# Voltage/Current variation according to the time and EMI

It is largely said that large voltage or current variation according to the time produces EMI. (Electromagnetic interference). When drawing the layout, care have to be taken on traces with high : $$\frac{dVoltage(t)}{dt}$$ and $$\frac{dCurrent(t)}{dt}$$.

Nevertheless I do not understand this principle. I do not know what is the relation between the current or voltage variation and magnetic or electric field. On the other hand, I can understand that large variation will lead to produce a lot of harmonics at high frequencies according to Fourier's theory. And so as the PCB are made smaller and smaller, the propagation will be easier as an antenna is perfectly transmitting/receiving when this length is equal to (if I remember correctly) to the waveform length divided by two.

Nevertheless, I do not know a formula which tells that the amplitude of the magnetic or electric field is higher if there is large current or voltage variation. The amplitude of the magnetic field or electric field space depends mainly on the current amplitude or voltage amplitude (and the distance).

So why no attention is paid on traces with high current or high voltage ?

If there is a formula which links voltage/current variation to magnetic/electric field, please let me know :D

## 2 Answers

EMI or electromagnetic interference is "inflicted" on an otherwise isolated circuit (circuit A) by an interfering circuit (circuit B) by a coupling of the two circuits magnetically and/or capacitively.

For magnetic interference it is the rate of change of current in a wire in circuit B that creates an alternating magnetic field that induces an interfering voltage in circuit A. This comes down to basic Faraday's law of induction: -

$$V = -N\dfrac{d\Phi}{dt}$$

Where N is the number of turns (usually 1 for EMI analysis) and $$\\Phi\$$ is the magnetic flux. So, if that flux is changing at a fast rate, the induced voltage into circuit A from circuit B is bigger and more problematic. The flux is proportional to current in the interfering circuit (B) and it can be shown that the previous equation also equals: -

$$V = -L\dfrac{di}{dt}$$

So, if circuit B has a rapidly changing electric current, it will induce more interference into circuit A (the unwilling recipient) than if the current is changing at a slower rate. If the distance between circuit A and circuit B gets larger, the inductive coupling gets smaller (usually quite rapidly with distance) and the interference gets less.

For electric field coupling there needs to be capacitance between circuit A and circuit B and we have this equation that describes the "injected" current into the unwilling recipient (circuit A) and circuit B (the interferer): -

$$I = C\dfrac{dv}{dt}$$

So, if the voltage is changing in circuit B (the interferer) relative to circuit A (the unwilling recipient) there is a current that will pass between them and that current magnitude is greater when the interfering voltage changes at a greater rate.

So why no attention is paid on traces with high current or high voltage ?

If the voltages and currents are DC or low frequency then there isn't much cause for alarm normally. If voltage and current are decent amplitude and high frequency then there can be great cause for concern and a lot of attention is paid to ensure that EMI is reduced.

• Thank you for your explanation :D Very clear ! I have just one question, you make the link between the rate of change of current and the rate of change of the magnetic flux, is there a relation which links the rate of change of voltage and the rate of change of "electric flux" ?
– Jess
Commented Apr 16, 2020 at 14:04
• They are proportional so your question boils down to is there a relationship between voltage and electric flux. Electric flux: hyperphysics.phy-astr.gsu.edu/hbase/electric/imgele/eflux.png Commented Apr 16, 2020 at 14:10
• My question was bad .... Magnetic field and current are also proportionnal. Nevertheless there is a relation which links the inductance, the rate of change the current and the magnetic flux. Is there a relation which links the rate of change of voltage and the rate of change of "electric flux", and the capacitor ? There should be some sort of duality, isn't it ?
– Jess
Commented Apr 16, 2020 at 14:22
• I expect there is duality just like there's duality to the permeability equation $B = \mu\cdot H$ but, off the top of my head it isn't manifesting. Commented Apr 16, 2020 at 14:25
• OK, electric flux density D $= \epsilon E$. Maybe that helps? And electric flux is D x area. Commented Apr 16, 2020 at 14:28

There is a direct relation between voltage/current magnitude and magnitude variation.

For a capacitor, this is I=CdU/dt, for an inductor it is U=LdI/dt.

If the timestep dt is very small, this leads to very high voltages/currents. This is why it is so important in EMI.