Redesign ChuaCircuit and add ChuaDiode

Modelica/Electrical/Analog/Examples/ChuaCircuit.mo

@@ -1,66 +1,100 @@
 within Modelica.Electrical.Analog.Examples;
-model ChuaCircuit "Chua's circuit, ns, V, A"
+model ChuaCircuit "Chua's circuit"
   extends Modelica.Icons.Example;
-
-  Modelica.Electrical.Analog.Basic.Inductor L(L=18, i(start=0, fixed=true)) annotation (Placement(transformation(
-        origin={-75,38},
-        extent={{-25,-25},{25,25}},
+  parameter Modelica.Units.SI.Resistance R=1900 "Try R={1850,1800,1750}";
+  SI.Voltage v1(start=+2.764331, fixed=true)=c1.v "Result: c1.v";
+  SI.Voltage v2(start=+0.744123, fixed=true)=c2.v "Result: c2.v";
+  Modelica.Electrical.Analog.Basic.Inductor inductor(i(fixed=true, start=0), L=18e-3)
+    annotation (Placement(transformation(
+        origin={-50,20},
+        extent={{-10,-10},{10,10}},
         rotation=270)));
-  Modelica.Electrical.Analog.Basic.Resistor Ro(R=12.5e-3) annotation (Placement(transformation(
-        origin={-75,-17},
-        extent={{-25,-25},{25,25}},
+  Modelica.Electrical.Analog.Basic.Resistor rL(R=14) annotation (Placement(transformation(
+        origin={-50,-20},
+        extent={{-10,-10},{10,10}},
         rotation=270)));
-  Modelica.Electrical.Analog.Basic.Conductor G(G=0.565) annotation (Placement(transformation(extent={{-25,38},
-            {25,88}})));
-  Modelica.Electrical.Analog.Basic.Capacitor C1(C=10, v(start=4, fixed=true)) annotation (Placement(transformation(
-        origin={25,3},
-        extent={{-25,-25},{25,25}},
+  Modelica.Electrical.Analog.Basic.Resistor resistor(R=R)    annotation (
+      Placement(transformation(
+        extent={{-10,-10},{10,10}},
+        rotation=0,
+        origin={0,40})));
+  Modelica.Electrical.Analog.Basic.Capacitor c1(C=10e-9)
+    annotation (Placement(transformation(
+        origin={20,0},
+        extent={{-10,-10},{10,10}},
         rotation=270)));
-  Modelica.Electrical.Analog.Basic.Capacitor C2(C=100, v(start=0, fixed=true)) annotation (Placement(transformation(
-        origin={-25,3},
-        extent={{-25,-25},{25,25}},
+  Modelica.Electrical.Analog.Basic.Capacitor c2(C=100e-9)
+    annotation (Placement(transformation(
+        origin={-20,0},
+        extent={{-10,-10},{10,10}},
         rotation=270)));
-  Modelica.Electrical.Analog.Examples.Utilities.NonlinearResistor Nr(
-    Ga(min=-1) = -0.757576,
-    Gb(min=-1) = -0.409091,
-    Ve=1) annotation (Placement(transformation(
-        origin={75,3},
-        extent={{-25,-25},{25,25}},
+  Modelica.Electrical.Analog.Examples.Utilities.NonlinearResistor chuasDiode(
+    Ga(min=-1) = -757.7576e-6,
+    Gb(min=-1) = -409.0909e-6,
+    Ve=1)     annotation (Placement(transformation(
+        origin={50,0},
+        extent={{-10,-10},{10,10}},
         rotation=270)));
-  Modelica.Electrical.Analog.Basic.Ground Gnd annotation (Placement(transformation(extent={{-25,-112},{25,
-            -62}})));
+  Modelica.Electrical.Analog.Basic.Ground Gnd annotation (Placement(transformation(extent={{-10,-60},
+            {10,-40}})));
 equation
-  connect(L.n, Ro.p) annotation (Line(points={{-75,13},{-75,8}}));
-  connect(C2.p, G.p) annotation (Line(
-      points={{-25,28},{-25,45.5},{-25,45.5},{-25,63}}, color={0,0,255}));
-  connect(L.p, G.p) annotation (Line(
-      points={{-75,63},{-25,63}}, color={0,0,255}));
-  connect(G.n, Nr.p) annotation (Line(
-      points={{25,63},{75,63},{75,28}}, color={0,0,255}));
-  connect(C1.p, G.n) annotation (Line(
-      points={{25,28},{25,45.5},{25,45.5},{25,63}}, color={0,0,255}));
-  connect(Ro.n, Gnd.p) annotation (Line(
-      points={{-75,-42},{-75,-62},{0,-62}}, color={0,0,255}));
-  connect(C2.n, Gnd.p) annotation (Line(
-      points={{-25,-22},{-24,-22},{-24,-62},{0,-62}}, color={0,0,255}));
-  connect(Gnd.p, C1.n) annotation (Line(
-      points={{0,-62},{25,-62},{25,-22}}, color={0,0,255}));
-  connect(Gnd.p, Nr.n) annotation (Line(
-      points={{0,-62},{75,-62},{75,-22}}, color={0,0,255}));
+  connect(inductor.n, rL.p) annotation (Line(points={{-50,10},{-50,-10}}));
+  connect(c2.p, resistor.p)
+    annotation (Line(points={{-20,10},{-20,40},{-10,40}},
+                                                 color={0,0,255}));
+  connect(inductor.p, resistor.p)
+    annotation (Line(points={{-50,30},{-50,40},{-10,40}},
+                                                 color={0,0,255}));
+  connect(resistor.n, chuasDiode.p)
+    annotation (Line(points={{10,40},{50,40},{50,10}}, color={0,0,255}));
+  connect(c1.p, resistor.n)
+    annotation (Line(points={{20,10},{20,40},{10,40}},
+                                               color={0,0,255}));
+  connect(rL.n, Gnd.p) annotation (Line(
+      points={{-50,-30},{-50,-40},{0,-40}}, color={0,0,255}));
+  connect(c2.n, Gnd.p) annotation (Line(
+      points={{-20,-10},{-20,-40},{0,-40}},           color={0,0,255}));
+  connect(Gnd.p,c1. n) annotation (Line(
+      points={{0,-40},{20,-40},{20,-10}}, color={0,0,255}));
+  connect(Gnd.p, chuasDiode.n)
+    annotation (Line(points={{0,-40},{50,-40},{50,-10}}, color={0,0,255}));
   annotation (
+    experiment(
+      StopTime=0.1,
+      Interval=1e-06,
+      Tolerance=1e-06),
+    Diagram(coordinateSystem(preserveAspectRatio=true,  extent={{-100,-100},{
+            100,100}})),
     Documentation(info="<html>
-<p>Chua&#39;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&#39;s diode. The chaotic behaviour is simulated.</p>
-<p>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 .</p>
+<p>This is a remake of the original implementation using realistic parameters for the components.</p>
+<p>Chua&#39;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&#39;s diode. </p>
+<p>It is possible to implement the nonlinear Chua&#39;s diode with two circuits called <a href=\"modelica://Modelica.Electrical.Analog.Examples.ChuaDiode\">NIC</a> 
+(negative impedance converter) using each an operational amplifier.</p>
+<p>
+The default paremeterization shows periodic behaviour at least after initial transients have vanished.<br>
+In the periodic region two attractors exist: Try initialization for v1 and v2 with exact negative values.<br>
+To investigate the path to chaos set (one after the other) R = {1900, 1850, 1800, 1750} Ohm and plot v2 vs. v1 as independent variable.<br>
+</p>
 <p><strong>Reference:</strong></p>
-<p>Kennedy, M.P.: Three Steps to Chaos - Part I: Evolution. IEEE Transactions on CAS I 40 (1993)10, 640-656</p>
+<ul>
+<li>Leon O. Chua, Chai Wah Wu, Anshan Huang and Guo-Qun Zhong: 
+    A Universal Circuit for Studying and Generating Chaos - Part I: Routes to Chaos. 
+    IEEE Transactions on Circuits and Systems, Vol. 40 (1993) 10, 732-744</li>
+<li>Michael Peter Kennedy: 
+    Three Steps to Chaos - Part I: Evolution. 
+    IEEE Transactions on Circuits and Systems, Vol. 40 (1993)10, 640-656</li>
+<li>Guo-Qun Zhong and F. Ayrom: 
+    Periodicity and Chaos in Chua&#39;s Circuit. 
+    IEEE Transactions on Circuits and Systems, Vol. 32 (1985) 5, 501-503</li>
+</ul>
 </html>",
    revisions="<html>
 <dl>
 <dt>
 <strong>Main Authors:</strong>
 </dt>
 <dd>
-Christoph Clau&szlig;
+    Christoph Clau&szlig;
     &lt;<a href=\"mailto:[email protected]\">[email protected]</a>&gt;<br>
     Andr&eacute; Schneider
     &lt;<a href=\"mailto:[email protected]\">[email protected]</a>&gt;<br>
@@ -69,9 +103,15 @@ Christoph Clau&szlig;
     Zeunerstra&szlig;e 38<br>
     D-01069 Dresden<br>
 </dd>
+<dt>
+<strong>Revision 2025:</strong>
+</dt>
+<dd>
+    Prof. Anton Haumer
+    &lt;<a href=\"mailto:[email protected]\">[email protected]</a>&gt;<br>
+    Estbavarian Technical University of Applied Sciences Regensburg<br>
+    D-93053 Regensburg, Germany<br>
+</dd>
 </dl>
-</html>"),
-    experiment(StopTime=5e4, Interval=1),
-    Diagram(coordinateSystem(preserveAspectRatio=true,  extent={{-100,-100},{
-            100,100}})));
+</html>"));
 end ChuaCircuit;

Modelica/Electrical/Analog/Examples/ChuaDiode.mo

@@ -0,0 +1,127 @@
+within Modelica.Electrical.Analog.Examples;
+model ChuaDiode "Demonstrate Chuas Diode"
+  extends Modelica.Icons.Example;
+  parameter SI.Voltage Vs=7.66667 "Supply voltage";
+  //NIC1+2
+  parameter SI.Resistance R1=220 "Pos. and neg. feedback resistance of NIC1";
+  parameter SI.Resistance Rg1=2200 "Resistance to ground of NIC1";
+  parameter SI.Resistance R2=22000 "Pos. and neg. feedback resistance of NIC2";
+  parameter SI.Resistance Rg2=3300 "Resistance to ground of NIC2";
+  //Results for NIC1+2
+  parameter SI.Voltage VLim1=Vs*Rg1/(Rg1 + R1) "NIC1: Left and right corner voltage";
+  parameter SI.Conductance gPos1=1/R1 "NIC1: Positive differential conductance";
+  parameter SI.Conductance gNeg1=-1/Rg1 "NIC1: Negative (inner) conductance";
+  parameter SI.Voltage VLim2=Vs*Rg2/(Rg2 + R2) "NIC2: Left and right corner voltage";
+  parameter SI.Conductance gPos2=1/R2 "NIC2: Positive differential conductance";
+  parameter SI.Conductance gNeg2=-1/Rg2 "NIC2: Negative (inner) conductance";
+  //Results for Chuas Diode
+  parameter SI.Conductance Ga=gNeg1 + gNeg2 "CHUA: Inner slope";
+  parameter SI.Voltage Ve=min(VLim1, VLim2) "CHUA: Inner limit";
+  parameter SI.Conductance Gb=if VLim1<VLim2 then gPos1 + gNeg2 else gNeg1 + gPos2
+    "CHUA: Intermediate slope";
+  parameter SI.Voltage Vp=max(VLim1, VLim2) "CHUA: Outer limit";
+  parameter SI.Conductance Gc=gPos1 + gPos2 "CHUA: Outer slope";
+  Modelica.Electrical.Analog.Basic.Resistor rPos1(R=R1) annotation (Placement(
+        transformation(
+        extent={{-10,-10},{10,10}},
+        rotation=0,
+        origin={-70,40})));
+  Modelica.Electrical.Analog.Ideal.OpAmpLimited opAmp1(Vps=+Vs, Vns=-Vs) annotation (Placement(
+        transformation(
+        extent={{10,10},{-10,-10}},
+        rotation=0,
+        origin={-70,10})));
+  Modelica.Electrical.Analog.Basic.Resistor rNeg1(R=R1) annotation (Placement(
+        transformation(extent={{-80,-10},{-60,-30}}, rotation=0)));
+  Modelica.Electrical.Analog.Basic.Resistor rg1(R=Rg1, i(start=0))  annotation (Placement(
+        transformation(
+        extent={{-10,-10},{10,10}},
+        rotation=270,
+        origin={-60,-40})));
+  Modelica.Electrical.Analog.Basic.Resistor rPos2(R=R2) annotation (Placement(
+        transformation(
+        extent={{10,-10},{-10,10}},
+        rotation=0,
+        origin={-30,40})));
+  Modelica.Electrical.Analog.Ideal.OpAmpLimited opAmp2(Vps=+Vs, Vns=-Vs) annotation (Placement(
+        transformation(
+        extent={{-10,10},{10,-10}},
+        rotation=0,
+        origin={-30,10})));
+  Modelica.Electrical.Analog.Basic.Resistor rNeg2(R=R2) annotation (Placement(
+        transformation(extent={{-20,-10},{-40,-30}}, rotation=0)));
+  Modelica.Electrical.Analog.Basic.Resistor rg2(R=Rg2, i(start=0))  annotation (Placement(
+        transformation(
+        extent={{-10,10},{10,-10}},
+        rotation=270,
+        origin={-40,-40})));
+  Modelica.Electrical.Analog.Basic.Ground ground
+    annotation (Placement(transformation(extent={{-10,-80},{10,-60}})));
+  Modelica.Electrical.Analog.Sources.SineVoltage source(V=8,    f=10)
+    annotation (Placement(transformation(extent={{-10,-10},{10,10}}, rotation=270)));
+  Modelica.Electrical.Analog.Sensors.CurrentSensor currentSensorA
+    annotation (Placement(transformation(extent={{-20,70},{-40,50}})));
+  Modelica.Electrical.Analog.Sensors.CurrentSensor currentSensorB
+    annotation (Placement(transformation(extent={{20,70},{40,50}})));
+  Modelica.Electrical.Analog.Examples.Utilities.NonlinearResistor chuasDiode(
+    Ga(min=-1) = Ga,
+    Gb(min=-1) = Gb,
+    Ve=Ve)    annotation (Placement(transformation(
+        origin={50,0},
+        extent={{-10,-10},{10,10}},
+        rotation=270)));
+equation
+  connect(opAmp1.in_n, rNeg1.n)
+    annotation (Line(points={{-60,4},{-60,-20}},  color={0,0,255}));
+  connect(opAmp1.out, rNeg1.p)
+    annotation (Line(points={{-80,10},{-80,-20}},color={0,0,255}));
+  connect(opAmp1.out, rPos1.p)
+    annotation (Line(points={{-80,10},{-80,40}},color={0,0,255}));
+  connect(opAmp1.in_p, rPos1.n)
+    annotation (Line(points={{-60,16},{-60,40}},color={0,0,255}));
+  connect(rNeg1.n, rg1.p)
+    annotation (Line(points={{-60,-20},{-60,-30}}, color={0,0,255}));
+  connect(opAmp2.out, rNeg2.p)
+    annotation (Line(points={{-20,10},{-20,-20}},color={0,0,255}));
+  connect(opAmp2.in_n, rNeg2.n)
+    annotation (Line(points={{-40,4},{-40,-20}},  color={0,0,255}));
+  connect(rPos2.n, opAmp2.in_p)
+    annotation (Line(points={{-40,40},{-40,16}},color={0,0,255}));
+  connect(rNeg2.n, rg2.p)
+    annotation (Line(points={{-40,-20},{-40,-30}}, color={0,0,255}));
+  connect(rPos2.p, opAmp2.out)
+    annotation (Line(points={{-20,40},{-20,10}},color={0,0,255}));
+  connect(source.n, ground.p)
+    annotation (Line(points={{0,-10},{0,-60}}, color={0,0,255}));
+  connect(rg1.n, ground.p)
+    annotation (Line(points={{-60,-50},{-50,-50},{-50,-60},{0,-60}},
+                                                           color={0,0,255}));
+  connect(ground.p, rg2.n)
+    annotation (Line(points={{0,-60},{-50,-60},{-50,-50},{-40,-50}},
+                                                           color={0,0,255}));
+  connect(currentSensorA.p, source.p)
+    annotation (Line(points={{-20,60},{0,60},{0,10}}, color={0,0,255}));
+  connect(currentSensorA.n, rPos2.n) annotation (Line(points={{-40,60},{-50,60},
+          {-50,40},{-40,40}},          color={0,0,255}));
+  connect(rPos1.n, rPos2.n) annotation (Line(points={{-60,40},{-40,40}},
+                     color={0,0,255}));
+  connect(source.p, currentSensorB.p)
+    annotation (Line(points={{0,10},{0,60},{20,60}}, color={0,0,255}));
+  connect(currentSensorB.n, chuasDiode.p)
+    annotation (Line(points={{40,60},{50,60},{50,10}}, color={0,0,255}));
+  connect(ground.p, chuasDiode.n)
+    annotation (Line(points={{0,-60},{50,-60},{50,-10}}, color={0,0,255}));
+  annotation (experiment(
+      StopTime=1.0,
+      Interval=0.001,
+      Tolerance=1e-06), Documentation(info="<html>
+<p>
+This example demonstrates how <a href=\"modelica://Modelica.Electrical.Analog.Examples.ChuaCircuit\">Chua&#39;s diode</a> can be implemented two OpAmp-circuits called NIC
+(negative impedance converter) using each an operational amplifier. The relations between the parameters of the OpAmp-circuit and the 
+ideal <a href=\"modelica://Modelica.Electrical.Analog.Examples.Utilities.NonlinearResistor\">nonlinear resistor</a> can be seen from the parameter calculations in the text layer.
+</p>
+<p>Plot <code>currentSensorA.i</code> and <code>currentSensorB.i</code> versus <code>source.v</code> to inspect the characteristic.</p>
+<p><strong>Note:</strong><br>
+The implementation using 2 NICs shows an outer positive slope which is not present in the ideal nonlinear resistor.</p>
+</html>"));
+end ChuaDiode;

Modelica/Electrical/Analog/Examples/package.order

@@ -4,6 +4,7 @@ CauerLowPassSC
 CharacteristicIdealDiodes
 CharacteristicThyristors
 ChuaCircuit
+ChuaDiode
 DifferenceAmplifier
 HeatingMOSInverter
 HeatingNPN_NORGate

Modelica/Resources/Reference/Modelica/Electrical/Analog/Examples/ChuaCircuit/comparisonSignals.txt

@@ -1,4 +1,4 @@
 time
-C1.v
-C2.v
-L.i
+v1
+v2
+inductor.i

Modelica/Resources/Reference/Modelica/Electrical/Analog/Examples/ChuaDiode/comparisonSignals.txt

@@ -0,0 +1,3 @@
+time
+currentSensorA.i
+currentSensorB.i