Understanding the Transient Electromagnetic Excitation Choices

Walter Frei, Comsol

In case you are modeling electrical indicators which are various arbitrarily in time, you possibly can typically use the computationally environment friendly Electrical Currents interface within the COMSOL Multiphysics software program to compute the response of the system by way of a time-dependent examine. Though there are a number of totally different excitation choices, we are going to normally wish to suppose when it comes to both an utilized present sign or a voltage sign touring alongside a transmission line. Let’s take a deeper take a look at why that is.

Introduction

Right here, we are going to take a look at the instance utilized in our earlier weblog put up, “Utilizing Completely different Physics Interfaces for RF Electromagnetic Heating Fashions”: frequency-domain excitations of a coaxial cable inserted right into a steel cavity full of a pattern of lossy dielectric materials. We are going to use the identical system and apply varied kinds of transient indicators to the coax in addition to evaluate the Electrical Currents physics interface with the Electromagnetic Waves, Transient physics interface, primarily when it comes to computing the whole dissipation throughout the materials. The rationale for evaluating these two interfaces is that the Electromagnetic Waves, Transient interface solves the total vectorial type of Maxwell’s equations, whereas the Electrical Currents interface solves for a simplified approximation of Maxwell’s equations by ignoring the magnetic fields and fixing solely for the scalar electrical potential. To cut back the computational price of those examples, the mannequin will likely be diminished to the 2D axisymmetric modeling airplane, as proven within the schematic beneath.

Present Excitation

We start with thrilling the system by way of a prescribed present, with a variation in time, as proven within the determine beneath. The sign is initially zero, after which steps as much as a most worth, which is then maintained. It’s potential to use smoothing to this step operate, which will likely be thought of later. The system begins in its unexcited state: the fields are initially zero all over the place. Given this preliminary situation and enter sign, the transient system response ought to strategy a nonzero steady-state answer after enough time, equal to a DC excitation of the system.

We are going to first construct a mannequin utilizing the Electromagnetic Waves, Transient interface since this interface captures all resistive, capacitive, and inductive phenomena. This interface is totally different from the Electromagnetic Waves, Frequency Area interface used beforehand, in that it doesn’t embrace an Impedance Boundary Situation, as this boundary situation solely has which means within the frequency area. Though it’s potential to explicitly mannequin the steel leads, we are going to as a substitute mannequin all metallic components as lossless, excellent conductors by way of the Excellent Electrical Conductor boundary situation. That is justified, because it was beforehand proven that the losses within the steel are comparatively negligible for this case.

We use the Lumped Port boundary situation, of kind Coaxial, and specify a transient utilized present. Be aware that the argument to the Step operate is entered in nondimensionalized items. The full simulated timespan is 150 ns, with outcomes saved each 1 ns. The plot beneath reveals the voltage sensed on the Lumped Port boundary situation (throughout the Electromagnetic Waves, Transient interface, which is abbreviated as TEMW within the determine beneath). The curve reveals the everyday response we should always count on from a resistive–capacitive system.

The identical scenario is modeled with the Electrical Currents interface, which considers solely resistive and capacitive results. On this interface, the Terminal boundary situation of kind Present will inject the required present on the interior conductor. The outer conductor and remaining exterior boundaries are all set to Floor. To match options, the utmost solver time step can be set to 1 ns, and the outcomes present wonderful settlement.

This plot reveals a comparability of the deposited warmth into the mannequin over time for each physics’ interfaces, and reveals settlement. We are able to additionally compute the built-in losses over time by way of the timeint() operator, which has the next syntax:

timeint(0,150e-9, intopSample(ec.Qh), ‘nointerp’),

the place the added ‘nointerp’ possibility evaluates the time integral of the mixing over the quantity utilizing solely the saved time steps, and each interfaces compute a complete deposited power of 46.8 nJ over this 0– 150 ns timespan, with lower than a 1% distinction. Based mostly on this information, it’s potential to conclude that, for this technique excited by this present sign, the Electrical Currents interface will give almost similar outcomes because the Electromagnetic Waves, Transient interface, and at decrease computational price.

Voltage Excitations in Electrical Currents

Subsequent, let’s use the identical step operate however as a substitute use it to modulate the Terminal Voltage throughout the Electrical Currents interface. That’s, we are going to attempt to immediately change the utilized voltage between the interior and outer conductor of the coaxial cable. We are able to attempt to clear up such a mannequin, however it would really result in a solver failure. This shouldn’t be too stunning, since a capacitive gadget resists an instantaneous change in voltage. That’s, the step enter to the voltage is nonphysical.

As a substitute of attempting to unravel such a nonphysical excitation, we are able to return to the Step operate and allow smoothing. With this alteration, we are able to clear up the mannequin over a shorter timespan of 5 ns, with outcomes saved each 0.01 ns, and with a tighter solver relative tolerance of 1e-5, as described in our “Controlling the Time-Dependent Solver Timesteps” information base entry.

This determine reveals the utilized voltage and the present via the terminal. Be aware that the present rises to over ten instances the steady-state present because the utilized voltage is rising. To know this, look at the expression for the present, as outlined throughout the Electrical Currents interface:

That is the sum of the conduction present and displacement present, and the electrical discipline is computed from . So, if the electrical potential as a operate of time is specified at a boundary, then each the conduction present and the displacement present into the mannequin are specified, and that’s nonphysical. Distinction this with the earlier case of an utilized present, the place solely the whole present is specified, and the mannequin computes what fraction of that complete present is displacement present or conduction present.

We must also ask if it’s potential to use a similar boundary situation within the Electromagnetic Waves, Transient interface. This isn’t potential; this interface makes use of the magnetic vector potential formulation, which doesn’t admit such an excitation situation. Even when it was potential by way of the numerical technique, the sort of excitation isn’t bodily believable since it will indicate a sort of suggestions management drawback.

It’s nonetheless legitimate to make use of the voltage excitation within the Electrical Currents interface within the time area, however solely in these particular instances the place the resultant displacement present on the terminal boundary is comparatively a lot smaller than the conduction present. That’s, use the voltage boundary situation just for these instances the place the gadget is sort of purely resistive. The case we’re right here, although, requires that we glance to a extra sensible boundary situation.

Transmission Traces, Lumped Ports, and Terminated Terminal Situations

Inside the Electromagnetic Waves, Transient interface, let’s now take one other take a look at the Lumped Port boundary situation. The Present kind was already mentioned, and the Circuit kind will likely be mentioned later, so we are going to now give attention to the Cable kind. The Cable possibility presents the flexibility to outline a voltage sign and a cable impedance. This offers us a situation that may be understood within the context of an infinite lossless transmission line of specified impedance, for instance , with a supply positioned alongside the infinite cable. This supply imposes a present such {that a} sign propagates in each instructions alongside the transmission line away from the supply, and such that the sensed voltage will likely be equal to the outlined sign. Because the sign propagates in each instructions, the magnitude of this imposed present is That is primarily based on the required voltage sign, V(t), and the required cable impedance — assuming that the system impedance matches the cable impedance. In truth, the cable impedance will likely be totally different from the system impedance, Zs, so the sign will likely be partially mirrored by the system mannequin and again into the transmission line. So, the enter sign is entered at this boundary when it comes to voltage, however truly imposes a set present in addition to a parallel load equal to the cable impedance. We are able to consider the sign coming from the present supply as being break up into the cable and system, with some fraction of that sign mirrored again. In most actual sources, there could be some sort of circulator or isolator that will stop the mirrored sign from interacting with the present supply, and divert the mirrored sign to a matched dissipative load.

The circuit equal interpretation of the Lumped Port boundary situation, of kind Cable. The highest determine reveals the assumed case: The sign propagates from the present supply into the cable and system, of matched impedance. The supply sits throughout the cable, so the sign propagates in each instructions. The underside determine reveals the modeled case: The mismatched impedance of the system results in a fraction of the sign being mirrored again into the cable.

The analogous boundary situation throughout the Electrical Currents interface is the Terminal situation of kind Terminated. Right here, we are able to equally enter a cable impedance, however as a substitute want to use an influence, quite than voltage, the place the ability is .

The mannequin will be solved utilizing finer output time steps and tolerances for each physics. The outcomes will be evaluated when it comes to measured voltage and present in addition to losses and built-in losses over time, as proven beneath. There are a number of options to comment on:

1. The sensed voltage and present from the Electromagnetic Waves, Transient interface reveals ripples, or waves, within the sign. That is anticipated. These ripples are because of the frequency content material of the enter sign and in addition come up resulting from reflections of the sign from the supplies, boundary circumstances, and geometry of the system mannequin.
2. The sensed voltage is almost twice the utilized voltage. This is because of the truth that this boundary situation will also be considered a Norton equal of a voltage supply, however with a Norton resistance equal to the cable impedance, which, on this case, is comparatively small in comparison with the resistance of the system being modeled.
3. The answer from the Electrical Currents interface doesn’t have any ripples since this interface explicitly ignores the inductive results, however the total form could be very related and provides the identical steady-state answer.
4. The losses agree effectively, and the whole deposited power agrees to inside 1%.

We are able to thus conclude that the Electrical Currents interface is an excellent approximation of the total Electromagnetic Waves, Transient interface, for this technique and excitation kind.

Plot of measured voltage and measured present when modeling an utilized smoothed step voltage sign propagating alongside a transmission line.

 

Comparability of computed losses with the pattern materials when a smoothed step voltage sign is utilized.

Electrical Circuit Connections

Wanting on the circuit diagram within the earlier determine, it seems as if the Lumped Port, of kind Cable, represents a resistor connected to the system. We might examine this interpretation by as a substitute utilizing the Lumped Port, of kind Circuit, and including a lumped present supply and a lumped resistor in parallel with the system by way of the Electrical Circuits interface. The strategy of connecting these physics interfaces is just like what was proven in our weblog put up “Understanding the Excitation Choices for Modeling Electrical Currents”. This similar excitation will be reproduced by connecting the Electrical Currents interface to the Electrical Circuits interface by way of the Terminal situation of kind Circuit.

A extra complicated matching circuit, together with capacitors, inductors, and transformers, may be carried out within the Electrical Circuit interface. It may be affordable to make use of a voltage supply characteristic throughout the Electrical Circuits interface so long as the extra parts are added to the circuit to forestall any sort of nonphysical excitation. Nonlinear lumped gadgets, diodes and transistors, will also be included, though these will lead to a set of equations which are extra computationally intensive to unravel, and may require additional modification of solver settings.

A Fast Phrase About Deposited Energy

Wanting again on the weblog put up about frequency-domain excitations of this technique, we additionally carried out an excitation that will deposit a identified energy into the system. Such a excitation relies on suggestions, which means that it displays some state of the mannequin and feeds data again to the enter. Such suggestions is affordable in a frequency-domain mannequin, underneath the implicit assumption that the suggestions occurs over a number of cycles. It’s a lot much less motivated for a time-domain mannequin, the place any suggestions would even have to incorporate the dynamics and delay of the management system. Such time-domain suggestions isn’t motivated for programs and timespans just like what now we have checked out right here.

Closing Remarks

We’ve checked out varied methods of thrilling a system with a time-domain sign inside each the Electrical Currents interface and the Electromagnetic Waves, Transient interface. For the actual system and the sign that was being thought of, these two interfaces produce very related outcomes. The Electrical Currents interface is suitable when the electrical power within the excited system is way better than the magnetic power. The alternate case, when the system is primarily inductive and the magnetic fields are a lot better than the electrical fields, will likely be checked out individually in a future weblog put up.

We’ve seen that each one excitations are basically specifying the present going into the system mannequin. The case of a voltage sign propagating alongside a transmission line is just a Norton equal: a present supply with an exterior resistance — representing the transmission line — parallel to the system mannequin. In the end, the selection between these excitation choices representing a present supply, a voltage sign propagating alongside a transmission line, or including an Electrical Circuit interface is dependent upon the kind of supply that you’re working with.

The indicators which have been checked out listed below are fairly easy, however we regularly want to think about extra difficult transient indicators, and particularly indicators which are periodic. Such indicators lend themselves to some very environment friendly modeling methods, which will likely be addressed in a following article, so keep tuned!