Open any mobile phone, Wi-Fi router or GPS receiver and you will not find coaxial cables or waveguides inside — the microwave signals travel along flat copper tracks on a circuit board. These are planar transmission lines: microstrip, stripline and coplanar waveguide. They are a standard topic in microwave engineering and appear in BCS (Telecom/EEE), BTCL and university exams. This post explains each type with an animated field picture, design formulas, a worked 50 Ω example and MCQs.
- Planar lines are conductors patterned on flat dielectric substrates — compatible with printed circuit boards (PCB) and integrated circuits (MIC/MMIC).
- Microstrip: strip above a ground plane; field partly in air → quasi-TEM, εeff between 1 and εr; easiest to make.
- Stripline: strip buried between two ground planes; field fully in the dielectric → pure TEM, shielded, no radiation.
- Coplanar waveguide (CPW): signal and ground on the same surface → easy to connect components in shunt.
- Guide wavelength λg = λ0/√εeff; on FR-4 a 3 mm-wide track on 1.6 mm board is about 50 Ω.
1. Why Planar Transmission Lines?
At microwave frequencies even a few centimetres of conductor behaves as a transmission line. Rectangular waveguides and coaxial cables work well but are bulky, heavy and expensive to integrate with transistors and chips. Planar lines are made by photolithography on a substrate (FR-4, Rogers/PTFE laminates, alumina, GaAs), so whole circuits — filters, couplers, matching networks, antennas — can be printed together, cheaply and repeatably.
2. Types and Field Patterns (Animation)
3. Microstrip Line in Detail
A microstrip consists of a conducting strip of width W on a dielectric substrate of thickness h and relative permittivity εr, with a ground plane underneath. Because the field lies partly in the dielectric and partly in air, the mode is quasi-TEM and the line behaves as if filled with an effective permittivity:
εeff = (εr + 1)/2 + (εr − 1)/2 · 1/√(1 + 12h/W)Characteristic impedance (for W/h ≥ 1, Hammerstad):
Z0 = 120π / { √εeff [ W/h + 1.393 + 0.667 ln(W/h + 1.444) ] }- Wider strip or thinner substrate → lower Z0; narrow strip → higher Z0.
- Phase velocity v = c/√εeff; guide wavelength λg = λ0/√εeff.
- Losses: conductor loss, dielectric loss (tan δ of the substrate) and radiation from discontinuities (which microstrip patch antennas exploit).
4. Stripline in Detail
A stripline (triplate line) places the strip in the middle of a dielectric sandwiched between two ground planes. The field is completely within a homogeneous dielectric, so it supports a pure TEM mode with εeff = εr and v = c/√εr. It is self-shielded (low radiation and crosstalk) and has wider bandwidth with no dispersion, but it is harder to fabricate and to mount components on (vias are needed). It is used in multilayer PCBs, couplers and filters.
5. Coplanar Waveguide and Slot Line
- Coplanar waveguide (CPW): a centre strip flanked by two ground planes on the same surface. Shunt components and transistor connections need no vias — popular in MMICs and on-wafer probing.
- Slot line: a narrow slot in a metal layer; the field is across the slot. Used in some antennas and balanced circuits.
- Suspended stripline: a thin substrate suspended in air inside a metal channel — low loss, used in high-performance filters.
6. Comparison Table
| Property | Microstrip | Stripline | Coplanar waveguide |
|---|---|---|---|
| Mode | Quasi-TEM | TEM | Quasi-TEM |
| εeff | Between 1 and εr | = εr | ≈ (εr + 1)/2 |
| Radiation / crosstalk | Some | Very low (shielded) | Low–moderate |
| Dispersion | Small, increases with f | None | Small |
| Fabrication & component mounting | Easiest | Harder (buried strip) | Easy; no vias for shunt parts |
| Typical use | RF PCBs, patch antennas, MICs | Multilayer boards, couplers, filters | MMICs, on-wafer probing |
7. Advantages and Disadvantages
| Advantages | Disadvantages |
|---|---|
| Small size, light weight, low profile | Higher loss than waveguide or coax |
| Low cost, mass production by photolithography | Lower power-handling capability |
| Easy integration with active devices (MIC/MMIC) | Radiation and coupling (microstrip) |
| Good repeatability and reliability | Limited Q-factor for resonators/filters |
| Wide bandwidth (stripline) | Dimensions tolerances become critical at mm-wave |
8. Worked Example: Designing a 50 Ω Microstrip
Given: FR-4 board, εr = 4.4, h = 1.6 mm, strip width W = 3.0 mm. Find εeff, Z0 and the length of a quarter-wave section at 2.4 GHz.
- W/h = 3.0/1.6 = 1.875
- εeff = 2.7 + 1.7/√(1 + 12/1.875) = 2.7 + 1.7/2.72 ≈ 3.32
- Z0 = 376.99 / {1.823 × [1.875 + 1.393 + 0.667 ln(3.319)]} ≈ 376.99/7.42 ≈ 50.8 Ω
- λ0 at 2.4 GHz = 12.5 cm ⇒ λg = 12.5/1.823 ≈ 6.86 cm ⇒ λg/4 ≈ 1.71 cm
The same strip in a stripline (εeff = 4.4) would have a shorter wavelength: λg = 12.5/√4.4 ≈ 5.96 cm.
9. Practice MCQs (click to see answer)
1. The dominant mode in a stripline is: (a) TE₁₀ (b) TM₀₁ (c) TEM (d) Quasi-TEM
2. The mode in a microstrip line is: (a) Pure TEM (b) Quasi-TEM (c) TE₁₀ (d) TM₁₁
3. Effective permittivity of microstrip lies: (a) Below 1 (b) Between 1 and εr (c) Above εr (d) Equal to εr
4. Increasing the strip width of a microstrip ______ its characteristic impedance. (a) Increases (b) Decreases (c) Does not change (d) Doubles
5. Which planar line has signal and ground conductors on the same surface? (a) Microstrip (b) Stripline (c) Coplanar waveguide (d) Coaxial line
6. Which planar line is fully shielded with negligible radiation? (a) Microstrip (b) Stripline (c) Slot line (d) Twin-lead
7. Guide wavelength in microstrip is: (a) λ₀√εeff (b) λ₀/√εeff (c) λ₀εeff (d) λ₀
8. A main disadvantage of microstrip compared with waveguide is: (a) Larger size (b) Lower power handling and higher loss (c) Higher cost (d) Difficult fabrication
10. বাংলায় দ্রুত রিভিশন
- প্ল্যানার ট্রান্সমিশন লাইন: সমতল ডাইইলেকট্রিক সাবস্ট্রেটের উপর ছাপা পরিবাহী — PCB ও IC-র সাথে সহজে যুক্ত হয়।
- মাইক্রোস্ট্রিপ: গ্রাউন্ড প্লেনের উপর স্ট্রিপ; ক্ষেত্র আংশিক বাতাসে → কোয়াসি-TEM; εeff ১ ও εr-এর মাঝে; তৈরি করা সবচেয়ে সহজ।
- স্ট্রিপলাইন: দুই গ্রাউন্ড প্লেনের মাঝে স্ট্রিপ; বিশুদ্ধ TEM, শিল্ডেড, বিকিরণ নেই।
- কোপ্ল্যানার ওয়েভগাইড: সিগন্যাল ও গ্রাউন্ড একই তলে — MMIC-তে জনপ্রিয়।
- λg = λ₀/√εeff; চওড়া স্ট্রিপ → কম Z₀। FR-4 (εr = 4.4, h = 1.6 mm)-এ ৩ মিমি চওড়া ট্র্যাক ≈ ৫০ Ω।
Related Posts
- Microstrip Line: Structure & Advantages
- Stripline Transmission Line
- Equivalent Circuit of a Transmission Line
- Microwaves: Properties & Bands
References: David M. Pozar, Microwave Engineering; K. C. Gupta et al., Microstrip Lines and Slotlines; E. O. Hammerstad, “Equations for Microstrip Circuit Design”, 1975. Images and animations: original work by Totalecer.