Introduction

Microwaves (about 300 MHz to 300 GHz, λ = 1 m to 1 mm) have wavelengths comparable to or smaller than the size of the circuit. Because of this, a microwave system behaves very differently from a conventional low-frequency (LF) system, where circuits are tiny compared with the wavelength.

Key idea: electrical size

• At 50 Hz, λ = 6000 km, so a 10 cm wire has no phase change along it. Voltage and current are the same everywhere on the wire, and lumped circuit theory (KVL, KCL) is valid.
• At 10 GHz, λ = 3 cm, so the same 10 cm wire is more than 3 wavelengths long. Voltage and current change in magnitude and phase along it, so the circuit must be treated as distributed, using transmission-line and field (Maxwell) theory.

Comparison of behaviour

Effects of these differences

1. Reflections and standing waves: a mismatched load reflects power, so impedance matching (stubs, quarter-wave transformers) becomes essential.
2. Higher losses: skin effect and dielectric loss grow with frequency, so low-loss substrates and waveguides are used.
3. Special active devices: ordinary transistors fail because of transit time, so microwave tubes (klystron, TWT, magnetron) and special diodes (Gunn, IMPATT) are used.
4. New analysis method: voltage and current are hard to define and measure, so scattering (S-) parameters, which are based on incident and reflected waves, are used instead of Z/Y parameters.

Example

A 1 cm PCB track has no effect at 1 MHz. At 7.5 GHz (λ = 4 cm) it is a quarter wavelength long, so it can turn a short circuit into an open circuit.

Microwave systems work at 300 MHz to 300 GHz, where the wavelength is comparable to the circuit size. Conventional low-frequency (LF) systems work at frequencies where the circuit is very small compared with λ. This one difference changes the operating principles of the whole system.

Comparison based on operating principles

Main consequence: LF engineers think in terms of voltage and current. Microwave engineers think in terms of waves, power flow, reflection, and matching.

Areas of application of microwave systems

1. Communication: terrestrial microwave links (backhaul), satellite communication (C, Ku, Ka bands), cellular mobile (GSM, LTE, 5G), Wi-Fi, Bluetooth, WiMAX.
2. Radar: air-traffic control, weather radar, police speed radar, military tracking, automotive radar at 77 GHz.
3. Navigation: GPS (L-band, 1575.42 MHz), aircraft landing systems, DME.
4. Broadcasting: direct-to-home satellite TV (Ku band), TV relay links.
5. Remote sensing: microwave radiometers, synthetic aperture radar (SAR) for earth observation.
6. Industrial and domestic heating: microwave ovens (2.45 GHz), drying, vulcanising rubber.
7. Medical: diathermy, hyperthermia cancer treatment, MRI RF coils, microwave imaging.
8. Scientific: radio astronomy, plasma heating, particle accelerators, spectroscopy.
9. Electronic warfare: jamming and surveillance.

The IEEE (Standard 521) gives letter names to the radar and microwave bands. Microwaves broadly cover 300 MHz to 300 GHz.

IEEE frequency band classification

Advantages of microwaves over lower frequencies

1. Large bandwidth: a 1% bandwidth at 10 GHz is 100 MHz, which carries many channels or high data rates.
2. High antenna gain from small antennas: gain ≈ 4πA/λ², so a small dish at microwave frequencies gives a narrow, high-gain beam.
3. Line-of-sight propagation: low interference, and the same frequency can be reused in nearby areas.
4. Ionosphere penetration: makes satellite and space communication possible.
5. Radar: target size is comparable to λ, so radar cross-section and resolution are good.
6. Less fading and noise: man-made and atmospheric noise is low.
7. Small components: λ-sized circuits are compact, such as MMICs and patch antennas.
8. Molecular resonances: allow heating, spectroscopy, and remote sensing.

Disadvantages

1. Line of sight only: towers or repeaters are needed every 40–50 km because of earth curvature.
2. Atmospheric attenuation: rain fade above about 10 GHz, and oxygen and water-vapour absorption.
3. Costly components and tight tolerances: precise machining, special substrates, and expensive test equipment.
4. Lumped analysis fails: field and S-parameter analysis is needed, which makes design complex.
5. Low device power and efficiency: ordinary transistors fail because of transit time, so special tubes and diodes are needed.
6. Higher losses: skin effect and dielectric loss rise with frequency.
7. Radiation hazards: high power densities can heat tissue, so safety limits apply.

Microwaves are electromagnetic waves (300 MHz–300 GHz) that travel at the speed of light, c = 3 × 10⁸ m/s, even in vacuum. Acoustic and seismic waves are mechanical waves. They need a material medium and are slow: about 343 m/s in air, about 1500 m/s in water, and a few km/s in rock.

Advantages of microwaves over acoustic/seismic waves

1. No medium needed: microwaves travel through vacuum, so they serve satellite and space links. Acoustic waves cannot.
2. Very high speed: signal delay is about 10⁶ times smaller, so radar ranging and real-time communication are fast.
3. Huge bandwidth: carrier frequencies in the GHz range carry Mbps to Gbps of data. Acoustic channels carry only kHz of bandwidth.
4. Long range in air: line-of-sight links of 50 km or more, and satellite links of 36,000 km. Acoustic waves in air die out within metres to kilometres.
5. Directive, compact antennas: λ is in cm, so narrow beams come from small dishes.
6. Weather-independent below about 10 GHz: microwaves pass through cloud, fog and smoke. Acoustic waves are disturbed by wind and temperature gradients.
7. Fine resolution for imaging and radar.

Disadvantages of microwaves compared with acoustic/seismic waves

1. Poor penetration of water and earth: microwaves are absorbed by conducting media such as sea water and wet soil. Sonar (acoustic) is used under water, and seismic waves probe deep underground for oil and earthquake study.
2. Line of sight: blocked by hills and buildings, while low-frequency seismic waves travel through the earth.
3. Expensive equipment: microwave sources, waveguides and analyzers cost far more than transducers and geophones.
4. Rain and atmospheric loss above about 10 GHz.
5. Health and safety limits on radiated power.
6. Licensing: the spectrum is regulated, while acoustic methods need no licence.

Microwave bands (300 MHz–300 GHz, λ = 1 m to 1 mm) lie between radio waves and infrared. Their main features come from the short wavelength.

• Electrically large circuits: circuit size is comparable to λ, so distributed (transmission-line) analysis is used instead of lumped KVL/KCL.
• Wave-based description: S-parameters, reflection coefficient and VSWR replace voltage and current.
• Wide bandwidth: large information capacity, for example 100 MHz is only 1% of 10 GHz.
• Line-of-sight propagation: microwaves pass through the ionosphere (used for satellites) and are not reflected back like HF waves.
• High-gain, small antennas: horns, parabolic dishes and patch arrays give narrow beams. Gain = 4πAe/λ².
• Skin effect: current flows in a thin surface layer, which raises conductor loss.
• Transit-time limits: ordinary tubes and transistors fail, so klystrons, magnetrons, TWTs, Gunn and IMPATT diodes are used.
• Radiation from discontinuities: bends, gaps and open ends radiate, so shielding and careful layout are needed.
• Atmospheric effects: rain attenuation above about 10 GHz, and absorption peaks at 22 GHz (water vapour) and 60 GHz (oxygen).
• Molecular resonance: used for heating (2.45 GHz ovens) and spectroscopy.
• Reflection from targets: objects comparable to λ reflect well, which is the basis of radar.

Applications: radar, satellite and terrestrial links, mobile phones, Wi-Fi, GPS, ovens, and medical diathermy.

Behaviour of passive components: low frequency vs microwave

At low frequency a resistor, inductor or capacitor acts as an ideal lumped element. At microwave frequencies its leads and body are a large fraction of λ, so parasitics (lead inductance, stray capacitance, skin effect) dominate.

Real resistor at microwave frequency:
      Ls       R       Ls
  o--^^^^---/\/\/---^^^^--o
        |              |
        +------||------+
              Cs (stray)

So at microwave frequencies L and C are made from short-circuited or open-circuited stubs, and resonators are made from cavities.

Real-world protocols of three microwave communication systems

1. Wi-Fi (IEEE 802.11 WLAN)

• Bands: 2.4 GHz ISM (2.400–2.4835 GHz), 5 GHz (5.15–5.85 GHz), and 6 GHz for Wi-Fi 6E.
• Channels: 20/40/80/160 MHz wide. At 2.4 GHz there are 13 channels 5 MHz apart, and only 1, 6 and 11 do not overlap.
• Modulation: OFDM with BPSK up to 1024-QAM (802.11ax). 802.11b used DSSS/CCK.
• Access: CSMA/CA with optional RTS/CTS. Duplexing is TDD.
• Rates: 11 Mbps (b), 54 Mbps (a/g), 600 Mbps (n, MIMO), about 9.6 Gbps (ax).
• Security: WPA2/WPA3 (AES).

2. Cellular mobile (GSM / LTE / 5G NR)

• GSM: 900/1800 MHz, 200 kHz carriers, GMSK modulation, TDMA with 8 time slots per carrier, FDD (uplink 890–915 MHz, downlink 935–960 MHz).
• LTE (4G): 700 MHz–2.6 GHz, 1.4–20 MHz bandwidth, OFDMA downlink and SC-FDMA uplink, up to 64-QAM, MIMO, FDD or TDD.
• 5G NR: FR1 below 6 GHz and FR2 at 24–52 GHz (mm-wave), up to 400 MHz bandwidth, flexible numerology, massive MIMO and beamforming.
• Architecture: mobile station, base station (BTS/eNodeB/gNB), core network. Frequency reuse in hexagonal cells, with handover between cells.

3. Satellite communication

• Geostationary orbit at 35,786 km. One-way delay is about 120 ms (about 240 ms up and down).
• Bands: C band (uplink 5.925–6.425 GHz, downlink 3.7–4.2 GHz, written 6/4 GHz), Ku band (14/12 GHz), Ka band (30/20 GHz).
• A transponder receives the uplink, translates the frequency down, amplifies with a TWTA or SSPA, and retransmits. Typical transponder bandwidth is 36 MHz.
• Access: FDMA, TDMA, CDMA. Example: VSAT networks with QPSK/8PSK and DVB-S2.
• Uplink is at the higher frequency because the ground station can afford more power to overcome the greater loss.

Unique differences: microwave vs conventional LF systems

Specifications/protocols of five microwave communication systems

1. Wi-Fi (IEEE 802.11 WLAN)

• Bands: 2.4 GHz ISM (2.400–2.4835 GHz), 5 GHz (5.15–5.85 GHz), and 6 GHz for Wi-Fi 6E.
• Channels: 20/40/80/160 MHz wide. At 2.4 GHz there are 13 channels 5 MHz apart, and only 1, 6 and 11 do not overlap.
• Modulation: OFDM with BPSK up to 1024-QAM (802.11ax). 802.11b used DSSS/CCK.
• Access: CSMA/CA with optional RTS/CTS. Duplexing is TDD.
• Rates: 11 Mbps (b), 54 Mbps (a/g), 600 Mbps (n, MIMO), about 9.6 Gbps (ax).
• Security: WPA2/WPA3 (AES).

2. Cellular mobile (GSM / LTE / 5G NR)

• GSM: 900/1800 MHz, 200 kHz carriers, GMSK modulation, TDMA with 8 time slots per carrier, FDD (uplink 890–915 MHz, downlink 935–960 MHz).
• LTE (4G): 700 MHz–2.6 GHz, 1.4–20 MHz bandwidth, OFDMA downlink and SC-FDMA uplink, up to 64-QAM, MIMO, FDD or TDD.
• 5G NR: FR1 below 6 GHz and FR2 at 24–52 GHz (mm-wave), up to 400 MHz bandwidth, flexible numerology, massive MIMO and beamforming.
• Architecture: mobile station, base station (BTS/eNodeB/gNB), core network. Frequency reuse in hexagonal cells, with handover between cells.

3. Satellite communication

• Geostationary orbit at 35,786 km. One-way delay is about 120 ms (about 240 ms up and down).
• Bands: C band (uplink 5.925–6.425 GHz, downlink 3.7–4.2 GHz, written 6/4 GHz), Ku band (14/12 GHz), Ka band (30/20 GHz).
• A transponder receives the uplink, translates the frequency down, amplifies with a TWTA or SSPA, and retransmits. Typical transponder bandwidth is 36 MHz.
• Access: FDMA, TDMA, CDMA. Example: VSAT networks with QPSK/8PSK and DVB-S2.
• Uplink is at the higher frequency because the ground station can afford more power to overcome the greater loss.

4. Terrestrial microwave link (point-to-point backhaul)

• Bands: 6, 7, 8, 11, 13, 15, 18, 23 and 38 GHz, with E-band at 70/80 GHz.
• Line of sight with at least 60% of the first Fresnel zone clear. Hop length 30–50 km at 6 GHz, a few km at 23–38 GHz.
• Modulation: adaptive QPSK up to 4096-QAM. Channel width 7–56 MHz (up to 112 MHz).
• Duplexing: FDD with a duplexer. Protection: 1+1 hot standby, and space or frequency diversity.
• Parabolic dishes of 0.3–3 m, 30–45 dBi gain.

5. Bluetooth (IEEE 802.15.1)

• Band: 2.4 GHz ISM. 79 channels of 1 MHz (Classic) or 40 channels of 2 MHz (Low Energy).
• FHSS at 1600 hops/s. Modulation GFSK (1 Mbps), with π/4-DQPSK or 8DPSK for EDR (2–3 Mbps).
• Piconet of 1 master and up to 7 active slaves, using TDD slots of 625 µs.
• Range: 10 m (Class 2, 2.5 mW) to 100 m (Class 1, 100 mW).

Microwave vs traditional low-frequency systems (operating principle)

Why S-parameter analysis is a must at microwave frequencies

1. V and I are not well defined: in a waveguide there is no unique voltage or current, only fields. S-parameters use incident and reflected wave amplitudes (a, b), which are always defined.
2. Open and short circuits cannot be made: Z, Y and h parameters need ports to be open or shorted. At microwave frequencies a "short" has inductance and an "open" radiates, and active devices often oscillate under these conditions. S-parameters are measured with all ports terminated in matched loads (Z0), which is stable and easy to do.
3. Direct measurement: a vector network analyzer measures |S| and phase directly, as ratios of power waves.
4. Physical meaning: S11 is the input reflection coefficient (return loss), and |S21|² is the power gain or insertion loss.
5. Network properties are easy to see: reciprocal means S = Sᵀ, and lossless means S is unitary (S*ᵀS = I).
6. Easy cascading and shifting of reference planes: moving a port reference only multiplies Sij by a phase factor e^(-jβl). With T-parameters, cascaded networks reduce to matrix multiplication.

Uses of microwaves in communication systems

1. Terrestrial point-to-point microwave links (backhaul for mobile networks and TV relay).
2. Satellite communication (telephony, DTH TV, VSAT, Internet).
3. Cellular mobile communication (GSM, CDMA, LTE, 5G).
4. Wireless LAN (Wi-Fi) and WiMAX.
5. Personal area networks (Bluetooth, ZigBee).
6. Navigation (GPS, radar beacons, aircraft landing systems).
7. Radar (a communication of target information).
8. Deep-space and telemetry links.

Communication protocols of three of them

1. Wi-Fi (IEEE 802.11 WLAN)

• Bands: 2.4 GHz ISM (2.400–2.4835 GHz), 5 GHz (5.15–5.85 GHz), and 6 GHz for Wi-Fi 6E.
• Channels: 20/40/80/160 MHz wide. At 2.4 GHz there are 13 channels 5 MHz apart, and only 1, 6 and 11 do not overlap.
• Modulation: OFDM with BPSK up to 1024-QAM (802.11ax). 802.11b used DSSS/CCK.
• Access: CSMA/CA with optional RTS/CTS. Duplexing is TDD.
• Rates: 11 Mbps (b), 54 Mbps (a/g), 600 Mbps (n, MIMO), about 9.6 Gbps (ax).
• Security: WPA2/WPA3 (AES).

2. Cellular mobile (GSM / LTE / 5G NR)

• GSM: 900/1800 MHz, 200 kHz carriers, GMSK modulation, TDMA with 8 time slots per carrier, FDD (uplink 890–915 MHz, downlink 935–960 MHz).
• LTE (4G): 700 MHz–2.6 GHz, 1.4–20 MHz bandwidth, OFDMA downlink and SC-FDMA uplink, up to 64-QAM, MIMO, FDD or TDD.
• 5G NR: FR1 below 6 GHz and FR2 at 24–52 GHz (mm-wave), up to 400 MHz bandwidth, flexible numerology, massive MIMO and beamforming.
• Architecture: mobile station, base station (BTS/eNodeB/gNB), core network. Frequency reuse in hexagonal cells, with handover between cells.

3. Satellite communication

• Geostationary orbit at 35,786 km. One-way delay is about 120 ms (about 240 ms up and down).
• Bands: C band (uplink 5.925–6.425 GHz, downlink 3.7–4.2 GHz, written 6/4 GHz), Ku band (14/12 GHz), Ka band (30/20 GHz).
• A transponder receives the uplink, translates the frequency down, amplifies with a TWTA or SSPA, and retransmits. Typical transponder bandwidth is 36 MHz.
• Access: FDMA, TDMA, CDMA. Example: VSAT networks with QPSK/8PSK and DVB-S2.
• Uplink is at the higher frequency because the ground station can afford more power to overcome the greater loss.

Lumped vs distributed circuit analysis

Lumped analysis treats R, L and C as concentrated at points connected by ideal wires. It is valid when the circuit size is much smaller than λ (a rule of thumb is l < λ/10). Distributed analysis treats R, L, G and C as spread along the line per unit length. Voltage and current then vary with position, which is needed when the size is about λ or larger.

Distributed model of a length Δz of line:
  o--R'Δz--L'Δz--+------o
                 |
              G'Δz  C'Δz
                 |
  o--------------+------o

Areas of application of microwave systems

Communication (terrestrial links, satellite, cellular, Wi-Fi), radar (ATC, weather, military, automotive), navigation (GPS), broadcasting (DTH TV), remote sensing, industrial and domestic heating (2.45 GHz ovens), medical (diathermy, hyperthermia), and radio astronomy.

Detailed protocols of two microwave communication systems

1. Wi-Fi (IEEE 802.11 WLAN)

• Bands: 2.4 GHz ISM (2.400–2.4835 GHz), 5 GHz (5.15–5.85 GHz), and 6 GHz for Wi-Fi 6E.
• Channels: 20/40/80/160 MHz wide. At 2.4 GHz there are 13 channels 5 MHz apart, and only 1, 6 and 11 do not overlap.
• Modulation: OFDM with BPSK up to 1024-QAM (802.11ax). 802.11b used DSSS/CCK.
• Access: CSMA/CA with optional RTS/CTS. Duplexing is TDD.
• Rates: 11 Mbps (b), 54 Mbps (a/g), 600 Mbps (n, MIMO), about 9.6 Gbps (ax).
• Security: WPA2/WPA3 (AES).

2. Satellite communication

• Geostationary orbit at 35,786 km. One-way delay is about 120 ms (about 240 ms up and down).
• Bands: C band (uplink 5.925–6.425 GHz, downlink 3.7–4.2 GHz, written 6/4 GHz), Ku band (14/12 GHz), Ka band (30/20 GHz).
• A transponder receives the uplink, translates the frequency down, amplifies with a TWTA or SSPA, and retransmits. Typical transponder bandwidth is 36 MHz.
• Access: FDMA, TDMA, CDMA. Example: VSAT networks with QPSK/8PSK and DVB-S2.
• Uplink is at the higher frequency because the ground station can afford more power to overcome the greater loss.

Behaviour of circuits: low frequency vs RF/microwave

Classification of microwave bands and applications (IEEE letter bands)

At low frequency, a transmission line (for example a pair of wires) is only a connection. At microwave frequency the same line is several wavelengths long, so it becomes a circuit element whose behaviour depends on its length, its characteristic impedance and the load.

Low-frequency behaviour

• Length ≪ λ, so there is no phase change from end to end, and V and I are the same at both ends.
• Modelled with lumped series R and L, and sometimes shunt C (power line models).
• Load impedance is seen directly at the input: Zin ≈ ZL.
• Losses are mainly I²R. Skin effect and radiation are negligible.
• Mismatch does not matter much, and there are no standing waves.
• Two-wire lines, twisted pair and ordinary cable are used.

Microwave behaviour

• Length is comparable to λ, so the line is treated as distributed with R′, L′, G′, C′ per metre.
• Voltage and current are waves: V(z) = V⁺e^(-γz) + V⁻e^(γz), with γ = α + jβ.
• Characteristic impedance Z0 = √((R′ + jωL′)/(G′ + jωC′)) ≈ √(L′/C′).
• Input impedance changes with length: Zin = Z0 (ZL + jZ0 tan βl)/(Z0 + jZL tan βl).
  • A λ/4 line inverts the impedance: Zin = Z0²/ZL.
  • A λ/2 line repeats the load.
  • Shorted or open stubs act as pure L or C.
• Mismatch gives reflection Γ = (ZL − Z0)/(ZL + Z0), standing waves and VSWR, so matching is required.
• Skin effect (δ = 1/√(πfμσ)) and dielectric loss raise the attenuation. Open lines radiate, so coax, waveguide, microstrip or stripline are used.
• Higher-order modes appear when the cross-section approaches λ/2.

Summary table

Example

A 7.5 cm shorted line at 1 GHz (λ = 30 cm) is λ/4 long, so it looks like an open circuit. At 50 Hz the same piece of wire is a dead short.

Behaviour of microwave circuits

Microwave circuits (300 MHz–300 GHz) have dimensions comparable to the wavelength, so they behave as distributed circuits.

1. Phase changes along conductors: every interconnection is a transmission line. Its input impedance depends on length: Zin = Z0(ZL + jZ0 tan βl)/(Z0 + jZL tan βl).
2. Reflections and standing waves: any mismatch reflects power (Γ ≠ 0), so matching networks are needed.
3. Parasitic effects: lead inductance and stray capacitance change R, L and C. Each component has a self-resonant frequency.
4. Skin effect: current flows in a few µm of the surface, which increases loss.
5. Radiation: open lines and discontinuities radiate, so closed structures (waveguides, shielded microstrip) are used.
6. Transit-time limits: ordinary active devices fail, so klystrons, magnetrons, Gunn diodes and HEMTs are used.
7. S-parameters: V and I are hard to define, so networks are described by incident and reflected waves.

Advantages of microwave frequencies

• Wide bandwidth and high data capacity.
• Small, high-gain, highly directive antennas.
• Line-of-sight propagation allows frequency reuse.
• Microwaves pass through the ionosphere, so satellite links are possible.
• Good radar resolution and target reflection.
• Low atmospheric and man-made noise.
• Compact components (MMIC).

Disadvantages

• Line of sight only, so repeaters or towers are needed.
• Rain and atmospheric attenuation at higher bands.
• Costly components, precise fabrication, and expensive test equipment.
• Complex field-based analysis and design.
• Low efficiency of active devices and higher losses.
• Radiation health hazards.

Classification of signal frequencies into waves and rays

The electromagnetic spectrum, from low to high frequency:

The "waves" (radio, up to EHF) are used for communication. Microwaves are 300 MHz–300 GHz.

Advantages of microwave signals

1. Large bandwidth, so high data rates and many channels.
2. High antenna gain with small antennas (G = 4πAe/λ²).
3. Line-of-sight propagation allows frequency reuse.
4. Microwaves pass through the ionosphere, so they are used for satellite and space links.
5. Low fading and low noise.
6. Good radar resolution.
7. Compact circuits and antennas.

Disadvantages

1. Line of sight only, so towers and repeaters are needed (about 50 km spacing).
2. Rain and gas attenuation above about 10 GHz.
3. Expensive components and precise fabrication.
4. Lumped circuit theory fails, so design is complex.
5. Transit-time effects need special devices with low efficiency.
6. Higher conductor and dielectric loss.
7. Biological hazards at high power.

Lumped vs distributed circuit analysis

In lumped analysis, each element (R, L, C) is concentrated at one point and connected by ideal wires. It is valid when the circuit is much smaller than λ (about λ/10 or less). In distributed analysis, the parameters are spread along the line per unit length (R′, L′, G′, C′). Voltage and current vary in amplitude and phase with position. This is needed at RF and microwave frequencies.

Uses of microwave bands

• L band: GPS, mobile phones.
• S band: Wi-Fi, Bluetooth, microwave ovens (2.45 GHz), weather radar.
• C band: satellite communication (6/4 GHz), 5 GHz Wi-Fi.
• X band: military and marine radar.
• Ku/Ka bands: DTH TV, VSAT, broadband satellites, 5G mm-wave.
• W band: automotive radar (77 GHz).
• Others: medical diathermy, remote sensing, radio astronomy.

Microwave frequency bands and their major applications (IEEE letter bands)

How microwave transmission lines differ from LF lines

1. Electrical length: an LF line is much shorter than λ and acts as a plain connection. A microwave line is several λ long, so it is distributed and has phase delay βl.
2. Input impedance: at LF, Zin ≈ ZL. At microwave frequency, Zin = Z0(ZL + jZ0 tan βl)/(Z0 + jZL tan βl), which changes with length. A λ/4 line inverts the impedance.
3. Reflections: a mismatch at microwave frequency produces Γ, standing waves and VSWR, so matching is needed.
4. Structure: LF lines are two-wire lines or ordinary cables. Microwave lines are coax, rectangular or circular waveguides, microstrip, stripline and coplanar waveguide, with closed or shielded fields.
5. Modes: LF lines carry TEM. Microwave waveguides carry TE/TM modes with a cutoff frequency.
6. Losses: microwave lines suffer skin-effect loss (∝ √f), dielectric loss and radiation, so low-loss materials are used.
7. Use as components: microwave line sections serve as stubs, filters, couplers and resonators.
8. Analysis: Smith chart and S-parameters instead of simple circuit laws.