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CauerLowPassSC.mo
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CauerLowPassSC.mo
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within Modelica.Electrical.Analog.Examples;
model CauerLowPassSC "Cauer low-pass filter with operational amplifiers and switched capacitors"
extends Modelica.Icons.Example;
parameter SI.Capacitance l1=1.304 "Filter coefficient i1";
parameter SI.Capacitance l2=0.8586 "Filter coefficient i2";
parameter SI.Capacitance c1=1.072 "Filter coefficient c1";
parameter SI.Capacitance c2=1/(1.704992^2*l1)
"Filter coefficient c2";
parameter SI.Capacitance c3=1.682 "Filter coefficient c3";
parameter SI.Capacitance c4=1/(1.179945^2*l2)
"Filter coefficient c4";
parameter SI.Capacitance c5=0.7262 "Filter coefficient c5";
Modelica.Electrical.Analog.Basic.Capacitor C1(C=c1 + c2,v(start=0, fixed=true))
annotation (Placement(transformation(extent={{-193,30},{-173,50}})));
Modelica.Electrical.Analog.Basic.Capacitor C2(C=c2,v(start=0, fixed=true))
annotation (Placement(transformation(extent={{-241,-70},{-221,-50}})));
Modelica.Electrical.Analog.Basic.Capacitor C3(C=l1,v(start=0, fixed=true))
annotation (Placement(transformation(extent={{-91,30},{-71,50}})));
Modelica.Electrical.Analog.Basic.Capacitor C4(C=c4,v(start=0, fixed=true))
annotation (Placement(transformation(extent={{-31,50},{-11,70}})));
Modelica.Electrical.Analog.Basic.Capacitor C5(C=c2)
annotation (Placement(transformation(extent={{-31,-100},{-11,-80}})));
Modelica.Electrical.Analog.Ideal.IdealOpAmp3Pin Op1
annotation (Placement(transformation(extent={{-201,-50},{-161,-10}})));
Modelica.Electrical.Analog.Basic.Ground G
annotation (Placement(transformation(extent={{-189,-76},{-175,-60}})));
Modelica.Electrical.Analog.Ideal.IdealOpAmp3Pin Op2
annotation (Placement(transformation(extent={{-101,-50},{-61,-10}})));
Modelica.Electrical.Analog.Ideal.IdealOpAmp3Pin Op3
annotation (Placement(transformation(extent={{5,-50},{45,-10}})));
Modelica.Electrical.Analog.Basic.Ground G1
annotation (Placement(transformation(extent={{-88,-76},{-74,-60}})));
Modelica.Electrical.Analog.Basic.Capacitor C6(C=c2 + c3 + c4)
annotation (Placement(transformation(extent={{8,30},{28,50}})));
Modelica.Electrical.Analog.Ideal.IdealOpAmp3Pin Op4
annotation (Placement(transformation(extent={{99,-50},{139,-10}})));
Modelica.Electrical.Analog.Ideal.IdealOpAmp3Pin Op5
annotation (Placement(transformation(extent={{199,-50},{239,-10}})));
Modelica.Electrical.Analog.Basic.Capacitor C7(C=l2,v(start=0, fixed=true))
annotation (Placement(transformation(extent={{109,30},{129,50}})));
Modelica.Electrical.Analog.Basic.Capacitor C8(C=c4)
annotation (Placement(transformation(extent={{159,-130},{179,-110}})));
Modelica.Electrical.Analog.Basic.Capacitor C9(C=c4 + c5)
annotation (Placement(transformation(extent={{207,10},{227,30}})));
protected
Modelica.Electrical.Analog.Interfaces.NegativePin n1
annotation (Placement(transformation(extent={{-215,-22},{-211,-18}})));
protected
Modelica.Electrical.Analog.Interfaces.NegativePin n2
annotation (Placement(transformation(extent={{-215,18},{-211,22}})));
protected
Modelica.Electrical.Analog.Interfaces.NegativePin n3
annotation (Placement(transformation(extent={{-215,38},{-211,42}})));
protected
Modelica.Electrical.Analog.Interfaces.NegativePin n4
annotation (Placement(transformation(
origin={-161,40},
extent={{2,2},{-2,-2}},
rotation=180)));
protected
Modelica.Electrical.Analog.Interfaces.NegativePin n5
annotation (Placement(transformation(extent={{-115,-32},{-111,-28}})));
protected
Modelica.Electrical.Analog.Interfaces.PositivePin p1
annotation (Placement(transformation(extent={{-155,-122},{-149,-118}})));
protected
Modelica.Electrical.Analog.Interfaces.NegativePin n6
annotation (Placement(transformation(extent={{-63,38},{-59,42}})));
protected
Modelica.Electrical.Analog.Interfaces.NegativePin n7
annotation (Placement(transformation(extent={{-7,-32},{-3,-28}})));
protected
Modelica.Electrical.Analog.Interfaces.NegativePin n8
annotation (Placement(transformation(extent={{-7,18},{-3,22}})));
protected
Modelica.Electrical.Analog.Interfaces.PositivePin p2
annotation (Placement(transformation(extent={{-7,38},{-3,42}})));
protected
Modelica.Electrical.Analog.Interfaces.PositivePin out1
annotation (Placement(transformation(extent={{43,-122},{47,-118}})));
protected
Modelica.Electrical.Analog.Interfaces.PositivePin p3
annotation (Placement(transformation(extent={{57,78},{61,82}})));
protected
Modelica.Electrical.Analog.Interfaces.NegativePin n9
annotation (Placement(transformation(extent={{85,18},{89,22}})));
protected
Modelica.Electrical.Analog.Interfaces.NegativePin n10
annotation (Placement(transformation(extent={{85,-32},{89,-28}})));
protected
Modelica.Electrical.Analog.Interfaces.NegativePin n11
annotation (Placement(transformation(extent={{137,38},{141,42}})));
public
Modelica.Electrical.Analog.Basic.Ground G2
annotation (Placement(transformation(extent={{11,-76},{25,-60}})));
protected
Modelica.Electrical.Analog.Interfaces.NegativePin n12
annotation (Placement(transformation(extent={{237,58},{241,62}})));
protected
Modelica.Electrical.Analog.Interfaces.NegativePin n13
annotation (Placement(transformation(extent={{237,18},{241,22}})));
protected
Modelica.Electrical.Analog.Interfaces.PositivePin p4
annotation (Placement(transformation(extent={{187,18},{193,22}})));
protected
Modelica.Electrical.Analog.Interfaces.NegativePin n14
annotation (Placement(transformation(extent={{187,-32},{193,-28}})));
public
Modelica.Electrical.Analog.Basic.Ground G3
annotation (Placement(transformation(extent={{112,-76},{126,-60}})));
Modelica.Electrical.Analog.Basic.Ground G4
annotation (Placement(transformation(extent={{212,-76},{226,-60}})));
Modelica.Electrical.Analog.Sources.StepVoltage V(startTime=1, V=1)
annotation (Placement(transformation(
origin={-241,-150},
extent={{-10,-10},{10,10}},
rotation=90)));
Modelica.Electrical.Analog.Basic.Ground Ground1
annotation (Placement(transformation(extent={{-247,-182},{-235,-170}})));
Modelica.Electrical.Analog.Examples.Utilities.SwitchedCapacitor R4(clock=0.1, R=-1, Capacitor(v(start=0, fixed=true))) annotation (Placement(transformation(extent={{-140,-40},{
-120,-20}})));
Modelica.Electrical.Analog.Examples.Utilities.SwitchedCapacitor R5(clock=0.1, R=-1, Capacitor(v(start=0, fixed=true))) annotation (Placement(transformation(extent={{-140,-80},{
-120,-60}})));
Modelica.Electrical.Analog.Examples.Utilities.SwitchedCapacitor R8(clock=0.1, R=-1, Capacitor(v(start=0, fixed=true))) annotation (Placement(transformation(extent={{60,10},{80,30}})));
Modelica.Electrical.Analog.Examples.Utilities.SwitchedCapacitor R9(clock=0.1, R=-1, Capacitor(v(start=0, fixed=true))) annotation (Placement(transformation(extent={{60,-40},{80,
-20}})));
Modelica.Electrical.Analog.Examples.Utilities.SwitchedCapacitor R1(clock=0.1,
R=1, Capacitor(v(start=0, fixed=true))) annotation (Placement(transformation(extent={{-240,-30},{
-220,-10}})));
Modelica.Electrical.Analog.Examples.Utilities.SwitchedCapacitor R2(clock=0.1,
R=1, Capacitor(v(start=0, fixed=true))) annotation (Placement(transformation(extent={{-240,10},{-220,
30}})));
Modelica.Electrical.Analog.Examples.Utilities.SwitchedCapacitor R3(clock=0.1,
R=1, Capacitor(v(start=0, fixed=true))) annotation (Placement(transformation(extent={{-200,70},{-180,
90}})));
Modelica.Electrical.Analog.Examples.Utilities.SwitchedCapacitor Rp1(clock=0.1,
R=1, Capacitor(v(start=0, fixed=true))) annotation (Placement(transformation(extent={{-32,10},{-12,
30}})));
Modelica.Electrical.Analog.Examples.Utilities.SwitchedCapacitor R7(clock=0.1,
R=1, Capacitor(v(start=0, fixed=true))) annotation (Placement(transformation(extent={{-32,-40},{-12,
-20}})));
Modelica.Electrical.Analog.Examples.Utilities.SwitchedCapacitor R10(clock=0.1,
R=1, Capacitor(v(start=0, fixed=true))) annotation (Placement(transformation(extent={{160,-40},{180,
-20}})));
Modelica.Electrical.Analog.Examples.Utilities.SwitchedCapacitor R11(clock=0.1,
R=1, Capacitor(v(start=0, fixed=true))) annotation (Placement(transformation(extent={{208,50},{228,
70}})));
equation
connect(Op1.in_p,G. p) annotation (Line(points={{-201,-42},{-201,-50},{-181,-50},{-181,-60},{-182,-60}},
color={0,0,255}));
connect(G1.p,Op2. in_p) annotation (Line(points={{-81,-60},{-81,-50},{-101,-50},{-101,-42}},
color={0,0,255}));
connect(n1,Op1. in_n) annotation (Line(points={{-213,-20},{-208,-20},{-208,-18},{-201,-18}},
color={0,0,255}));
connect(C2.n,n1) annotation (Line(points={{-221,-60},{-213,-60},{-213,-20}}, color={0,0,255}));
connect(n1,n2)
annotation (Line(points={{-213,-20},{-213,20}}, color={0,0,255}));
connect(n2,n3)
annotation (Line(points={{-213,20},{-213,40}}, color={0,0,255}));
connect(n3,C1. p)
annotation (Line(points={{-213,40},{-193,40}}, color={0,0,255}));
connect(C1.n,n4)
annotation (Line(points={{-173,40},{-161,40}}, color={0,0,255}));
connect(n4,Op1. out) annotation (Line(points={{-161,40},{-161,-30}}, color={0,
0,255}));
connect(C5.p,Op1. out) annotation (Line(points={{-31,-90},{-161,-90},{-161,
-30}}, color={0,0,255}));
connect(n5,Op2. in_n) annotation (Line(points={{-113,-30},{-113,-18},{-101,-18}},
color={0,0,255}));
connect(C3.p,n5) annotation (Line(points={{-91,40},{-113,40},{-113,-30}}, color={0,0,255}));
connect(C2.p,p1) annotation (Line(points={{-241,-60},{-241,-120},{-152,-120}}, color={0,0,255}));
connect(C3.n,n6)
annotation (Line(points={{-71,40},{-61,40}}, color={0,0,255}));
connect(n6,Op2. out)
annotation (Line(points={{-61,40},{-61,-30}}, color={0,0,255}));
connect(n7,Op3. in_n) annotation (Line(points={{-5,-30},{-5,-18},{5,-18}}, color={0,0,255}));
connect(C5.n,n7) annotation (Line(points={{-11,-90},{-5,-90},{-5,-30}}, color={0,0,255}));
connect(n7,n8) annotation (Line(points={{-5,-30},{-5,20}}, color={0,0,255}));
connect(C6.p,p2)
annotation (Line(points={{8,40},{-5,40}}, color={0,0,255}));
connect(n8,p2)
annotation (Line(points={{-5,20},{-5,40}}, color={0,0,255}));
connect(C4.n,p2) annotation (Line(points={{-11,60},{-5,60},{-5,40}}, color={
0,0,255}));
connect(C6.n,Op3. out) annotation (Line(points={{28,40},{45,40},{45,-30}}, color={0,0,255}));
connect(Op3.out,out1)
annotation (Line(points={{45,-30},{45,-120}}, color={0,0,255}));
connect(p1,out1) annotation (Line(points={{-152,-120},{45,-120}}, color={0,0,
255}));
connect(out1,C8. p) annotation (Line(points={{45,-120},{159,-120}}, color={0,
0,255}));
connect(C4.p,p3) annotation (Line(points={{-31,60},{-41,60},{-41,80},{59,80}}, color={0,0,255}));
connect(n9,n10)
annotation (Line(points={{87,20},{87,-30}}, color={0,0,255}));
connect(n10,Op4. in_n) annotation (Line(points={{87,-30},{87,-18},{99,-18}}, color={0,0,255}));
connect(n9,C7. p) annotation (Line(points={{87,20},{87,40},{109,40}}, color={
0,0,255}));
connect(C7.n,n11)
annotation (Line(points={{129,40},{139,40}}, color={0,0,255}));
connect(n11,Op4. out)
annotation (Line(points={{139,40},{139,-30}}, color={0,0,255}));
connect(G2.p,Op3. in_p) annotation (Line(points={{18,-60},{5,-60},{5,-42}}, color={0,0,255}));
connect(p3,n12) annotation (Line(points={{59,80},{239,80},{239,60}}, color={
0,0,255}));
connect(C9.n,n13)
annotation (Line(points={{227,20},{239,20}}, color={0,0,255}));
connect(n12,n13)
annotation (Line(points={{239,60},{239,20}}, color={0,0,255}));
connect(n13,Op5. out)
annotation (Line(points={{239,20},{239,-30}}, color={0,0,255}));
connect(C9.p,p4)
annotation (Line(points={{207,20},{190,20}}, color={0,0,255}));
connect(p4,n14)
annotation (Line(points={{190,20},{190,-30}}, color={0,0,255}));
connect(Op5.in_n,n14) annotation (Line(points={{199,-18},{190,-18},{190,-30}}, color={0,0,255}));
connect(C8.n,n14) annotation (Line(points={{179,-120},{190,-120},{190,-30}}, color={0,0,255}));
connect(Op4.in_p,G3. p) annotation (Line(points={{99,-42},{99,-60},{119,-60}}, color={0,0,255}));
connect(Op5.in_p,G4. p) annotation (Line(points={{199,-42},{199,-60},{219,-60}}, color={0,0,255}));
connect(V.p, Ground1.p) annotation (Line(points={{-241,-160},{-241,
-170}}, color={0,0,255}));
connect(R4.n, n5) annotation (Line(
points={{-120,-30},{-116,-30},{-116,-30},{-113,-30}}, color={0,0,255}));
connect(Op1.out, R4.p) annotation (Line(
points={{-161,-30},{-140.2,-30}}, color={0,0,255}));
connect(R5.p, p1) annotation (Line(
points={{-140.2,-70},{-152,-70},{-152,-120}}, color={0,0,255}));
connect(R5.n, n5) annotation (Line(
points={{-120,-70},{-116,-70},{-116,-70},{-113,-70},{-113,-30}}, color={0,0,255}));
connect(p3, R8.p) annotation (Line(
points={{59,80},{59.8,80},{59.8,20}}, color={0,0,255}));
connect(R8.n, n9) annotation (Line(
points={{80,20},{84,20},{84,20},{87,20}}, color={0,0,255}));
connect(Op3.out, R9.p) annotation (Line(
points={{45,-30},{59.8,-30}}, color={0,0,255}));
connect(R9.n, n10) annotation (Line(
points={{80,-30},{84,-30},{84,-30},{87,-30}}, color={0,0,255}));
connect(R1.p, V.n) annotation (Line(
points={{-240.2,-20},{-250,-20},{-250,-130},{-241,-130},{-241,-140}}, color={0,0,255}));
connect(R1.n, n1) annotation (Line(
points={{-220,-20},{-216,-20},{-216,-20},{-213,-20}}, color={0,0,255}));
connect(R2.n, n2) annotation (Line(
points={{-220,20},{-218,20},{-218,20},{-213,20}}, color={0,0,255}));
connect(R2.p, n6) annotation (Line(
points={{-240.2,20},{-240,20},{-240,100},{-61,100},{-61,40}}, color={0,0,255}));
connect(R3.p, n3) annotation (Line(
points={{-200.2,80},{-213,80},{-213,40}}, color={0,0,255}));
connect(R3.n, n4) annotation (Line(
points={{-180,80},{-170,80},{-170,80},{-161,80},{-161,40}}, color={0,0,255}));
connect(Rp1.n, n8) annotation (Line(
points={{-12,20},{-8,20},{-8,20},{-5,20}}, color={0,0,255}));
connect(Rp1.p, n11) annotation (Line(
points={{-32.2,20},{-52,20},{-52,100},{139,100},{139,40}}, color={0,0,255}));
connect(Op2.out, R7.p) annotation (Line(
points={{-61,-30},{-32.2,-30}}, color={0,0,255}));
connect(R7.n, n7) annotation (Line(
points={{-12,-30},{-8,-30},{-8,-30},{-5,-30}}, color={0,0,255}));
connect(R10.p, Op4.out) annotation (Line(
points={{159.8,-30},{139,-30}}, color={0,0,255}));
connect(R10.n, n14) annotation (Line(
points={{180,-30},{186,-30},{186,-30},{190,-30}}, color={0,0,255}));
connect(R11.n, n12) annotation (Line(
points={{228,60},{234,60},{234,60},{239,60}}, color={0,0,255}));
connect(R11.p, p4) annotation (Line(
points={{207.8,60},{190,60},{190,20}}, color={0,0,255}));
annotation (Diagram(coordinateSystem(preserveAspectRatio=true, extent={{-250,
-200},{250,200}})),
experiment(StopTime=60, Interval=0.04),
Documentation(revisions="<html>
<ul>
<li><em>January 13, 2006</em>
by Christoph Clauss<br>
included into Modelica Standard Library</li>
<li><em>September 15, 2005</em>
by Peter Trappe designed and by Teresa Schlegel<br>
initially modelled.</li>
</ul>
</html>", info="<html>
<p>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.</p>
<p>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.</p>
<p>This model is identical to the CauerLowPassOPV example. But the resistors are realized by switched capacitors (see <a href=\"modelica://Modelica.Electrical.Analog.Examples.Utilities.SwitchedCapacitor\">SwitchedCapacitor</a>). There are two different types of instances, one with a value of <code>R=1</code> and one with a value of <code>R=-1</code>.</p>
<p>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.</p>
<p>Due to the recharging of the capacitances after switching the performance of simulation is not as good as in the CauerLowPassOPV example.</p>
</html>"));
end CauerLowPassSC;