.net barcode reader free Development of the rectangular waveguide from parallel transmission lines in Software

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Development of the rectangular waveguide from parallel transmission lines
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One way of visualizing how a waveguide works is to develop the theory of waveguides from the theory of elementary parallel transmission lines (see Chap 3) Figure 19-3A shows the basic parallel transmission line which was introduced in Chap 3 The line
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Development of the rectangular waveguide from parallel transmission lines 371 consists of two parallel conductors separated by an air dielectric Because air won t support the conductors, ceramic or other material insulators are used as supports There are several reasons why the parallel transmission line per se is not used at microwave frequencies Skin effect increases ohmic losses to a point that is unacceptable Also, the insulators supporting the two conductors are significantly more
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19-2 Rectangular waveguide (end view)
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End view of two wire line 19-3 Development of waveguide from parallel line
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372 Microwave waveguides and antennas lossy at microwave frequencies than at lower frequencies Finally, radiation losses increase dramatically Figure 19-3B shows the electric fields surrounding the conductors The fields add algebraically (either constructively or destructively), resulting in pinching of the resultant field along one axis, and bulging along the other This geometry increases radiation losses at microwave frequencies Now let s consider the quarter-wavelength shorted stub The looking-in impedance of such a stub is infinite When placed in parallel across a transmission line (Fig 19-4A) the stub acts like an insulator In other words, at its resonant frequency, the stub is a metallic insulator, and can be used to physically support the transmission line Again, because the impedance is infinite, we can connect two quarterwavelength stubs in parallel with each other across the same points on the transmission line (Fig 19-4B) without loading down the line impedance This arrangement effectively forms a half-wavelength pair The impedance is still infinite, so no harm is done Likewise, we can parallel a large number of center-fed half-wavelength pairs along the line, as might be the case when a long line is supported at multiple points The waveguide is analogous to an infinite number of
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Two wire transmission line
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19-4A Quarter-wave stub analogy
/4 Short circuit
19-4B Quarter-wave stub analogy extended /4
Propagation modes in waveguides 373
19-4C Quarter-wave stub analogy extended even further /4
center-fed half-wave pairs of quarter-wave shorted stubs connected across the line The result is the continuous metal pipe structure of the common rectangular waveguide (Fig 19-4C) On first glance, relating rectangular waveguide to quarter-wavelength shorted stubs seems to fall down, except at the exact resonant frequency It turns out, however, that the analogy also holds up at other frequencies, so long as the frequency is higher than a certain minimum cutoff frequency The waveguide thus acts like a highpass filter There is also a practical upper frequency limit In general, waveguides support a bandwidth of 30 to 40 percent of cutoff frequency As shown in Fig 19-5, the center line of the waveguide (which represents the points where the conductors are in the parallel line analogy) becomes a shorting bar between segments, and that bar widens or narrows according to operating frequency Thus, the active region is still a quarter-wavelength shorted stub Below the cutoff frequency, the structure disappears entirely, and the waveguide acts like a parallel transmission line with a low-impedance inductive reactance shorted across the conductors When modeled as a pair of quarter-wavelength stubs, the a dimension of the waveguide is a half-wavelength long The cutoff frequency is defined as the frequency at which the a dimension is less than a half-wavelength
Propagation modes in waveguides
The signal in a microwave waveguide propagates as an electromagnetic wave, not as a current Even in a transmission line, the signal propagates as a wave because the current in motion down the line gives rise to electric and magnetic fields, which behave as an electromagnetic field The specific type of field found in transmission lines, however, is a transverse electromagnetic (TEM) field The term transverse implies things at right angles to each other, so the electric and magnetic fields are perpendicular to the direction of travel In addition to the word transverse, these right-angle waves are said to be normal or orthogonal to the direction of travel three different ways of saying the same thing: right-angledness
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