How do I calculate the width for a 50 ohm microstrip?

The width depends on the substrate thickness (h), dielectric constant (Er), and copper thickness (t). For FR-4 (Er = 4.4) with 0.2 mm dielectric height and 35 micrometer copper: a 50 ohm trace is approximately 0.36 mm wide (w/h ratio of about 1.8). For Rogers RO4003C (Er = 3.38) at the same thickness: the 50 ohm width is about 0.44 mm. The general rule: lower Er means wider traces for a given impedance, and wider traces mean lower conductor loss and easier fabrication. Most PCB design tools include impedance calculators, but for quick estimation: Z0 is approximately (87/sqrt(Er+1.41)) times ln(5.98h/(0.8w+t)) for w/h less than or equal to 1.

What are the loss mechanisms in microstrip?

Three loss mechanisms dominate. Conductor loss: the signal current concentrates in a skin-depth-thin layer on the trace surface and ground plane. It scales as sqrt(f) due to skin effect and increases with surface roughness above 5 GHz. Dielectric loss: energy absorbed by the substrate material, proportional to frequency times tan delta. Radiation loss: the open structure of microstrip (no top ground) allows energy to radiate from discontinuities (bends, T-junctions, open stubs) and from the fringing fields at the trace edges. Radiation loss becomes significant above about 20 GHz and limits the useful frequency range of microstrip. At mmWave frequencies, stripline (enclosed between two ground planes) is preferred because it does not radiate.

When should I use stripline or CPW instead of microstrip?

Stripline embeds the signal trace between two ground planes, providing complete shielding and zero radiation loss. Use it for routing sensitive signals through inner layers, for filters requiring high isolation, and above 20 GHz where microstrip radiation becomes problematic. The disadvantage is that components cannot be mounted directly on a stripline trace because it is buried. Coplanar waveguide (CPW) places the signal trace and ground on the same surface layer with narrow gaps between them. CPW is preferred for MMIC probing (ground-signal-ground probes connect directly), for flip-chip mounting, and for frequencies above 40 GHz where it provides better mode control than microstrip. Its disadvantage is sensitivity to the gap dimension and potential for parasitic parallel-plate modes.

PCB Design

Microstrip

Every RF signal on a PCB travels through a microstrip line: a copper trace on the top surface, a dielectric substrate below it, and a solid ground plane on the bottom. This sandwich forms a transmission line whose characteristic impedance is set by four numbers: trace width, substrate height, dielectric constant, and copper thickness. Get any of them wrong and the impedance deviates from 50 Ω, causing reflections, ripple, and signal loss. At 1 GHz, a 10% impedance mismatch is a minor nuisance (0.1 dB return loss degradation). At 28 GHz, the same mismatch on a 20 mm trace creates standing waves that can shift a filter's passband by 100 MHz. Controlled impedance is not a suggestion; it is the law of microwave PCB design.

Category: PCB Design

Target: 50 Ω (RF), 100 Ω (differential)

Determined By: w, h, ε_r, t

Choosing the Right Transmission Line

Type	Shielding	Radiation Loss	Component Access	Max Freq.	Best For
Microstrip	Partial (open top)	Moderate (>20 GHz)	Full access (top layer)	~30 GHz	Most RF PCBs, filters, matching
Stripline	Full (enclosed)	Zero	None (buried)	~60 GHz	Inner-layer routing, isolation
GCPW	Good (coplanar ground)	Low	Full (top layer)	~110 GHz	mmWave, MMIC, flip-chip
Embedded microstrip	Moderate	Low	Limited	~40 GHz	Multilayer with solder mask
Suspended stripline	Full	Zero	None	~40 GHz	Low-loss filters, diplexers

Microstrip impedance (w/h ≤ 1):
Z₀ ≈ (87 / √(ε_r + 1.41)) × ln(5.98h / (0.8w + t))

Effective permittivity:
ε_eff ≈ (ε_r+1)/2 + (ε_r−1)/2 × (1/√(1+12h/w))

50 Ω trace widths (h = 0.2 mm, t = 35 μm):
FR-4 (ε_r = 4.4): w ≈ 0.36 mm
RO4003C (ε_r = 3.38): w ≈ 0.44 mm
PTFE (ε_r = 2.2): w ≈ 0.58 mm

Common Questions

Frequently Asked Questions

How to calculate 50 Ω width?

Depends on h, ε_r, t. FR-4 at 0.2 mm height: w ≈ 0.36 mm. Rogers RO4003C: w ≈ 0.44 mm. Lower ε_r = wider traces = easier fabrication and lower conductor loss. Use PCB stackup calculators for production.

What causes microstrip loss?

Three mechanisms: conductor loss (√f, skin effect + roughness), dielectric loss (f × tanδ), radiation loss (from discontinuities, significant above 20 GHz). At mmWave, stripline or GCPW preferred because they do not radiate.

When to use stripline or CPW?

Stripline: inner-layer routing, full shielding, high isolation, above 20 GHz. CPW: MMIC probing (GSG pads), flip-chip, above 40 GHz. Microstrip: the default for most RF PCBs because components mount directly on the signal trace.

Related Terms

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PCB Layout

Microstrip Impedance Calculator

Enter substrate height, dielectric constant, trace width, and copper weight. Compute Z₀, effective permittivity, wavelength, and loss per cm at your operating frequency.

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