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Pi $CellContext`f; $CellContext`tau1 = ( Subscript[$CellContext`\[Tau], 1] = $CellContext`L2/$CellContext`R1$$); $CellContext`tau2 = ( Subscript[$CellContext`\[Tau], 2] = $CellContext`R2$$ $CellContext`C1); $CellContext`wc1 = 1/$CellContext`tau1; $CellContext`wc2 = 1/$CellContext`tau2; $CellContext`logwmin = Log[10, Min[{$CellContext`wc1, $CellContext`wc2}]] - 2; $CellContext`logwmax = Log[10, Max[{$CellContext`wc1, $CellContext`wc2}]] + 2; $CellContext`max1 = $CellContext`R0$$ + $CellContext`R2$$; \ $CellContext`max2 = If[(($CellContext`R1$$ - $CellContext`R2$$) Subscript[$CellContext`\[Tau], 1]^2 Subscript[$CellContext`\[Tau], 2]^2 + ($CellContext`R1$$ $CellContext`R2$$ Subscript[$CellContext`\[Tau], 2]^2 ( Subscript[$CellContext`\[Tau], 1]^3 - Subscript[$CellContext`\[Tau], 1] Subscript[$CellContext`\[Tau], 2]^2)^2)^ Rational[1, 2])/($CellContext`R2$$ Subscript[$CellContext`\[Tau], 1]^4 Subscript[$CellContext`\[Tau], 2]^2 - $CellContext`R1$$ Subscript[$CellContext`\[Tau], 1]^2 Subscript[$CellContext`\[Tau], 2]^4) > 0, $CellContext`R0$$ + (($CellContext`R1$$ + $CellContext`R2$$) Subscript[$CellContext`\[Tau], 1]^2 ( Subscript[$CellContext`\[Tau], 1]^2 - Subscript[$CellContext`\[Tau], 2]^2) - 2 ($CellContext`R1$$ $CellContext`R2$$ Subscript[$CellContext`\[Tau], 2]^2 ( Subscript[$CellContext`\[Tau], 1]^3 - Subscript[$CellContext`\[Tau], 1] Subscript[$CellContext`\[Tau], 2]^2)^2)^Rational[1, 2])/( Subscript[$CellContext`\[Tau], 1]^2 - Subscript[$CellContext`\[Tau], 2]^2)^2, 0]; $CellContext`max3 = If[(($CellContext`R1$$ - $CellContext`R2$$) Subscript[$CellContext`\[Tau], 1]^2 Subscript[$CellContext`\[Tau], 2]^2 - ($CellContext`R1$$ $CellContext`R2$$ Subscript[$CellContext`\[Tau], 2]^2 ( Subscript[$CellContext`\[Tau], 1]^3 - Subscript[$CellContext`\[Tau], 1] Subscript[$CellContext`\[Tau], 2]^2)^2)^ Rational[1, 2])/($CellContext`R2$$ Subscript[$CellContext`\[Tau], 1]^4 Subscript[$CellContext`\[Tau], 2]^2 - $CellContext`R1$$ Subscript[$CellContext`\[Tau], 1]^2 Subscript[$CellContext`\[Tau], 2]^4) > 0, $CellContext`R0$$ + (($CellContext`R1$$ + $CellContext`R2$$) Subscript[$CellContext`\[Tau], 1]^2 ( Subscript[$CellContext`\[Tau], 1]^2 - Subscript[$CellContext`\[Tau], 2]^2) + 2 ($CellContext`R1$$ $CellContext`R2$$ Subscript[$CellContext`\[Tau], 2]^2 ( Subscript[$CellContext`\[Tau], 1]^3 - Subscript[$CellContext`\[Tau], 1] Subscript[$CellContext`\[Tau], 2]^2)^2)^Rational[1, 2])/( Subscript[$CellContext`\[Tau], 1]^2 - Subscript[$CellContext`\[Tau], 2]^2)^2, 0]; $CellContext`max = Max[{$CellContext`R0$$ + $CellContext`R1$$, $CellContext`R0$$ + \ $CellContext`R2$$, $CellContext`max2, $CellContext`max3}]; $CellContext`cond = Or[ And[(-$CellContext`L2) $CellContext`R1$$^2 + $CellContext`C1 \ $CellContext`R1$$^2 $CellContext`R2$$^2 > 0, (-$CellContext`C1) $CellContext`L2^2 $CellContext`R2$$^2 + \ $CellContext`C1^2 $CellContext`L2 $CellContext`R1$$^2 $CellContext`R2$$^2 > 0], And[(-$CellContext`L2) $CellContext`R1$$^2 + $CellContext`C1 \ $CellContext`R1$$^2 $CellContext`R2$$^2 < 0, (-$CellContext`C1) $CellContext`L2^2 $CellContext`R2$$^2 + \ $CellContext`C1^2 $CellContext`L2 $CellContext`R1$$^2 $CellContext`R2$$^2 < 0]]; ParametricPlot[ Evaluate[{{ Re[ $CellContext`Z[I 10^$CellContext`logw]], -Im[ $CellContext`Z[ I 10^$CellContext`logw]]}}], {$CellContext`logw, \ $CellContext`logwmin, $CellContext`logwmax}, Epilog -> { AbsolutePointSize[5], Point[{$CellContext`R0$$, 0}], If[$CellContext`cond, Point[{($CellContext`C1 $CellContext`R0$$ $CellContext`R1$$ \ $CellContext`R2$$ + $CellContext`L2 ($CellContext`R0$$ + $CellContext`R1$$ + \ $CellContext`R2$$))/($CellContext`L2 + $CellContext`C1 $CellContext`R1$$ \ $CellContext`R2$$), 0}], {}], Red, AbsolutePointSize[6], Point[ Evaluate[{ Re[ $CellContext`Z[I $CellContext`\[Omega]]], -Im[ $CellContext`Z[I $CellContext`\[Omega]]]}]], Black, Text[ StringJoin["f/Hz = ", ToString[$CellContext`f]], Scaled[{0.02, 0.95}], {-1, 0}], Text[ StringJoin["R1/\[CapitalOmega] = ", ToString[$CellContext`R0$$]], Scaled[{0.02, 0.875}], {-1, 0}], Text[ StringJoin[ "\!\(\*SubscriptBox[\(R\), \(ZIR\)]\)/\[CapitalOmega] = ", ToString[ Re[ $CellContext`Z[I $CellContext`\[Omega]]]]], Scaled[{0.02, 0.8}], {-1, 0}], If[$CellContext`cond, Text[ StringJoin[ "\!\(\*SubscriptBox[\(R\), \(ImZ\\ = 0\)]\)/\[CapitalOmega] = ", ToString[($CellContext`C1 $CellContext`R0$$ $CellContext`R1$$ \ $CellContext`R2$$ + $CellContext`L2 ($CellContext`R0$$ + $CellContext`R1$$ + \ $CellContext`R2$$))/($CellContext`L2 + $CellContext`C1 $CellContext`R1$$ \ $CellContext`R2$$)]], Scaled[{0.02, 0.725}], {-1, 0}], {}]}, Frame -> True, FrameLabel -> {"Re Z", "- Im Z"}, Evaluate[ If[$CellContext`cond, FrameTicks -> {{ 0, {$CellContext`R0$$, "R1"}, {$CellContext`R0$$ + $CellContext`R1$$, "R1+R2"}, {$CellContext`R0$$ + $CellContext`R2$$, "R1+R3"}}, { 0}, {0, {($CellContext`C1 $CellContext`R0$$ $CellContext`R1$$ \ $CellContext`R2$$ + $CellContext`L2 ($CellContext`R0$$ + $CellContext`R1$$ + \ $CellContext`R2$$))/($CellContext`L2 + $CellContext`C1 $CellContext`R1$$ \ $CellContext`R2$$), "\!\(\*SubscriptBox[\(R\), \(Im\\ Z\\ = \\ 0\)]\)"}}, None}, FrameTicks -> {{ 0, {$CellContext`R0$$, "R1"}, {$CellContext`R0$$ + $CellContext`R1$$, "R1+R2"}, {$CellContext`R0$$ + $CellContext`R2$$, "R1+R3"}}, { 0}, {0}, None}]], PlotRange -> {{ 0, 1.05 $CellContext`max}, {(-0.45) $CellContext`max, 0.45 $CellContext`max}}, PlotStyle -> AbsoluteThickness[2], BaseStyle -> {FontFamily -> "Helvetica", FontSize -> 10}]), "Specifications" :> { Style["Simulation of electrolyte resistance", Bold, Medium], Style["measurement for the R1+R2/L2+R3/C3 circuit", Bold, Medium], Dynamic[ Show[$CellContext`fRRLRC]], Delimiter, Style[ "Circuit parameters value", 12, Bold], {{$CellContext`R0$$, 1, "R1/\[CapitalOmega]"}, 0.1, 5, 0.1, Appearance -> "Labeled"}, {{$CellContext`R1$$, 4., "R2/\[CapitalOmega]"}, 0.1, 5., 0.1, Appearance -> "Labeled"}, {{$CellContext`R2$$, 2., "R3/\[CapitalOmega]"}, 0.1, 5., 0.1, Appearance -> "Labeled"}, {{$CellContext`logL2$$, -1., "log(L2/H)"}, -2., 1., 0.1, Appearance -> "Labeled"}, {{$CellContext`logC$$, -1., "log(C3/F)"}, -1., 1., 0.1, Appearance -> "L2abeled"}, Delimiter, Style[ "Frequency measurement", 12, Bold], {{$CellContext`logf$$, 5., "log(f/Hz)"}, -3., 5., 0.1, Appearance -> "Labeled"}}, "Options" :> {FrameLabel -> { Style[ "ER@SE/LEPMI, 2009. Hosted by Bio-Logic@www.bio-logic.info", Medium]}, ControlPlacement -> Left}, "DefaultOptions" :> {}], ImageSizeCache->{701., {201.84375, 207.15625}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, Initialization:>(($CellContext`Z1[ Pattern[$CellContext`p$, Blank[]]] := $CellContext`L2 $CellContext`p$ \ $CellContext`R1$$/($CellContext`L2 $CellContext`p$ + $CellContext`R1$$); \ $CellContext`Z2[ Pattern[$CellContext`p$, Blank[]]] := $CellContext`R2$$/( 1 + $CellContext`R2$$ $CellContext`C1 $CellContext`p$); $CellContext`Z[ Pattern[$CellContext`p$, Blank[]]] := $CellContext`R0$$ + $CellContext`Z1[$CellContext`p$] + \ $CellContext`Z2[$CellContext`p$]; Cap[ Pattern[$CellContext`xO, Blank[]], Pattern[$CellContext`yO, Blank[]], Pattern[$CellContext`L, Blank[]], Pattern[$CellContext`l, Blank[]]] := Graphics[{ AbsoluteThickness[$CellContext`trfin], Line[{{$CellContext`xO, $CellContext`yO}, {$CellContext`xO + \ $CellContext`L - $CellContext`L/20, $CellContext`yO}}], Line[{{$CellContext`xO + $CellContext`L + $CellContext`L/ 20, $CellContext`yO}, {$CellContext`xO + 2 $CellContext`L, $CellContext`yO}}], AbsoluteThickness[$CellContext`trepais], Line[{{$CellContext`xO + $CellContext`L - $CellContext`L/ 20, $CellContext`yO - $CellContext`l/ 2}, {$CellContext`xO + $CellContext`L - $CellContext`L/ 20, $CellContext`yO + $CellContext`l/2}}], Line[{{$CellContext`xO + $CellContext`L + $CellContext`L/ 20, $CellContext`yO - $CellContext`l/ 2}, {$CellContext`xO + $CellContext`L + $CellContext`L/ 20, $CellContext`yO + $CellContext`l/2}}]}]; $CellContext`Res[ Pattern[$CellContext`xO, Blank[]], Pattern[$CellContext`yO, Blank[]], Pattern[$CellContext`L, Blank[]], Pattern[$CellContext`l, Blank[]]] := Graphics[{ AbsoluteThickness[$CellContext`trfin], Line[{{$CellContext`xO, $CellContext`yO}, {$CellContext`xO + \ $CellContext`L/2, $CellContext`yO}}], Line[{{$CellContext`xO + 3 ($CellContext`L/2), $CellContext`yO}, {$CellContext`xO + 2 $CellContext`L, $CellContext`yO}}], AbsoluteThickness[$CellContext`tr], Line[{{$CellContext`xO + $CellContext`L/ 2, $CellContext`yO - $CellContext`l/ 2}, {$CellContext`xO + $CellContext`L/ 2 + $CellContext`L, $CellContext`yO - $CellContext`l/2}}], Line[{{$CellContext`xO + $CellContext`L/ 2 + $CellContext`L, $CellContext`yO - $CellContext`l/ 2}, {$CellContext`xO + $CellContext`L/ 2 + $CellContext`L, $CellContext`yO + $CellContext`l - \ $CellContext`l/2}}], Line[{{$CellContext`xO + $CellContext`L/ 2 + $CellContext`L, $CellContext`yO + $CellContext`l - \ $CellContext`l/ 2}, {$CellContext`xO + $CellContext`L/ 2, $CellContext`yO + $CellContext`l - $CellContext`l/2}}], Line[{{$CellContext`xO + $CellContext`L/ 2, $CellContext`yO + $CellContext`l - $CellContext`l/ 2}, {$CellContext`xO + $CellContext`L/ 2, $CellContext`yO - $CellContext`l/2}}]}]; $CellContext`Ind[ Pattern[$CellContext`xO, Blank[]], Pattern[$CellContext`yO, Blank[]], Pattern[$CellContext`r, Blank[]]] := Graphics[{ AbsoluteThickness[$CellContext`trfin], Line[{{$CellContext`xO, $CellContext`yO}, {$CellContext`xO + 1.2 ($CellContext`r/2), $CellContext`yO}}], Line[{{$CellContext`xO + $CellContext`r/2 + 9 ($CellContext`r/10), $CellContext`yO}, {$CellContext`xO + 2 $CellContext`r, $CellContext`yO}}], AbsoluteThickness[$CellContext`tr], Circle[{$CellContext`xO + $CellContext`r/2 + 2 ($CellContext`r/10), $CellContext`yO}, $CellContext`r/ 10, {(-Pi)/4, Pi}], Circle[{$CellContext`xO + $CellContext`r/2 + 3.5 ($CellContext`r/10), $CellContext`yO}, $CellContext`r/ 10, {(-Pi)/4, 5 (Pi/4)}], Circle[{$CellContext`xO + $CellContext`r/2 + 5 ($CellContext`r/10), $CellContext`yO}, $CellContext`r/ 10, {(-Pi)/4, 5 (Pi/4)}], Circle[{$CellContext`xO + $CellContext`r/2 + 6.5 ($CellContext`r/10), $CellContext`yO}, $CellContext`r/ 10, {(-Pi)/4, 5 (Pi/4)}], Circle[{$CellContext`xO + $CellContext`r/2 + 8 ($CellContext`r/10), $CellContext`yO}, $CellContext`r/10, { 0, 5 (Pi/4)}]}]; $CellContext`RpC[ Pattern[$CellContext`x0, Blank[]], Pattern[$CellContext`y0, Blank[]], Pattern[$CellContext`L, Blank[]], Pattern[$CellContext`l, Blank[]]] := Block[{}, { Graphics[{ AbsoluteThickness[$CellContext`trfin], Line[{{$CellContext`x0, $CellContext`y0}, {$CellContext`x0, \ $CellContext`y0 + $CellContext`L}}], Line[{{$CellContext`x0 + 2 $CellContext`L, $CellContext`y0}, {$CellContext`x0 + 2 $CellContext`L, $CellContext`y0 + $CellContext`L}}], Line[{{$CellContext`x0 - $CellContext`L/ 2, $CellContext`y0 + $CellContext`L/ 2}, {$CellContext`x0, $CellContext`y0 + $CellContext`L/2}}], Line[{{$CellContext`x0 + 2 $CellContext`L, $CellContext`y0 + $CellContext`L/ 2}, {$CellContext`x0 + 2 $CellContext`L + $CellContext`L/ 2, $CellContext`y0 + $CellContext`L/2}}]}], $CellContext`Res[$CellContext`x0, $CellContext`y0, $CellContext`L, \ $CellContext`l], Cap[$CellContext`x0, $CellContext`L, $CellContext`L, \ $CellContext`l]}]; $CellContext`RpL[ Pattern[$CellContext`x0, Blank[]], Pattern[$CellContext`y0, Blank[]], Pattern[$CellContext`L, Blank[]], Pattern[$CellContext`l, Blank[]], Pattern[$CellContext`r, Blank[]]] := Block[{}, { Graphics[{ AbsoluteThickness[$CellContext`trfin], Line[{{$CellContext`x0, $CellContext`y0}, {$CellContext`x0, \ $CellContext`y0 + $CellContext`L}}], Line[{{$CellContext`x0 + 2 $CellContext`L, $CellContext`y0}, {$CellContext`x0 + 2 $CellContext`L, $CellContext`y0 + $CellContext`L}}], Line[{{$CellContext`x0 - $CellContext`L/ 2, $CellContext`y0 + $CellContext`L/ 2}, {$CellContext`x0, $CellContext`y0 + $CellContext`L/2}}], Line[{{$CellContext`x0 + 2 $CellContext`L, $CellContext`y0 + $CellContext`L/ 2}, {$CellContext`x0 + 2 $CellContext`L + $CellContext`L/ 2, $CellContext`y0 + $CellContext`L/2}}]}], $CellContext`Res[$CellContext`x0, $CellContext`y0, $CellContext`L, \ $CellContext`l], $CellContext`Ind[$CellContext`x0, $CellContext`y0 + $CellContext`L, \ $CellContext`r]}]); Typeset`initDone$$ = True), SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, 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