1. Theory

  • Definition: Empirical FET models fit measured MESFET and HEMT characteristics with closed-form functions chosen for shape and smoothness rather than derived from device physics; the Curtice, Statz, TriQuint TOM and Angelov models are the most widely used (Brinson; Aoki; RF Essentials).
  • MESFET models: Curtice combines a square-law transfer curve with a tanh knee; Statz adds a doping-profile term and a cubic knee; the TOM models add a power-law exponent, subthreshold conduction and output-conductance compression (Brinson; Brinson and Jahn).
  • Angelov model: The drain current is , with a polynomial of the gate voltage around the peak-transconductance point, which reproduces the bell-shaped transconductance of HEMTs and its derivatives for distortion (RF Essentials; Aoki).
  • Role today: Empirical models remain common for RF power amplifiers, while ASM-HEMT and the MIT virtual-source model are the CMC standard physics-based GaN models (Aoki; RF Essentials).

2. Working Principle

  • Separable fitting: The current is a product of a gate-voltage function, a knee function of and an output-conductance factor, so each can be fitted from transfer and output curves separately (Brinson; RF Essentials; my reading).
  • Transconductance shaping: Because near the peak, the tanh form gives a peaked whose higher derivatives control intermodulation (computed, after RF Essentials).
  • Charges: Gate charges built from tanh functions of and give charge-conserving, bias-dependent capacitances (RF Essentials; Aoki).
  • Dispersion: Separate DC and RF current branches, or a delay , represent traps and transit delay that make RF behaviour differ from DC (RF Essentials; Brinson and Jahn).

3. Applications

  • GaN and GaAs power amplifiers: Large-signal design, load-pull and harmonic tuning with Angelov models (RF Essentials; Aoki).
  • Mixers and oscillators: Nonlinear capacitance and harmonic generation (RF Essentials).
  • InP HEMT circuits: Millimetre-wave models built on Angelov equations (Li et al.).
  • Legacy and quick designs: Curtice models for small-signal GaAs MESFET amplifiers and estimates (RF Essentials).

MESFET Models

NameFormulaRelated FormulaeVariables/Constants
Curtice quadratic model








Statz (Raytheon) model
TriQuint TOM models



Angelov Model

NameFormulaRelated FormulaeVariables/Constants
Angelov drain current






Angelov gate charge and gate current





Charges and Dispersion

NameFormulaRelated FormulaeVariables/Constants
Charges, delay and dispersion in empirical models



Important Questions

Ques: How do the Curtice and Statz models describe a MESFET?

With a transfer function times a knee function. The Curtice model is (Brinson and Jahn; Brinson), and its level 2 variant smooths the pinch-off with a softplus overdrive (Brinson). Statz divides the square law by , so the transfer curve becomes linear at high overdrive, and replaces the tanh with a cubic below , reaching saturation with zero slope there (Brinson). With and , the Curtice current at zero gate bias is 11.2 at 3 ; Statz with an assumed B = 0.5 gives 5.1 (computed). Curtice uses fixed capacitances, while Statz adds a junction-like gate charge, which improves large-signal accuracy. Reference: M. Brinson and S. Jahn, ‘Compact device - circuit macromodel specification: A Curtice level 1 MESFET model’, Qucs documentation (2007) (fetch-tool summary); M. Brinson, ‘Verilog-A compact device models for GaAs MESFETs’, Qucs report (2008) (some equations garbled in the extract) (fetch-tool summary).

Ques: Why do the two Qucs reports give different Curtice defaults?

They describe different implementations. Brinson and Jahn’s 2007 level 1 macromodel uses , and , while Brinson’s 2008 Verilog-A MESFET report uses , and , both with . At zero gate bias and 3 the first gives 119 and the second 11.2 (computed), a factor of ten, and their knees lie at about 3.75 and 1.33 (computed). Neither set describes a particular device; the 2008 values are closer to a typical small GaAs MESFET, whose pinch-off is a volt or two (background knowledge), so they are the more realistic placeholders (my reading). Brinson and Jahn’s VBR default of 1010 also appears to be a typo for . Defaults should never be used without extraction. Reference: M. Brinson and S. Jahn, ‘Compact device - circuit macromodel specification: A Curtice level 1 MESFET model’, Qucs documentation (2007) (fetch-tool summary); M. Brinson, ‘Verilog-A compact device models for GaAs MESFETs’, Qucs report (2008) (some equations garbled in the extract) (fetch-tool summary).

Ques: Why does the Angelov model use the tanh of a polynomial?

To reproduce the peaked transconductance of HEMTs. In with (RF Essentials), the current at equals and the transconductance is at its maximum, while the current saturates at (computed). and make the curve asymmetric, matching its fall at high gate bias, and because tanh is infinitely differentiable, the second and third derivatives that set intermodulation are smooth. For Li et al.’s InP HEMT, with and an assumed , the peak would be 6.5 (computed). Li et al. modified the equations for strong drain-induced barrier lowering in their 70 device. Reference: RF Essentials, ‘What is the Angelov model for a GaN HEMT and when is it appropriate to use?’, RF Knowledge Base (April 2026; author not named) (fetch-tool summary); T. Li, W. Li and J. Liu, ‘An improved large signal model of InP HEMTs’, Journal of Semiconductors 39(5), 054003 (2018) (abstract, tables and captions only) (fetch-tool summary).

Ques: Does the Angelov current include a (1 + lambda Vds) factor?

In the original model, yes. The RF Essentials page writes the current as without it, and Aoki’s ADS listing, as extracted, reads Ids = IPK0(1 + tanh(x1p))tanh(Alphap Vds), but the same slides list LAMBDA among the parameters. Angelov’s published model includes for output conductance (background knowledge), and a parameter named LAMBDA would have no role otherwise, so the extracted fragment is probably truncated (it was limited to 72 characters) and the RF Essentials form a simplification (my reading). With the two agree. A typical of 0.01 (assumed) raises the current by 30 per cent from 0 to 30 (computed), so dropping it would be significant for GaN power devices. Reference: RF Essentials, ‘What is the Angelov model for a GaN HEMT and when is it appropriate to use?’, RF Knowledge Base (April 2026; author not named) (fetch-tool summary); H. Aoki, ‘Basic physical properties and compact models of high-speed, high-voltage compound transistors (introduction to GaN HEMT physics and modelling)’, slides in Japanese, 317th Gunma University Analog Integrated Circuit Workshop (15 December 2016) (parentheses dropped in the extract) (fetch-tool summary).

Ques: How do empirical models capture dispersion and trapping?

By separating DC and RF behaviour. RF Essentials describes Angelov implementations with separate DC and RF drain-current sources, each with its own parameters, so that trap-induced current collapse makes RF load lines and efficiency differ from DC predictions. Aoki shows Angelov fits to pulsed I-V of a GaN HEMT, which removes the slow thermal and trap states from the DC curves. The Curtice model only adds a fixed delay to the drain current, 10 by default (Brinson and Jahn), a 36-degree phase lag at 10 (computed), which represents transit delay rather than traps. A two-branch model cannot represent the bias history of traps, which ASM-HEMT and MVSG handle with RC trap networks (ASM-HEMT and MVSG pages), so empirical models should be extracted from pulsed data at the intended quiescent point. Reference: RF Essentials, ‘What is the Angelov model for a GaN HEMT and when is it appropriate to use?’, RF Knowledge Base (April 2026; author not named) (fetch-tool summary); H. Aoki, ‘Basic physical properties and compact models of high-speed, high-voltage compound transistors (introduction to GaN HEMT physics and modelling)’, slides in Japanese, 317th Gunma University Analog Integrated Circuit Workshop (15 December 2016) (parentheses dropped in the extract) (fetch-tool summary); M. Brinson and S. Jahn, ‘Compact device - circuit macromodel specification: A Curtice level 1 MESFET model’, Qucs documentation (2007) (fetch-tool summary); ASM-HEMT Model page of this vault; MVSG Model page of this vault.

Ques: How accurate are Angelov models for power-amplifier design?

Good at the fundamental, weaker at harmonics. RF Essentials gives typical accuracies of 0.5 to 1 for gain and saturated output power and 2 to 5 per cent for power-added efficiency, but 3 to 5 for the second harmonic, 5 to 8 for the third and 3 to 6 for IM3 and IM5. The third harmonic is the most sensitive because it depends on the third derivative of the current and charges. Accuracy improves with pulsed-IV extraction, careful charge fitting and validation against harmonic load-pull, and for critical uses such as 5G base-station amplifiers the page recommends measuring device harmonics. Aoki shows such validation for a GaN HEMT at 7 , with power and drain current against input power for 50 and efficiency-optimal loads. Reference: RF Essentials, ‘What is the Angelov model for a GaN HEMT and when is it appropriate to use?’, RF Knowledge Base (April 2026; author not named) (fetch-tool summary); H. Aoki, ‘Basic physical properties and compact models of high-speed, high-voltage compound transistors (introduction to GaN HEMT physics and modelling)’, slides in Japanese, 317th Gunma University Analog Integrated Circuit Workshop (15 December 2016) (parentheses dropped in the extract) (fetch-tool summary).

Ques: When should an empirical model be used instead of ASM-HEMT or MVSG?

When a fast, well-fitted large-signal model of one device matters more than scalability. RF Essentials prefers Angelov over Curtice for GaN HEMTs, GaAs pHEMT amplifiers and designs needing accurate harmonics, and keeps Curtice for simple small-signal MESFET amplifiers, estimates and legacy designs. Aoki lists ASM-HEMT and the MIT virtual-source model as the two CMC standard GaN HEMT models. Physics-based models scale with gate width, length and field-plate geometry and connect parameters to process, while empirical fits usually apply to one geometry and bias range (background knowledge for the scaling argument). In practice, foundry kits for GaN often provide both: standard models for scalable cells and Angelov-type models for power-amplifier cells, re-extracted for each device (my reading, after RF Essentials’ note on re-extraction). Reference: RF Essentials, ‘What is the Angelov model for a GaN HEMT and when is it appropriate to use?’, RF Knowledge Base (April 2026; author not named) (fetch-tool summary); H. Aoki, ‘Basic physical properties and compact models of high-speed, high-voltage compound transistors (introduction to GaN HEMT physics and modelling)’, slides in Japanese, 317th Gunma University Analog Integrated Circuit Workshop (15 December 2016) (parentheses dropped in the extract) (fetch-tool summary).

References

  1. M. Brinson and S. Jahn, “Compact device - circuit macromodel specification: A Curtice level 1 MESFET model,” Qucs documentation, 2007. Available: https://qucs.sourceforge.net/docs/report/curtice.pdf
  2. M. Brinson, “Verilog-A compact device models for GaAs MESFETs,” Qucs report, 2008. Available: https://qucs.sourceforge.net/docs/report/MESFET.pdf
  3. RF Essentials, “What is the Angelov model for a GaN HEMT and when is it appropriate to use?,” RF Knowledge Base, Apr. 2026 (author not named). Available: https://rfessentials.com/rf-knowledge-base/what-is-the-angelov-model-for-a-gan-hemt-and-when-is-it-appropriate-to-use/
  4. T. Li, W. Li and J. Liu, “An improved large signal model of InP HEMTs,” Journal of Semiconductors, vol. 39, no. 5, 054003, 2018. Available: https://www.jos.ac.cn/article/doi/10.1088/1674-4926/39/5/054003
  5. H. Aoki, “Basic physical properties and compact models of high-speed, high-voltage compound transistors (introduction to GaN HEMT physics and modelling),” slides (in Japanese), 317th Gunma University Analog Integrated Circuit Workshop, Dec. 2016. Available: https://kobaweb.ei.st.gunma-u.ac.jp/lecture/ProfAoki_07.pdf

Related pages in this vault: MVSG Model, ASM-HEMT Model, Metal Semiconductor Field Effect Transistor (MESFET), Ebers-Moll and Gummel-Poon Models, GaAs InP High Electron Mobility Transistor (HEMT), GaN HEMT (degradation), Diode Compact Models, GaN HEMT, Power Device Compact Models.