Microwave Passive Components
A complete guide to microwave passive components — directional couplers, hybrid rings, baluns, ferrite circulators, isolators, cavity resonators, waveguide components and power dividers. Theory, S-parameter signatures, design equations and real-world applications throughout.
Microwave Passive Component Families
Passive microwave components manipulate RF signals without amplification — splitting, combining, routing, filtering, attenuating or transforming signals. Unlike lumped components at low frequencies, microwave passives are typically distributed structures whose physical dimensions are comparable to the wavelength. Understanding the S-parameter signature of each component is essential for system design.
Directional Couplers
A directional coupler is a 4-port device that samples a portion of the signal travelling in one direction on a transmission line, while ideally not responding to signals in the reverse direction. The key figures of merit are coupling factor C, directivity D, insertion loss IL, and isolation I.
D = −20·log₁₀(|S41|/|S31|) = I − C dB (directivity)
I = −20·log₁₀(|S41|) dB (isolation — power at isolated port)
IL = −20·log₁₀(|S21|) dB (insertion loss — through port)
Ideal: IL = 10·log₁₀(1−10^(−C/10)) dB (lossless) · D > 20 dB typical > 30 dB excellent
Port numbering: 1=input, 2=through, 3=coupled, 4=isolated
Coupled-Line Coupler
The most common microwave coupler — two parallel transmission lines coupled over a quarter wavelength. The coupling factor is determined by the even- and odd-mode impedances of the coupled section.
Z_0e = Z_0·√((1+C_linear)/(1−C_linear)) (even-mode impedance)
Z_0o = Z_0·√((1−C_linear)/(1+C_linear)) (odd-mode impedance)
Length = λ_g/4 at centre frequency
Branch-Line Hybrid (90° Hybrid)
The branch-line hybrid is a 4-port 3 dB coupler where the output ports have a 90° phase difference. It is widely used in balanced amplifiers, IQ mixers, and antenna feed networks.
Z_through = Z_0/√2 = 50/√2 = 35.4 Ω (horizontal arms)
Z_shunt = Z_0 = 50 Ω (vertical arms)
S-parameters (ideal): |S21|=|S31|=−3 dB, ∠S21−∠S31=−90°, S41=0 (isolated)
Bandwidth: −1 dB from ≈ 0.75f₀ to 1.25f₀ (33% fractional BW)
Rat-Race Ring (180° Hybrid)
The rat-race consists of a 3λ/2 ring with four ports. At the sum port, signals add in phase; at the difference port, they add 180° out of phase. It is the standard 180° hybrid in microwave systems.
Port spacing: 1–2 = λ/4, 2–3 = λ/4, 3–4 = λ/4, 4–1 = 3λ/4
Sum port (Σ): ports 2 and 4 add in-phase → output at port 1
Difference port (Δ): ports 2 and 4 add 180° → output at port 3
Bandwidth narrower than branch-line: ≈ 20% BW at −1 dB
Baluns
A balun (balanced-unbalanced transformer) converts between a single-ended (unbalanced) coaxial port and a balanced (differential) two-terminal port. The balanced output has two equal-amplitude signals 180° out of phase, with no common-mode component. Critical for mixers, dipole antenna feeds, push-pull PAs and differential LNAs.
| Balun Type | Mechanism | Bandwidth | Best For |
|---|---|---|---|
| Coaxial sleeve (choke) | λ/4 short-circuit sleeve chokes CM current on coax outer | Narrowband (~10%) | Antenna feeds, simple applications |
| Marchand balun | Two coupled λ/4 sections — broadband phase balance | Octave bandwidth | Mixers, push-pull PAs, broadband |
| Transformer balun | Wound toroid — magnetic coupling | DC to 3 GHz | VHF/UHF, HF transceivers |
| Wilkinson + 180° hybrid | Rat-race hybrid as balun | 20% | PCB integration, lab measurements |
| MMIC balun | On-chip coupled lines or active balun | Multi-octave | mm-Wave ICs, high integration |
Marchand Balun
Z_c = √(Z_in × Z_out/2) (coupling impedance for 1:1 transformation)
For 50 Ω in → 50 Ω balanced out (25 Ω each side):
Z_c = √(50 × 25) = 35.4 Ω
Phase balance: better than ±2° across octave bandwidth in planar implementation
Amplitude balance: better than ±0.3 dB across band
Circulators & Isolators
Ferrite devices are non-reciprocal — their S-parameters differ when ports are swapped. This arises because magnetised ferrite material breaks time-reversal symmetry: electromagnetic waves interact differently depending on their propagation direction relative to the biasing magnetic field.
Circulator
A 3-port circulator routes power cyclically: signal enters port 1 → exits port 2 → enters port 2 → exits port 3 → enters port 3 → exits port 1. Reverse signals are strongly attenuated (isolation >20 dB). The S-matrix of an ideal circulator is:
S21=S32=S13=1 (0 dB, lossless forward) · S12=S23=S31=0 (−∞ dB, no reverse)
Real circulator specs:
Insertion loss: 0.3–0.6 dB (ferrite loss + connector)
Isolation: 18–30 dB (frequency dependent — best at design centre)
VSWR: 1.15:1 – 1.3:1 · Power handling: 1 mW – 100 W CW
| Application | Why a Circulator | Circulator Spec |
|---|---|---|
| Antenna duplexer | TX and RX share one antenna without a filter | High isolation (30 dB), low IL, power handling |
| PA output protection | Absorbs reflected power from mismatched load — protects PA | Power handling = PA Pout, good VSWR |
| Reflection amplifier | Amplifier reflects signal (negative resistance device) — circulator separates input/output | Very low IL, phase stability |
| Radar T/R switch | High isolation between high-power TX and sensitive RX | High power handling, fast recovery |
| VNA port isolation | Improves raw directivity of VNA bridges | Very high directivity (>35 dB) |
Isolator
An isolator is a 2-port circulator with port 3 terminated in a matched load. Signals pass forward with low loss; reverse signals are absorbed in the termination. Used after every PA output and LO source to prevent load impedance variations from pulling the frequency or causing instability.
VSWR_in ≈ 1.2:1 (port 1 sees matched load regardless of port 2 termination)
Power handling: 10 mW – 50 W average (peak power higher)
Frequency range: typically 1 decade (e.g. 2–4 GHz or 8–12 GHz)
Note: isolators are single-frequency-range devices — you need a different isolator for each band
Microwave Resonators
A resonator stores energy oscillating between electric and magnetic fields. The quality factor Q characterises how well it stores energy — higher Q means lower loss, sharper resonance, and better phase noise in oscillators and better selectivity in filters.
Q_u = Q_L/(1 − |S21_peak|²)^½ (unloaded Q — intrinsic material Q)
Q_ext = 1/(1/Q_L − 1/Q_u) (external Q — coupling to ports)
1/Q_L = 1/Q_u + 1/Q_ext
For minimum insertion loss: Q_ext = Q_u → IL = 6 dB (half power to resonator losses)
Cavity Resonators
Metallic cavities are the highest-Q passive resonators — Q factors of 1,000 to 50,000 at microwave frequencies. They are used in low-phase-noise oscillators, filter banks for satellite transponders, and radar receiver preselectors.
For TE₁₀₁: m=1, n=0, p=1 → f_res = (c/2)·√((1/a)² + (1/d)²)
Approximate Q for copper cavity:
Q_u ≈ (π/2)·(f_res/f₀)·(a·d/2)·(2/δ) / (total surface area contribution)
Rule of thumb: copper cavity Q ≈ 150·√(V[cm³])·√(f[GHz]) (very approximate)
Example: 2 cm³ copper cavity at 5 GHz → Q ≈ 150·√2·√5 ≈ 150×1.414×2.236 ≈ 474
| Resonator Type | Q Range | Size | Tuneable? | Application |
|---|---|---|---|---|
| Lumped LC (chip) | 20–200 | Tiny | Varactor | VCO tank, IC filters |
| Microstrip ring/stub | 50–300 | Small | PIN diode | PCB bandpass filters |
| SAW resonator | 1,000–10,000 | Very small | No | Mobile phone duplexers, timing |
| BAW/FBAR resonator | 1,000–3,000 | Tiny (die) | No | 5G FR1 duplexers, WiFi filters |
| Dielectric resonator | 5,000–30,000 | Compact | Mechanical | DRO, base station filters |
| Coaxial resonator | 2,000–8,000 | Medium | Screw trim | Combline filters, diplexers |
| Rectangular cavity | 5,000–50,000 | Large | Tuning screw | Radar filters, test equipment |
| Superconducting cavity | >10⁹ | Large | No | Particle accelerators, quantum computing |
Dielectric Resonator (DR)
Dielectric resonators (DRs) use high-εr ceramics (εr = 20–100) to miniaturise cavities by a factor of √εr. A DR with εr=38 at 5 GHz is √38 = 6.2× smaller than an air cavity. Q factors of 5,000–30,000 make them ideal for DROs (dielectric resonator oscillators) and high-Q bandpass filters for base stations.
Or: f_res ≈ c/(2√εr·D) for simple sphere approximation
Temperature stability: τf (ppm/°C) determined by ceramic composition. Near-zero τf ceramics available (e.g. Ba(Mg₁/₃Ta₂/₃)O₃ at τf ≈ 0 ppm/°C, Q·f = 400,000 GHz)
Coupling: magnetic coupling to microstrip or coax via proximity — coupling coefficient adjusted by distance between DR and line
Waveguide Components
Rectangular metallic waveguides are hollow conducting tubes that propagate TE and TM modes above the cutoff frequency. They offer the lowest loss of any transmission medium at microwave frequencies — essential for high-power radar, satellite uplinks and mm-wave systems where coaxial loss becomes prohibitive.
| Component | Function | Key Spec | Application |
|---|---|---|---|
| E-plane T junction | 3-port power divider — series T in E-plane | Equal split, input VSWR | Power distribution in waveguide systems |
| H-plane T junction | 3-port shunt T — power split with phase reversal | Equal split, input VSWR | Antenna array feeds |
| Magic-T | 4-port hybrid (E+H plane T combined) — sum and difference ports | Isolation >30 dB, equal split | Balanced mixers, radar T/R, bridge circuits |
| Iris | Conducting aperture in waveguide wall — inductive or capacitive | Susceptance value | Waveguide filter coupling elements |
| Waveguide coupler | Two waveguides share a common wall with coupling holes | Coupling factor, directivity | Power monitoring in high-power radar |
| Tuning screw | Metallic screw penetrating into waveguide — capacitive susceptance | Tuning range, power handling | Filter tuning, impedance matching |
| Waveguide-to-coax transition | Probe or loop coupling from coax to waveguide | Return loss, insertion loss | Interface between coaxial and waveguide systems |
f_operating = 1.25×f_c to 1.9×f_c (usable range before next mode)
λ_g = λ/√(1−(f_c/f)²) (guide wavelength, longer than free space)
Z_TE = 377/√(1−(f_c/f)²) Ω (TE₁₀ wave impedance, >377 Ω)
Attenuators & Phase Shifters
Fixed Attenuators
Attenuators reduce signal level without reflections — they present 50 Ω at all ports regardless of source or load impedance. Pi and T resistor networks are the standard topologies.
R2 = Z_0·(10^(A/10)−1)/(2·10^(A/20)) (series resistor)
For 10 dB: R1=R3=96.2 Ω, R2=35.1 Ω · For 3 dB: R1=R3=292 Ω, R2=17.6 Ω
P_R1 = P_R3 = P_in·(1−10^(−A/10))·(R2/Z_0)/(1+R2/Z_0)² (power dissipation)
Phase Shifters
| Type | Mechanism | Phase Range | Application |
|---|---|---|---|
| Switched-line | PIN diodes switch between two TL lengths | Fixed steps (e.g. 180°, 90°, 45°) | Phased array beam steering (digital) |
| Loaded-line | Shunt varactors on TL change effective εr | Continuous, 0–60° per section | Analogue phase steering, continuous beam scan |
| Reflection-type | Hybrid + varactor loads → phase via reflection | Continuous 0–360° | IQ modulator, vector modulator |
| MEMS phase shifter | Capacitive MEMS switches on distributed TL | 4–6 bits (up to 360°) | mm-Wave phased arrays (5G, automotive radar) |
| Ferrite phase shifter | Magnetic biasing of ferrite in waveguide | 0–360°, latching | High-power radar phased arrays |