Modelica.Electrical.Analog.Basic

Information

This package contains very basic analog electrical components such as resistor, conductor, condensator, inductor, and the ground (which is needed in each electrical circuit description. Furthermore, controlled sources, coupling components, and some improved (but nevertheless basic) are in this package.

Package Content

Name	Description
Ground	Ground node
Resistor	Ideal linear electrical resistor
HeatingResistor	Temperature dependent electrical resistor
Conductor	Ideal linear electrical conductor
Capacitor	Ideal linear electrical capacitor
Inductor	Ideal linear electrical inductor
SaturatingInductor	Simple model of an inductor with saturation
Transformer	Transformer with two ports
M_Transformer	Generic transformer with free number of inductors
Gyrator	Gyrator
EMF	Electromotoric force (electric/mechanic transformer)
TranslationalEMF	Electromotoric force (electric/mechanic transformer)
VCV	Linear voltage-controlled voltage source
VCC	Linear voltage-controlled current source
CCV	Linear current-controlled voltage source
CCC	Linear current-controlled current source
OpAmp	Simple nonideal model of an OpAmp with limitation
OpAmpDetailed	Detailed model of an operational amplifier
VariableResistor	Ideal linear electrical resistor with variable resistance
VariableConductor	Ideal linear electrical conductor with variable conductance
VariableCapacitor	Ideal linear electrical capacitor with variable capacitance
VariableInductor	Ideal linear electrical inductor with variable inductance

Modelica.Electrical.Analog.Basic.Ground

Information

Ground of an electrical circuit. The potential at the ground node is zero. Every electrical circuit has to contain at least one ground object.

Connectors

Name	Description
p

Modelica.Electrical.Analog.Basic.Resistor

Information

The linear resistor connects the branch voltage v with the branch current i by i*R = v. The Resistance R is allowed to be positive, zero, or negative.

Parameters

Name	Description
R	Resistance at temperature T_ref [Ohm]
T_ref	Reference temperature [K]
alpha	Temperature coefficient of resistance (R_actual = R*(1 + alpha*(T_heatPort - T_ref)) [1/K]
useHeatPort	=true, if HeatPort is enabled
T	Fixed device temperature if useHeatPort = false [K]

Connectors

Name	Description
p	Positive pin (potential p.v > n.v for positive voltage drop v)
n	Negative pin
heatPort

Modelica.Electrical.Analog.Basic.HeatingResistor

Information

This is a model for an electrical resistor where the generated heat is dissipated to the environment via connector heatPort and where the resistance R is temperature dependent according to the following equation:

    R = R_ref*(1 + alpha*(heatPort.T - T_ref))

alpha is the temperature coefficient of resistance, which is often abbreviated as TCR. In resistor catalogues, it is usually defined as X [ppm/K] (parts per million, similarly to percentage) meaning X*1.e-6 [1/K]. Resistors are available for 1 .. 7000 ppm/K, i.e., alpha = 1e-6 .. 7e-3 1/K;

Via parameter useHeatPort the heatPort connector can be enabled and disabled (default = enabled). If it is disabled, the generated heat is transported implicitly to an internal temperature source with a fixed temperature of T_ref.

If the heatPort connector is enabled, it must be connected.

Parameters

Name	Description
R_ref	Resistance at temperature T_ref [Ohm]
T_ref	Reference temperature [K]
alpha	Temperature coefficient of resistance (R = R_ref*(1 + alpha*(heatPort.T - T_ref)) [1/K]
useHeatPort	=true, if HeatPort is enabled
T	Fixed device temperature if useHeatPort = false [K]

Connectors

Name	Description
p	Positive pin (potential p.v > n.v for positive voltage drop v)
n	Negative pin
heatPort

Modelica.Electrical.Analog.Basic.Conductor

Information

The linear conductor connects the branch voltage v with the branch current i by i = v*G. The Conductance G is allowed to be positive, zero, or negative.

Parameters

Name	Description
G	Conductance at temperature T_ref [S]
T_ref	Reference temperature [K]
alpha	Temperature coefficient of conductance (G_actual = G_ref/(1 + alpha*(T_heatPort - T_ref)) [1/K]
useHeatPort	=true, if HeatPort is enabled
T	Fixed device temperature if useHeatPort = false [K]

Connectors

Name	Description
p	Positive pin (potential p.v > n.v for positive voltage drop v)
n	Negative pin
heatPort

Modelica.Electrical.Analog.Basic.Capacitor

Information

The linear capacitor connects the branch voltage v with the branch current i by i = C * dv/dt. The Capacitance C is allowed to be positive or zero.

Parameters

Name	Description
C	Capacitance [F]

Connectors

Name	Description
p	Positive pin (potential p.v > n.v for positive voltage drop v)
n	Negative pin

Modelica.Electrical.Analog.Basic.Inductor

Information

The linear inductor connects the branch voltage v with the branch current i by v = L * di/dt. The Inductance L is allowed to be positive, or zero.

Parameters

Name	Description
L	Inductance [H]

Connectors

Name	Description
p	Positive pin (potential p.v > n.v for positive voltage drop v)
n	Negative pin

Modelica.Electrical.Analog.Basic.SaturatingInductor

Information

This model approximates the behaviour of an inductor with the influence of saturation, i.e., the value of the inductance depends on the current flowing through the inductor. The inductance decreases as current increases.

The parameters are:

• Inom...nominal current
• Lnom...nominal inductance at nominal current
• Lzer...inductance near current = 0; Lzer has to be greater than Lnom
• Linf...inductance at large currents; Linf has to be less than Lnom

Parameters

Name	Description
Inom	Nominal current [A]
Lnom	Nominal inductance at Nominal current [H]
Lzer	Inductance near current=0 [H]
Linf	Inductance at large currents [H]

Connectors

Name	Description
p	Positive pin (potential p.v > n.v for positive voltage drop v)
n	Negative pin

Modelica.Electrical.Analog.Basic.Transformer

Information

The transformer is a two port. The left port voltage v1, left port current i1, right port voltage v2 and right port current i2 are connected by the following relation:

         | v1 |         | L1   M  |  | i1'; |
         |    |    =    |         |  |     |
         | v2 |         | M    L2 |  | i2'; |

L1, L2, and M are the primary, secondary, and coupling inductances respectively.

Parameters

Name	Description
L1	Primary inductance [H]
L2	Secondary inductance [H]
M	Coupling inductance [H]

Connectors

Name	Description
p1	Positive pin of the left port (potential p1.v > n1.v for positive voltage drop v1)
n1	Negative pin of the left port
p2	Positive pin of the right port (potential p2.v > n2.v for positive voltage drop v2)
n2	Negative pin of the right port

Modelica.Electrical.Analog.Basic.M_Transformer

Information

The model M_Transformer is a model of a transformer with the possibility to choose the number of inductors. Inside the model, an inductance matrix is built based on the inductance of the inductors and the coupling inductances between the inductors given as a parameter vector from the user of the model.

An example shows that approach:
The user chooses a model with three inductors, that means the parameter N has to be 3. Then he has to specify the inductances of the three inductors and the three coupling inductances. The coupling inductances are no real existing devices, but effects that occur between two inductors. The inductivities (main diagonal of the inductance matrix) and the coupling inductivities have to be specified in the parameter vector L. The length dimL of the parameter vector is calculated as follows: dimL=(N*(N+1))/2

The following example shows how the parameter vector is used to fill in the inductance matrix. To specify the inductance matrix of a three inductances transformer (N=3):

the user has to allocate the parameter vector L[6] , since Nv=(N*(N+1))/2=(3*(3+1))/2=6. The parameter vector must be filled like this: L=[1,0.1,0.2,2,0.3,3] .

Inside the model, two loops are used to fill the inductance matrix to guarantee that it is filled in a symmetric way.

Parameters

Name	Description
N	number of inductors
L[dimL]	inductances and coupling inductances [H]
Lm[N, N]	[H]

Connectors

Name	Description
p[N]	Positive pin
n[N]	Negative pin

Modelica.Electrical.Analog.Basic.Gyrator

Information

A gyrator is a two-port element defined by the following equations:

    i1 =  G2 * v2
    i2 = -G1 * v1

where the constants G1, G2 are called the gyration conductance.

Parameters

Name	Description
G1	Gyration conductance [S]
G2	Gyration conductance [S]

Connectors

Name	Description
p1	Positive pin of the left port (potential p1.v > n1.v for positive voltage drop v1)
n1	Negative pin of the left port
p2	Positive pin of the right port (potential p2.v > n2.v for positive voltage drop v2)
n2	Negative pin of the right port

Modelica.Electrical.Analog.Basic.EMF

Information

EMF transforms electrical energy into rotational mechanical energy. It is used as basic building block of an electrical motor. The mechanical connector flange can be connected to elements of the Modelica.Mechanics.Rotational library. flange.tau is the cut-torque, flange.phi is the angle at the rotational connection.

Parameters

Name	Description
useSupport	= true, if support flange enabled, otherwise implicitly grounded
k	Transformation coefficient [N.m/A]

Connectors

Name	Description
p
n
flange
support	Support/housing of emf shaft

Modelica.Electrical.Analog.Basic.TranslationalEMF

Information

EMF transforms electrical energy into translational mechanical energy. It is used as basic building block of an electrical linear motor. The mechanical connector flange can be connected to elements of the Modelica.Mechanics.Translational library. flange.f is the cut-force, flange.s is the distance at the translational connection.

Parameters

Name	Description
useSupport	= true, if support flange enabled, otherwise implicitly grounded
k	Transformation coefficient [N/A]

Connectors

Name	Description
p
n
flange
support	Support/housing

Modelica.Electrical.Analog.Basic.VCV

Information

The linear voltage-controlled voltage source is a TwoPort. The right port voltage v2 is controlled by the left port voltage v1 via

    v2 = v1 * gain. 

The left port current is zero. Any voltage gain can be chosen.

Parameters

Name	Description
gain	Voltage gain

Connectors

Name	Description
p1	Positive pin of the left port (potential p1.v > n1.v for positive voltage drop v1)
n1	Negative pin of the left port
p2	Positive pin of the right port (potential p2.v > n2.v for positive voltage drop v2)
n2	Negative pin of the right port

Modelica.Electrical.Analog.Basic.VCC

Information

The linear voltage-controlled current source is a TwoPort. The right port current i2 is controlled by the left port voltage v1 via

    i2 = v1 * transConductance. 

The left port current is zero. Any transConductance can be chosen.

Parameters

Name	Description
transConductance	Transconductance [S]

Connectors

Name	Description
p1	Positive pin of the left port (potential p1.v > n1.v for positive voltage drop v1)
n1	Negative pin of the left port
p2	Positive pin of the right port (potential p2.v > n2.v for positive voltage drop v2)
n2	Negative pin of the right port

Modelica.Electrical.Analog.Basic.CCV

Information

The linear current-controlled voltage source is a TwoPort. The right port voltage v2 is controlled by the left port current i1 via

    v2 = i1 * transResistance. 

The left port voltage is zero. Any transResistance can be chosen.

Parameters

Name	Description
transResistance	Transresistance [Ohm]

Connectors

Name	Description
p1	Positive pin of the left port (potential p1.v > n1.v for positive voltage drop v1)
n1	Negative pin of the left port
p2	Positive pin of the right port (potential p2.v > n2.v for positive voltage drop v2)
n2	Negative pin of the right port

Modelica.Electrical.Analog.Basic.CCC

Information

The linear current-controlled current source is a TwoPort. The right port current i2 is controlled by the left port current i1 via

    i2 = i1 * gain. 

The left port voltage is zero. Any current gain can be chosen.

Parameters

Name	Description
gain	Current gain

Connectors

Name	Description
p1	Positive pin of the left port (potential p1.v > n1.v for positive voltage drop v1)
n1	Negative pin of the left port
p2	Positive pin of the right port (potential p2.v > n2.v for positive voltage drop v2)
n2	Negative pin of the right port

Modelica.Electrical.Analog.Basic.OpAmp

Information

The OpAmp is a simple nonideal model with a smooth out.v = f(vin) characteristic, where "vin = in_p.v - in_n.v". The characteristic is limited by VMax.v and VMin.v. Its slope at vin=0 is the parameter Slope, which must be positive. (Therefore, the absolute value of Slope is taken into calculation.)

Parameters

Name	Description
Slope	Slope of the out.v/vin characteristic at vin=0

Connectors

Name	Description
in_p	Positive pin of the input port
in_n	Negative pin of the input port
out	Output pin
VMax	Positive output voltage limitation
VMin	Negative output voltage limitation

Modelica.Electrical.Analog.Basic.OpAmpDetailed

Information

The OpAmpDetailed model is a general operational amplifier model. The emphasis is on separating each important data sheet parameter into a sub-circuit independent of the other parameters. The model is broken down into five functional stages input, frequency response, gain, slew rate and an output stage. Each stage contains data sheet parameters to be modeled. This partitioning and the modelling of the separate submodels are based on the description in [CP92].

Using [CP92] Joachim Haase (Fraunhofer Institute for Integrated Circuits, Design Automation Division) transferred 2001 operational amplifier models into VHDL-AMS. Now one of these models, the model "amp(macro)" was transferred into Modelica.

Reference:

[CP92] Conelly, J.A.; Choi, P.: Macromodelling with SPICE. Englewood Cliffs: Prentice-Hall, 1992

Parameters

Name	Description
Rdm	Input resistance (differential input mode) [Ohm]
Rcm	Input resistance (common mode) [Ohm]
Cin	Input capacitance [F]
Vos	Input offset voltage [V]
Ib	Input bias current [A]
Ios	Input offset current [A]
vcp	Correction value for limiting by p_supply [V]
vcm	Correction value for limiting by msupply [V]
Avd0	Differential amplifier [dB]
CMRR	Common-mode rejection [dB]
fp1	Dominant pole [Hz]
fp2	Pole frequency [Hz]
fp3	Pole frequency [Hz]
fp4	Pole frequency [Hz]
fz	Zero frequency [Hz]
sr_p	Slew rate for increase [V/s]
sr_m	Slew rate for decrease [V/s]
Rout	Output resistance [Ohm]
Imaxso	Maximal output current (source current) [A]
Imaxsi	Maximal output current (sink current) [A]
Ts	sampling time [s]

Connectors

Name	Description
p	Positive pin of the input port
m	Negative pin of the input port
outp	Output pin
p_supply	Positive output voltage limitation
m_supply	Negative output voltage limitation

Modelica.Electrical.Analog.Basic.VariableResistor

Information

The linear resistor connects the branch voltage v with the branch current i by
i*R = v
The Resistance R is given as input signal.

Attention!!!
It is recommended that the R signal should not cross the zero value. Otherwise depending on the surrounding circuit the probability of singularities is high.

Parameters

Name	Description
T_ref	Reference temperature [K]
alpha	Temperature coefficient of resistance (R_actual = R*(1 + alpha*(T_heatPort - T_ref)) [1/K]
useHeatPort	=true, if HeatPort is enabled
T	Fixed device temperature if useHeatPort = false [K]

Connectors

Name	Description
p	Positive pin (potential p.v > n.v for positive voltage drop v)
n	Negative pin
heatPort
R	[Ohm]

Modelica.Electrical.Analog.Basic.VariableConductor

Information

The linear conductor connects the branch voltage v with the branch current i by
i = G*v
The Conductance G is given as input signal.

Attention!!!
It is recommended that the G signal should not cross the zero value. Otherwise depending on the surrounding circuit the probability of singularities is high.

Parameters

Name	Description
T_ref	Reference temperature [K]
alpha	Temperature coefficient of conductance (G_actual = G/(1 + alpha*(T_heatPort - T_ref)) [1/K]
useHeatPort	=true, if HeatPort is enabled
T	Fixed device temperature if useHeatPort = false [K]

Connectors

Name	Description
p	Positive pin (potential p.v > n.v for positive voltage drop v)
n	Negative pin
heatPort
G	[S]

Modelica.Electrical.Analog.Basic.VariableCapacitor

Information

The linear capacitor connects the branch voltage v with the branch current i by
i = dQ/dt with Q = C * v.
The capacitance C is given as input signal. It is required that C ≥ 0, otherwise an assertion is raised. To avoid a variable index system, C = Cmin, if 0 ≤ C < Cmin, where Cmin is a parameter with default value Modelica.Constants.eps.

Besides the Cmin parameter the capacitor model has got the two parameters IC and UIC that belong together. With the IC parameter the user can specify an initial value of the voltage over the capacitor, which is defined from positive pin p to negative pin n (v=p.v - n.v).

Hence the capacitor is charged at the beginning of the simulation. The other parameter UIC is of type Boolean. If UIC is true, the simulation tool uses

the IC value at the initial calculation by adding the equation v= IC. If UIC is false, the IC value can be used (but it does not need to!) to calculate the initial values in order to simplify the numerical algorithms of initial calculation.

Parameters

Name	Description
Cmin	lower bound for variable capacitance [F]
IC	Initial Value [V]
UIC

Connectors

Name	Description
p	Positive pin (potential p.v > n.v for positive voltage drop v)
n	Negative pin
C	[F]

Modelica.Electrical.Analog.Basic.VariableInductor

Information

The linear inductor connects the branch voltage v with the branch current i by
v = d Psi/dt with Psi = L * i .
The inductance L is as input signal. It is required that L ≥ 0, otherwise an assertion is raised. To avoid a variable index system, L = Lmin, if 0 ≤ L < Lmin, where Lmin is a parameter with default value Modelica.Constants.eps.

Besides the Lmin parameter the inductor model has got the two parameters IC and UIC that belong together. With the IC parameter the user can specify an initial value of the current that flows through the inductor.

Hence the inductor has an initial current at the beginning of the simulation. The other parameter UIC is of type Boolean. If UIC is true, the simulation tool uses

the IC value at the initial calculation by adding the equation i= IC. If UIC is false, the IC value can be used (but it does not need to!) to calculate the initial values in order to simplify the numerical algorithms of initial calculation.

Parameters

Name	Description
Lmin	lower bound for variable inductance [H]
IC	Initial Value [A]
UIC

Connectors

Name	Description
p	Positive pin (potential p.v > n.v for positive voltage drop v)
n	Negative pin
L	[H]