Simulation Techniques for Inductor Coil Design

🔹 New Resource: Inductor Guide 🔹 I'm excited to share my detailed and practical Inductor Guide, which covers everything from basic principles to advanced selection and simulation techniques. ✅ Topics Covered: - Inductor Fundamentals (Core, Frequency, and Phase Behavior) - DC-DC Converter Design with Inductor Selection Examples - Real-World Calculations (Time Constant, Current Ripple) - Inductor Types and Core Selection Strategy - LTSpice Simulation Results - Practical Selection Checklist for Power Supplies and Filters This guide is designed to help engineers, students, and hardware designers understand inductor behavior beyond textbook definitions. 📥 Download the PDF attached and let me know your feedback! I’d love to hear your experience with inductor selection or EMI challenges in your projects. #HardwareDesign #PowerElectronics #Inductors #PCBDesign #DCtoDCConverter #SignalIntegrity #ComponentSelection #PowerDesign #ElectronicsEngineering #EngineeringResources

Inductor is tricky design because silicon is not a friendly medium for magnetics. ⸻ 1. Fabrication of Inductor on Silicon Inductors are planar spiral inductors, made using the top metal layers. Steps: 1. Substrate: Start with silicon wafer (p-type). 2. Isolation: Field oxide or STI separates active devices. 3. Metals: Multiple interconnect metal layers are deposited. 4. Inductor layout: • A spiral pattern is drawn in the topmost thick metal layer (for reduced resistance, usually copper or thick aluminum). • Can be circular, square, or octagonal spiral. 5. Vias: If multi-level spirals are used, vias connect metals. 6. Passivation: Inductor is covered by dielectric layers for protection. 7. Optional improvements: • Patterned Ground Shield (PGS): A special shield layer under the inductor to reduce substrate loss. • MEMS techniques: Suspend the inductor above silicon to reduce parasitics. Note: On-silicon inductors are low-Q compared to off-chip inductors, because silicon is lossy and eddy currents + parasitic capacitance degrade performance. ⸻ 2. Modeling of On-Chip Inductor We need to capture electrical + substrate parasitics. Two main approaches: Analytical lumped models and Electromagnetic (EM) simulation models. (a) Lumped-Element Equivalent Circuit A typical spiral inductor is modeled as: Rs Ls ---/\/\/\----+ | Cpar | GND But in reality, it’s more complex (π or T models). Components: • Ls: Self-inductance of spiral. • Rs: Series resistance of metal track (depends on width, thickness, and skin effect). • Cox: Capacitance to substrate through oxide. • Csi: Capacitance from metal to silicon substrate. • Rsub: Resistance of silicon substrate (models substrate losses). • Mutual coupling: If multiple turns → mutual inductance. Complete π-model looks like: • Series branch: L_s + R_s • Shunt branches: C_{ox}, C_{si}, R_{sub} • Sometimes also a substrate network of R_{si} || C_{si}. ⸻ (b) Key Parameters • Inductance (L): L =mu_0 N^2 A/l_{avg} where N = turns, A = average area, l_{avg} = mean path length. • Q-factor: Q = (omega *L)/(R_{s} + R_{loss}) High-Q is desired (>10 for RF), but on-silicon often < 10. • Self-Resonant Frequency (SRF): f_{SRF} =1/2*pi*sqrt{L*C_{par}} Beyond this frequency, inductor behaves capacitive. ⸻ (c) Modeling Approaches in Practice 1. Analytical models: For first-order design 2. Extraction using EM solvers (2.5D/3D): Tools like HFSS, Momentum, or EMX simulate inductance, resistance, and parasitics accurately. 3. Foundries provide PDK libraries with fitted equivalent circuits. ⸻ 3. Challenges in Silicon Inductor Design • Substrate losses: Eddy currents + capacitive coupling to lossy Si. • Low Q-factor: Much worse than PCB/air-core inductors. • Large area: Spirals consume lots of die area. • Frequency limit: SRF limits usage in GHz range. ⸻ Key design metrics are L, Q-factor, and SRF.

Controlled Nonlinear Inductors - The Saturated Step Principle I take inspiration from a previous post of mine related to a Coilcraft inductor, which featured a particular geometric structure, to describe a rather uncommon but very interesting construction technique known as the saturated step (stepped air-gap). The saturated step core, unlike what can be achieved using distributed-gap powder cores, allows the design of an inductor with two (or more) distinct inductance levels as a function of the operating current. The goal is to obtain a predefined inductance value, sufficiently linear over a specific current range, consistent with the requirements of the application. Beyond a certain current threshold, the inductance is intentionally reduced, introducing a second operating regime. I designed my first saturated step inductor back in 1988, for an application that required controlling the maximum operating frequency under light-load conditions, in order to prevent the switching frequency from increasing uncontrollably. Of course, this solution also has limitations, and it is presented here for demonstration purposes only. In particular, the portion of the core subjected to high magnetic flux density tends to generate more heat; for this reason, it is good practice to keep the ratio between low-current inductance and high-current inductance within 15–20% (purely indicative values, to be evaluated case by case). For those who want to experiment or explore the concept further, I have prepared a simple Python program which, based on the input parameters, computes and plots the inductance versus current characteristic. Two fundamental rules derived from experience: never reduce the main air gap (G1) to zero remain conservative when defining the maximum flux density in the high-current operating condition At the link below, you can download the complete document, together with the Python code used to analyze and verify the behavior of the system. Link to download: - Full document https://lnkd.in/ebgdaqDc - Python script https://lnkd.in/eQ-kVRFP - Config file https://lnkd.in/e8A_BP-f #powerconvertion #inductor #powerdesign #converters #pwm

PyPEEC is a 3D quasi-magnetostatic PEEC solver developed at Dartmouth College that can simulate a large variety of magnetic components (inductors, transformers, air coils, etc.). The open-source tool contains a mesher, a solver (static and frequency domain), and advanced plotting capabilities. Python Source Code and Documentation: https://pypeec.otvam.ch Paper in the Journal of Open Source Software: https://lnkd.in/gmtXCyKe PyPEEC is based on the FFT-accelerated PEEC method (first described and implemented in MATLAB by R. Torchio, https://lnkd.in/gd5aU44X). This method is very well-suited for geometries that can be efficiently meshed with a regular voxel structure. Finally, keep in mind that PyPEEC is an academic tool and not a competitor to commercial FEA software... #python #opensource #magnetic #powerelectronics #dartmouth

 🚀 Today I'm releasing py2femm — the FEA companion for open-source power-electronics design. A few years back I open-sourced pyplecs to automate PLECS simulations. py2femm is its younger brother: where pyplecs handles the topology, py2femm handles the finite-element world behind the schematic — thermal, magnetic, electrostatic. Power electronics design is never just the circuit. It's:  → Will this heatsink drop 20 °C or 200 °C?  → Does my inductor saturate under peak current?  → What's the parasitic capacitance between that bus bar and the chassis? FEMM answers all of these. The pain is doing it at scale — parametric sweeps, CI pipelines, shared licenses — from a Windows GUI.  py2femm gives you:  ✅ Pure Python API for magnetics, electrostatics, heat flow, current flow  ✅ REST server — run FEMM from a notebook, a Linux box, or CI  ✅ Cross-platform via Wine / Docker / Windows  ✅ Built-in parametric engine — 360-config factorial heatsink sweep in ~10 min  The open-source power-electronics toolbox keeps getting stronger:  🔹 #pyplecs topology-level simulation (PLECS)  🔹 OpenMagnetics — the gold standard for magnetic design  🔹 #py2femm — thermal, EM field, and boundary-condition workflows Together they let you go from topology → magnetic sizing → thermal sign-off. All in Python. All open  source. All reproducible.  🔗 Repo: https://lnkd.in/e6_C_UHg  📚 Docs: https://lnkd.in/evdzkdVS  📜 License: AGPL-3.0  If you design converters, what examples would you want to see next?  #PowerElectronics #OpenSource #FEMM #FEA #Python #MagneticDesign #ThermalDesign #ConverterDesign

RF Basics: On-chip Inductor Modeling: Most of the engineers are scared of inductor 🙂. Inductor is one of the most important and widely used component in RF circuits such as LNA, Mixers, PA, VCO, impedance matching, filtering, etc.. Accurate and more reliable model for inductor is the extraction done through wafer level measurement and curve fitting. Also, 3D EM simulators such as HFSS, CST Studio, 3D EMPro, etc. are quiet accurate. An "extracted on-chip inductor model" refers to a simplified representation of an on-chip inductor's behavior, typically derived from measured data or simulations. These models are used in circuit simulation and design to predict the inductor's performance without needing to perform complex 3D electromagnetic simulations. Types of On-Chip Inductor Models: Distributed Models: These models consider the inductor as a distributed structure, taking into account the effects of its physical dimensions on its inductance and other parameters. Frequency-Dependent Models: These models, account for the change in the inductor's properties with frequency, such as the frequency-dependent effects of skin effect and substrate interaction. Compact Frequency-Independent Models: These models aim to capture the overall behavior of the inductor with a simplified set of parameters, suitable for various frequency ranges. Extraction Methods: Direct Extraction: This method directly extracts model parameters from measured data, such as S-parameters or Y-parameters. Simultaneous Optimization: This method combines direct extraction with optimization algorithms to refine model parameters and improve accuracy. Curve Fitting: This method uses curve fitting techniques to find the best fit for a predefined model structure based on measured data. Applications: RFIC Design: On-chip inductors are essential for matching impedances, filtering signals, and providing reactive elements in RF integrated circuits. Power Supply Design: Inductors play a crucial role in power supply circuits for filtering, smoothing voltage, and storing energy. Simulation and Optimization: Extracted models enable efficient circuit simulation and optimization, leading to more accurate and reliable designs. Key Considerations: Accuracy vs. Complexity: A balance needs to be struck between model accuracy and the complexity of the extraction method. Frequency Range: The model's validity should be verified across the relevant frequency range of interest. Process Technology: On-chip inductor models are often tailored to specific process technologies and fabrication techniques. In essence, an extracted on-chip inductor model is a valuable tool for characterizing and predicting the behavior of these crucial components in integrated circuits. 🙏🙏🙏🙏🙏