Section 6.3 · Further exercises · 9 of 10
Exercise 6.3.9: Why low-emissivity windows block mobile phones
About the further exercises of Section 6.3
Ten further exercises at normal incidence, in the spirit of the problems, the home exercises and the worked examples of this section, each group of five graded from easy to harder. They use only the toolbox at the head of this subsection.
Why low-emissivity windows block mobile phones
#Energy-saving windows carry a transparent metallic coating of sheet resistance (ohms per square). At GHz model the coated pane as a free-standing resistive sheet in air (the mm glass is electrically thin and is ignored). Across the sheet is continuous while jumps by the surface current . (a) Show that the incident wave sees the impedance , and find and in terms of . (b) Find the reflected, transmitted and absorbed fractions for and , and the transmission loss in dB. (c) Which absorbs the most, and how much? (d) Which would let the signal through with only dB loss?
Behind the sheet there is only a transmitted wave in air, so there . The sheet adds the current to the magnetic field without changing : in circuit language, a resistor connected across the line. Since air is on both sides, , and the rest of the power is absorbed in the coating.
With the field on the sheet, , so
, and :
gives , . Then , : and , the most a thin sheet can absorb.
: , so , far too resistive to reflect heat radiation.
The Joule loss per unit area is . Divided by it gives . gives , a perfect conductor, and gives , no sheet .
A low-emissivity coating is a silver layer about nm thick between dielectric antireflection layers: thin enough to pass most visible light, conductive enough (–) to reflect the long-wave infrared of a heated room and, as computed here, the microwaves of mobile networks. Measured losses of – dB are common. The remedy is to scribe the coating with a laser into a fine grid of isolated patches, which interrupts the currents at microwave frequencies while keeping the infrared reflection.
cf. Worked example 6.3.2