EM Wave & Antenna

Plane wave along +k, then a far-field pattern in spherical coordinates. Units on the readout are the real ones.

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Linear · +k

E
B × c
S
+k

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|E| peak

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Frequency: —
Wavelength: —
k: —
|B| = |E|/c: —
S avg: —

Wave

Frequency

Wavelength

E0 V/m

Polarization

E angle deg

Time

View speed cyc/s

Poynting vector

Free-space plane wave along +x, labeled +k. Phase is kx − ωt. Linear E and B share that cosine, stay perpendicular to each other and to k, and |B| = |E|/c. B arrows are drawn × c so the ratio looks equal; the readout is tesla. E angle is from +y toward +z. Circular sense is IEEE, looking along +k: clockwise is RHCP. E0 is the major-axis peak. S = E × H points along +k. Average power is E0²(1+AR²)/(2 Z0), with Z0 = μ0 c, μ0 = 4π×10⁻⁷ H/m, and c = 299792458 m/s. The axis is two wavelengths. View speed only slows the picture.

D0: —
E-plane HPBW: —
H-plane: —
First nulls: —
Peak: —

Antenna

L/λ

Ground

Perfect ground plane

h/λ

Scale

Far field, lossless, so the peak number is directivity in dBi. The z-dipole uses F(θ) = [cos(π L/λ · cosθ) − cos(π L/λ)] / sinθ. A half-wave dipole is about 2.15 dBi with an E-plane HPBW near 78°. Extra lobes show up once L is past about 1.25λ. The PEC sheet is the xy plane. A vertical current at height h is imaged in phase: the field is multiplied by 2 cos(2π h/λ · cosθ), and the lower hemisphere is zero. The patch is the thin-substrate rectangular model (Balanis two-slot): length L along x, width W along y, infinite ground already included, so h is not applied. E-plane is φ = 0. Dipole H-plane is θ = 90°. Patch H-plane is φ = 90°. dB radius floors at −40 dB.