Source — Power MOSFET/GaN HEMT Non-Linear Capacitance Extraction
Raw source:
raw/articles/2026-08-14_joe-nonlinear-capacitance-power-fet.md(immutable)
Author: Joe Chang. Status: ongoing (technical report draft).
One-line summary
Use large-signal dynamic charge measurement (Q_G, Q_GS, Q_GD, Q_oss) to back out continuous non-linear capacitance curves (C_gs, C_gd, C_ds), solving the problem that datasheet small-signal AC capacitance distorts in the low V_DS region and causes errors in DPT (double-pulse test) simulation.
Core arguments
- Limitations of small-signal AC capacitance: the datasheet’s C_iss/C_oss/C_rss are measured at V_GS=0V, fixed DC bias, 1MHz/25mV AC ripple. As V_DS→0V, C_gd surges 10–100×, the instrument can’t measure accurately at low bias, and the curve distorts in the low-voltage region.
- Advantage of charge conservation: Q_G and Q_oss are continuous transient integrals over the entire switching trajectory (Q=∫C(v)dv). Through charge conservation in the Miller plateau and overdrive regions, one can back out the low-voltage peak capacitance and the knee/transition voltage, yielding an accurate large-signal behavioral model.
- Three-step extraction method: (1) C_gs and V_plat (Miller plateau voltage); (2) non-linear C_gd(V_DS) curve (Lorentzian/smooth-step); (3) C_ds(V_DS) for GaN HEMT (sigmoidal/Hill function).
- GaN specifics: no PN-junction body diode; C_ds consists of the metal geometry capacitance C_metal and the 2DEG field-plate depletion capacitance C_2DEG, described by a sigmoidal function.
- Verification and application: use Q_oss numerical integration (trapezoidal) to back-validate; apply to the ZVS dead time t_dead,min = 2·Q_oss(V_in)/I_magnetizing.
Key formulas (extraction skeleton)
- C_gs ≈ C_iss − C_rss
- V_plat = Q_GS / C_gs
- C_gd,low = (Q_G − Q_GS − Q_GD)/(V_drive − V_plat) − C_gs
- C_gd(V_DS) = C_rss + (C_gd,low − C_rss) / [1 + (V_DS/V_trans,gd)²]
- V_trans,gd ≈ (Q_GD − C_rss·V_test) / [(C_gd,low − C_rss)·π/2]
- C_ds(V_DS) = C_metal + C_2DEG / [1 + (V_DS/V_trans)^k] (GaN, k=2.5)
- Q_oss(V_DS) = ∫₀^{V_DS} [C_ds(v) + C_gd(v)] dv
Implementation
In SPICE, non-linear capacitance is implemented with a behavioral current source (i = C(v)·ddt(v)), ensuring charge conservation and transient convergence, with a complete subcircuit example (see Section 6 of the raw source).
Links to other pages
- Domain aggregate: power-semiconductor-modeling
- Core concepts: non-linear-capacitance-extraction, charge-conservation-qv, miller-plateau, zvs-dead-time
- Entities: power-mosfet, gan-hemt, 2deg, spice
- Note: in the raw source, the V_trans,gd section and the C_ds,test section each contain one leftover editor-suggestion fragment (not part of the physics text). The summary follows the correct physical formulation; for verbatim proofreading, refer back to the raw source.