# Ideal Diode and Ideal Switch instability problem

**URL:** <https://discourse.julialang.org/t/ideal-diode-and-ideal-switch-instability-problem/107769>\
**Category:** Modelling & Simulations\
**Tags:** question, modelingtoolkit\
**Created:** [December 18, 2023, 1:33pm UTC](https://discourse.julialang.org/t/ideal-diode-and-ideal-switch-instability-problem/107769 "2023-12-18T13:33:58Z")\
**Posts on this page:** 12\
**Page:** 1

<div class="post-metadata">

**Author:** ![luca.andriotto](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/luca.andriotto/32/205202_2.png) [@luca.andriotto](https://discourse.julialang.org/u/luca.andriotto)\
**Post date:** [December 18, 2023, 1:33pm UTC](https://discourse.julialang.org/t/ideal-diode-and-ideal-switch-instability-problem/107769/1 "2023-12-18T13:33:58Z")

</div>

Greetings,

I am new to Julia community and, in particular, to the use of `ModelingToolkit` package. I would like to implement an `IdealDiode` component to be replaced by a short circuit when the controlled variable (i.e. integral of the current flowing into the Diode) has reached one of the two thresholds (being either 0 or `Vin_th`).

Initially, i had thought of implementing a model for a simple ideal diode and a model of an ideal controlled switch. Such devices would be connected in parallel in the final circuit.

I had faced some difficulties:

- Ideal Diode returns instability (dt \< dtmin) probably dued to the rising edge. This is why I have decided to go for a Shockley Diode.
- Ideal Switch works this way: if controlled variable is \<= 0 or \>= `Vin_th`, the switch is closed, so that the diode is excluded. The switch is otherwise open. I am getting the very same error. I decided to introduce a `tanh` function in the current equation of such device in order to reduce this behavior.

These workarounds seem not to have worked when simulating, considering the full circuit. In some Threads on Discourse and in the Documentation, I’ve read about Callbacks but I haven’t understood how to write them properly and where to insert them in the DSL code and if there exist some macro helping in this process. Should I drop the usage of new macros (i.e. @mtkmodel, @mtkbuild …) for the old format in order to add Callbacks?

Another possibility could be to use conditionals, in order to include/exclude the IdealDiode in the circuit but i don’t think this will solve instability, in the end. I write here to ask some suggestion to avoid workarounds and for some help facing these problems directly.

This is the code i used for modeling. Forgive my English, it’s not my first language. Thanks in advance for any feedback.

Used libraries

```julia
using ModelingToolkit
using ModelingToolkitStandardLibrary.Blocks
using ModelingToolkitStandardLibrary.Electrical
using OrdinaryDiffEq
using Plots

```

Diode

```julia
@mtkmodel Diode begin
    @extend v, i = oneport = OnePort()
    @parameters begin
        threshold = 0, [description = "Voltage Threshold"]
    end
    @components begin
        input = RealInput()
    end
    @equations begin
        0 ~ ifelse(input.u > 0, v, i)
    end
end

```

ver. 2

```julia
exlin(x, max_x) = ifelse(x > max_x,
                         exp(max_x)*(1 + x - max_x),
                         exp(x))
@mtkmodel Diode begin
    @extend v, i = oneport = OnePort()
    @parameters begin
        Ids = 1e-6,
        [description = "Reverse-bias current"]
        max_exp = 15,
        [description = "Value after which linearization is applied"]
        R = 1e8,
        [description = "Diode Resistance"]
        Vth = 1e-3,
        [description = "Threshold voltage"]
        k = 1e3,
        [description = "Speed of exponential"]
    end
    @equations begin
        i ~ Ids * (exlin(k * (v - Vth) / Vth, max_exp) - 1) + (v / R)
    end
end

```

Switch:

```julia
@mtkmodel Switch begin
    @extend v, i = oneport = OnePort()
    @parameters begin
        V_FRC, [description = "Airway Volume at FRC"]
    end
    @variables begin
        ∫i(t) = 0, [description = "Current integral"]
    end
    @equations begin
        0 ~ ifelse(∫i / V_FRC <= 0, v,
                   ifelse(∫i / V_FRC < 0.9, i, v))
    end
end

```

Switch ver. 2

```julia
@mtkmodel Switch begin
    @extend v, i = oneport = OnePort()
    @parameters begin
        V_FRC, [description = "Airway Volume at FRC"]
        Rclosed = 1e-12, [description = "Switch Resistance when Closed"]
        Ropen = 2.5e5, [description = "Switch Resistance when Open"]
        k = 1e3
    end
    @variables begin
        ∫i(t) = 0, [description = "Current integral"]
        R(t) = 0, [description = "Switch Resistance"]
    end
    @equations begin
        R ~ Rclosed + (Ropen - Rclosed) * (1 / 2) * (tanh(k * (∫i / V_FRC) * (1 - (∫i / V_FRC))))
        v ~ R * i
    end
end

```

For performing the simulation I’ve used:

```julia
@mtkbuild system = System()
prob = ODEProblem(system, Pair[], (0, 2));
sol = solve(prob, Rodas4());

```

---

<div class="post-metadata">

**Author:** ![ufechner7](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/ufechner7/32/51363_2.png) [@ufechner7](https://discourse.julialang.org/u/ufechner7)\
**Post date:** [December 18, 2023, 3:54pm UTC](https://discourse.julialang.org/t/ideal-diode-and-ideal-switch-instability-problem/107769/2 "2023-12-18T15:54:17Z")

</div>

You can find one (complex) example how to use callbacks in my tutorial: [Examples · Tethers.jl](https://ufechner7.github.io/Tethers.jl/dev/examples/#Using-a-callback-2)

In priciple you just have to define:  
@named sys = ODESystem(eqs, t; continuous\_events = cb)

and `cb` must be an array of equations that passes zero when your switches switch…

What I am doing in my code is to create an array of equations, because I have **segment** elements that can “switch”.

Did you read the documentation: [Event Handling and Callback Functions · ModelingToolkit.jl](https://docs.sciml.ai/ModelingToolkit/stable/basics/Events/) ?

---

<div class="post-metadata">

**Author:** ![pierre-haessig](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/pierre-haessig/32/217129_2.png) [@pierre-haessig](https://discourse.julialang.org/u/pierre-haessig)\
**Post date:** [December 18, 2023, 10:54pm UTC](https://discourse.julialang.org/t/ideal-diode-and-ideal-switch-instability-problem/107769/3 "2023-12-18T22:54:50Z")

</div>

> [@luca.andriotto](#):
>
> I would like to implement an `IdealDiode` component to be replaced by a short circuit when the controlled variable (i.e. integral of the current flowing into the Diode) has reached one of the two thresholds (being either 0 or `Vin_th`).

Hi, can you elaborate on this Diode model. Is it specific to your circuit? Because I don’t see in general the need to account for the _integral_ of the current to model the switching transition of a Diode.

That being said, I’m familiar with Modelica’s [Diode model](https://doc.modelica.org/Modelica%204.0.0/Resources/helpDymola/Modelica_Electrical_Analog_Ideal.html#Modelica.Electrical.Analog.Ideal.IdealDiode) (based on switching between large and small resistance values), but have no experience in doing so in `ModelingToolkit`.

---

<div class="post-metadata">

**Author:** ![pierre-haessig](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/pierre-haessig/32/217129_2.png) [@pierre-haessig](https://discourse.julialang.org/u/pierre-haessig)\
**Post date:** [December 18, 2023, 11:04pm UTC](https://discourse.julialang.org/t/ideal-diode-and-ideal-switch-instability-problem/107769/4 "2023-12-18T23:04:21Z")

</div>

For the reference, these are the simplified, compactified equations of Modelica Standard Libary’s 4.0 `IdealDiode`:

```Modelica
parameter Real Ron = 1e-5
    "Forward state-on differential resistance (closed resistance)";
parameter Real Goff = 1e-5
    "Backward state-off conductance (opened conductance)";

 Real v "voltage drop";
 Real i "current";
 Boolean off(start=true) "Switching state";
 Real s "Auxiliary variable for actual position on the ideal diode characteristic";
  /* s = 0: knee point
     s < 0: below knee point, blocking
     s > 0: above knee point, conducting */

equation

  v = s * (if off then 1 else Ron);
  i = s * (if off then Goff else 1) ;
  off = s < 0;

```

Would this approach be implementable in MTK?

References:

- [IdealSemiconductor.mo](https://github.com/modelica/ModelicaStandardLibrary/blob/master/Modelica/Electrical/Analog/Interfaces/IdealSemiconductor.mo)
- [IdealDiode.mo](https://github.com/modelica/ModelicaStandardLibrary/blob/master/Modelica/Electrical/Analog/Ideal/IdealDiode.mo)

---

<div class="post-metadata">

**Author:** ![langestefan](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/langestefan/32/207923_2.png) [@langestefan](https://discourse.julialang.org/u/langestefan)\
**Post date:** [November 16, 2024, 7:51pm UTC](https://discourse.julialang.org/t/ideal-diode-and-ideal-switch-instability-problem/107769/5 "2024-11-16T19:51:51Z")

</div>

Hi! Has there been any progress on this? I would also like to use a diode in ModelingToolkit.jl

The Modelica implementation seems fine: [Diode - Simple diode with heating port](https://reference.wolfram.com/system-modeler/libraries/Modelica/Modelica.Electrical.Analog.Semiconductors.Diode.html)

If there hasn’t been any progress then I will try to make a PR for it. Shouldn’t be that hard to do.

---

<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [November 17, 2024, 8:59am UTC](https://discourse.julialang.org/t/ideal-diode-and-ideal-switch-instability-problem/107769/6 "2024-11-17T08:59:28Z")

</div>

Do you need discontinuity detection for this?

---

<div class="post-metadata">

**Author:** ![langestefan](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/langestefan/32/207923_2.png) [@langestefan](https://discourse.julialang.org/u/langestefan)\
**Post date:** [November 17, 2024, 10:02am UTC](https://discourse.julialang.org/t/ideal-diode-and-ideal-switch-instability-problem/107769/7 "2024-11-17T10:02:53Z")

</div>

No, if we use the Shockley diode equation like Modelica then it is continuous.

For reference: [Shockley diode equation](https://www.desmos.com/calculator/cxaxpocr7h)

---

<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [November 17, 2024, 11:20am UTC](https://discourse.julialang.org/t/ideal-diode-and-ideal-switch-instability-problem/107769/8 "2024-11-17T11:20:34Z")

</div>

Yeah if there’s no derivative discontinuities it should be implementable, I just don’t think anyone has done it yet.

---

<div class="post-metadata">

**Author:** ![langestefan](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/langestefan/32/207923_2.png) [@langestefan](https://discourse.julialang.org/u/langestefan)\
**Post date:** [November 18, 2024, 4:43pm UTC](https://discourse.julialang.org/t/ideal-diode-and-ideal-switch-instability-problem/107769/9 "2024-11-18T16:43:26Z")

</div>

I implemented the diode.

There isn’t a place to put common constants yet so I just put them inside the component. If you want I can also make a separate PR for that?

I also implemented the thermal diode which has an additional thermalport and models the temperature dependent behaviour, I’ll make a separate PR for that once I have added tests.

```julia
"""
        Diode(; name, Is = 1e-12, n = 1)

Ideal diode based on the Shockley diode equation.

# States

    - See [OnePort](@ref)

# Connectors
    
    - `p` Positive pin
    - `n` Negative pin

# Parameters
     
    - `Is`: [`A`] Saturation current
    - `n`: Ideality factor
"""
@mtkmodel Diode begin
    begin
        k = 1.380649e-23 # Boltzmann constant (J/K)
        q = 1.602176634e-19 # Elementary charge (C)
    end

    @extend v, i = oneport = OnePort(; v = 0.0)
    @parameters begin
        Is = 1e-6, [description = "Saturation current (A)"]
        n = 1, [description = "Ideality factor"]
        T = 300.15, [description = "Ambient temperature"]
    end
    @equations begin
        i ~ Is * (exp(v * q / (n * k * T)) - 1)
    end
end

```

Made a small demo with an AC source:

 ![afbeelding](https://global.discourse-cdn.com/julialang/original/3X/6/f/6f4de6df1a63cc8298407f1473d271cca432207a.png)

---

<div class="post-metadata">

**Author:** ![langestefan](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/langestefan/32/207923_2.png) [@langestefan](https://discourse.julialang.org/u/langestefan)\
**Post date:** [November 18, 2024, 7:18pm UTC](https://discourse.julialang.org/t/ideal-diode-and-ideal-switch-instability-problem/107769/10 "2024-11-18T19:18:13Z")

</div>

PR here: [Add diode component by langestefan · Pull Request #343 · SciML/ModelingToolkitStandardLibrary.jl · GitHub](https://github.com/SciML/ModelingToolkitStandardLibrary.jl/pull/343)

---

<div class="post-metadata">

**Author:** ![junmorenodi99](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/junmorenodi99/32/217862_2.png) [@junmorenodi99](https://discourse.julialang.org/u/junmorenodi99)\
**Post date:** [July 24, 2025, 6:46am UTC](https://discourse.julialang.org/t/ideal-diode-and-ideal-switch-instability-problem/107769/11 "2025-07-24T06:46:02Z")

</div>

Hi everyone,

I’m fairly new to the Julia community, so apologies if some of this is basic. I’d like to revisit the topic of the Ideal Switch in MTK. Has anyone submitted a PR for a controllable switch yet? I’m working on my own based on @luca.andriotto’s model, but I’m running into a few issues:

1. The declaration with the internal integral ∫i(t) makes the system under-determined.
2. The declaration of R(t) as a time-dependent variable leads me to a “Variable R is not a function of independent variable t” error.

Any pointers or references to prior work are greatly appreciated!

(If there isn’t an existing discussion or PR, I’ll open a dedicated issue)

---

<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [July 24, 2025, 9:44am UTC](https://discourse.julialang.org/t/ideal-diode-and-ideal-switch-instability-problem/107769/12 "2025-07-24T09:44:11Z")

</div>

I dont think the standard library has a controllable switch. Open an issue with the code you are trying as without seeing what you are running we cannot help you. But what was posted here was for MTK v8 and a lot has changed so its easier to put it into a thread/library where it can be maintained rather than just a thread post