EM field topology around parallel conductors - various signals

[designteam]

I would like to know what the electric and magnetic field topology is for the following conditions relating to parallel conductors, "A" and "B".

All signals are identical except for phase and point of connection.

A1 __________________ A2
B1 __________________ B2

1. In phase signals applied to A1 and B2, A2 and B1 grounded.
2. Anti-phase signals applied to A1 and B2, A2 and B1 grounded.

Same as above but with one signal offset from the other by 100% of its peak voltage.

I am looking for a visual description of what the resulting E and B fields would look like along the lateral plane of interaction.

 

[D.A.(Tony)Stewart]

Both E & H fields , let us assume the wavelengths much greater than 10x the distance of the standing wave or in other words the frequency of this example is much lower than 10% of resonant frequency of the wire pair.

For in-phase signals starting from the same end, this is effectively example 2 with opposite phase starting from opposite ends.

The in-phase coupling capacitance and inductance between the conductors cancels and thus in theory has nulls E&H fields only at the intersection between the two lines, so it is not null everywhere between, but very low for a 3D view but null for the 2D view.

The external common mode inductance to earth or any distance ground plane is reduced in 1/2 and capacitance doubled which affects the H and E fields respectively.

Each line will have a distributed inductance and distributed leakage capacitance thru air to nearby conductors.

This is how power transmission lines reduce flux density around the 4 wires in parallel separated by gaps, resulting 1/2 the transmission line impedance with a larger diameter effective wire bundle and lower radiated H field density tends to reduce susceptibility to arc flash is reduced from dielectric breakdown just like a large smooth surface requires a large external voltage to breakdown than a sharp point.

In the case of anti-phase signals in parallel as in case 1 with in-phase, but from reverse ends, the opposite is true.

This antiphase lowers emanated E&H far fields by cancellation which reduces stray emissions for E&H fields. The higher distributed ( i.e. depends on length) coupling inductance and capacitance now lowers the differential impedance to shunt ingress from outside disturbances and defines its characteristic impedance as a ratio of root L/C between the conductors.

Twisting the pairs provides even better far field uniformity to reduce emissions (egress) and interference (ingress).

As magnetic fields get weaker with rising frequency due to source inductance and Z=Lf*2pi, we are usually only concerned on wires below 100MHz and for conducted noise < 30MHz for H fields.,

But for E fields as Capacitance reduces in impedance with rising f, so additional shielding around the pair or a ground track on either side of the differential pair improves the far field ingress and egress, meaning it reduces interference to other conductors and visa versa which we generalize as a two way Electro-Magnetic Interference or EMI

 

[designteam]

Thank you for your explanation. Due to my lack of experience, I had a bit of trouble following some parts.

I should also mention that my orientation is not EMI prevention but rather to experiment with low E and H field frequency transmitters. Hence I am interested in the emitted field itself, not a means for reducing interference.

There were two examples given in my original post. In neither was there the case of two in-phase signals fed into the same ends of both wires. Perhaps a more specific explanation would help.

Let's say I have a length of two-conductor speaker wire arranged as a wide-area bifilar loop. The signal is a 100Hz sine wave at 1Vpp, and resistance to ground is 10R.

In example 1, I feed the exact same signal (in phase) into opposite ends of each wire, with the other ends connected to the ground resistor. My understanding is the E and H fields will tend to cancel due to the opposing current.

In example 2, I feed one signal into the end of one wire, and an inverted copy into the opposite end of the other wire. The remaining ends are again connected to the common ground resistance. In this case a sinusoidal voltage potential appears between each winding. The currents in adjacent wires do not cancel since when one is rising, the other is falling by the same amount, and vice versa. Note that this is different from feeding the same two signals in at one end where currents do not oppose.

What I am wondering about example 2 is the following. What is the difference in field emissions between this arrangement and two turns in parallel of the same wire carrying the same signal, i.e. as in a single winding air core coil? Will either the E or H field be disproportionately suppressed or amplified?

The second part of my original post asked how the emitted field would change if the signals in example 2 were given a DC offset from each other. It seems to me that this would create a steady DC current, directly related to the offset voltage, that cancels. In comparison with the condition above, how would this affect the emission characteristics of the two wires?

 

[FvM]

I don't think that your description is clear enough to discuss the generated E field.

For the H field, only wire currents matter. You clarified that frequencies are low (100 Hz), it's a simple magnetic field problem and you don't need care about wavelength or travel time of signals.

We can further assume that the wire pair distance is low enough neglect it and respective dipole fields, the field looks like being generated by one wire carrying a sum current. As you say, the sum is zero in the first case and twice the individual current in the second.

There's no essential difference between low frequency AC or DC currents.

 

[designteam]

Thank you for your concise reply. The problem appears simpler than I first thought.

However, I point out the in spite of the voltages of the signal and its inverted copy adding in example 2, the currents of each oppose since each signal is fed in from a different end of the wire pair. Does this in fact have no effect in terms of the emitted fields?

While I claim no expertise in this area, it seems to me that the voltage potential between the two wires would produce a 100Hz electrical field aligned with the plane of intersection between them. And, although the currents oppose, they do not sum to zero because there is a 100Hz positive/negative charge symmetry between the two conductors and this would produce a magnetic field at right angle.

Any further comments would be appreciated.

I have a slightly related question, if no one minds. In example 1 of my original post, the currents are said to cancel each other out. Let's assume for the moment that the wires are the only resistive load. Why then is about the same amount of power, for example from an amplifier, required to drive a load consisting of opposed currents as ones which are unopposed? Doesn't this demonstrate there is little or no actual cancellation?

 

[FvM]

I suggest to specify the setup precisely, including a drawing and an equivalent circuit. Otherwise we could easily talk on cross purposes.

(...) since each signal is fed in from a different end of the wire pair. Does this in fact have no effect in terms of the emitted fields?

The position of the driving source does not matter for the field generated by the wire itself, as long as signal travel times can be neglected, only magnitude and phase of the sum current counts.

But current flows always in loops and the return path contributes to the total field. In so far it's reasonable to close the double wire to a loop so that the return path has zero length.

While I claim no expertise in this area, it seems to me that the voltage potential between the two wires would produce a 100Hz electrical field aligned with the plane of intersection between them. And, although the currents oppose, they do not sum to zero because there is a 100Hz positive/negative charge symmetry between the two conductors and this would produce a magnetic field at right angle.

As already mentioned, voltage (generating an E field) and current (H field) can and should be analyzed separately as long as the circuit dimensions are small compared to wavelength. That's surely the case for 100 Hz (λ = 3000 km). But you don't need to refer to voltage when analyzing the magnetic field of a double wire line. In addition to the concentric field of the current sum, there's a dipole field depending on the current difference and wire distance. The dipole field decays fast and is effectively suppressed by twisting the wires. It can be only sensed in the wire's vicinity.

 

[designteam]

At your suggestion I have included a drawing of the three examples of interest. Let's assume a 100Hz 2Vpp signal and all load resistance in the coils.

In the new examples 2 and 3, I have put a DC offset on the signals. In 3, one signal is inverted.

As previously stated, I am trying to understand the differences between magnetic the emitted electric and magnetic fields of each configuration.

Please note that the wires are parallel, in contact with each other and not twisted.

 

[D.A.(Tony)Stewart]

At your suggestion I have included a drawing of the three examples of interest. Let's assume a 100Hz 2Vpp signal and all load resistance in the coils.

In the new examples 2 and 3, I have put a DC offset on the signals. In 3, one signal is inverted.

As previously stated, I am trying to understand the differences between magnetic the emitted electric and magnetic fields of each configuration.

Please note that the wires are parallel, in contact with each other and not twisted.

View attachment 122607

As 100Hz is treated the same as DC, visualize a solenoid with an iron rod in the centre and consider the next force at the 1st peak of the sine wave as if it was just DC.

A. Example 1 & 3 have zero net force.
B. Example 2 has a net force exactly double that of either source with only a single wire loop.

 

[FvM]

In addition to the points I already mentioned:

- the driving source is shorted by the wire, there's only a small voltage (according to the loop inductance) at the wire and respecitively only a small electrical field.

- AC and DC currents can be analysed separately.
AC-wise, configuration 1 and 2 are identical (AC magnetic field cancels out). DC-wise, configuration 2 and 3 are identical, both DC currents add.

Please note that the wires are parallel, in contact with each other and not twisted.

Yes, noted. For an analysis of the dipole field involved by the two wires, the exact geometry (wire diameter and separation) must be considered. Because these field components are rather small, I don't see much sense in the analysis for the present problem.

 

[designteam]

Yes, I did want to look at AC and DC separately since the device is a kind of "transmitter", and dealing with them differently is the purpose of the different antenna configurations.

Based upon the last two replies, I have summarized below to the best of my understanding. Please refer to previous drawing and correct as necessary. Thank you.

1. AC cancels, DC cancels
2. AC cancels, DC adds
3. AC adds, DC adds

The remaining possibility(?) is AC adds, DC cancels. Is there any way to do this with a setup similar to that shown in my drawing?

I am also interested in the electric field since the bifilar coil consists of numerous concentric turns, although only one has been shown on the drawing for simplicity. I assume where AC and/or DC current does not cancel there will be an electric field at right angle.

For example, if these were a planar coils, the magnetic field would be axial and the electric field radial.

 

[designteam]

I had a rethink on my previous post, and was wondering why the DC in 2 and 3 would add given the they are moving counter to each other in adjacent conductors. Does this not imply cancellation?

 

[D.A.(Tony)Stewart]

I assume you are only interested in the Fields in the center of the loop and not at the ends or between the wires.

Thus you can use a weakly coupled transformer analogy.

As others suggested you had it right now in #10


As I indicated from the start only the 3rd loop has an AC field inside and far-field effects.

Neglect the fields between the wires and at leaky gap at the terminations, where the fields rise sharply.

Maxwell's s 450 page book A Treatise on Electricity and Magnetism circa 1873 is an eye opener, It is absorbing as he properly defines all the math and experiments to prove his Laws of Nature.

In the Appendix he draws accurate graphic lines of forces for wire pairs, plates and grids but in and discusses the all the works of Faraday, Laplace, Poisson, Green, Gauss, Fourier, Weber, Neumann, Lorenz, Weidemann, Reiss, Beer, Hamilton, Thomson, Volta, Varley, Holtz, Coulomb, Ritter, Leyden, Ohm, and many more.. in which he would later finalize the Unified Field Theory defined in Maxwell's Equations, still true today.

He was kind in his criticisms to incorrect opinions from his elders.

Maxwell talks about Fourier's incorrect expressions of heat and power vectors and then states

"It is remarkable that Ohm himself,misled by the analogy between electricity and heat,
... entertained an opinion of this kind, and was thus, by means of an erroneous opinion, led to employ the equations of Fourier to express the true laws of conduction of electricity through a long wire, long before the real reason of the propriateness of these equations had been suspected.

 

[designteam]

Thank you for explaining further. I will consider the question solved and another lesson learned. But what do CM and DM stand for?

And is it possible to have a case where AC adds and DC cancels?

 

[D.A.(Tony)Stewart]

Thank you for explaining further. I will consider the question solved and another lesson learned. But what do CM and DM stand for?

And is it possible to have a case where AC adds and DC cancels?

Common Mode (CM) means common to both lines but phase depends on "dot" orientation of coil. meaning same direction or connection of ends reversed.

Differential Mode (DM) as in #3 could have a common mode DC if you simply reverse one battery polarity then they cancel.

A Low inductance wire wound resistor is one like your dual coil.

You take magnet wire fold in half then twist the both ends as a pair... .

Then the open end inductance for each half cancels each other out and you end up with a wire resistor but lower inductance. (but then you end up where you started !)

This is a good way to make a power resistor in the milliohm scale with low inductance if all you have is magnet wire.

 

[designteam]

I must be thick, but I don't understand how in examples 2 and 3 DC can "add" as you state.

I thought when you have a current each flowing in an opposite direction in two adjacent conductors, the currents oppose, cancel, and there is no resulting magnetic field.

If so, in example 2 AC and DC would both cancel, and in 3 AC would add and DC cancel.

You probably feel you have already explained it and I am missing some point. Anyway, I just thought I would mention it.