A Widlar current source is a specialized bipolar junction transistor (BJT) current mirror circuit that uses an emitter degeneration resistor to generate highly stable, microamp-level output currents from a much larger reference current. In practical analog design, this topology fundamentally changes how we bias circuits by allowing engineers to create tiny, precise bias currents without resorting to impractically large, chip-area-hogging resistors or extreme transistor geometrical scaling. If you tried to pull 10 µA from a 1 mA reference using a basic current mirror, you would need to scale the output transistor's emitter area to 1/100th of the reference transistor—a manufacturing nightmare in silicon and a thermal matching nightmare on the bench.
Think of the emitter resistor as a restrictive valve in a water pipe: the flow (current) through it creates a pressure drop (voltage) that automatically chokes off further flow, stabilizing the system at a much lower rate than the main supply line.
Topology Comparison: Where the Widlar Fits
Before breaking out the soldering iron or opening your SPICE simulator, it is critical to understand where the Widlar topology sits among other standard current mirrors. Each topology solves a specific analog design problem, and choosing the wrong one will ruin your circuit's headroom or output impedance.
| Topology | Output Impedance | Low-Current Capability | Voltage Headroom Required | Transistor Count |
|---|---|---|---|---|
| Basic Mirror | Moderate ($r_o$) | Poor (requires area scaling) | Low ($V_{CE(sat)}$) | 2 |
| Widlar Mirror | High ($r_o \times \beta$) | Excellent (via $R_E$ degeneration) | Low ($V_{CE(sat)} + V_{RE}$) | 2 + Resistor |
| Wilson Mirror | Very High ($\beta \times r_o / 2$) | Poor (1:1 ratio primarily) | High ($2 \times V_{BE}$) | 3 |
| Cascode Mirror | Extremely High ($\beta \times r_o$) | Moderate | Very High ($V_{CE(sat)} + V_{BE}$) | 4 |
As the table demonstrates, the Widlar is the undisputed champion for low-current generation while maintaining relatively low voltage headroom. The Wilson and Cascode mirrors are designed for high output impedance (keeping the current stable despite varying load voltages), but they are terrible choices if your primary goal is stepping down a milliamp reference to a microamp output.
The Math: A Worked Numeric Example
Let’s design a Widlar current source on the bench to generate a precise 10 µA output current ($I_{OUT}$) from a 1 mA reference current ($I_{REF}$). We will assume an ambient temperature of 27°C (300K), which gives us a thermal voltage ($V_T$) of approximately 25.85 mV.
The governing equation for the Widlar emitter resistor ($R_E$) is derived from the Shockley diode equation:
$$R_E = \frac{V_T}{I_{OUT}} \ln\left(\frac{I_{REF}}{I_{OUT}}\right)$$
Plugging in our target values:
- Calculate the ratio: $I_{REF} / I_{OUT} = 1000 \text{ µA} / 10 \text{ µA} = 100$.
- Find the natural log: $\ln(100) \approx 4.605$.
- Calculate $\Delta V_{BE}$: $25.85 \text{ mV} \times 4.605 = 119.04 \text{ mV}$. This is the voltage drop that must appear across $R_E$.
- Solve for $R_E$: $119.04 \text{ mV} / 10 \text{ µA} = 11,904 \text{ } \Omega$.
In the real world, you cannot buy an 11.904 kΩ resistor. Looking at the standard E96 1% resistor series, the closest values are 11.8 kΩ (E96 code 1182) or 12.0 kΩ (E96 code 1202).
- Using 11.8 kΩ yields an actual $I_{OUT}$ of approximately 10.09 µA.
- Using 12.0 kΩ yields an actual $I_{OUT}$ of approximately 9.92 µA.
For most analog biasing applications, the 12.0 kΩ resistor is perfectly acceptable and much easier to source. Notice how a basic current mirror would have required a 1.2 MΩ resistor to pull 10 µA directly from a 12V rail, which introduces massive thermal noise and parasitic capacitance. The Widlar elegantly sidesteps this.
Where You Meet This in Practice
You rarely build a Widlar current source from scratch for a hobby project unless you are designing a custom analog front-end, but you interact with them constantly inside integrated circuits.
- Operational Amplifier Bias Networks: The classic LM741 and the ubiquitous LM358 use Widlar-style current sources to bias their input differential pairs. The input stage requires microamp-level tail currents to achieve high input impedance and low offset voltage, and the Widlar topology generates these from the chip's master milliamp-level bias rail.
- Low-Power Sensor Interfaces: When designing discrete circuitry for battery-powered IoT sensors, you often need to bias photodiodes or thermistors with exact, tiny currents to minimize self-heating and preserve battery life. A discrete Widlar source powered by a low-dropout regulator (LDO) provides a cheaper, lower-noise alternative to dedicated digital-to-analog converters (DACs).
- Current Limiting Circuits: The Widlar topology is frequently used as the sensing element in foldback current limiters inside linear power supplies, where a small voltage drop across a sense resistor needs to be amplified into a precise trip threshold.
Common Confusions and Pitfalls
When troubleshooting or designing analog bias networks, engineers frequently mix up the Widlar with other topologies or fall victim to second-order semiconductor effects.
Confusing it with the Wilson Mirror: The Wilson current mirror uses three transistors and negative feedback to achieve massive output impedance, making the output current immune to load voltage changes. The Widlar uses two transistors and a resistor specifically to scale down current. If your load voltage is swinging wildly and your Widlar current is drifting, you don't need a different resistor; you need to add a cascode transistor on top of the Widlar output to shield it from the Early effect.
Ignoring Base Current Errors: The math above assumes the transistors have infinite current gain ($\beta$). In reality, a standard small-signal NPN like the 2N3904 has a $\beta$ of around 100 to 300. At a 1 mA reference current, the base currents steal roughly 10 µA from the reference leg. If you are designing for extreme precision, you must add a third transistor (a beta-helper or base-current cancellation transistor) to buffer the base nodes, ensuring the reference current perfectly matches the collector current of the input transistor.
Frequently Asked Questions
Can I build a Widlar current source with MOSFETs?
Yes, but the math changes entirely. MOSFETs operate on a square-law relationship (in saturation) rather than the exponential relationship of BJTs. A MOSFET Widlar requires solving a quadratic equation for the source degeneration resistor, and it is highly sensitive to threshold voltage ($V_{th}$) mismatch, which is notoriously worse than BJT $V_{BE}$ mismatch in standard CMOS processes.
Why not just use a constant current diode (JFET)?
Constant current diodes (like the J500 series) are simple two-terminal parts, but their tolerance is typically terrible (often ±20% or worse), and their current is fixed at manufacture. The Widlar allows you to dial in an exact, programmable current using standard 1% resistors and a master reference.
For deeper reading on semiconductor biasing networks and the derivations of these mirror topologies, the Electronics Tutorials guide on transistor current sources provides excellent baseline schematics, while Wikipedia's breakdown of the Widlar current source offers a rigorous look at the small-signal output impedance calculations.
