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I am currently trying to model parts of an electronic system in Simulink using standard (discrete) blocks.

I'd like to model two capacitors connected in parallel incl. their series resistances (ESR). In SPICE this would look like this:

enter image description here

Writing down some equations for voltages and currents was straightforward:

$$ i_{total} = i_{C1} + i_{C2} $$ $$ i_{C1} = (V_{ES}-V_{C1}) / R1 $$ $$ i_{C2} = (V_{ES}-V_{C2}) / R2 $$ $$ V_{ES} = V_{C1} + i_{C1} \times R1 = V_{C2} + i_{C2} \times R2 $$

My main problem now is that I do not find a formulation for how the total current splits into \$i_{C1}\$ and \$i_{C2}\$, since this depends on the voltage \$V_{ES}\$.

Another problem with my approach: I have the current \$i_{total}\$ as my block input and I try to find the correct "split ratio" to feed it into my integrators (= ideal caps). Since the voltages on the capacitors rise at different rates, I would also have to take the current flow between the caps into account, such that with \$t \rightarrow \infty \$ and no input current \$V_{ES} = V_{C1} = V_{C2}\$.

Does anyone have a suggestion?

MoTex_42
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    130 ohm ESR sounds highly unlikely for such a huge capacitor. It is probably ~4 order of magnitude lower, unless you add a discrete resistor. – tobalt Nov 18 '22 at 17:58
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    When we are talking about supercaps, this is absolutely realistic - unfortunately: [CPH3225A](https://eu.mouser.com/ProductDetail/Seiko-Semiconductors/CPH3225A?qs=3etwrb1wR%252BhUOph6lAO7eg%3D%3D) – MoTex_42 Nov 18 '22 at 18:07
  • Are you looking to create time-domain expressions? – jonk Nov 18 '22 at 18:08
  • I am interested in the time-domain-behavior, yes. The Simulink model is executed at discrete time steps. – MoTex_42 Nov 18 '22 at 18:09
  • Thanks for the link. Didn't know such small supercaps existed – tobalt Nov 18 '22 at 18:16
  • @MoTex_42 not generally true. I'm using ultracaps with around 2 milliohm internal resistance and are 300 farads in value. Presumably you can model them in spice? – Andy aka Nov 18 '22 at 19:19
  • SPICE Simulation works fine but I am trying to model a more complex reconfigurable system that I am not able to simulate in SPICE. I was able to model a single (real) cap but I don't know how to approach the parallel cap configuration :/ – MoTex_42 Nov 18 '22 at 22:19
  • Looks like `I1` is the charging current and lasts for 1.8s while `I2` is the discharge current that's just a short 1ms burst at the 2.0s point. How about you transform the network to its Laplace transform? You can then use the Laplace transforms of the "inputs" i.e. the pulse currents (consider them scaled step functions e.g. \$10\text{m} \cdot u(t) - 10\text{m} \cdot u(t-1.8)\$). Plus you can use superposition easily since one is zero while the other isn't. If you don't use Laplace you can use straight time-domain convolution with the differential equations, but that's harder in my opinion. – Ste Kulov Nov 19 '22 at 05:06

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