demonstrates how to export two inductors and connect them together in a target system. This requires that one of the inductors (here: DirectInductor) is defined to have states and the current and derivative of current are provided in the interface. The other inductor (here: InverseInductor) requires voltage according to the provided input current and derivative of current.

Connecting a conductance element between two inductors
The fourth part (Conductor4) demonstrates how to export a conductance element that needs only currents for its conductance law and connect this conductance law in a target system between two inductors.

Bear in mind that separating physical components and connecting them via adaptor signals requires to place appropriate ground components to define electric potential within the subcircuits.

Extends from Modelica.​Icons.​Example (Icon for runnable examples).


Model Modelica.​Electrical.​Analog.​Examples.​ResonanceCircuits
Resonance circuits: example to demonstrate generation of FMUs (Functional Mock-up Units)

Information

This example demonstrates how to couple the components of a parallel resonance circuit (upper part) and a series resonance circuit (lower part) not directly but using adaptors between physical connectors and input/output signals. Taking into account which derivatives are required, these components can be exported as input/output blocks (e.g. in form of an FMU - Functional Mock-up Unit). Connecting these input/output blocks should give the same results as connecting the physical components directly.

Bear in mind that separating physical components and connecting them via adaptor signals requires to place appropriate ground components to define electric potential within the subcircuits.

Extends from Modelica.​Icons.​Example (Icon for runnable examples).

Parameters

TypeNameDefaultDescription
CapacitanceC0.01Capacitance
InductanceL0.01Inductance
final FrequencyfRes(2 * pi * sqrt(L * C)) ^ (-1)Source frequency
Realres1f/fResonanace
Frequencyfres * fResSource frequency

Model Modelica.​Electrical.​Analog.​Examples.​InvertingAmp
Inverting amplifier

Information

This is an inverting amplifier. Resistance R1 can be chosen, R2 is defined by the desired amplification k.

Extends from Modelica.​Icons.​Example (Icon for runnable examples).

Parameters

TypeNameDefaultDescription
VoltageVps15Positive supply
VoltageVns-15Negative supply
VoltageVin5Amplitude of input voltage
Frequencyf10Frequency of input voltage
Realk2Desired amplification
ResistanceR11000Arbitrary resistance
ResistanceR2k * R1Calculated resistance to reach desired amplification k

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