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3.1 Transmission Lines: Coaxial, Twin-Lead, and Characteristic Impedance
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
3.1 Transmission Lines: Coaxial, Twin-Lead, and Characteristic Impedance
Key Takeaways Explain This Topic AI
Transmission lines transport radio frequency (RF) energy between transceivers and antennas with minimal radiation or attenuation loss.
Coaxial cable is an unbalanced feedline whose characteristic impedance is governed by dielectric constant and the ratio of outer shield to inner conductor diameter.
Twin-lead and open-wire line are balanced feedlines offering exceptionally low dielectric loss and high efficiency under mismatched conditions.
Characteristic impedance (Z0) is an inherent property of line geometry and dielectric material, completely independent of physical cable length.
Physical length equals electrical length multiplied by the velocity factor (VF = 1 / sqrt(er)), which ranges from 0.66 for solid PE to 0.98 for open-wire line.
Last updated: July 2026
3.1 Transmission Lines: Coaxial, Twin-Lead, and Characteristic Impedance
ACMA Exam Focus: Transmission lines (feedlines) are critical links in every amateur radio station. Understanding how physical geometry and dielectric materials dictate characteristic impedance ( Z 0 Z_0 Z 0 ), velocity factor ( V F VF V F ), physical-to-electrical length conversions, and attenuation at higher frequencies is essential for the ACMA Standard Theory examination.
1. Purpose of Transmission Lines
A transmission line (or feedline) is a specialised conductor system designed to transport radio frequency (RF) electromagnetic energy from a transmitter to an antenna, or from an antenna to a receiver, with maximum efficiency and minimal power loss.
An ideal transmission line accomplishes two fundamental goals:
Zero Radiation Loss: It guides RF energy without radiating electromagnetic fields into space along its length.
Zero Signal Pickup: It prevents ambient electromagnetic noise (man-made interference, impulse noise, neighbouring transmissions) from coupling into the receiver.
In practical amateur radio installations, transmission lines fall into two primary structural categories: unbalanced coaxial cables and balanced parallel-conductor lines (twin-lead, ladder line, and open-wire line).
2. Coaxial Cable Construction
Coaxial cable (coax) is the most widely used feedline in modern radio stations. Its name derives from the coaxial geometry: both inner and outer conductors share the exact same central longitudinal axis. +-------------------------------------------------------------+
- | Outer Protective Jacket (PVC / PE) |
- | +-------------------------------------------------------+ |
- | | Outer Metallic Braid / Shield (Grounded Return) | |
- | | +-------------------------------------------------+ | |
- | | | Solid or Foam Dielectric Insulator (er) | | |
- | | | +-------------------------------------------+ | | |
- | | | | Centre Conductor (Solid / Stranded Copper) | | | |
- | | | +-------------------------------------------+ | | |
- | | +-------------------------------------------------+ | |
- | +-------------------------------------------------------+ |
- +-------------------------------------------------------------+
A standard coaxial line consists of four concentric layers:
Inner (Centre) Conductor: Solid or stranded high-conductivity copper (or copper-clad steel). It carries the primary RF signal voltage and current.
Dielectric Insulator: A flexible insulating sheath surrounding the inner conductor. Common materials include Solid Polyethylene ( ε r ≈ 2.25 \varepsilon_r \approx 2.25 ε r ≈ 2.25 ) , Foam Polyethylene ( ε r ≈ 1.3 − 1.5 \varepsilon_r \approx 1.3 - 1.5 ε r ≈ 1.3 − 1.5 ) , and PTFE / Air-Spaced Polyethylene ( ε r ≈ 1.1 − 1.5 \varepsilon_r \approx 1.1 - 1.5 ε r ≈ 1.1 − 1.5 ) . The dielectric maintains exact concentric spacing between conductors.
Outer Shield (Braid / Foil): Woven tinned-copper braid, aluminium foil, or solid corrugated copper (hardline). The outer shield acts as the return path for RF current and forms an electromagnetic shield. Because the outer shield is held at ground potential, coax is an unbalanced line .
Outer Protective Jacket: Tough, weather-resistant Polyvinyl Chloride (PVC) or Polyethylene (PE) jacket protecting the cable against moisture ingress, ultraviolet (UV) degradation, and mechanical abrasion.
3. Parallel-Conductor Lines: Twin-Lead and Open-Wire Line
Parallel-conductor lines consist of two identical parallel wires separated by a uniform insulating gap along their entire length.
Twin-Lead Ribbon Line: Two stranded copper wires embedded within a continuous flat ribbon of solid polyethylene insulation.
Open-Wire / Ladder Line: Two solid or stranded wires held at a fixed spacing by plastic or ceramic insulating spacers (spreaders) positioned at regular intervals. Air acts as the primary dielectric between conductors.
Balanced vs. Unbalanced Operation
Parallel-conductor lines are balanced transmission lines . Equal and opposite RF currents flow in the two conductors relative to ground. The electromagnetic fields produced by the equal and opposite currents cancel each other completely in space, preventing line radiation provided the conductor spacing is small relative to the operating wavelength ( S ≪ λ S \ll \lambda S ≪ λ ).
- Parameter Coaxial Cable Open-Wire / Ladder Line
- Line Type Unbalanced Balanced
- Shielding Fully shielded (low local noise pickup) Unshielded (susceptible to near-field metallic objects)
- Dielectric Loss Moderate to High (solid PE) Extremely Low (air dielectric)
- SWR Loss Tolerance Poor (high dielectric heating under SWR) Excellent (handles high SWR with minimal loss)
Typical Impedance 50 Ω 50\,\Omega 50 Ω , 75 Ω 75\,\Omega 75 Ω 300 Ω 300\,\Omega 300 Ω , 450 Ω 450\,\Omega 450 Ω , 600 Ω 600\,\Omega 600 Ω
- 4. Characteristic Impedance ( Z 0 Z_0 Z 0 )
- Definition
The characteristic impedance ( Z 0 Z_0 Z 0 ) of a uniform transmission line is the ratio of RF voltage to RF current of a single wave propagating along an infinitely long loss-free line: Z 0 = V forward I forward = L C Z_0 = \frac{V_{\text{forward}}}{I_{\text{forward}}} = \sqrt{\frac{L}{C}} Z 0 = I forward V forward = C L
where L L L is inductance per unit length (henries/metre) and C C C is capacitance per unit length (farads/metre).
CRITICAL ACMA CONCEPT: Characteristic impedance is determined exclusively by the physical dimensions (conductor diameter and spacing) and the relative permittivity ( ε r \varepsilon_r ε r ) of the dielectric material. It is completely independent of physical cable length . A 1-metre length of RG-58 coaxial cable has an identical characteristic impedance ( 50 Ω 50\,\Omega 50 Ω ) to a 100-metre roll of RG-58.
- Mathematical Formulas for Z 0 Z_0 Z 0
- 1. Coaxial Cable
For a coaxial line with inner conductor diameter d d d , outer shield inner diameter D D D , and dielectric relative permittivity ε r \varepsilon_r ε r : Z 0 = 138 ε r log 10 ( D d ) Z_0 = \frac{138}{\sqrt{\varepsilon_r}} \log_{10}\left(\frac{D}{d}\right) Z 0 = ε r 138 lo g 10 ( d D )
2. Parallel-Conductor Line (Twin-Lead / Open-Wire)
For two parallel conductors of diameter d d d separated by centre-to-centre distance S S S in a dielectric of relative permittivity ε r \varepsilon_r ε r : Z 0 = 276 ε r log 10 ( 2 S d ) Z_0 = \frac{276}{\sqrt{\varepsilon_r}} \log_{10}\left(\frac{2S}{d}\right) Z 0 = ε r 276 lo g 10 ( d 2 S )
From these formulas, we observe:
Increasing conductor spacing ( S S S or D D D ) increases Z 0 Z_0 Z 0 .
Increasing conductor diameter ( d d d ) decreases Z 0 Z_0 Z 0 .
Increasing dielectric constant ( ε r \varepsilon_r ε r ) decreases Z 0 Z_0 Z 0 .
5. Standard Transmission Line Impedances
In amateur and commercial radio engineering, specific standard impedances are used:
50 Ω 50\,\Omega 50 Ω Coax (RG-58, RG-213, LMR-400): Standard for amateur HF/VHF/UHF transceivers. 50 Ω 50\,\Omega 50 Ω is an optimum engineering compromise between maximum power-handling capability (which occurs at ∼ 30 Ω \sim 30\,\Omega ∼ 30 Ω for air-dielectric coax) and minimum attenuation loss (which occurs at ∼ 77 Ω \sim 77\,\Omega ∼ 77 Ω ).
75 Ω 75\,\Omega 75 Ω Coax (RG-59, RG-6): Standard for television distribution and matching half-wave dipole antennas in free space (which have a natural resonant feedpoint impedance of ≈ 73 Ω \approx 73\,\Omega ≈ 73 Ω ).
300 Ω 300\,\Omega 300 Ω Twin-Lead: Standard ribbon line used for folded dipoles and FM receiver antennas.
450 Ω 450\,\Omega 450 Ω Ladder Line / 600 Ω 600\,\Omega 600 Ω Open-Wire: Extremely low-loss balanced feedlines used with antenna tuning units (ATUs) for multi-band doublet antennas.
- 6. Velocity Factor ( V F VF V F ) and Physical vs. Electrical Length
- Velocity Factor Definition
Radio waves travel in a vacuum at the speed of light ( c ≈ 3 × 10 8 m/s c \approx 3 \times 10^8\text{ m/s} c ≈ 3 × 1 0 8 m/s ). However, when an electromagnetic wave travels through a dielectric material inside a transmission line, it slows down.
The Velocity Factor ( V F VF V F ) is the ratio of the speed of an electromagnetic wave in the transmission line ( v v v ) to the speed of light in a vacuum ( c c c ): V F = v c = 1 ε r VF = \frac{v}{c} = \frac{1}{\sqrt{\varepsilon_r}} V F = c v = ε r 1
Dielectric Velocity Factors
Dielectric Insulation Type Relative Permittivity ( ε r \varepsilon_r ε r ) Typical Velocity Factor ( V F VF V F )
- Solid Polyethylene (Solid PE) ≈ 2.25 \approx 2.25 ≈ 2.25 0.66
- Foam Polyethylene (Foam PE) ≈ 1.4 − 1.6 \approx 1.4 - 1.6 ≈ 1.4 − 1.6 0.80 - 0.85
- Solid PTFE (Teflon) ≈ 2.1 \approx 2.1 ≈ 2.1 0.69 - 0.70
- Semi-air-spaced / Air-spaced PE ≈ 1.1 − 1.2 \approx 1.1 - 1.2 ≈ 1.1 − 1.2 0.90 - 0.93
- Open-Wire Line (Air) ≈ 1.05 \approx 1.05 ≈ 1.05 0.95 - 0.98
- Physical vs. Electrical Length Calculation
Because the wave travels slower in the cable, the wavelength in the transmission line ( λ line \lambda_{\text{line}} λ line ) is shorter than the wavelength in free space ( λ free \lambda_{\text{free}} λ free ): λ line = λ free × V F \lambda_{\text{line}} = \lambda_{\text{free}} \times VF λ line = λ free × V F
To calculate the physical length ( L phys L_{\text{phys}} L phys ) required for a specific electrical fraction of a wavelength (such as a quarter-wave matching stub, 1 4 λ \frac{1}{4}\lambda 4 1 λ ): L free = 300 f MHz metres L_{\text{free}} = \frac{300}{f_{\text{MHz}}} \text{ metres} L free = f MHz 300 metres L phys = L elec × V F = ( 300 f MHz × fraction ) × V F metres L_{\text{phys}} = L_{\text{elec}} \times VF = \left( \frac{300}{f_{\text{MHz}}} \times \text{fraction} \right) \times VF \text{ metres} L phys = L elec × V F = ( f MHz 300 × fraction ) × V F metres
Worked Example
Problem: Calculate the physical length in metres of a quarter-wavelength ( 1 4 λ \frac{1}{4}\lambda 4 1 λ ) matching stub cut for 14.1 MHz 14.1\text{ MHz} 14.1 MHz using solid polyethylene coaxial cable ( V F = 0.66 VF = 0.66 V F = 0.66 ).
Solution:
Calculate free-space wavelength: λ free = 300 14.1 = 21.277 metres \lambda_{\text{free}} = \frac{300}{14.1} = 21.277\text{ metres} λ free = 14.1 300 = 21.277 metres .
Calculate electrical quarter-wavelength: L elec = 21.277 4 = 5.319 metres L_{\text{elec}} = \frac{21.277}{4} = 5.319\text{ metres} L elec = 4 21.277 = 5.319 metres .
Multiply by Velocity Factor: L phys = 5.319 × 0.66 = 3.51 metres L_{\text{phys}} = 5.319 \times 0.66 = \mathbf{3.51\text{ metres}} L phys = 5.319 × 0.66 = 3.51 metres .
7. Dielectric Loss and Frequency Attenuation
Transmission lines suffer signal loss (attenuation), expressed in decibels per 100 metres ( dB / 100 m \text{dB}/100\text{ m} dB /100 m ). Feedline attenuation increases significantly as frequency increases due to two primary physical mechanisms:
Skin Effect (Conductor Loss): At direct current (DC), electric current flows uniformly across the entire cross-sectional area of a wire. As frequency increases, electromagnetic induction forces alternating RF current to flow exclusively in a paper-thin layer on the outer surface of the inner conductor and inner surface of the shield. This drastically reduces the effective conductive cross-section, causing AC resistance to rise proportional to f \sqrt{f} f .
Dielectric Hysteresis Loss: Alternating electric fields cause rapid polarisation cycles of molecules within the dielectric insulator, generating heat. Dielectric loss increases linearly with operating frequency ( f f f ).
Attenuation Comparison Across Bands ( dB / 100 m \text{dB}/100\text{ m} dB /100 m )
Coaxial Cable Type 3.5 MHz (80 m) 28 MHz (10 m) 146 MHz (2 m) 435 MHz (70 cm)
RG-58 (Thin Coax) 2.2 dB 2.2\text{ dB} 2.2 dB 6.5 dB 6.5\text{ dB} 6.5 dB 16.5 dB 16.5\text{ dB} 16.5 dB 31.0 dB 31.0\text{ dB} 31.0 dB
RG-213 (Thick Coax) 1.1 dB 1.1\text{ dB} 1.1 dB 3.2 dB 3.2\text{ dB} 3.2 dB 8.5 dB 8.5\text{ dB} 8.5 dB 16.2 dB 16.2\text{ dB} 16.2 dB
LMR-400 (Low-Loss Foam) 0.7 dB 0.7\text{ dB} 0.7 dB 2.1 dB 2.1\text{ dB} 2.1 dB 4.9 dB 4.9\text{ dB} 4.9 dB 8.8 dB 8.8\text{ dB} 8.8 dB
Practical Takeaway: Thin RG-58 is acceptable for short HF patch leads, but unusable for long VHF/UHF feedline runs due to excessive attenuation.