A Widlar current mirror is a bipolar junction transistor (BJT) circuit that uses an emitter degeneration resistor on the output transistor to generate a precise, scaled-down microamp output current from a much larger milliamp reference current. If you are designing low-power sensor biasing networks, analog IC front-ends, or discrete 4-20mA loop transmitters, this topology is your primary tool for generating tiny bias currents without resorting to impractically large resistors or mismatched transistor geometries.
The Core Mechanism: How Emitter Degeneration Scales Current
In a basic BJT current mirror, two identical transistors share the same base-emitter voltage (VBE), forcing the output current to exactly match the reference current. To get a smaller output current in a basic mirror, you would have to either use a massive, area-hogging resistor or fabricate an output transistor with a physically smaller emitter area than the reference transistor. On a silicon die, mismatched transistor areas introduce thermal and process variation errors. On a breadboard, you simply cannot buy discrete transistors with a precise 1:100 area ratio.
The Widlar topology solves this by leaving the transistors perfectly matched (same geometry, same VBE characteristics) but inserting a single resistor (RE) in the emitter leg of the output transistor (Q2). Because the collector current of a BJT is exponentially related to its VBE, a tiny voltage drop across RE drastically reduces the effective VBE of Q2 relative to Q1. This logarithmic relationship allows you to step down the current by orders of magnitude using a very reasonable resistor value.
Think of it like a high-pressure water main (the reference current) feeding two pipes. One pipe is wide open (Q1). The second pipe (Q2) has a severe physical restriction (the emitter resistor) that chokes the flow down to a mere trickle, even though both pipes are connected to the exact same main pressure.
Worked Numeric Example: Designing a 10 µA Source from 1 mA
Let us design a discrete Widlar mirror on the bench. We have a 5V supply and want to generate a stable 10 µA bias current for a high-impedance sensor amplifier, using a 1 mA reference current.
Step 1: Set the Reference Current (Iref)
We use a standard resistor (Rref) from the 5V rail to the diode-connected Q1. Assuming a typical VBE of 0.65V for Q1 at 1 mA:
Rref = (VCC - VBE) / Iref = (5V - 0.65V) / 0.001A = 4,350 Ω.
Bench pick: Use a standard 4.32kΩ (E96 series) 1% resistor.
Step 2: Calculate the Emitter Degeneration Resistor (RE)
The Widlar equation relates the two currents via the thermal voltage (VT), which is approximately 25.85 mV at room temperature (300K):
RE = (VT / Iout) * ln(Iref / Iout)
Plugging in our target values:
RE = (0.02585V / 0.00001A) * ln(0.001 / 0.00001)
RE = 2585 * ln(100)
RE = 2585 * 4.605 = 11,904 Ω
Step 3: Component Selection and Tolerance
The closest standard 1% (E96) resistor value is 11.8kΩ. If we use 11.8kΩ, our actual output current shifts slightly:
11,800 = (0.02585 / Iout) * 4.605
Iout ≈ 10.09 µA.
For a discrete sensor bias network, a 0.9% deviation is well within acceptable limits. For monolithic ICs, laser-trimmed resistors dial this in perfectly.
Where You Meet the Widlar Current Mirror in Practice
You will rarely see a Widlar mirror drawn as a standalone block on a system-level schematic, but it is hiding inside almost every classic analog IC you use. According to the Texas Instruments LM741 Datasheet, the internal bias network relies heavily on a Widlar configuration to generate the microamp-level tail currents for the input differential pair from the master milliamp-level reference current.
- Op-Amp Bias Networks: The LM358 and LM324 use Widlar-style degeneration to keep quiescent current low while maintaining stable biasing across temperature.
- Bandgap Voltage References: Circuits like the LM385 or TL431 use Widlar mirrors to generate the proportional-to-absolute-temperature (PTAT) currents required to cancel out the negative temperature coefficient of a diode.
- 4-20mA Current Loops: In industrial process control, discrete Widlar mirrors are often used in the transmitter front-end to establish precise low-level bias currents for the sense amplifiers before the main power stage scales it up to the 20mA loop current.
Common Confusions: Widlar vs. Wilson vs. Basic Mirrors
When reading application notes from sources like All About Circuits, engineers frequently mix up the specific problem each mirror topology solves. Here is how to separate them:
| Topology | Primary Purpose | Output Impedance | Key Limitation |
|---|---|---|---|
| Basic Mirror | 1:1 current copying | Low (ro) | Poor current scaling; Early effect causes current drift with VCE changes. |
| Widlar Mirror | Stepping down current (mA to µA) | High (due to RE degeneration) | Requires calculation; not ideal for exact 1:1 copying. |
| Wilson Mirror | High output impedance & 1:1 copying | Very High (β * ro / 2) | Requires higher compliance voltage (headroom); poor for low-voltage rails. |
| Cascode Mirror | Maximum output impedance | Extremely High | Eats up massive voltage headroom; complex biasing required. |
Decision Tree: Which Current Mirror Topology to Pick
Do not default to a basic mirror just because it is the first one taught in textbooks. Use this decision matrix to terminate your design phase with a concrete topology or part number.
| If your circuit requirement is... | Then pick this topology or part | Concrete Bench / BOM Pick |
|---|---|---|
| I need a precise microamp bias current derived from a milliamp reference to save space/power. | Widlar Current Mirror | BCM847BS dual transistor + 11.8kΩ E96 emitter resistor |
| I need an exact 1:1 copy of a current, and my load voltage will vary widely (need high output impedance). | Wilson Current Mirror | Matched quad array (e.g., ALD1101) wired as Wilson |
| I am operating on a 1.8V or 3.3V rail and cannot afford the VCE headroom loss of a Wilson/Cascode. | Basic Mirror with Early-effect compensation | Low-VCE(sat) transistors like BC847BPDW1 |
| I need a highly accurate, temperature-stable current source and do not want to calculate discrete resistor tolerances. | Integrated Current Source IC | TI REF200UA (dual 100µA precision current source) |
FAQ: Practical Bench Questions
Does the Widlar mirror work with MOSFETs?
Technically, you can add a source-degeneration resistor to a MOSFET current mirror to scale current. However, because MOSFETs follow a square-law (or subthreshold exponential) relationship rather than the strict BJT exponential equation, the math changes entirely. In modern CMOS IC design, engineers usually just adjust the W/L (width/length) ratio of the MOSFET gates to scale current, making the discrete resistor unnecessary. The Widlar topology remains primarily a BJT/bipolar domain.
How does temperature affect my calculated 10 µA output?
The thermal voltage (VT) in the Widlar equation is directly proportional to absolute temperature (VT = kT/q). As your circuit heats up from 27°C to 70°C, VT rises from ~25.85mV to ~29.5mV. Because RE is fixed, your output current will increase slightly with temperature (roughly +14% over that 43°C span). If your application requires absolute temperature independence, you must pair the Widlar mirror with a PTAT (Proportional To Absolute Temperature) compensation network or use a bandgap reference IC.
What happens if my output transistor enters saturation?
Like all current mirrors, the Widlar requires the output transistor (Q2) to remain in the active region to regulate current. The minimum voltage required across Q2 (from collector to emitter) is its VCE(sat), typically around 0.2V for small-signal NPNs. If your load pulls the collector voltage below VE + 0.2V, the mirror breaks down, output impedance plummets, and the current will drop off sharply. Always verify your load compliance voltage on the bench with an oscilloscope.
