inductance, or both. A point is eventually reached where the inductance and the capacitance can be reduced no further. This is the highest frequency at which a conventional circuit can oscillate. ">
In ordinary electronic equipment a resonant circuit consists of a coil and a capacitor that are connected either in series or in parallel. The resonant frequency of the circuit is increased by reducing the capacitance, the inductance, or both. A point is eventually reached where the inductance and the capacitance can be reduced no further. This is the highest frequency at which a conventional circuit can oscillate.
The upper limit for a conventional resonant circuit is between 2000 and 3000 megahertz. At these frequencies, the inductance may consist of a coil of one-half turn, and the capacitance may simply be the stray capacitance of the coil. Tuning a one-half turn coil is very difficult and tuning stray capacitance is even more difficult. In addition, such a circuit will handle only very small amounts of current.
NEETS, Module 10, Introduction to Wave Propagation explained that a 1/4l section of transmission line can act as a resonant circuit. The same is true of a 1/4l section of waveguide. Since a waveguide is hollow, it can also be considered as a RESONANT CAVITY.
By definition, a resonant cavity is any space completely enclosed by conducting walls that can contain oscillating electromagnetic fields and possess resonant properties. The cavity has many advantages and uses at microwave frequencies. Resonant cavities have a very high Q and can be built to handle relatively large amounts of power. Cavities with a Q value in excess of 30,000 are not uncommon. The high Q gives these devices a narrow bandpass and allows very accurate tuning. Simple, rugged construction is an additional advantage.
Although cavity resonators, built for different frequency ranges and applications, have a variety of shapes, the basic principles of operation are the same for all.
One example of a cavity resonator is the rectangular box shown in figure 1-58, view (A). It may be thought of as a section of rectangular waveguide closed at both ends by conducting plates. The frequency at which the resonant mode occurs is 1/2l of the distance between the end plates. The magnetic and electric field patterns in the rectangular cavity are shown in view (B).
Figure 1-58A. - Rectangular waveguide cavity resonator. RESONATOR SHAPE
Figure 1-58B. - Rectangular waveguide cavity resonator.
FIELD PATTERNS OF A SIMPLE MODE
The rectangular cavity is only one of many cavity devices that are useful as high-frequency resonators. Figure 1-59 shows the development of a cylindrical resonant cavity from an infinite number of quarter-wave sections of transmission line. In view (A) the 1/4l section is shown to be equivalent to a resonant circuit with a very small amount of inductance and capacitance. Three 1/4l sections are joined in parallel in view (B). Note that although the current-carrying ability of several 1/4l sections is greater than that of any one section, the resonant frequency is unchanged. This occurs because the addition of inductance in parallel lowers the total inductance, but the addition of capacitance in parallel increases the total capacitance by the same proportion. Thus, the resonant frequency remains the same as it was for one section. The increase in the number of current paths also decreases the total resistance and increases the Q of the resonant circuit. View (C) shows an intermediate step in the development of the cavity. View (D) shows a completed cylindrical resonant cavity with a diameter of 1/2l at the resonant frequency.
Figure 1-59A. - Development of a cylindrical resonant cavity. QUARTER-WAVE SECTION EQUIVALENT TO LC CIRCUIT
Figure 1-59B. - Development of a cylindrical resonant cavity. QUARTER-WAVE LINES JOINED
Figure 1-59C. - Development of a cylindrical resonant cavity. CYLINDRICAL RESONANT CAVITY BEING FORMED FROM QUARTER-WAVE SECTIONS
Figure 1-59D. - Development of a cylindrical resonant cavity. CYLINDRICAL RESONANT CAVITY
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