SIT Curve Fitting Tutorial

Step-by-step guide to digitizing and modeling Static Induction Transistor characteristics

Characteristic Curve Digitizer SIT Curve Fitter

Overview

This tutorial guides you through creating a SPICE model for a Static Induction Transistor (SIT) from published characteristic curves. SITs are solid-state devices that exhibit triode-like characteristics.

The workflow consists of two main phases:

Digitization - Extract numerical data points from a graph image using the Characteristic Curve Digitizer
Curve Fitting - Fit the digitized data to the Rothacher SIT model using the SIT Curve Fitter

The result is a behavioral SPICE subcircuit that accurately models the SIT's I-V characteristics.

About Static Induction Transistors

SITs are voltage-controlled devices with characteristics similar to vacuum tube triodes:

Normally-on - Conduct current with zero gate voltage
Triode-like curves - No distinct saturation region like MOSFETs
Popular types - 2SK82, 2SK180, PASS-SIT-1

Phase 1: Digitizing the Curves

First, use the Characteristic Curve Digitizer to extract data points from a published SIT characteristic curve.

Obtain a Source Image

Find an SIT output characteristics graph showing I_d vs V_d curves at various V_g values. Good sources include:

Manufacturer datasheets (Sony, Tokin, Yamaha)
Application notes and technical papers
Curve Tracer Images

Save the graph as a PNG or JPG image file.

Note: SIT curves use different notation than triodes: V_g (gate voltage) instead of V_gk, V_d (drain voltage) instead of V_ak, and I_d (drain current) instead of I_a.

Load the Image

Open the Characteristic Curve Digitizer and click "Choose File" to load your image. Enter the device name as the project name (e.g., "2SK180").

Calibrate the Axes

Define three calibration points:

Origin - Click "Set Origin" then click on the (0,0) point
X-Axis Point - Click "Set X-Axis" then click on a known V_d value (e.g., 80V)
Y-Axis Point - Click "Set Y-Axis" then click on a known I_d value (e.g., 1.5A)

Enter the actual voltage and current values in the calibration fields.

Important: Some SIT datasheets show current in milliamps (mA) but the curve fitter expects Amps. Make sure to convert: 1500mA = 1.5A. Set your Y calibration accordingly.

Create Data Series

Each curve at a different V_g value becomes a separate series. Click "Add Series" and enter the gate voltage. For SITs, V_g values are typically 0, -2, -4, -6, -8, -10, -12V, etc.

Digitize Points

With a series selected, click along the curve to add data points:

Work from left to right along each curve
Add extra points in the "knee" region where current rises sharply
Include points in the linear region at higher V_d
Press Z to undo mistakes
Use zoom for precision in crowded areas

Tip: SIT curves often have a distinct knee where the device turns on. Capture several points in this transition region for better model accuracy.

Repeat for All Curves

Create a series for each V_g curve shown in the datasheet. Include curves from V_g = 0V down to the most negative value shown.

Export the Data

Click "Download CSV" to save your digitized data. The file will be named based on your project name (e.g., "2SK180.csv").

CSV File Format

The exported CSV uses the same format as the triode data:

Series 1: 0, 0.385,0.015 0.399,0.121 0.537,0.202 ... Series 2: -2, 1.280,0.023 1.927,0.091 ...

Each series header contains "Series N: Vg" where Vg is the gate voltage, followed by "Vd,Id" data pairs.

Phase 2: Fitting the Rothacher Model

Now use the SIT Curve Fitter to find optimal model parameters.

Load the CSV Data

Click "Choose File" and select your exported CSV. The data summary shows the number of curves and total data points loaded.

Review Initial Parameters

The default values work for most SITs. If you have prior knowledge of the device, you can adjust:

K - Gain constant (affects overall current magnitude)
X - Power law exponent (typically 1.5-2.5)
μ (mu) - Amplification factor (typically 5-50)
V_ct - Threshold voltage offset
N - Logarithmic coefficient

Run the Curve Fit

Click "Run Curve Fit" to start optimization. The Nelder-Mead algorithm will iteratively adjust parameters to minimize the error between the model and your data.

Evaluate the Fit

Check the results:

RMSE - Should be small relative to typical currents (< 0.01A is good)
Visual comparison - Fitted curves should closely follow the data points
Knee region - Pay attention to how well the turn-on behavior is captured

Troubleshooting: If the fit is poor, try adjusting the initial μ value. SITs with very different characteristics may need different starting points. You can also try running the fit multiple times as the optimizer may find different local minima.

Adjust Plot Scale

Use the "Vd Max" and "Id Max" fields to adjust the plot range to match your device's operating region. Click "Update Plot" to refresh.

Export the SPICE Model

The SPICE Subcircuit Model panel shows a behavioral model using the fitted parameters. Click "Copy to Clipboard" or "Download .txt" to save.

The Rothacher SIT Model

I_d = K × (V_g + V_ct + N×ln(V_d) + V_d/μ)^X

This model captures the key behaviors of SITs:

Parameter	Description	Physical Meaning
K	Gain constant	Overall transconductance scaling
X	Power exponent	Controls curve shape (1.5 = space charge, 2.0 = square law)
μ (mu)	Amplification factor	Ratio of V_d change to V_g change for constant I_d
V_ct	Threshold offset	Effective pinch-off voltage adjustment
N	Log coefficient	Models the drain voltage influence on channel

Key Model Features

Logarithmic term - The ln(V_d) term models the gradual turn-on characteristic
No saturation - Unlike MOSFETs, current continues rising with V_d
Triode-like μ - The V_d/μ term creates triode-like plate resistance

Using the SPICE Model

The generated subcircuit can be used in LTspice, ngspice, or other SPICE simulators:

.SUBCKT 2SK180 D G S * Rothacher SIT Model * Parameters: K=0.0234, X=1.82, mu=12.5, Vct=3.21, N=1.45 B1 D S I=... .ENDS

Connecting the Model

The subcircuit has three terminals:

D - Drain (connects to positive supply through load)
G - Gate (input signal)
S - Source (typically grounded or to current source)

Example Circuit

* Simple SIT amplifier test .include 2SK180_model.txt X1 drain gate 0 2SK180 Vdd drain_supply 0 48 Rload drain_supply drain 1k Vbias gate 0 -4 .dc Vbias -12 0 0.1 .end

Tips for Best Results

Include the V_g=0 curve - This anchors the model at zero gate voltage
Check μ reasonableness - The fitted μ should be comparable to datasheet values if available
Verify with known operating point - Check that the model predicts correct current at a typical bias point

Example Workflow: 2SK180

Obtain 2SK180 datasheet with output characteristics
Load image into Graph Digitizer
Calibrate: X-axis 0-100V, Y-axis 0-2A
Create series for V_g = 0, -2, -4, -6, -8, -10, -12V
Digitize 15-20 points per curve, focusing on knee region
Export as "2SK180.csv"
Load into SIT Curve Fitter
Run fit with default parameters
Verify RMSE < 0.02A and good visual fit
Download SPICE model for simulation

Open Characteristic Curve Digitizer Open SIT Curve Fitter

Model: "A Concise Model for Static Induction Transistor IV Characteristics" by Michael Rothacher, Linear Audio Vol 6