La longueur d’onde de l’énergie électromagnétique Barry OLNEY, responsable de la société In Circuit Design, expert en conception de carte électronique numérique dite “High-Speed”, nous donne ici quelques éléments de réponse au sujet du comportement des signaux rapides…

The speed of light is the one universal physi­ cal constant that we are yet to break. lt is the limit of the velocity at which conventional matter and information can attain in our uni­ verse-without warping space-time, of course. At a lightning 299,792,458 m/s, it is the max­ inmm speed at which massless particles (or waves) of light, electromagnetic energy, and gravitational waves travel in a vacuum. In this month’s colmnn, I will look at how to simply measure the speed of light and how the wave­ length of electromagnetic energy relates to the multilayer PCB.

One morning recently, whilst eating my vegemite toast (as Australians do), I was read­ ing my weekly New Scientist Magazine and came across an interesting article on how to measure the speed of light using a chocolate bar and a microwave aven. Here’s how it works.

A microwave oven’s magnetron (RF trans­ mitter) oscillates at 2.45 GHz. Electromagnetic energy in this frequency range has an inter­ esting property: lt is absorbed by water, fats, and sugars. The microwaves, in the turned cavity, penetrate the food and excite the mol­ ecules heating the food throughout-provided the turntable is rotating. But for this exercise, the chocolate bar needs to be stationary, so remove the turntable.

Since the chocolate bar  is  not  rotating,  the microwaves are not evenly distributed throughout the bar, and regions of chocolate will begin to melt in the high-intensity areas. Chilling the bar first makes the molten areas more distinct. This will take approximately 50 seconds on high power. Take care not to exceed 60 seconds, or you may have a mess to clean (lick) up.

Electromagnetic energy  travels  in  a wave through a vac­uum or air at the speed of light. The distance between the peaks of the wave is the wavelength of the energy. As the wave travels, the peaks and troughs heat the choc­ olate. By measuring the distance between these hot spots, one can  determine  the half wavelength of the energy (Figure 1).

You should get about 60 mm between the melted globs. I got 58 mm after 45 seconds. However, there is plenty of leeway in the dubious accu­ racy of my plastic ruler and failing eyesight. Doubling this (120 mm) gives you the wave­ length related to a frequency of 2.45 GHz. The following equation is used to calculate the velocity (v), where fis frequency and lambda (11.)is the wavelength.

Equation 1:

For an extremely rough measurement, this is very close to the actual velocity of light (299,792 ,458 m/s). Note that light will travel a little slower in the air than a perfect vacuum.

Now, let’s look at how this relates to the speed of electromagnetic energy in multilayer PCBs. If you have a digital signal running at a dock rate of 2.45 GHz, then one would expect

the wavelength to be 120 mm. Wrong! Unfor­ tunately, the relative permeability or  dielec­ tric constant (Dk) of the  surrounding  materi­ als impacts the velocity of propagation at the speed of light (c).

Equation 2:

A vacuum has a Dk = 1, air= 1.0006 and typ­ ical FR-4 = 4. Then, salve Equation 2 for the wavelength, including the Dk of the dielectric rnaterial:

Equation 3:

Therefore, the FR-4 material in a stripline configuration slows the propagation speed and decreases the wavelength of the electrornagnetic wave down by about half (Figure 2). But that all depends on the exact dielectric con­ stant of the surrounding materials.

For the top layer 1, the electromagnetic energy travels in a combination of prepreg, sol­ der mask, and air (Figure 3). The effective Dk will be around  2.68 with  a propagation speed of 1.83 x 108 m/s. For layer 4, there is a com­ bination of prepreg and  core  with an  effec­ tive Dk of 4.03 and a speed of 1.49 x 108 m/s. This should be simulated by a field solver, as it depends on the combination of materials and their Dks, order, and thickness. From this, one can see that the propagation speed of the elec­ tromagnetic energy is always faster on the outer mierostrip layers than the inner stripline layers. At high frequencies, short traces (partieu­ larly stubs or unterminated traces) on a PCB can act as a monopole or loop antenna. Dif­ ferential-mode radiation is the electromagnetic radiation caused by currents consisting of har­ monie frequency components flowing in a loop in the PCB. The radiation is proportional to the current loop area and the square of the fre­ quency of the signal. Common-mode radiation is the electromagnetic radiation caused by cur­ rent flowing in an unterminated trace (or ter­ minated with a high-input impedance device) and may require load terminating resistors to eliminate reflections. The radiation resembles that of a monopole antenna, and the magni­ tude is proportional to the current per line length and frequency.

Trace antennas form a monopole with a quarter wavelength (À/4) at the resonant frequency. Monopoles require a ground plane; this fonns the other quarter wavelength to radiate  efficiently,  which  is  not  desirable in this case. lt functions as an open resona­ tor, oscillating with standing waves along its length. The radiation pattern is practically omni-directional.

Unfortunately, the high-frequency compo­ nents of the fundamental (lowest frequency in a complex wave) radiate more readily because their shorter wavelengths are comparable to trace lengths, which act as antennas. Conse­ quently, although the amplitude of the har­ monie frequency components decreases as the frequency increases, the radiated frequency varies depending on the characteristics of the antennas/traces.

At 2.45 GHz, an 18-mm trace on the outer, microstrip layers may radiate while on  the inner stripline layers, 15 mm (600 mils) is suf­ ficient. And as we increase  the  frequency  to 10 GHz, the maximum length is just 3.75 mm (150 mils), which is incredibly short.  Strip­  line traces are embedded between two planes, which dramatically reduces radiation with the exception of the fringing fields from the edge  of the board. However, the outer mierostrip layers will radiate; hence critical, high-speed traces should be avoided on these layers.

Since the wavelength of electromagnetic energy depends on the signal frequency and dielectrie constant of the surrounding materi­ als, a low Dk (circled in Figure 4) is preferred for high-speed design. Fortunately, low-loss materials generally have this characteristic.

Key Points

• Microwave energy is absorbed by water, fats, and sugars.
• Electromagnetic energy travels in a wave through a vacuum or air at the speed of light.
• The distance between the peaks  and troughs of the energy is a half wavelength.
• The dielectric constant of the surrounding materials impacts the velocity of propaga­ tion of the signal.
• The FR-4 material in a stripline configu­ ration slows the propagation speed and decreases the wavelength of the electro­ magnetic wave down by about half.
• In a microstrip (outer layer), the electro­ magnetic energy travels in a combination of prepreg, solder mask, and air, which reduces the effective Dk.
• In a stripline, there is a combination of prepreg and core.
• The propagation speed of the electromag­ netic energy is always faster on the outer microstrip layers than the inner stripline layers.
• At high frequencies, short traces (particularly stubs or unterminated traces) on a PCB can actas a monopole or loop antenna.
• Trace antennas form a monopole with a quarter wavelength (À/4) at the resonant frequency.
• High-frequency components of the fonda­ mental radiate more readily because their shorter wavelengths are comparable to trace lengths.
• Outer microstrip layers will radiate; hence critical, high-speed traces should be avoided on these layers.
• A low-Dk material is preferred for high­ speed designs.

La longueur d’onde de l’énergie électromagnétique
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