Transmission Lines and Cabling Notes

Transmission Lines, Wave Propagation, and Antennas

Introduction (Chapter 12)

• Focus on transmission lines, wave propagation, and antennas.
• Chapter 12 focuses on transmission lines (cabling).
• Common cabling types: Cat 5, Cat 5e, Cat 6, Coax.
• Sections covered in Chapter 12:
  • Introduction to Transmission Lines
  • Types of Transmission Lines
  • Electrical Characteristics of Transmission Lines

Objectives

• Describe operational characteristics of twisted pair and coaxial cable.
• Distinguish between balanced and unbalanced lines.
• Describe physical characteristics of standard transmission lines; calculate characteristic impedance ($Z_0$).
• Discuss losses in transmission lines.

Introduction to Transmission Lines

• Transmission lines are typically two-wire but can also be waveguides or fiber optic.
• Waveguides are wireless conduits, directing signals through a wireless pipe.
• At radio frequencies, wired transmission lines behave differently than at low frequencies or DC circuits; they act like complex circuits.
• Capacitance and inductance affect the line's performance.
• Impedance matching is crucial to prevent energy reflection (standing waves).
• Standing waves are expressed as a ratio in dB; they're unwanted and result from impedance mismatch.
• Characteristic impedance ($Z_0$) must be considered for smooth signal transmission.

Types of Transmission Lines

• Basic form: flat lead (rarely used as a transmission line).
  • High radiation loss and excessive noise pickup.
  • Better suited as an antenna.
  • Also called twin lead or two-wire ribbon.
  • Example: Used as an antenna for music-on-hold system at West Valley School District.
• Twisted Pair (Cat 5, Cat 5e, Cat 6):
  • Twisting prevents noise pickup.
  • Cat 5 has four pairs of two wires with different twist rates.
  • Twisting maintains even phase, minimizing interference from exterior noise.

Cat 5e

• Most common twisted pair cable; can be shielded (STP) or unshielded (UTP).
• Exterior insulation (various colors) indicates footage marks and cable type.
• UTP vs. STP:
  • STP has additional protection (aluminum foil) inside the exterior insulation.
  • Foil prevents external interference and emission of high frequencies.
  • STP is more expensive and used when necessary (e.g., near fluorescent lights or high-voltage lines).
• Data networks:
  • Color-coded (blue, orange, green, brown).
  • Terminated with RJ45 connectors.
  • Crimper tool used for termination.
• Two standards: TIA 568A, TIA 568B
  • 568B is more commonly used.
  • Difference lies in the swapping of orange-white and green-white pairs.
  • Federal jobs often use 568A.

25-Pair Cable

• Contains 25 pairs, used heavily in ITCS 4 for phone systems.
• Primary colors: blue, orange, green, brown, slate.
• Secondary colors: white, red, black, yellow, violet.
• Pairs are color-coded (e.g., blue-white, orange-white, blue-red, etc.).
• Terminated on 66 or 110 blocks using a punch-down tool.

Progression of 568B Categories

• Category 1 & 2: referred to, but not established.
• Category 4: obsolete.
• Category 3:
  • Used for telephone installations (landlines).
  • Untwisted, four wires.
  • Up to 16 Mbps bandwidth.
• Cat 5:
  • Computer networks.
  • Up to 100 MHz, 100 Mbps.
  • 100-meter length.
• Cat 5e:
  • Computer networks.
  • 100 MHz, up to 1000 Mbps.
  • Improved noise performance.
• Cat 6:
  • Current standard for high-speed networks.
  • Up to 256 MHz, 1000 Mbps.
  • Four pairs separated by a plastic insulator.
• Cat 7:
  • Proposed higher standard (up to 600 MHz).

Cable Testing

• Essential for ensuring cable integrity after termination.
• Crosstalk:
  • Measures signal coupling between pairs (in dB).
  • Compares energy in distributed pair vs. distributing pair.
  • Limited by shielding and different twist rates.
  • Two types: near-end crosstalk (NEXT) and far-end crosstalk (FEXT).
• Cable tester with master and dummy load units used for testing.
• Patch cables, manufactured or created, should be tested before implementation.

Different Twist Rates

• Prevents crosstalk.
• Varying twist rates help cancel out interference by ensuring that any induced charge is negated over the length of the wire, preventing any net charge at the end.

Delay Skew

• Measures propagation delay differences between the fastest and slowest pairs.
• Velocity depends on twist rate, capacitance, and inductance.
• Increased bit rates lead to more errors due to propagation delay differences.

Other Measurements

• Attenuation to Crosstalk Ratio (ACR):
  • Compares attenuation and crosstalk; larger number is better.
• Power Sum Near-End Crosstalk (PSNEXT):
  • Measures total crosstalk across all pairs.
• Return Loss:
  • Measures reflected power vs. transmitted power (in dB).
  • $Return Loss = 10 \cdot log<em>{10}(\frac{P</em>{incident}}{P_{reflected}})$
  • Larger number is better.

Shielded Pair

• Metal shield around pairs (copper braid or aluminum foil).
• Shield isolates connectors from external noise and is grounded at both ends.
• Internal conductors are balanced to ground.
• Prevents signal radiation to other equipment.
• Available in UTP (unshielded) and STP (shielded) versions.

Quiz: Correct Statements about Twisted Transmission Lines

• Correct answers:
  • Twisting a cable pair prevents noise pickup.
  • Different twist rates in a multi-pair cable prevent crosstalk.

Coaxial Cable (Coax)

• Durable, used for broadband internet, cable TV, satellite TV.
• Components:
  • Insulating material (dielectric):
    • Air (rare).
    • Polyethylene (most common).
    • Teflon.
  • Two concentric conductors.
    • Inner conductor.
    • Copper braid shielding (flexibility).
• Outer shield is grounded.
• Excellent noise immunity, minimal radiation.

Coax Connectors

• BNC: Used with oscilloscopes.
• N-Type: Used for antennas.
  • Female end on antenna, male from transmitter.
• UHF (Ultra High Frequencies).
• F-Type: Used for cable TV, satellite TV, broadband internet.
• SMA (Subminiature Amphenol): Smaller version of F-Type.

Baluns (Balanced/Unbalanced)

• Used to connect coax (unbalanced) to twisted pair (balanced).
• Balanced lines:
  • Equal impedance to ground.
  • Examples: ribbon cable, twisted pair, shielded pair.
• Unbalanced lines:
  • Unequal impedance to ground.
  • Example: coaxial cable.
• Balun converts between balanced and unbalanced signals using a transformer.

Electrical Characteristics of Transmission Lines

• At high frequencies, transmission lines act as complex circuits (with inductance, resistance, conductance, and capacitance).
• Resistance of wires and conductance insignificant.
• Characteristic impedance ($Z_0$) is impedance where there are no reflected waves (standing waves).
• $Z_0 = \sqrt{\frac{L}{C}}$, where L is the inductance and C is the capacitance.
  • The input impedance of a transmission line either infinitely long or terminated in a resistance equal to its characteristic impedance.

Example 12-1

• RG-8A/U coaxial cable: Capacitance = 29.8 pF/ft, Inductance = 73.75 nH/ft.
• Characteristic impedance is independent of length.
• $Z_0 = \sqrt{\frac{73.75 \times 10^{-9} H/ft}{29.8 \times 10^{-12} F/ft}} = 50 \Omega$
• For 1 mile:
  • $Z_0 = \sqrt{\frac{73.75 \times 5280 \times 10^{-9} H}{29.8 \times 5280 \times 10^{-12} F}} = 50 \Omega$

Formulas for Characteristic Impedance

• Twisted Pair:
  • $Z<em>0 = \frac{276}{\sqrt{\epsilon</em>r}} \cdot log<em>{10}(\frac{D}{d})$, where $\\epsilon</em>r$ is the dielectric constant, D is the distance between conductors, and d is the diameter of conductors.
• Coaxial Cable:
  • $Z<em>0 = \frac{138}{\sqrt{\epsilon</em>r}} \cdot log_{10}(\frac{D}{d})$

Example 12-2

• Parallel wireline: distance-to-diameter ratio = 2, air dielectric.
  • $Z<em>0 = 276 \cdot log</em>{10}(2 \times 2) = 166 \Omega$
• Air dielectric coaxial line: distance-to-diameter ratio = 2.35.
  • $Z<em>0 = 138 \cdot log</em>{10}(2.35) = 51.2 \Omega$
• RG-8A/U coaxial cable: D = 0.285 inches, d = 0.08 inches, polyethylene dielectric ($\epsilon_r$ = 2.3).
  • $Z<em>0 = \frac{138}{\sqrt{2.3}} \cdot log</em>{10}(\frac{0.285}{0.08}) = 50 \Omega$

Handout Examples

• Capacitance = 0.2 nF/m, Inductance = 200 nH/m
  • $Z_0 = \sqrt{\frac{200 \times 10^{-9}}{0.2 \times 10^{-9}}} = 31.6 \Omega$
• 1000 m coaxial cable: inner conductor diameter = 1.5 mm, polyethylene insulator thickness = 14 mm.
  • $Z<em>0 = \frac{138}{\sqrt{2.3}} \cdot log</em>{10}(\frac{14}{1.5}) = 88.268 \Omega$
• 500 m twisted pair: conductor diameter = 0.8 mm, distance between conductors = 4 mm, Teflon insulator.
  • $Z<em>0 = \frac{276}{\sqrt{2.1}} \cdot log</em>{10}(\frac{4}{0.8} \times 2) = 190.46 \Omega$

Quiz Question

• 100 m coaxial cable has $Z_0$ = 50 ohms. What is the impedance if cable is cut in half?
  • Still 50 ohms (characteristic impedance is independent of length).

Transmission Line Losses

• Signal amplitude attenuates along the wire due to characteristic impedance.
• Three major losses:
  • Copper Loss (Power Losses):
    • Minimize line length.
    • Skin effect: lower current in conductor center.
  • Dielectric Losses:
    • Proportional to voltage across dielectric and increases with frequency.
    • every dielectric has a breakdown voltage that needs to be taken in consideration.
  • Radiation/Inductive Losses:
    • Reduce by terminating line with resistive load equal to line's characteristic impedance and proper shielding.

Conclusion

• Covered operational characteristics of twisted pair and coaxial cable.
• Distinguished between balanced and unbalanced lines.
• Described physical characteristics of standard transmission lines, and calculating characteristic impedance.
• Discussed losses in transmission lines.