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--- simulating_a_time-varying_capacitor_in_spice [2024/09/10 10:16] – bm
+++ simulating_a_time-varying_capacitor_in_spice [2024/09/10 11:51] (current) – bm
@@ Line 20: / Line 20: @@
 <code>
-.subckt inductor + - params: IL0=0
+.subckt capacitor + - params: VC0=0
-.func L(time) {5m+3m*sin(2*pi*100k*time)}
+.func C(time) {5n+3n*sin(2*pi*100k*time)}
-gcurr + - value={(sdt(V(+,-))+IL0*L(0))/L(time)}
+hvolt + - value={(sdt(I(hvolt))+VC0*C(0))/C(time)}
 .ends
 </code>
-The current through the inductor (see equation above) is modeled via a G-type current source ''gcurr''. The integral is realized via the ''sdt'' function in SPICE. The initial value at time t=0 of the inductor must be given as parameter.
+Current Dependent Voltage Source
+The voltage over the capacitor (see equation above) is modeled via a current dependent voltage source ''hvolt''. The integral is realized via the ''sdt'' function in SPICE. The initial value at time t=0 of the capacitor must be given as parameter.
 First, we save the code for this subcircuit into a .txt-file and, for example, place this file in the same folder as your SPICE circuit file.
@@ Line 32: / Line 34: @@
 Next, open the text file in LT Spice, right click on the first word ".subckt", and select "Create symbol".
-The program asks you if you wish to automatically create a symbol. Click "yes". A .asy file is created which contains your custom time-varying inductor, typically in the folder 'C:Users\YourUserName\AppData\Local\LTspice\lib\sym\AutoGenerated'
+The program asks you if you wish to automatically create a symbol. Click "yes". A .asy file is created which contains your custom time-varying capacitor, typically in the folder 'C:Users\YourUserName\AppData\Local\LTspice\lib\sym\AutoGenerated'
-To use the time-varying inductor in a circuit, click "component" (F2) and insert the custom inductor by searching "inductor" in the window.
+To use the time-varying capacitor in a circuit, click "component" (F2) and insert the custom capacitor by searching "capacitor" in the window.
-Plotting the value of the inductance in SPICE in function of time is not straightforward. Let us just check some individual times: we compare the value of the current through and voltage over the inductor (i) in the case of the time-varying inductor at time $t_i$ (after the transition period), and (ii) in the case of a static inductor with value $L(t_i)$.
+Plotting the value of the capacitance in SPICE in function of time is not straightforward. Let us just check some individual times: we compare the value of the current through and voltage over the capacitor (i) in the case of the time-varying capacitor at time $t_i$ (after the transition period), and (ii) in the case of a static capacitor with value $C(t_i)$.
 Case (i): We apply a high frequency source in order to create an envelope facilitating comparison between both cases.
+{{:simulating_a_time-varying_capacitor_in_spice-1.png|}}
-{{:simulating_a_time-varying_inductor_in_spice-1.png|}}
+At a certain time, e.g., t=50µs, the value of the capacitor equals $C$(50µs)=  5 nF + 3 nF.sin(2π.100 kHz.50µs)=5 nF.
-At a certain time, e.g., t=50µs, the value of the inductor equals $L$(50µs)= 5 mH + 3 mH.sin(2π.100 kHz.50 µs)=5 mH.
 If we then zoom in at the simulation at t=50µs, we find the peak value of voltage over and current through the inductor.
-Case (ii): We compare this value with a static inductor of 5 mH:
+Case (ii): We compare this value with a static inductor of 5 nF:
+{{:simulating_a_time-varying_capacitor_in_spice-2.png|}}
-{{:simulating_a_time-varying_inductor_in_spice-2.png|}}
 We find that both the current and voltage correspond to case (i).
-We do the same for a lot of other values of time, and always find a correspondence between both cases. This is not a rigid proof, but it gives us sufficient confidence that the inductor was modeled correctly in SPICE.
+We do the same for a lot of other values of time, and always find a correspondence between both cases. This is not a rigid proof, but it gives us sufficient confidence that the capacitor was modeled correctly in SPICE.