Six simulations for thirteen lectures

Every module bundles two or three lectures into one live model. Move a slider and the geometry, the spectrum, the constellation or the budget all recompute — so the equation on the slide becomes something the class can push on. Numbers follow Roddy, Satellite Communications, and the ITU-R recommendations the course cites.

How to run these in class

Start from the worked example. Each module opens on the preset used in the lecture, so the readout matches the number already on the slide. Then change one input and ask what should happen before releasing the mouse.
The presets are the course's own cases — Ho Chi Minh City to VINASAT-1, Ka-band rain in Ho Chi Minh City, a C-band GEO budget, a 550 km LEO pass.
Everything is computed, not animated artwork. If a student disputes a figure, open the step list inside the panel: each line shows the formula and its intermediate value.

Runs offline — no network needed once the page has loaded.

Lecture 1Lecture 2Lecture 3Roddy ch. 1–3

Orbits, Coverage and Look Angles

One force balance sets everything else. Pick an altitude and the period, speed, horizon, pass length and propagation delay all follow from Kepler's third law — then point a real dish at a real satellite and read off azimuth, elevation and slant range.

Orbit explorer

§1.5 force balance · §1.6 orbit classes · §2.4 Kepler's third law

Altitude h550 km Elevation mask ε10°

T = 2π·√(a³/μ) v = √(μ/a) μ = 398 600 km³/s² a = Rᴇ + h

GEO look angles

§3.2 azimuth, elevation and range — Example 3.4, Ho Chi Minh City to VINASAT-1

Station latitude10.82° N Station longitude106.63° E Satellite longitude132.00° E

What to draw out of this module

Altitude buys period, and period costs everything else. Drag from 550 km to GEO: the period goes from about 96 minutes to a sidereal day, one satellite's coverage grows from 3 % to 42 % of the globe, and the pass stops ending — but the one-way delay goes from 2 ms to 119 ms and the free-space loss rises by roughly 35 dB.
There is no altitude that wins. Ask the class which column they would sacrifice for a voice call, for a GNSS fix, for a broadcast TV channel. Each answer picks a different row of the readout.
Elevation is the hidden variable. Raise the mask from 0° to 20° and watch the usable pass collapse. This is the same angle that drives atmospheric and rain loss in Module 2.
Check the worked example. The default preset reproduces Example 3.4 — Ho Chi Minh City to VINASAT-1 at 132° E gives roughly 111.6° azimuth, 58° elevation, 36 620 km range.

Rᴇ = 6378.14 km · a_GSO = 42 164 km · sidereal day = 86 164.1 s

Lecture 4Lecture 9ITU-R P.838 · P.618

Propagation, Rain Fade and Polarization

The atmosphere is the one part of the path that changes while you are using it. Here is the full ITU rain-attenuation procedure step by step, and the polarization geometry that decides whether a second channel on the same frequency is a gift or a source of interference.

Rain attenuation — the ITU procedure

§4.4 specific attenuation γ = k·R^α · effective path · time-percentage scaling

Frequency20.0 GHz Elevation angle θ50° Rain rate R₀.₀₁95 mm/h Rain height h_R4.90 km

Polarization and cross-polar isolation

§4.6–4.7 mismatch loss · §4.9 XPD and frequency reuse · §4.10 Faraday rotation

Receiver tilt misalignment0° Axial ratio of wave1.0 (linear→∞) Carrier frequency4.0 GHz Total electron content50 TECU

L_pol = −20·log₁₀|cos Δτ| Faraday Ω ≈ 2.36×10⁴ · B_av · TEC / f²

What to draw out of this module

Rain fade is a frequency cliff, not a slope. Hold the rain rate at the Ho Chi Minh City value and step C → Ku → Ka. The attenuation goes from under a decibel to tens of decibels for exactly the same storm. This is the single strongest argument in the course for why tropical Ka-band systems need adaptive coding.
Elevation is a lever you can actually pull. At 20 GHz in Ho Chi Minh City, dropping from 50° to 15° triples the slant path through the rain cell and takes the 0.01 % fade from about 35 dB to 64 dB. It is the reason a Vietnamese earth station prefers a satellite near its own longitude.
Horizontal polarization always suffers more — raindrops flatten as they fall, so they present a wider cross-section to a horizontal field. Toggle the polarization and watch k and α move.
Frequency reuse is only as good as the worst fade. In the right-hand panel, rain depolarization and Faraday rotation both eat the cross-polar discrimination that dual-polarization capacity depends on.

k and α interpolated log-log from ITU-R P.838-3 · path reduction from ITU-R P.618 · Faraday with B_av ≈ 3×10⁻⁵ T

Lecture 5Lecture 10Roddy ch. 6, 12

Antennas, Beams and Free-Space Loss

Gain is not amplification — it is concentration, and the bill arrives as beamwidth. Size a reflector and watch the main lobe narrow, the sidelobes appear and the pointing tolerance shrink; then steer a phased array electronically and see the same aperture rule at work.

Parabolic reflector

§5.9 gain and efficiency · §5.10 effective aperture · §5.12 beamwidth and sidelobes

Diameter D3.0 m Frequency12.0 GHz Aperture efficiency η0.65 Mispointing0.00°

G = η(πD/λ)² θ₃dB ≈ 70λ/D A_eff = Gλ²/4π far field d > 2D²/λ

Phased array beam steering

§5.14 array factor and electronic steering · §5.15 Friis transmission

Number of elements N16 Element spacing d0.50 λ Steer angle θ₀0°

AF(θ) = sin(Nψ/2) / (N·sin(ψ/2)), ψ = kd·sinθ + β, β = −kd·sinθ₀

Grating lobes appear once d/λ > 1/(1+|sin θ₀|) — push the spacing past half a wavelength and a second beam walks in from the horizon.

What to draw out of this module

Six decibels of gain costs half the beamwidth. Double D and the gain rises 6 dB while θ₃dB halves. Then add mispointing: a 9 m C-band dish off by a quarter of a degree has already given back most of what the extra aperture bought.
The same λ/D rule governs both panels. A 16-element array at half-wavelength spacing has the same beamwidth as a reflector two apertures wide — concentration depends on electrical size, never on the technology.
Steering is not free. Push θ₀ toward 60° and watch the main lobe broaden and the gain drop: the array's projected aperture shrinks as cos θ₀.
Grating lobes are an aliasing problem. Spacing beyond half a wavelength under-samples the aperture, exactly as a sample rate below Nyquist does in Module 5.

Uniformly illuminated circular aperture, |2J₁(u)/u|² with u = (πD/λ)sin θ · uniform linear array factor

Lecture 6Lecture 10Roddy ch. 12

The Space Link Budget

The accounting sheet the whole course converges on. Uplink and downlink are computed separately, combined the way powers add, and then rained on — so the class can watch the famous double penalty do its work: the signal falls and the noise temperature rises at the same instant.

Uplink · downlink · combined

§10.2 EIRP · §10.3 free-space loss · §10.5 system noise · §10.6 G/T · §10.10 combined C/N

Downlink frequency4.00 GHz Satellite EIRP34.0 dBW Earth-station dish D3.0 m LNA noise temperature45 K Feeder loss before LNA0.50 dB Elevation angle35° Rain attenuation on downlink0.0 dB Information bit rate36 Mbit/s

Downlink waterfall

every term from satellite transmitter to demodulator input

System noise temperature

§10.5 antenna noise, lossy feeder and the amplifier cascade

T_s = T_ant/L_f + T_F(1 − 1/L_f) + T_LNA + T₂/G₁ + T₃/(G₁G₂)

What to draw out of this module

Put the low-noise amplifier at the feed. Push the feeder loss from 0.5 dB to 3 dB and the system temperature climbs steeply — a decibel of loss ahead of the LNA costs signal and adds noise in the same stroke. This is why the LNB is bolted to the dish and not to the television.
The double penalty. Drag the rain slider. The carrier drops by the attenuation, and the antenna temperature rises toward the physical temperature of the rain cell, because an absorber is also an emitter. The C/N falls faster than the attenuation alone would predict — always ask the class to predict the ratio before they see it.
Combined C/N is dominated by the weaker link. Powers add as reciprocals, so improving an already-strong uplink changes almost nothing. Make them find the knee.
G/T is the only receiver number that matters. Trade dish diameter against LNA temperature and find two configurations with the same G/T but very different cost.

Boltzmann −228.6 dBW/K/Hz · T_m = 275 K for the rain medium · sky noise from a simple elevation/zenith-opacity model

Lecture 7Lecture 8Roddy ch. 10–11

Digital Signals, Modulation and Coding

Where the decibels earned in Modules 3 and 4 are finally spent on bits. Add noise to a live constellation and count the errors, close the eye with the wrong filter roll-off, then buy back the margin with a code — and watch the Shannon wall refuse to move.

Constellation under noise

§7.10 digital carrier modulation · §7.11 BER and E_b/N₀

E_b/N₀8.0 dB Symbols drawn1500

BER curves and coding gain

§8.8 coding gain · §8.10 the Shannon limit · §8.11 turbo and LDPC

The dashed red wall at −1.59 dB is Shannon's bound as bandwidth grows without limit. No code reaches it; every code in the course is a claim about how close you can get and how much complexity that costs.

Eye diagram and intersymbol interference

§7.9 Nyquist, raised-cosine filtering and the eye

Roll-off factor α0.35 Timing offset0 % Noise0.00

Hamming (7,4) — break it and watch it heal

§8.3 generator matrix, parity-check matrix and the syndrome

Message bits d₁d₂d₃d₄1011

Flip one bit anywhere in the seven and the syndrome names its position exactly. Flip two and the syndrome still points somewhere — confidently, and at the wrong bit. That gap is what d_min = 3 means.

What to draw out of this module

BPSK and QPSK cost the same energy per bit. Switch between them at a fixed E_b/N₀ and the measured error rate barely moves — QPSK simply packs two bits into the same symbol. Then try 16QAM and watch the price of spectral efficiency appear.
Coding gain is real decibels. Pick a target of 10⁻⁵ and read the horizontal distance between the uncoded curve and the turbo curve: close to 9 dB, obtained by changing software rather than hardware. The same 9 dB would otherwise mean eight times the transmitter power.
The eye closes from two directions. Reduce the roll-off toward zero for a narrow spectrum and ISI closes the eye horizontally; add noise and it closes vertically. Sampling instant matters as much as signal-to-noise.
Single-error correction is a geometric fact. With d_min = 3 the spheres of radius one around each codeword do not touch; with two errors you land inside the wrong sphere. Demonstrate the double-error failure deliberately — it lands better than the success case.

Gray-mapped constellations · theory curves from the Q-function · coding gains at BER 10⁻⁵ from Lecture 8

Lecture 11Lecture 12Lecture 13

Multiple Access, Networks and Services

One transponder, many users. Three ways to divide it, a transport protocol that was never designed for a half-second round trip, and the positioning service that turns the same geometry from Module 1 into a fix on the ground.

Sharing one transponder

§11.3 FDMA · §11.6 TDMA frames and guard time · §11.8 CDMA

Active users6 Guard band / guard time8 % Transponder bandwidth36 MHz

TCP over a satellite link

§12.8 congestion control · §12.9 bandwidth-delay product · §12.12 split connections

Link rate10 Mbit/s Receive window64 kB Packet loss rate0.10 %

GNSS trilateration and dilution of precision

§13.16 GPS principle, clock bias, DOP and differential correction

Satellites in view4 Spread across the sky90° Pseudorange error σ5.0 m

Squeeze the satellites into one patch of sky and the position ellipse stretches without any single measurement getting worse. Geometry, not ranging accuracy, is what fails in an urban canyon.

Digital television — from pixels to transponder

§13.3 bit rates for digital TV · §13.4 MPEG compression · §13.5 FEC overhead

Format1080i HD Compression ratio60 : 1 FEC code rate3/4

What to draw out of this module

All three access schemes pay a tax. FDMA pays in guard bands and intermodulation backoff, TDMA pays in guard time and preamble, CDMA pays in processing gain and self-interference. Raise the user count and watch which one degrades first.
A GEO hop breaks TCP arithmetic. At 540 ms round trip a 64 kB window caps throughput near 1 Mbit/s no matter how fast the link is. Show the bandwidth-delay product, then open the window and watch the ceiling lift — this is exactly what RFC 2488 recommends.
Loss is interpreted as congestion. Add a tenth of a percent of packet loss and the Mathis-model throughput collapses on a long link, because TCP reads satellite bit errors as a signal to slow down.
Compression is what makes DTH possible. Uncompressed HD needs roughly a gigabit per second; a transponder has tens of megabits. Everything between those two numbers is MPEG, and the FEC rate then decides how much of the channel carries payload at all.

Mathis throughput bound · GDOP from the geometry matrix · studio rates per ITU-R BT.601 / BT.709