EEL4514C Communication Systems and Components, Fall 2026, Lecture 19

Overview

Mingyue Ji transitions from amplitude modulation to angle modulation, reviewing QAM, analog TV, and frequency-division multiplexing before introducing phase modulation (PM) and frequency modulation (FM). The lecture defines phase and instantaneous frequency, derives PM/FM signal forms, and explains angle modulation’s constant-envelope power advantage alongside the bandwidth distortion that nonlinear amplification can cause in DSB-SC.

Key takeaways

QAM carries two independent messages on orthogonal cosine and sine carriers, but coherent demodulation requires the receiver to know the transmitted carrier phase.
FDM prevents user overlap by assigning separate frequency bands; the telephone hierarchy described supports up to 600 users by grouping 12-user channels into larger aggregates.
The defining relationship for angle modulation is ωi(t) = dθ(t)/dt, which makes PM respond to m(t) and FM respond to the integral of m(t) in its phase.
PM and FM maintain constant carrier amplitude, giving average power A²/2 and easing amplifier design compared with amplitude-varying AM or DSB-SC.
A cubic nonlinearity acting on DSB-SC produces a component at 3ωc and can expand bandwidth to roughly three times the message bandwidth.

Chapters

0:00 QAM Uses Orthogonal Carriers for Two Message Channels

QAM replaces the message and its Hilbert transform in an SSB-style signal with independent messages M1 and M2 on cosine and sine carriers.
The cosine and sine components are orthogonal, allowing separate recovery with coherent multiplication and low-pass filtering.
QAM requires accurate carrier-phase synchronization and is used in analog TV color transmission as well as Wi-Fi and 5G/6G.

2:30 AM Applications: Broadcast Radio, Analog TV, and Telephone Speech

AM broadcast uses long wavelengths; the example discussed has a wavelength of about 353 meters, requiring a physically large antenna.
U.S. analog TV combines black-and-white video, color, and analog sound in separate spectral components; video uses vestigial-sideband (VSB) transmission.
TV color uses QAM, with VSB on the I channel and DSB-SC on the Q channel; the lecture highlights the distinct spectrum shapes of the components.
Long-distance telephone systems carry speech over roughly 4 kHz of bandwidth and use single-sideband (SSB) signaling for efficiency.

5:08 Multiplexing Shares Communication Channels Across Users

Frequency-division multiplexing (FDM) assigns different frequency bands to users; first-generation mobile systems used FDMA, or frequency-division multiple access.
Time-division multiplexing separates users by time slots, while code-division systems such as 3G CDMA use low-correlation sequences to distinguish transmissions.
Multiple antennas can separate users spatially through beamforming; the course focuses primarily on exploiting the frequency domain.
The telephone hierarchy groups 12 users, combines five groups into a supergroup, and combines 10 supergroups into a master group, supporting up to 600 users.

8:09 Angle Modulation Begins with Phase and Frequency

Lecture 19 starts a roughly five-lecture unit on angle modulation, with a midterm planned after the unit.
Angle modulation changes the carrier’s angle, or phase, rather than encoding the message in its amplitude.
The modulated carrier is represented as s(t) = A cos(θ(t)), where θ(t) is the time-varying phase.

10:00 Why Angle Modulation Can Reduce the Impact of Noise

In amplitude modulation, received noise or interference directly alters the amplitude that carries the message, so it appears in the recovered output.
Angle modulation places the information in the carrier’s phase or frequency instead of its amplitude; amplitude disturbances therefore need not directly corrupt the encoded message.
The lecture also notes that angle modulation can improve signal-to-noise ratio as bandwidth increases, but demodulator design is more complex than a simple AM envelope detector.

16:30 Instantaneous Frequency Is the Derivative of Phase

For a carrier cos(ωct), the phase is θ(t) = ωct and the angular frequency is constant at ωc.
For a general angle-modulated signal, instantaneous angular frequency is ωi(t) = dθ(t)/dt.
Frequency measures how quickly phase changes; recovering phase from frequency therefore requires integration.

22:09 Phase Modulation Makes Carrier Phase Follow the Message

PM defines θ(t) = ωct + kp m(t), where kp is phase sensitivity and kp m(t) is measured in radians.
If m(t) is measured in volts, kp has units of radians per volt.
The PM signal is sPM(t) = A cos(ωct + kp m(t)); its instantaneous angular frequency is ωc + kp dm(t)/dt.
Digital PSK is a phase-modulation example: binary symbols can be represented by phases such as 0 and π.

27:57 Frequency Modulation Integrates the Message into Phase

FM defines instantaneous angular frequency as ωi(t) = ωc + kf m(t), with kf as frequency sensitivity.
Because frequency is the derivative of phase, FM phase is θ(t) = ωct + kf ∫₀ᵗ m(α)dα.
The resulting signal is sFM(t) = A cos(ωct + kf ∫₀ᵗ m(α)dα); FM is widely used for analog audio broadcasting.
PM and FM fit a generalized model in which the message passes through a filter before affecting the carrier angle; PM uses a scaled impulse response, while FM uses a constant-gain response.

32:05 Constant-Envelope Angle Modulation Keeps Transmitted Power Fixed

Assuming the carrier frequency is much higher than the message bandwidth, m(t) changes very little during one carrier period.
With constant amplitude A, the average power of an angle-modulated carrier is approximately A²/2, independent of the message waveform.
A constant-envelope signal simplifies power-amplifier design compared with AM or DSB-SC, whose amplitudes vary with the input.

35:13 Nonlinear DSB-SC Amplification Generates Extra Bandwidth

Angle modulation is nonlinear in the message: applying PM to m1(t) + m2(t) does not produce the sum of the two separately modulated signals.
To illustrate nonlinear distortion, the lecture passes a DSB-SC signal through y(t) = a s(t) + b s³(t), using cosine-product identities to expand the cubic term.
The cubic term creates components at the carrier frequency and at 3ωc; the third-harmonic component carries a term proportional to m³(t).
For a message bandwidth W, the third-harmonic products can expand the transmitted bandwidth to about 3W, making nonlinear amplification problematic for DSB-SC.

Summary, takeaways, and chapters were generated by AI from the video's transcript and may contain errors. The video belongs to its creator, Mingyue Ji.