Wireless 101
M07 · L01
Module 7 · Lesson 1

Where the Wave Leaves the Wire

Everything so far has happened inside a conductor. At some point the signal has to leave, cross open space, and be caught again. The component that does both is the antenna.

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Wireless 101
M07 · L01
The mechanism

Only Acceleration Radiates

A charge sitting still has a static field. A steady current has a static field too — a DC circuit radiates nothing. Change a charge’s velocity and a kink in the field peels off at c and never comes back.

Larmor radiated power
P_{\text{rad}} = \frac{q^2 a^2}{6\pi \varepsilon_0 c^3}
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Wireless 101
M07 · L01
What an antenna is

A Transducer, Like a Speaker

A speaker turns a signal into a pressure wave. An antenna turns a guided wave — bound to a coax or a trace — into an unguided one that needs no conductor. Same information, different form.

And it is passive
Gain redistributes power. It never adds any.
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Wireless 101
M07 · L01
Size follows λ

Half a Wavelength

Too short a wire and radiation resistance collapses, so the power just warms the metal. The natural length is λ/2 — and c = fλ turns a frequency straight into centimetres of hardware.

1 MHz
150 m
100 MHz
1.5 m
2.4 GHz
6.25 cm
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Wireless 101
M07 · L01
Three regions

Near Field, Far Field

Region boundaries, largest dimension D
r < 0.62\sqrt{\tfrac{D^3}{\lambda}} \;\Big|\; r > \tfrac{2D^2}{\lambda}

Inside the first radius energy sloshes without escaping. Between them the wave is leaving but the pattern is still forming. Only beyond the second does the antenna have the gain it is sold with.

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Wireless 101
M07 · L01
Try it

Size and Distance

Sweep 30 MHz to 30 GHz and watch λ, the dipole, and the three field regions rearrange. The far-field radius honours the r > 3λ floor when D is small.

Freq 1.02 GHz · λ 29.5 cm
Size D D 1.0 m · far 6.78 m
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Wireless 101
M07 · L01
Worked example

A 1 m Dish at 10 GHz

  • λ = 3×10⁸/10¹⁰ = 3 cm
  • Reactive: 0.62√(1/0.03) = 3.6 m
  • Far field: 2×1²/0.03 = 66.7 m

Sixty-seven metres of range to measure one dish — which is why near-field scanners exist.

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Wireless 101
M07 · L01
The best deal in the subject

Reciprocity

Any linear, passive antenna behaves identically transmitting and receiving: same pattern, same gain, same impedance. An antenna 20 dB stronger toward the horizon is 20 dB more sensitive toward the horizon.

What it buys you
Measure once. Use the number both ways.
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Wireless 101
M07 · L01
The receive picture

Effective Aperture

Gain as collecting area
A_e = \frac{\lambda^2}{4\pi}\, G

An isotropic antenna collects 0.72 m² at 100 MHz but only 0.72 cm² at 10 GHz — 10,000× less. That λ² is why low bands need big antennas and high bands need gain.

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Wireless 101
Knowledge Check

Check what stuck

Four questions from this lesson. Answer to see why — the explanation appears whether you were right or wrong. Nothing is scored or saved.

Question 1 of 0
Score 0/0

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Wireless 101
M07 · L01
Recap

What you learned

  • Accelerating charge radiates; steady current does not
  • An antenna is a passive transducer, sized by λ/2
  • Reactive, Fresnel, then far field beyond 2D²/λ
  • Reciprocity: identical on transmit and receive
  • Ae = (λ²/4π)G — gain is collecting area
Up next in Module 7
Antenna Parameters →
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