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4.4 Critical Frequency, Maximum Usable Frequency (MUF), and Fading
ACMA Amateur Radio Standard Recognition Certificate - Theory Exam
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1 Chapter 1: Electrical Principles and Components
1.1 Mathematics, Units and Metric Prefixes 1.2 DC Circuits, Voltage, Current, and Ohm's Law 1.3 Power, Energy, and Resistance Calculations 1.4 Resistor Colour Code and Component Symbol Identification 1.5 Capacitors: Construction, Ratings and Safety 1.6 Inductors: Construction, Factors Affecting Inductance and Combinations 1.7 Capacitor and Inductor Combination Calculations 1.8 AC Circuits, Frequency, Wavelength, and RMS Values 1.9 Reactance and Impedance in AC Circuits 1.10 Resonance, Q Factor and Tuned Circuits 1.11 Transformers: Turns Ratio, Impedance Matching and Eddy Currents 1.12 Rectifiers, PIV and Power Supply Smoothing 1.13 Active Components: Semiconductors, Diodes, and Transistors 1.14 Transistor and FET Symbols, Configurations and External Behaviour
2 Chapter 2: Transmitters and Receivers
2.1 Superheterodyne Receiver Architecture and Block Diagrams 2.2 Frequency Converters, IF Amplifiers and Transceiver Sharing 2.3 Receiver Performance: Sensitivity, Selectivity, and AGC 2.4 Signal-to-Noise Ratio and Receiver Noise Performance 2.5 Transmitter Architecture, Oscillators and Frequency Synthesisers 2.6 Transmission Quality: Frequency Drift, Parasitic Oscillation and Over-Modulation 2.7 Modulation Techniques: AM, FM, and SSB 2.8 Amplifier Classes and Power Amplifiers (Class A, B, C, and AB) 2.9 Modulation, Duty Cycle and Rated Transmitter Power 2.10 Transceiver Control: ALC, Squelch, and Digital Modes 2.11 Digital Transmission Modes and Bandwidth
3 Chapter 3: Transmission Lines and Antennas
3.1 Transmission Lines: Coaxial, Twin-Lead, and Characteristic Impedance 3.2 Standing Wave Ratio (SWR) and Reflection Loss 3.3 Impedance Matching, Baluns, and Antenna Tuning Units (ATUs) 3.4 Resonant Antennas: Dipoles, Verticals, and End-Fed Antennas 3.5 Angle of Radiation, Antenna Height and Current Distribution 3.6 Directional Antennas: Yagis, Gain and Radiation Patterns 3.7 Effective Radiated Power: System Gains and Losses
4 Chapter 4: Radio Wave Propagation
4.1 Electromagnetic Waves: Velocity, Wavelength and Polarisation 4.2 Ground Wave, Direct Wave and Line-of-Sight Propagation 4.3 Ionospheric Layers (D, E, F1, F2) and Skywave Propagation 4.4 Critical Frequency, Maximum Usable Frequency (MUF), and Fading 4.5 Solar Activity, Sunspot Cycles, and VHF Anomalous Propagation 4.6 Seasonal and Diurnal Effects on Band Selection
5 Chapter 5: Electrical and RF Measurements
5.1 Multimeter Operation: Voltage, Current, and Resistance Measurements 5.2 RF Power and SWR Measurement (PEP vs. Average Power) 5.3 Frequency Counters, Dummy Loads, and Test Equipment 5.4 Frequency Standards, Crystal Calibrators and Standard-Frequency Transmissions
6 Chapter 6: Interference and Electromagnetic Compatibility (EMC)
6.1 Harmonic Emissions, Spurious Signals, and Transmitter Filtering 6.2 How Interference Enters Television and Broadcast Receivers 6.3 Masthead Amplifier Overload and Audio-Stage Demodulation 6.4 Electromagnetic Interference (EMI), Breakthrough, Ferrites, and EMC 6.5 Filter Types, Response Curves and EMC Filter Selection 6.6 EMC Good Practice: Minimum Power, Balanced Antennas and Feedline Routing 6.7 Vehicle EMC and Resolving Community Interference Complaints
7 Chapter 7: Safety and Environmental Hazards
7.1 Mains Voltage Safety, Earthing, and High-Voltage Capacitors 7.2 Equipment Approval, Mains Wiring and Fuse Practice 7.3 Station Layout, Cabling and Emergency Shut-Off 7.4 Lightning Protection and Station Security 7.5 Electric Shock: Prevention, Rescue and Emergency Response 7.6 Battery, Chemical and Hearing Safety in the Amateur Station 7.7 RF Exposure: EMR Hazards and Safe Distance 7.8 Antenna Erection, Siting and Power Line Safety
4.4 Critical Frequency, Maximum Usable Frequency (MUF), and Fading
Key Takeaways Explain This Topic AI
Critical frequency (fc) is the highest frequency that will be refracted back to Earth when transmitted at vertical incidence (90 degrees elevation).
Maximum Usable Frequency (MUF) for an oblique skywave path is calculated using the Secant Law: MUF = fc / cos(theta) = fc * sec(theta).
Lowest Usable Frequency (LUF) is the minimum frequency providing readable communication, bounded by D-layer absorption and background noise.
Optimum Working Frequency (OWF or FOT) is established at approximately 85% of the MUF (OWF = 0.85 * MUF) to ensure reliable communication resistant to ionospheric fluctuations.
Skywave fading is caused by multipath phase interference, Faraday polarisation rotation, and dynamic ionospheric movement.
Last updated: July 2026
4.4 Critical Frequency, Maximum Usable Frequency (MUF), and Fading
Predicting HF propagation conditions requires understanding how operating frequency, elevation angle, and ionospheric ionisation levels interact. Radio operators must select frequencies between defined upper and lower limits to achieve reliable skywave communication.
Measuring the Ionosphere: Ionosondes
The ionosphere is monitored using specialised radar systems called vertical incidence ionosondes . An ionosonde transmits short pulses of RF energy straight up into the ionosphere ( 90 ∘ 90^\circ 9 0 ∘ elevation angle, vertical incidence) while sweeping across frequencies from 1 MHz to 20+ MHz.
By measuring the time delay of returned echoes, the ionosonde determines the virtual height of the ionospheric layers and generates a graphical plot known as an ionogram .
Critical Frequency ( f c f_c f c )
The Critical Frequency ( f c f_c f c or f o f_o f o ) is the highest frequency that will be refracted back to Earth when transmitted vertically ( 90 ∘ 90^\circ 9 0 ∘ elevation angle) . Critical Frequency Concept
- f > fc (Escapes to space)
- | ^ f = fc (Critical Threshold)
- | /
- | / f < fc (Refracted back)
- +-------------|-/--------------------+ Ionospheric F Layer
- | |/ |
- | / |
- | / |
- | / |
- =====|==========/=========================|=====
- Transmitter
If a vertical signal frequency is below f c f_c f c , it is refracted back to Earth.
If a vertical signal frequency is above f c f_c f c , the ionospheric electron density is insufficient to bend the wave back down, and the signal passes straight through into space.
Maximum Usable Frequency (MUF)
In practical amateur communications, signals are transmitted at oblique angles (elevation angles below 90 ∘ 90^\circ 9 0 ∘ ) rather than vertically. When a wave enters the ionosphere obliquely at an angle of incidence θ \theta θ (measured relative to the normal of the ionospheric layer), the wave undergoes greater total refraction over a longer path within the layer.
Consequently, the Maximum Usable Frequency (MUF) for an oblique path is significantly higher than the vertical critical frequency ( f c f_c f c ).
The Secant Law / MUF Formula
The mathematical relationship between Critical Frequency ( f c f_c f c ) and MUF for an angle of incidence θ \theta θ is expressed by the Secant Law : MUF = f c cos θ = f c × sec θ \text{MUF} = \frac{f_c}{\cos\theta} = f_c \times \sec\theta MUF = cos θ f c = f c × sec θ
Where:
f c f_c f c is the Critical Frequency for vertical incidence.
θ \theta θ is the angle of incidence at the ionospheric layer (relative to the normal/perpendicular).
ψ \psi ψ is the takeoff angle (radiation elevation angle above the Earth's horizon). Angle Geometry at Ionosphere
- | Normal (Perpendicular)
- |
- | / Angle of Incidence (theta)
- |/
- ----------------------------+----------------------------- Ionospheric Layer
- /
- / Radiation Path
- /
- ====(Takeoff Angle psi)==/================================= Earth's Surface
- Impact of Radiation Takeoff Angle ( ψ \psi ψ )
Low Radiation Takeoff Angle ( ψ → 0 ∘ \psi \to 0^\circ ψ → 0 ∘ ): The signal strikes the ionosphere at a shallow glancing angle (large incidence angle θ → 90 ∘ \theta \to 90^\circ θ → 9 0 ∘ ). Because cos θ \cos\theta cos θ becomes small, the MUF \text{MUF} MUF becomes very high, enabling maximum single-hop distances.
High Radiation Takeoff Angle ( ψ → 90 ∘ \psi \to 90^\circ ψ → 9 0 ∘ ): The signal strikes the ionosphere nearly vertically ( θ → 0 ∘ , cos θ → 1 \theta \to 0^\circ, \cos\theta \to 1 θ → 0 ∘ , cos θ → 1 ). The MUF drops down toward f c f_c f c .
Worked Calculation: MUF
Problem: A vertical ionosonde measures a critical frequency f c = 7.0 MHz f_c = 7.0 \text{ MHz} f c = 7.0 MHz . Calculate the Maximum Usable Frequency (MUF) for an oblique propagation path where the angle of incidence θ = 60 ∘ \theta = 60^\circ θ = 6 0 ∘ .
Step 1: Determine cos ( 60 ∘ ) \cos(60^\circ) cos ( 6 0 ∘ ) . cos ( 60 ∘ ) = 0.5 \cos(60^\circ) = 0.5 cos ( 6 0 ∘ ) = 0.5
Step 2: Apply the MUF formula. MUF = f c cos θ = 7.0 MHz cos ( 60 ∘ ) = 7.0 MHz 0.5 = 14.0 MHz \text{MUF} = \frac{f_c}{\cos\theta} = \frac{7.0 \text{ MHz}}{\cos(60^\circ)} = \frac{7.0 \text{ MHz}}{0.5} = 14.0 \text{ MHz} MUF = cos θ f c = cos ( 6 0 ∘ ) 7.0 MHz = 0.5 7.0 MHz = 14.0 MHz
Answer: The MUF for this path is 14.0 MHz (the 20-metre amateur band).
Lowest Usable Frequency (LUF)
While the MUF establishes the upper boundary for HF communication over a given path, the Lowest Usable Frequency (LUF) defines the lower boundary .
D-Layer Absorption: At lower frequencies, D-layer absorption increases rapidly ( A ∝ 1 / f 2 A \propto 1/f^2 A ∝ 1/ f 2 ).
Background Atmospheric Noise: Natural noise levels rise at lower frequencies.
If the operating frequency drops below the LUF, signal absorption in the D layer becomes so severe that received signal strength falls below the noise floor, rendering communication impossible.
Unlike the MUF (which is determined purely by ionospheric electron density and geometric path angle), the LUF depends on transmitter power and antenna gain . Increasing transmitter power or antenna gain can lower the effective LUF by overcoming absorption losses.
Optimum Working Frequency (OWF / FOT)
Operating exactly at the MUF is risky. The ionosphere is dynamic, and minor fluctuations in electron density can cause the MUF to drop suddenly, causing the operating frequency to exceed the MUF and pass through into space.
To ensure reliable, stable skywave communication, operators choose the Optimum Working Frequency (OWF) —also known in international notation as FOT ( Fréquence Optimale de Travail ): OWF = FOT = 0.85 × MUF \text{OWF} = \text{FOT} = 0.85 \times \text{MUF} OWF = FOT = 0.85 × MUF
Operating at 85% of the MUF provides an optimal compromise:
It remains comfortably below the MUF to prevent unexpected fade-outs.
It remains far enough above the LUF to avoid heavy D-layer absorption and background noise. HF Propagation Frequency Window
- Frequency (MHz)
- ^
- | Unusable (Passes into Space)
- ======+=================================================== MUF
- | Fluctuating Buffer
- -----|--------------------------------------------------- OWF / FOT (85% of MUF)
- | OPTIMAL COMMUNICATION WINDOW
- | (Low absorption, high stability)
- ======+=================================================== LUF
- | Unusable (Absorbed by D Layer)
- v
- Skywave Fading Mechanisms
Fading is the continuous variation in received signal strength over time. Skywave signals experience three primary fading mechanisms:
1. Multipath Fading (Interference Fading)
Multipath fading occurs when a signal travels from transmitter to receiver via two or more distinct paths of different lengths (e.g., a 1-hop path vs. a 2-hop path, or a low ray vs. a high Pedersen ray).
Because the path lengths differ, the arriving waves have relative phase differences. As ionospheric height fluctuates slightly, the arriving waves alternate between:
Constructive Interference: Waves arrive in phase ( 0 ∘ 0^\circ 0 ∘ phase difference), reinforcing each other (signal peak).
Destructive Interference: Waves arrive out of phase ( 180 ∘ 180^\circ 18 0 ∘ phase difference), canceling each other out (deep signal null).
2. Polarisation Rotation (Faraday Rotation)
As an EM wave travels through the ionised ionosphere in the presence of the Earth's magnetic field, the wave is split into ordinary and extraordinary modes that travel at slightly different phase velocities. This causes the wave's plane of polarisation to rotate continuously .
When the rotating wave arrives at a fixed linearly polarised receiving antenna (e.g., horizontal dipole), the signal strength drops whenever the polarisation vector becomes perpendicular to the receiving antenna.
3. Selective Fading
Selective fading affects specific frequencies within a signal's modulation bandwidth differently. For example, in an SSB or AM signal, the upper sideband may experience constructive interference while the lower sideband or carrier experiences destructive cancellation, causing severe audio distortion.