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Meander Line Calculator Meander Line Calculator Formulas Used: 1. Free-Space Wavelength (λ₀): \( \lambda_0 = \frac{c}{f} \) where \( c \) is the speed of light (\( 3 \times 10^8 \) m/s) and \( f \) is the frequency in Hz. 2. Effective Permittivity (εeff): \( \varepsilon_{eff} = \frac{\varepsilon_r + 1}{2} + \frac{\varepsilon_r - 1}{2} \times \left( \frac{1}{\sqrt{1 + 12 \frac{h}{W}}} \right) \) where \( \varepsilon_r \) is the relative permittivity of the substrate, \( h \) is the substrate thickness, and \( W \) is the meander line width. 3. Guided Wavelength (λg): \( \lambda_g = \frac{\lambda_0}{\sqrt{\varepsilon_{eff}}} \) 4. Meander Line Length (L_guided): \( L_{guided} = \frac{\lambda_g}{2} \) 5....

Beamwidths and Side lobe levels In addition to  directivity , the  radiation patterns of antennas  are also characterized by their beamwidths and sidelobe levels (if applicable). These concepts can be easily illustrated. Consider the radiation pattern given by: This pattern is actually fairly easy to generate using  Antenna Arrays , as will be seen in that section. The 3-dimensional view of this radiation pattern is given in Figure 1. Figure 1. 3D Radiation Pattern. The polar (polar angle measured off of z-axis) plot is given by: Figure 2. Polar Radiation Pattern. The  main beam  is the region around the direction of maximum radiation (usually the region that is within 3 dB of the peak of the main beam). The main beam in Figure 2 is centered at 90 degrees. The  sidelobes  are smaller beams that are away from the main beam. These sidelobes are usually radiation in undesired directions which can never be completely eliminated. The sidelobes in Figur...

  Radiation Pattern A  radiation pattern  defines the variation of the power radiated by an antenna as a function of the direction away from the antenna. This power variation as a function of the arrival angle is observed in the antenna's  far field . As an example, consider the 3-dimensional radiation pattern in Figure 1, plotted in  decibels (dB)  . Figure 1. Example radiation pattern for an Antenna (generated with FEKO software). This is an example of a donut shaped or toroidal radiation pattern. In this case, along the z-axis, which would correspond to the radiation directly overhead the antenna, there is very little power transmitted. In the x-y plane (perpendicular to the z-axis), the radiation is maximum. These plots are useful for visualizing which directions the antenna radiates. Typically, because it is simpler, the radiation patterns are plotted in 2-d. In this case, the patterns are given as "slices" through the 3d plane. The same pattern in Fig...

Frequency: Frequency is one of the most important concepts in the universe and to antenna theory, which we will see. But fortunately, it isn't too complicated. Beginner Level (or preliminaries): Antennas function by transmitting or receiving electromagnetic (EM) waves. Examples of these electromagnetic waves include the light from the sun and the waves received by your cell phone or radio. Your eyes are basically "receiving antennas" that pick up electromagnetic waves that are of a particular frequency. The colors that you see (red, green, blue) are each waves of different frequencies that your eyes can detect. All electromagnetic waves propagate at the same speed in air or in space. This speed (the speed of light) is roughly 671 million miles per hour (1 billion kilometers per hour). This is roughly a million times faster than the speed of sound (which is about 761 miles per hour at sea level). The speed of light will be denoted as c in the equations that follow. We like...