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EE 351 · Communication Systems

Week 5 · FM Broadcasting Systems

From AM radio to a real FM receiver

The broadcasting system first. The mathematics of frequency modulation last.

By the end you should be able to: explain why broadcasting moved from AM to VHF FM; compare MW, SW and FM-VHF coverage; describe how one FM carrier carries L, R and RDS; follow the receiver we built in MATLAB/Simulink; explain frequency reuse and who regulates it; and then say exactly what FM modulation does.

This deck follows the order used in class. Derivations, Bessel spectra and Carson's rule move to the Week 6 deck.

Roadmap

Nine questions, in the order we ask them

  1. Why did broadcasting move beyond AM?propagation, Armstrong, VHF
  2. Why does FM cover a city differently?MW vs SW vs FM-VHF, one landscape
  3. Why VHF?spectrum and fidelity
  4. How can one RF station carry L and R?M = L + R, D = L − R
  5. What is the 19 kHz tone, and why is RDS at 57 kHz?the multiplex
  6. What does a real receiver do?ADALM-Pluto + Simulink
  7. Why can the same frequency be reused?service contours, separation
  8. Who decides which frequencies may be used?ITU → CST → operator
  9. Only then: what exactly does FM modulation do?fi(t) = fc + kf m(t)

Part 1

Why did broadcasting move beyond AM?

Propagation first, then Armstrong, then the move to VHF.

Question 1 — Why did broadcasting move beyond AM?

Conventional AM lives in two places: MW and SW

Weeks 2–4 used AM. Broadcast AM sits in the MF / medium-wave band (about 530–1700 kHz) and in several HF / short-wave broadcast bands. What matters is not the table of numbers but how each band travels.

MF 0.3–3 MHz HF 3–30 MHz VHF 30–300 MHz 100 kHz1 MHz10 MHz100 MHz1 GHz MW broadcast SW (Saudi: 7.2–21.7 MHz) FM Band II 88–108 MHz log frequency axis · what service do we get this high?
MW and SW are both AM, but they use different physics to reach the listener. FM broadcasting sits two decades higher. SW values from the SBA international schedule (slide 7).

Question 1 — Why did broadcasting move beyond AM?

Medium wave: ground wave by day, a risky sky wave at night

Regional service. A medium-wave station covers its city and region mainly with the ground wave, which follows the curved Earth.

Not only ground wave. By day the D layer absorbs the sky wave. At night it fades, the wave reflects from the E and F layers and returns hundreds of kilometres away: far listeners, but also fading and interference between stations on the same frequency.

Switch Day / Night. Layer heights are to scale; ranges are order-of-magnitude, set by power and ground conductivity.†

Question 1 — Why did broadcasting move beyond AM?

Short wave: bounce off the ionosphere, cross a continent

SW (HF) broadcasting aims at the sky. The ionosphere returns the wave if the frequency is below the maximum usable frequency, which depends on the take-off angle:

\[ \mathrm{MUF}=\frac{f_c}{\cos i} \]

Low take-off angle → long hop → the first signal lands far away, leaving a skip zone. Hops repeat for multi-hop paths.

Try 21.7 MHz by day, then by night. Critical frequency is illustrative (7 MHz day, 3 MHz night).†

Question 1 — Why did broadcasting move beyond AM?

A real short-wave service: Saudi international broadcasting

ProgrammekHzλ m
06121824 h
Pashto باشتو983530.5
Pashto باشتو969530.9
Urdu أوردو1366021.9
Urdu أوردو1377521.8
Swahili سواحيلي1528519.6
Somali صومالي1372021.9
Farsi فارسي2165013.8
Farsi فارسي724041.4
Indonesian اندونيسي2167013.8
Bengali بنجالي969530.9
English انجليزي1759017.0
English انجليزي1384021.7
French فرنسي1766017.0
Turkestani تركستاني988530.3
Turkish تركي967531.0

Select a row for its target region. Notice Farsi: 21650 kHz in the morning, 7240 kHz from the afternoon; and 9695 kHz serves Bengali at 12–15 and Pashto at 17–19.

Source: SBA international schedule (SBA RadioChannel page, 13 Oct 2026), GMT+3. λ = c/f computed here; the page prints 19 m for Bengali on 9695 kHz, but 9695 kHz is 31 m.

Question 1 — Why did broadcasting move beyond AM?

Move much higher in frequency: the sky stops helping

1 MHz · MW ground wave follows the Earth the sky wave is absorbed by day 15 MHz · SW the ionosphere turns it back hundreds to thousands of km 100 MHz · FM passes through the ionosphere only the line-of-sight path stays
Above roughly 30 MHz† the ionosphere no longer returns the wave. Service becomes local: that is both a limitation and, as we will see, an opportunity.

Question 1 — Why did broadcasting move beyond AM?

Armstrong’s answer to “the static problem”

The motivation came before the equation: AM broadcasts suffered from static, which corrupts amplitude. Armstrong’s wideband FM varied the carrier’s frequency instead, giving better fidelity and far better resistance to noise.

1933Armstrong demonstrates FMagainst AM’s “static problem” 1934Multiplex trial: 2 programmes,telegraph, a fax page 1937400 ft Alpine, NJ tower(still in use) US band change42–50 MHz moved to88–108 MHz (Band II) early 1960sRegulators set ground rules;stereo multiplex designed mid 1970sFM stations outnumberAM stations
This is the historical United States path. Other regions did not follow it step by step: they planned VHF FM later, within the ITU framework. Source: Software Defined Radio Using MATLAB & Simulink and the RTL-SDR, §9.1 and §9.9.2 (Chapter 9).

Question 1 — Why did broadcasting move beyond AM?

Why FM sounds cleaner in static

Same message, same noise bursts. AM reads the height, so every burst adds to the audio. FM can hard-limit the height away and read only how fast the zero crossings come. Push the noise to the top: once the bursts rival the carrier, FM degrades too, abruptly (the threshold). One fixed noise record is used; another record would cross the threshold at another level.

Question 1 — Why did broadcasting move beyond AM?

FM went to VHF — history differs from today’s framework

30507090110MHz Historical US (Armstrong’s first allocation): 42–50 MHz US after the change: 88–108 MHz Saudi stations (SBA maps): 88.0 … 107.3 MHz seen
Two different statements: the U.S. history (42–50 → 88–108 MHz) and the present framework for Saudi Arabia, an ITU Region 1 country, where VHF FM is planned inside ITU Band II† and national allocations from CST. SBA frequencies read from the SBA RadioChannel region maps (13 Oct 2026).

Question 2 — Why does FM cover a city differently?

Three broadcast services, one landscape

Context: regional MW station. City and region by ground wave; night-time reach brings far listeners and interference.

Question 2 — Why does FM cover a city differently?

FM-VHF coverage: antenna height, terrain and the radio horizon

VHF travels in nearly straight lines, so coverage ends at the radio horizon. With standard atmospheric refraction:

\[ d\approx 4.12\left(\sqrt{h_1}+\sqrt{h_2}\right)\ \text{km} \]

(\(h\) in metres.) Distance grows like \(\sqrt h\): a mast four times taller gives only twice the reach. Terrain can still cast a shadow inside the horizon.

Try a 250 m city tower and a 1.5 m car antenna, then add the hill.†

Question 3 — Why VHF?

VHF did not demand a wider channel — it made room for one

MW band: 530–1700 kHz ≈ 1.2 MHz → about 117 channels × 10 kHz FM Band II: 88–108 MHz = 20 MHz → 100 channels × 200 kHz same scale · 20 MHz ≈ 17 × the whole MW band · each FM channel ≈ 20 × a MW channel

What did not change

The channel width is set by the deviation and the audio bandwidth, not by \(f_c\). A 1 MHz and a 100 MHz carrier could carry the same \(\Delta f\) in the same bandwidth.

What VHF changed

There was 20 MHz of spectrum to give the service. Wide channels meant higher fidelity (15 kHz audio) and room for extra multiplex services — stereo, then RDS.

MW band edges and 10 kHz spacing: course Week 6 deck. 10 kHz is the Americas raster; Region 1 uses 9 kHz.†

Question 3 — Why VHF?

“About 200 kHz”: U.S. channelization is not the Saudi plan

FCC · United States

Channels are 200 kHz wide, on a 200 kHz raster across 88–108 MHz.†

A comparison, not the authority for Saudi broadcasting.

Saudi Arabia · CST NFAT

Source of truth for Saudi allocations. The attached NFAT file arrived empty, so the band edges and channel raster are not asserted here.

Observed: SBA lists assignments to 0.1 MHz (e.g. 88.4, 94.2, 107.3), consistent with a 100 kHz grid.†

Does the signal fit?

Carson, \(\Delta f=75\) kHz:

  • 15 kHz audio → 180 kHz
  • 53 kHz stereo MPX → 256 kHz

Stations are band-limited (the book cites 200 kHz in the UK), keeping ~98% of the energy.

Carson and 256 kHz example: SDR book §9.3.2. 180 kHz mono estimate: Week 6 deck, slide 28.

Part 2

How can one RF station carry L, R and more?

Stereo, the MPX spectrum, the 19 kHz pilot and RDS.

Question 4 — How can one RF station carry L and R?

One broadcast, two kinds of listener

L (left mic) R (right mic) stereo encoderL+R · pilot · L−R FMtransmitter Mono radio (older)plays L + Rignores everything above 15 kHz Stereo radiofinds the 19 kHz pilot → “stereo” lamp onrebuilds L and R separately
Backward compatibility is the design constraint: stereo was added in the early 1960s without breaking the mono receivers already in homes. So the part that old radios play must be exactly the mono signal, L + R.

Question 4 — How can one RF station carry L and R?

Send the sum and the difference, not L and R

\[ M=L+R,\qquad D=L-R \]
\[ L=\frac{M+D}{2},\qquad R=\frac{M-D}{2} \]

\(M\) is what a mono radio plays. \(D\) is extra, for stereo receivers only. Try the four cases and watch \(D\) and \(M\).

Question 5 — What is the 19 kHz tone, and why is RDS at 57 kHz?

The multiplex: 19 · 38 · 57 kHz

Levels (45 / 10 / 22.5 + 22.5 / 2.6 + 2.6 %) and the RDS band: SDR book Figs 9.26, 9.28. DARC shape: ITU-R BS.1194-1 Fig. 1. Click a receiver to shade its bands.

Question 5 — What is the 19 kHz tone, and why is RDS at 57 kHz?

The suppressed 38 kHz carrier is rebuilt from the 19 kHz pilot

The \(L-R\) signal is DSB-SC: no carrier is transmitted, only its sidebands. To demodulate it coherently the receiver needs a 38 kHz carrier in the right phase.

The transmitter therefore sends a weak 19 kHz pilot and the receiver doubles it:

\[ D\cos^2\omega t=\tfrac{D}{2}\bigl[1+\cos 2\omega t\bigr] \]

A low-pass filter keeps \(D/2\). \(19,\ 38=2(19),\ 57=3(19)\ \text{kHz}\).

01519233853kHz L + R quiet gap pilot L − R(DSB-SC) 38 kHz carrier is not sent ×2 in the receiver
The pilot sits in the empty gap between the audio and the stereo sidebands, so it disturbs neither.

Question 5 — What is the 19 kHz tone, and why is RDS at 57 kHz?

RDS: a digital communication system inside an analog broadcast

RDS data1187.5 bit/s † BPSKbits → phase ×57 kHz = 3 × pilot + MPX≈ 5% deviation FM modulator→ antenna

Name

Station name shown on the display (PS).

RadioText

Song title, programme text (RT).

Type

Programme type: news, pop, speech (PTY).

Alt. freq.

Other frequencies carrying the same programme (AF).

Traffic

Traffic programme and announcement flags (TP/TA).

BPSK, 57 kHz DSB-SC, 3 × pilot, 55–59 kHz band, ≈ 5.2 % modulation: SDR book §9.9.2. ITU-R BS.643 (RDS) is cited in ITU-R BS.1194-1. 1187.5 bit/s (= 57 kHz / 48) and the service list follow IEC 62106†.

Check yourself

The 19 kHz pilot

A station switches its 19 kHz pilot off but still transmits \(L+R\) and the \(L-R\) sidebands. What does a stereo receiver do?

Part 3

What does a real receiver do?

The MATLAB / Simulink path we followed in the laboratory.

Question 6 — What does a real receiver do?

The Simulink receiver, one step at a time

ADALM-Pluto RX FMdemodulatorMPX spectrum analyserprobe here LPF 0–15 kHzL + R = M → de-emphasis → mono audio BPF 19 kHz×238 kHz BPF 23–53 kHz×LPF 15 kHzD = L − R matrixM + D → LM − D → RLRstereo audio BPF 55–59 kHz×LPF 2 kHzRDS bits×357 kHz

1 · ADALM-Pluto receiver. Tune to a station: the Pluto delivers complex baseband samples around that carrier. Nothing audio yet.

After SDR book §9.9.2 (Fig. 9.28) and Exercise 10.6; the Pluto replaces the RTL-SDR block. Pluto and Simulink block settings are not shown: they are not in the supplied material.

Question 6 — What does a real receiver do?

What each spectrum probe should show

Probe pointExpect to seeWhat it proves
After the FM demodulator (MPX)Energy 0–15 kHz, a line at 19 kHz, humps 23–53 kHz, a small bump near 57 kHzThe station is standard stereo FM; the demodulator works
After LPF 0–15 kHzOnly the audio band; nothing at 19 kHz or aboveL + R is isolated; this is what a mono radio plays
After BPF 19 kHz, then ×2One tone at 19 kHz, then one tone at 38 kHzThe pilot is present and doubling works
After the 38 kHz mixerL − R at baseband plus a copy near 76 kHzCoherent detection of DSB-SC; the 76 kHz copy is removed next
After M + D and M − DTwo different audio spectraL and R are independent: the stereo image
After BPF 55–59 kHzA narrow ~4 kHz featureRDS present (if the station sends it)

Why 15 kHz everywhere? If either channel exceeded 15 kHz, the audio would run into the pilot gap and the stereo sidebands.

After SDR book Exercises 10.5–10.6. The book’s MPX analyser uses a 240 kHz span.

Question 6 — What does a real receiver do?

The reverse path: from a stereo file to a Pluto transmitter

stereo audiofile: L, R LPF15 kHz matrixM, D × 0.45 × × 0.45 19 kHz × 0.10 RDS × 57 kHz Σ FM modΔf = 75 kHz SDR TXPluto 38 kHz MPX
The receiver of slide 24 run backwards. The weights 0.45 (L + R), 0.45 (L − R) and 0.10 (pilot) follow the book’s Simulink exercise. After the sum, the MPX is the message that the FM modulator turns into frequency variations: the topic of the last part of this lecture.

Part 4

Why can the same frequency be reused, and who decides?

Frequency reuse, then ITU → CST → operator.

Question 7 — Why can the same frequency be reused?

The same frequency, two cities, no conflict

FM’s VHF coverage is geographically limited. Two stations on the same frequency can serve two cities, if the second city lies outside the first station’s interference reach.

Reuse rule here: separation ≥ interference reach + service radius. Real planning uses protection ratios, terrain and propagation curves.†

On the SBA Riyadh-region map, 88.0 and 90.0 MHz each appear at two different towns.†

Question 7 — Why can the same frequency be reused?

Short wave reuses frequencies differently

FM-VHF: separate by distance

f₁f₁gapsame f · tens to hundreds of km apart

Each signal dies out at the radio horizon, so geography does the separating.

SW: sky waves cross continents

06121824 hBengaliPashtoboth on 9695 kHz

One signal can be heard thousands of km away, so planners also separate transmissions by time, frequency and beam direction. Coordination is international.

Schedule values: SBA international schedule (slide 7). The SW coordination statement is general practice†.

Question 8 — Who decides which frequencies may be used?

ITU → national regulator → station

ITUinternational allocation · coordination framework · Recommendationse.g. ITU-R BS.450, BS.412 CST · Saudi Arabianational regulator · National Frequency Allocation Table (NFAT)national allocations and assignments Station / operatore.g. SBA: a frequency per city, as on its region maps

The FCC is a comparison

The FCC is the U.S. regulator. It plays the same role as CST for the U.S., so it is a useful example, but it is not the authority for Saudi broadcasting.

CST NFAT · class material

The NFAT table we inspected in class belongs here. The attached file was empty, so no entry is quoted. to insert

Question 8 — Who decides which frequencies may be used?

Which ITU-R Recommendation answers which question?

RecommendationIt answers…In this lecture
ITU-R BS.450-4What does the transmitted FM signal look like? (the real transmission standard)†The multiplex of slides 19–20: pilot, stereo, RDS
ITU-R BS.412How far apart must stations be? (planning: protection ratios)Frequency reuse, slide 28. Cited in BS.1194-1 for protection ratios.
ITU-R BS.643The Radio Data System (RDS)Slide 21. Cited in BS.1194-1 (IEC 62106 is the companion specification).
ITU-R BS.1194-1A higher-rate data channel: DARC, an LMSK subcarrier at 76 kHz = 4 × 19 kHz, 16 kbit/sThe extension of slide 19. Compatible with stereo + RDS.

From BS.1194-1: the DARC sub-carrier is locked to the 4th harmonic of the pilot; its deviation is 4–10 % (±3 to ±7.5 kHz) depending on the stereo L − R level; the test multiplex used pilot ±6.75 kHz (9 %) and RDS ±3 kHz (4 %), slightly different from the book’s 10 % and 5.2 %: always check which document a number comes from.

BS.450-4 and BS.412 content is not reproduced from the attachments.

Part 5

Only now: what exactly does FM modulation do?

The message moves the instantaneous carrier frequency above and below fc.

Question 9 — What exactly does FM modulation do?

The message moves the frequency above and below \(f_c\)

\[ f_i(t)=f_c+k_f\,m(t) \]

The peak frequency deviation is

\[ \Delta f=k_f\,A_m \]

Raise the message amplitude and the frequency excursion grows. The carrier height never changes.

Question 9 — What exactly does FM modulation do?

Small excursion or large? Narrowband vs wideband FM

\[ \beta=\frac{\Delta f}{f_m} \]

\(\beta\) compares the frequency excursion with the message frequency. Small \(\beta\): narrowband FM. Large \(\beta\): wideband FM.

Broadcast FM is wideband FM: \(\Delta f=75\) kHz, \(f_m=15\) kHz, \(\beta=5\).

Question 9 — What exactly does FM modulation do?

Engineering card: how wide is the FM signal?

\[ B_{\text{FM}}\approx 2\,(\Delta f+B_m) \]

Carson’s rule: deviation plus message bandwidth, both sides of the carrier. It is an engineering estimate (about 98 % of the power), not an exact edge.

Message\(B_m\)\(B_{\text{FM}}\) at \(\Delta f=75\) kHz
Mono audio15 kHz180 kHz
Stereo MPX53 kHz256 kHz
+ RDS (to 59 kHz)59 kHz268 kHz

The MPX of Part 2 is the message \(m(t)\). Stations are band-limited near the channel width; the book cites 200 kHz for the UK. The full derivation, Bessel-function spectrum and examples are in the original Week 6 deck.

256 kHz example: SDR book §9.3.2. Mono and RDS rows computed from the same rule.

Check yourself

Deviation and modulation index

A broadcast station has \(\Delta f=75\) kHz and the highest message frequency is 15 kHz. What is \(\beta\), and is this narrowband or wideband FM?

References

Sources, and what still needs a source

Used

  • SDR book (Software Defined Radio Using MATLAB & Simulink and the RTL-SDR), Ch. 9 and 10.
  • ITU-R BS.1194-1, DARC (1998).
  • SBA RadioChannel page: international SW schedule and FM region maps, accessed 13 Oct 2026.
  • Lathi & Ding, Modern Digital and Analog Communication Systems, 5th ed., Ch. 5.

Marked † or “to insert”

  • ITU-R BS.450-4 and the CST NFAT: the attached files were empty.
  • IEC 62106 details (RDS rate, coding, services).
  • Region 1 FM band edges and raster; FCC channel plan.
  • Typical ranges for MW/SW, MUF values, SW coordination.

† = pending a source

EE 351 · Week 5 · FM broadcasting

One landscape, one multiplex, one carrier

AM’s MW and SW show how propagation shapes a service. VHF FM trades reach for spectrum: a local, high-fidelity service whose 200-kHz-class channel carries L + R, the 19 kHz pilot, L − R and RDS. The same frequency can be reused where coverage ends, under rules set by ITU and, in Saudi Arabia, CST. Only then does the frequency modulation \(f_i(t)=f_c+k_f m(t)\) have to be explained.

Next: the derivation, Bessel spectrum and examples in the Week 6 deck.

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