The field of radio frequency (RF) and microwave engineering generally covers the behaviorof alternating current signals with frequencies in the range of 100 MHz (1 MHz = 106Hz)to 1000 GHz (1 GHz = 109Hz). RF frequencies range from very high frequency (VHF)(30–300 MHz) to ultra high frequency (UHF) (300–3000 MHz), while the termmicrowaveis typically used for frequencies between 3 and 300 GHz, with a corresponding electricalwavelength betweenλ=c/f =10 cm andλ=1 mm, respectively. Signals with wavelengths on the order of millimeters are often referred to as millimeter waves. Figure 1.1shows the location of the RF and microwave frequency bands in the electromagnetic spectrum. Because of the high frequencies (and short wavelengths), standard circuit theoryoften cannot be used directly to solve microwave network problems. In a sense, standardcircuit theory is an approximation, or special case, of the broader theory of electromagnetics as described by Maxwell’s equations. This is due to the fact that, in general, thelumped circuit element approximations of circuit theory may not be valid at high RF andmicrowave frequencies. Microwave components often act asdistributed elements, wherethe phase of the voltage or current changes significantly over the physical extent of the device because the device dimensions are on the order of the electrical wavelength. At muchlower frequencies the wavelength is large enough that there is insignificant phase variationacross the dimensions of a component. The other extreme of frequency can be identified
as optical engineering, in which the wavelength is much shorter than the dimensions of the
component. In this case Maxwell’s equations can be simplified to the geometrical optics
regime, and optical systems can be designed with the theory of geometrical optics. Such
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