There are two variables that determine the primary frequency of any resonant cavity. The first variable is PHYSICAL SIZE. In general, the smaller the cavity, the higher its resonant frequency. The second controlling factor is the SHAPE of the cavity. Figure 1-60 illustrates several cavity shapes that are commonly used. Remember from the previously stated definition of a resonant cavity that any completely enclosed conductive surface, regardless of its shape, can act as a cavity resonator.
Figure 1-60. - Several types of cavities.
Cavity resonators are energized in basically the same manner as waveguides and have a similar field distribution. If the cavity shown in figure 1-61 were energized in the TE mode, the electromagnetic wave would reflect back and forth along the Z axis and form standing waves. These standing waves would form a field configuration within the cavity that would have to satisfy the same boundary conditions as those in a waveguide. Modes of operation in the cavity are described in terms of the fields that exist in the X, Y, and Z dimensions. Three subscripts are used; the first subscript indicates the number of 1/2l along the X axis; the second subscript indicates the number of 1/2l along the Y axis; and the third subscript indicates the number of 1/2l along the Z axis.
Figure 1-61. - Rectangular cavity resonator.
Energy can be inserted or removed from a cavity by the same methods that are used to couple energy into and out of waveguides. The operating principles of probes, loops, and slots are the same whether used in a cavity or a waveguide. Therefore, any of the three methods can be used with cavities to inject or remove energy.
The resonant frequency of a cavity can be varied by changing any of three parameters: cavity volume, cavity capacitance, or cavity inductance. Changing the frequencies of a cavity is known as TUNING. The mechanical methods of tuning a cavity may vary with the application, but all methods use the same electrical principles.
A mechanical method of tuning a cavity by changing the volume (VOLUME TUNING) is illustrated in figure 1-62. Varying the distance d will result in a new resonant frequency because the inductance and the capacitance of the cavity are changed by different amounts. If the volume is decreased, the resonant frequency will be higher. The resonant frequency will be lower if the volume of the cavity is made larger.
Figure 1-62. - Cavity tuning by volume.
CAPACITIVE TUNING of a cavity is shown in view (A) of figure 1-63. An adjustable slug or screw is placed in the area of maximum E lines. The distance d represents the distance between two capacitor plates. As the slug is moved in, the distance between the two plates becomes smaller and the capacitance increases. The increase in capacitance causes a decrease in the resonant frequency. As the slug is moved out, the resonant frequency of the cavity increases.
Figure 1-63A. - Methods of changing the resonant frequency of a cavity. CHANGING THE CAPACITANCE
Figure 1-63B. - Methods of changing the resonant frequency of a cavity. CHANGING THE INDUCTANCE
INDUCTIVE TUNING is accomplished by placing a nonmagnetic slug in the area of maximum H lines, as shown in view (B) of figure 1-63. The changing H lines induce a current in the slug that sets up an opposing H field. The opposing field reduces the total H field in the cavity, and therefore reduces the total inductance. Reducing the inductance, by moving the slug in, raises the resonant frequency. Increasing the inductance, by moving the slug out, lowers the resonant frequency.
Resonant cavities are widely used in the microwave range, and many of the applications will be studied in chapter 2. For example, most microwave tubes and transmitting devices use cavities in some form to generate microwave energy. Cavities are also used to determine the frequency of the energy traveling in a waveguide, since conventional measurement devices do not work well at microwave frequencies.
Q.50 What two variables determine the primary frequency of a resonant cavity?