(Equation 3.25 )
f = 1/T (Equation 3.26 )
(Equation 3.27 )where T is the period of the function and to is any value of t. Equation 3.27 shows that the rms value is obtained by squaring the function, integrating the square of the function over any period, dividing by the period, and taking the square root. Integrating over a period is equivalent to calculating the area between the function, f2, and the t axis. Dividing this area by T is equivalent to calculating the average, or mean, of f2 over one period. For example, the rms value of the f(t) shown in Figure 3.18 is calculated as follows: The area between the f2 (t) curve and the t axis between t o and t o + T is (25 x 30) + (4 x 10) = 790; hence the rms value of f is
(Equation 3.28 )where gp is the peak value of the sinusoid.
(Equation 3.29 )
In free space, v is equivalent to the speed of light (c). In a dielectric material the velocity of the wave is slower than that of free space.
Figure 3.20 shows a planewave. E and H could have any directions in the plane as long as they are perpendicular to each other. Far away from its source, a spherical wave can be considered to be approximately a planewave in a limited region of space, because the curvature of the spherical wavefronts is so small that they appear to be almost planar. The source for a true planewave would be a planar source, infinite in extent.
|electric circuit theory (Kirchhoff's laws)|
|microwave theory or electromagnetic-field theory|
|optics or ray theory|
d = 2 L2 / (Equation 3.30)
The values of S range from unity to infinity. For the standing wave shown in Figure 3.23(b) ,
S = . A wave pattern is called a standing wave only when nodes exist, so the minimum value of the sinusoid is zero.
where is the magnitude of the reflection coefficient--the ratio of the reflected wave's magnitude to the incident wave's magnitude. For a terminated transmission line (the load impedance is equal to the characteristic impedance), the reflection coefficient is zero and the standing-wave ratio is unity.
The relative cutoff frequencies for a few modes are shown in Figure 3.26. Both m and n cannot be zero for any mode, because that would require all the fields to be zero. For the same reason, neither m nor n can be zero for the TM modes.
Go to Chapter 3.3
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Last modified: June 24, 1997
© October 1986, USAF School of Aerospace Medicine, Aerospace Medical Division (AFSC), Brooks Air Force Base, TX 78235-5301