USAFA DFEC

ECE 495 — Electromagnetic Warfare and Survivability

Block 1: Radar Fundamentals
Lesson 2: EM Spectrum and Propagation
Juan Jurado, Col, USAF, Ph.D.
Permanent Professor and Head
Electrical and Computer Engineering
Fall 2026
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Block 1 · Lesson 2 · Where We Left Off

Where We Left Off

L1 framed the problem: kill chains, ES / EP / EA, the B-21 thread.

Before we can quantify any of it, we need the physics layer underneath.

Today
EM waves, propagation, polarization, and antenna basics — the building blocks of every equation in B1.

Block 1 · Lesson 2 · Objectives

Lesson Objectives

By the end of this lesson, you will be able to:

  • Identify the radar bands across the EM spectrum and connect them to mission
  • Compute wavelength and free-space path loss (FSPL)
  • Explain why polarization matters in EW
  • Relate antenna gain to aperture and beamwidth
Pick a frequency and you have picked everything downstream of it.

Block 1 · Lesson 2 · Part One

The Spectrum

Frequency choice is a chain of consequences: antenna size, resolution, weather loss, and how easy you are to jam.

Block 1 · Lesson 2 · Radar Bands

Radar Lives in a Narrow Slice

Seven IEEE letter bands, roughly 1 to 40 GHz, carry nearly every radar in this course.

L1–2 GHz
S2–4 GHz
C4–8 GHz
X8–12 GHz
Ku12–18 GHz
K18–27 GHz
Ka27–40 GHz

Block 1 · Lesson 2 · Radar Bands

The EM Spectrum: Radar Bands

BandFrequencyWavelengthTypical Use
L
1–2 GHz30–15 cmLong-range surveillance
S
2–4 GHz15–7.5 cmSurveillance, weather, ATC
C
4–8 GHz7.5–3.75 cmWeather, civil radar
X
8–12 GHz3.75–2.5 cmFire control, airborne
Ku
12–18 GHz2.5–1.7 cmSAR, comm
K
18–27 GHz1.7–1.1 cmShort-range, high-res
Ka
27–40 GHz11–7.5 mmMissile seekers, mmW
  • Lower frequency ⇒ longer range, larger antennas, coarser resolution
  • Higher frequency ⇒ finer resolution, smaller antennas, more atmospheric loss
  • Threat band tells you what mission it is doing

Block 1 · Lesson 2 · Wavelength

Wavelength and Frequency

\[ \lambda f = c, \qquad c \approx 3 \times 10^{8}~\text{m/s} \]
  • $\lambda$ sets antenna size, target interaction, and how the wave bends around obstacles
  • Pick the frequency, the wavelength is fixed — no negotiating
Quick mental math
$f = 3$ GHz ⇒ $\lambda = 10$ cm  (S-band)
$f = 10$ GHz ⇒ $\lambda = 3$ cm  (X-band)
$f = 30$ GHz ⇒ $\lambda = 1$ cm  (Ka-band)
Wavelength sets antenna size, propagation, and target interaction.

Block 1 · Lesson 2 · Part Two

Propagation

Energy spreads over a sphere. Everything from here is bookkeeping on how little of it comes back.

Block 1 · Lesson 2 · Free Space

Free-Space Propagation

A transmitter radiates power $P_t$ isotropically. At range $R$, power spreads over a sphere of area $4\pi R^2$.

Power density at $R$
\[ S = \frac{P_t}{4\pi R^2} \]
Captured by aperture $A_e$
\[ P_r = S \cdot A_e = \frac{P_t \, A_e}{4\pi R^2} \]
  • One-way loss scales as $1/R^2$ — the inverse square law
  • Radar is two-way and goes as $1/R^4$ — that is why L1's fourth-power law was harsh

Block 1 · Lesson 2 · Path Loss

Free-Space Path Loss in dB

Give the isotropic receiver its actual catch area, $A_e = \lambda^{2}/4\pi$, and invert $P_r$: $f$ enters through the antenna, not the medium. With $R$ in km and $f$ in GHz:

The working formula
\[ L_{\text{fs,dB}} = 20\log_{10} R + 20\log_{10} f + 92.45 \]
  • Doubling $R$ adds 6 dB
  • Doubling $f$ adds 6 dB
  • At 100 km, X-band is about 10 dB worse than S-band — before atmosphere
Every 6 dB matters: range and frequency both pay in 6 dB chunks.

Block 1 · Lesson 2 · Polarization

Polarization

Direction of the E-field as the wave propagates. Two flavors that matter:

Why EW cares

  • Antennas only receive their matched polarization efficiently — mismatch loss can be 20–30 dB
  • RAM and shaping behave differently for V vs. H — LO is polarization-dependent
  • Polarization agility is an EP technique (own radar) and an EA target (threat radar)
Two flavors
Linear: Vertical (V) or Horizontal (H)
Circular: Right-hand (RHC) or Left-hand (LHC)
Polarization is a survival angle.

Block 1 · Lesson 2 · Antennas

Antennas: Gain, Aperture, and Beamwidth

Gain and beamwidth
\[ G \approx \frac{4 \pi A_e}{\lambda^{2}}, \qquad \theta_{\text{BW}} \approx \frac{\lambda}{D} \]
  • $G$ is the focusing factor over isotropic — units: dBi
  • $A_e$ is the effective collecting area
  • $\theta_{\text{BW}}$ is the angular extent of the main lobe
  • More gain ⇔ larger aperture ⇔ narrower beam ⇔ less coverage
Gain you buy with aperture; coverage you pay with beamwidth.

Block 1 · Lesson 2 · Patterns

Antenna Patterns

Four common shapes you will see this semester:

  • Omni — nearly equal gain in all directions; low gain
  • Fan beam — wide in one plane, narrow in the other; search radars
  • Pencil beam — narrow in both planes; trackers and seekers
  • ESA (electronically scanned array) — pencil beam that steers without moving the antenna
A real pattern has a main lobe, side lobes, and back lobes. Side lobes are an EA vulnerability (jam through them) and an EP design target (suppress them).

Today's Interactive Demo: Free-Space Path Loss

Companion script: L2_FreeSpacePathLoss.m
In L3 we wrap FSPL into the full radar range equation
Live demo

Free-Space Path Loss Calculator

usafa-ece.github.io/ece-495-ew

Block 1 · Lesson 2 · Type-along

Your Turn

Laptops open, MATLAB up. Eleven lines, typed together.

Block 1 · Lesson 2 · Quick Exercise

Quick Exercise / Type-along: Where Did the 6 dB Go?

Same dish ($A_e = 1$ m$^2$), same target at 50 km. Type this with me:

c = 3e8;             % m/s
Ae = 1.0;            % m^2 -- same physical antenna at every frequency
R_km = 50;           % fixed range to the target
f_GHz = [5 10 20];   % C-band, X-band, K-band
lam  = c ./ (f_GHz*1e9);
G_dB = 10*log10(4*pi*Ae ./ lam.^2);
L_dB = 20*log10(R_km) + 20*log10(f_GHz) + 92.45;
net  = G_dB - L_dB;
fprintf('  f(GHz)  lam(cm)   G(dBi)  FSPL(dB)    net(dB)\n');
fprintf('%8.1f %8.2f %8.2f %9.2f %10.2f\n', [f_GHz; lam*100; G_dB; L_dB; net]);

Read the last column. What do you notice?

Who is lying — the formula, or the antenna?

Block 1 · Lesson 2 · Wrap-Up

Wrap-Up

Key ideas
  • EM spectrum is a menu — each band has a price and a benefit
  • $\lambda f = c$ and FSPL $\propto (R/\lambda)^{2}$ underpin everything in B1
  • Polarization and antenna gain are the levers we tune in B2 and B3
Next lesson
  • L3: The radar range equation — where FSPL, RCS, and gain all meet
  • Work the L3 pre-flight before class — you could be the one up front