Wireless 101
M07 · L02
Module 7 · Lesson 2

Reading the Spec Sheet

Every antenna ever sold is described by the same seven numbers. Learn them and you can compare a $3 whip to a $30,000 dish without seeing either one.

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Wireless 101
M07 · L02
Two numbers, one shape

Directivity vs Gain

Gain from directivity
G = e_{\mathrm{rad}} \, D

Directivity is geometry. Gain is geometry after losses. At 60% efficiency you lose 10·log(0.6) = 2.2 dB; at 90%, only 0.46 dB. Datasheets quote gain; simulators print directivity.

02 / 11
Wireless 101
M07 · L02
Gain over what?

dBi and dBd

Converting references
G_{\mathrm{dBi}} = G_{\mathrm{dBd}} + 2.15

A half-wave dipole has directivity 1.641 = 2.15 dBi (M2-L4). So a Yagi sold as 10 dBd is 12.15 dBi. Marketing quotes dBi; cautious engineers quote dBd.

03 / 11
Wireless 101
M07 · L02
Anatomy of a pattern

Lobes, Nulls, Cuts

  • Main lobe — the beam holding the peak
  • Side lobes — first one 13.3 dB down for a uniform aperture
  • Back lobe — front-to-back typically 20–35 dB
  • Nulls — a resource: aim one at an interferer
  • E-plane / H-plane — two orthogonal cuts, often nothing alike
04 / 11
Wireless 101
M07 · L02
The −3 dB width

Half-Power Beamwidth

Aperture beamwidth
\theta_{3\mathrm{dB}} \approx \frac{70 \, \lambda}{D_a}

A 1 m dish at 10 GHz (λ = 3 cm): 70 × 0.03 / 1 = 2.1°. Then G ≈ 30000/(2.1 × 2.1) = 6803 = 38.3 dBi — and the aperture formula independently says 38.2.

05 / 11
Wireless 101
M07 · L02
Try it

Pattern Explorer

Grow the aperture and watch the main lobe narrow, the side lobes multiply, and directivity climb. The second slider spends efficiency to turn D into G.

Aperture 6.0λ · D 26.6 dBi · 8.5°
Efficiency e 65% · G 24.7 dBi
06 / 11
Wireless 101
M07 · L02
Which way does E point?

Polarization

  • Linear — vertical, horizontal, or slant ±45°
  • Circular — RHCP and LHCP, field rotating once per cycle
  • Cross-polarized — infinite isolation in theory, 20–30 dB in practice
  • Linear to circular — a flat, predictable 3 dB
  • GPS uses RHCP — a known 3 dB beats an unknown fade
07 / 11
Wireless 101
M07 · L02
The 50 Ω world

Impedance and Matching

Reflection and VSWR
\mathrm{VSWR} = \frac{1 + |\Gamma|}{1 - |\Gamma|}

VSWR 2:1 gives Γ = 1/3, so |Γ|² = 11.1% reflected — a mere 0.51 dB lost, and 9.5 dB return loss. That is why 2:1 is the usual pass mark.

08 / 11
Wireless 101
M07 · L02
Where the watts go

Efficiency

Ohmic loss in the conductors, dielectric loss in the substrate. And the hard floor from M7-L1: shrink an antenna below resonant size and its radiation resistance collapses while its ohmic resistance does not — so small means inefficient.

Well built
90–95%
In a phone
40–50%
At e = 0.5
−3.0 dB
09 / 11
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

10 / 11
Wireless 101
M07 · L02
Recap

What you learned

  • G = e·D, and dBi = dBd + 2.15 — always check the reference
  • The pattern is the real spec: main lobe, side lobes, back lobe, nulls
  • HPBW ≈ 70λ/D → 2.1° for a 1 m dish at 10 GHz → 38.3 dBi
  • Polarization must match; VSWR 2:1 costs only 0.5 dB; small means lossy
Up next in Module 7
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