Theory

SPICE Tube Models — Beyond the Basics

Understanding Koren, Rydel, and Ayumi models for accurate tube simulation

SPICE was designed for semiconductors. Simulating vacuum tubes requires subcircuit models that replicate the tube's I-V characteristics using controlled sources. The three dominant model families each take a different approach to accuracy vs. complexity.

Koren Model
Closed-form equations
5-8 parameters per tube
Fast simulation
Good for triodes
Limited pentode accuracy
Rydel Model
Lookup table interpolation
Measured data-driven
Very accurate
Slower convergence
Needs real tube measurements
Ayumi Model
Enhanced Koren-type
Better pentode support
Screen current modeling
Good for guitar amps
Moderate complexity
Koren triode: I_p = (E1/K_g1)^x × (1 + sign(E1)) / 2
where E1 = V_pk/K_p × ln(1 + exp(K_p × (1/μ + V_gk/sqrt(K_vb + V_pk²))))
Calculator

Koren Model Explorer

See how Koren parameters affect the predicted plate current

μ100
Kp600
Kvb300
Kg11.1k
x1.4
Vpk200V
Vgk-2V
E10.235
Ip0.01mA
gm (est)0.00mA/V
Visualization

Koren Model IV Curves — 12AX7

Reference

SPICE Model Availability by Tube

Which models exist for your favorite tubes

TubeKorenRydelAyumiNotes
12AX7YesYesYesMost-modeled tube; all models accurate
12AT7YesYesYesGood agreement across models
12AU7YesYesYesLow-mu; Koren works well
6SN7YesSomeYesDual triode; match both sections
EL34LimitedYesYesScreen current model critical for pentode
KT88LimitedYesYesUltralinear tap modeling adds complexity
300BYesYesYesDHT — filament as cathode, simple model
6L6GCLimitedYesYesKink region needs special handling
Practice

Setting Up Tube Simulations

1. Choosing a Simulator

LTspice (free, Windows/Mac) is the most popular for tube circuits. It handles nonlinear subcircuits well and converges reliably. SPICE OPUS, Ngspice, and TINA-TI are alternatives. For pentodes, ensure your simulator supports multi-terminal subcircuits with the .SUBCKT syntax.

2. Convergence Tips

Tube circuits often fail to converge in DC operating point analysis. Solutions: (1) Add .OPTIONS RELTOL=0.003 ITL1=500 to relax tolerances, (2) Use .IC statements to set initial node voltages near the expected operating point, (3) Add 1GΩ resistors from each node to ground to prevent floating nodes, (4) For transformer-coupled circuits, use K-statement coupling with realistic leakage inductance.

3. Validating Your Model

Always validate against published tube data: (1) Plot Ip vs Vp at several Vg values and compare to datasheet curves, (2) Check gm at the operating point against the datasheet value, (3) Verify mu by measuring ΔVp/ΔVg at constant Ip, (4) For pentodes, verify screen current is realistic (typically 20-40% of plate current). A model that matches at one operating point may diverge badly at extremes.

4. What SPICE Cannot Do

SPICE models don't capture: microphonics (mechanical vibration coupling), aging (emission decline over time), warm-up transients (cathode temperature rise), or grid emission at very high temperatures. For guitar amplifiers, the interaction between speaker impedance curves and output transformer characteristics is critical but hard to model accurately — always build and test.

Quiz de synthèse

Testez vos connaissances

Question 1 / 5

What is the primary advantage of the Koren tube model over table-based models like Rydel?