Calculator
Formula Used
The calculator uses the common NPN Widlar current sink model.
Reference current:
IREF = (VCC - VBE1) / RREF
Beta corrected mirror current:
K = IREF × (A2 / A1) × β / (β + 2)
Widlar current equation:
IOUT = K × e^(-IOUT × RE / VT)
Target emitter resistor:
RE = (VT / ITARGET) × ln(K / ITARGET)
Compliance estimate:
VCMIN ≈ IOUT × RE + VCEsat
Maximum load resistance:
RLOAD(max) = (VCC - VCMIN) / IOUT
How to Use This Calculator
- Enter the supply voltage and reference resistor.
- Enter the assumed reference transistor base emitter voltage.
- Add the output emitter resistor used in the Widlar branch.
- Set emitter area ratio if the transistors are not equal.
- Enter beta, Early voltage, load resistance, and collector voltage.
- Choose temperature based VT or enter manual thermal voltage.
- Press Calculate to view current, compliance, power, and load limits.
- Use CSV or PDF to save the result.
Example Data Table
| VCC | RREF | VBE | RE | Area Ratio | Approximate Use |
|---|---|---|---|---|---|
| 12 V | 100 kΩ | 0.70 V | 10 kΩ | 1 | Microamp analog bias |
| 15 V | 150 kΩ | 0.68 V | 22 kΩ | 1 | Low power differential pair |
| 5 V | 47 kΩ | 0.65 V | 6.8 kΩ | 2 | Compact bias stage |
| 9 V | 82 kΩ | 0.70 V | 15 kΩ | 1 | Sensor front end bias |
Widlar Current Source Design Guide
A Widlar current source is a modified bipolar current mirror. It adds an emitter resistor to the output transistor. That resistor lowers the output current far below the reference current. This is useful when a circuit needs microamp bias without using very large resistors.
Why the Widlar method is useful
A simple mirror often needs a reference current near the desired output current. That can waste power in low current stages. The Widlar source avoids that problem. A small voltage develops across the emitter resistor. This voltage reduces the base emitter voltage of the output transistor. The result is a smaller collector current.
Important design details
The calculation is not a straight linear step. The output current appears inside an exponential equation. This calculator solves that equation by iteration. It also estimates finite beta loss, Early effect, load compliance, resistor power, and output resistance. These checks help expose weak designs before parts are selected.
Thermal voltage and temperature
Thermal voltage changes with temperature. At room temperature it is near 25.85 mV. A higher temperature increases thermal voltage. That changes the current and the required emitter resistor. Use the temperature option when you want a design that follows a selected operating condition.
Compliance and load limits
The source must keep the output transistor in active mode. The collector voltage must remain above the emitter voltage by a safe margin. If the load resistor is too high, the collector voltage drops too far. The current then falls out of regulation. The compliance result warns about that condition.
Practical accuracy
Real circuits have transistor mismatch, resistor tolerance, beta spread, and temperature drift. Integrated Widlar sources work better because matched transistors sit close together. Discrete versions still work, but accuracy is limited. Use this calculator for planning, comparison, and sanity checks. For final hardware, test the current across temperature and supply range.
Reading the results
Start with the solved current. Then check emitter voltage and minimum collector voltage. Next review load margin and power loss. A good design has safe compliance, modest resistor heating, and enough output resistance. Adjust the reference resistor or emitter resistor until the numbers fit your circuit. Recheck values after choosing real component tolerances.
FAQs
What is a Widlar current source?
It is a bipolar current mirror with an emitter resistor in the output transistor. The resistor reduces output current below the reference current, making small bias currents easier to create.
Why is the equation iterative?
The output current appears inside an exponential term and also outside it. A direct linear solution is not enough, so the calculator uses numerical solving.
What does thermal voltage mean?
Thermal voltage is tied to absolute temperature. It is about 25.85 mV near room temperature. It affects the base emitter voltage relationship.
What is emitter area ratio?
Emitter area ratio compares the output transistor emitter area with the reference transistor emitter area. A larger ratio can increase the available mirror current.
Why include beta correction?
Real transistors draw base current. Beta correction estimates current lost to base drive. This makes the result more realistic than an ideal mirror model.
What is compliance voltage?
Compliance voltage is the minimum collector voltage needed to keep the output transistor active. Below this point, the current source may stop regulating.
Can this calculator replace circuit simulation?
No. It gives strong first estimates. Use simulation and hardware testing for final circuits, especially across temperature, tolerance, and supply variation.
Why is my target current rejected?
A Widlar source reduces current below the corrected mirror current. If the target is higher than that limit, the chosen reference path cannot support it.