Microstrip Inductor Calculator

Calculate total inductance, characteristic impedance (Z₀), effective dielectric constant (εeff), and unit‑length inductance for a microstrip transmission line.

mm
Dielectric thickness (e.g., 0.8 – 3.2 mm for common PCBs)
mm
Conductor width on top of substrate
FR4 ≈ 4.6, Rogers 4003 ≈ 3.55, Alumina ≈ 9.8
mm
Physical length of the microstrip conductor
MHz
For inductive reactance XL = 2πfL
mm
(1 oz = 0.035 mm)
? FR4 50Ω (W=3.0mm, H=1.6mm, εr=4.6)
? Rogers 4003C 50Ω (W=2.9mm, H=1.524mm, εr=3.55)
⚡ High‑Z inductor (W=0.5mm, H=1.6mm, εr=4.6)
? Alumina (εr=9.8, W=1.2mm, H=0.635mm)
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Microstrip Inductor Theory & Design

A microstrip line consists of a conducting trace separated from a ground plane by a dielectric substrate. When designed as a high‑impedance line (narrow trace relative to substrate height), it behaves as a distributed inductor with predictable inductance per unit length. The total inductance is derived from the characteristic impedance and effective permittivity: L0 = Z₀ · √εeff / c₀ , where c₀ is the speed of light. This calculator implements closed‑form expressions from Hammerstad & Jensen, widely adopted in RF engineering (ref. “Microstrip Lines and Slotlines” by Gupta et al.).

εeff = εr+1/2 + εr−1/2 · 1/√(1+12H/W)

Z₀ = (60/√εeff)·ln(8H/W+W/4H) (W/H ≤ 1) or (120π/√εeff)/[W/H+1.393+0.667 ln(W/H+1.444)] (W/H ≥ 1)

L0 (nH/mm) = Z₀ · √εeff / 300

Thickness correction: ΔW = (t/π)·ln(1 + 4H/t)   (Wheeler approximation)

Why Use an Interactive Microstrip Inductor Tool?

  • Rapid prototyping: Instantly obtain inductance and impedance for PCB inductors without expensive EM simulations.
  • Educational depth: Visualize the cross‑section and understand how W/H ratio influences inductance.
  • Optimization: Design high‑impedance lines for RF chokes or matching networks.
  • Verified formulas: Based on IEEE‑standard microstrip models, consistent with industry EDA tools.

Step‑by‑Step Calculation Methodology

1. Compute effective permittivity εeff using the well‑known empirical model by Hammerstad.
2. Determine characteristic impedance Z₀ based on the ratio W/H (two distinct regimes).
3. Calculate unit‑length inductance L0 = Z₀ · √εeff / 300 (exact conversion from H/m to nH/mm).
4. Multiply by physical length to obtain total inductance Ltotal = L0 × Lengthmm.
5. Optionally compute inductive reactance XL = 2πf Ltotal and electrical length in degrees.
The model assumes a lossless line with negligible dispersion (quasi‑static approximation), adequate up to several GHz.

Application Case Study: 2.4 GHz Bandpass Filter

Design Example: High‑Impedance Inductor for L‑matching network

An engineer needs a 4.7 nH inductor on a 1.6mm FR4 board. Using this calculator with W = 0.7 mm, H = 1.6 mm, εr = 4.6 gives L0 ≈ 1.18 nH/mm. To obtain 4.7 nH, required length = 4.7 / 1.18 ≈ 3.98 mm. The characteristic impedance is about 92 Ω, which provides sufficient inductive behaviour. The tool quickly verifies the trade‑off between line width and achievable inductance, enabling compact PCB inductors without spiral coils.

Limitations & Practical Notes

  • Frequency dependence: At very high frequencies (>5‑10 GHz), dispersive effects slightly modify εeff and Z₀; this calculator provides quasi‑static results.
  • Conductor thickness: For thick copper (>0.035mm), corrections can slightly reduce Z₀. The optional thickness factor is approximated as a first‑order adjustment.
  • Nearby components: Mutual coupling and discontinuities affect real inductance; for critical designs use EM validation.
  • Self‑resonance: At high frequencies, parasitic capacitance creates self‑resonance; the model does not include SRF.

Authoritative References & Standards

  • Hammerstad, E. and Jensen, Ø. (1980). “Accurate Models for Microstrip Computer-Aided Design”. IEEE MTT-S.
  • Wheeler, H. A. (1964). “Transmission-Line Properties of a Strip on a Dielectric Sheet”. IEEE Trans. Microwave Theory Tech.
  • Pozar, D. M. “Microwave Engineering”, 4th Edition, Wiley.
  • IPC-2141A “Controlled Impedance Circuit Boards and High-Speed Logic Design”.
Substrate εr H (mm) W (mm) for 50Ω L0 (nH/mm) Typical use
FR4 std 4.6 1.6 2.95 0.77 General purpose RF
Rogers 4350B 3.48 1.524 3.2 0.70 High-frequency PCB
Alumina 96% 9.8 0.635 0.58 0.56 Hybrid microwave ICs
Low-loss PTFE 2.2 0.8 2.42 0.88 Satellite / mmWave

Euler-Like Insight: Relationship Between L₀ and Z₀

Microstrip inductance per unit length is directly proportional to characteristic impedance: high‑impedance lines (narrow traces) yield larger inductance, making them suitable for compact inductive elements. For a fixed substrate, reducing W from 3 mm to 0.5 mm can increase L₀ by a factor of 2–3, demonstrating the design flexibility.

Frequently Asked Questions

The analytical model matches full‑wave simulations within 2‑5% for typical PCB geometries (0.2 ≤ W/H ≤ 10). It is trusted for initial design and educational purposes.

For standard 1oz copper (35 µm), effect on Z₀ is < 1‑2%. The optional thickness correction uses incremental width adjustment to improve accuracy for heavy copper.

No, this calculator applies only to straight microstrip lines. For spiral inductors, use a planar spiral inductor calculator.

Quasi‑static model works well up to ~5 GHz for typical FR4. For higher frequencies, consider dispersive formulas (not implemented here).
References: Microwaves101 | Hammerstad & Jensen (1980) | Pozar "Microwave Engineering" (2021). Tool last updated May 2026 – GetZenQuery tech team.