Widlar Current Mirror

A Widlar current mirror adds a single resistor in series with the output transistor's emitter, and that one resistor exploits the logarithmic relationship between a bipolar transistor's base-emitter voltage and its collector current to generate an output current dramatically smaller than the reference current — microamps from milliamps — without needing either an impractically large emitter resistor or a wastefully large reference current, which is precisely the problem a plain current mirror with matched device sizing cannot solve efficiently.

The logarithmic VBE-current relationship is what makes a huge current ratio achievable with a small, practical resistor, which is the entire point of the circuit. A bipolar transistor's collector current depends exponentially on its base-emitter voltage, which means the inverse relationship — how much base-emitter voltage difference you need to force a given current ratio — is logarithmic rather than linear: generating a 100-to-1 current ratio needs only about 60 millivolts of VBE mismatch at room temperature (ln(100) times the thermal voltage, roughly 26 millivolts), and that modest voltage dropped across a resistor carrying only the small output current requires just a few kilohms, not the impractically large resistor a naive linear scaling argument might suggest.

Trying to hit the same current ratio with device sizing alone, instead of a resistor, runs into real silicon-area and matching limits fast. A plain current mirror can scale output current relative to reference current by making the output transistor's emitter area some ratio of the reference transistor's — but pushing that ratio to 100-to-1 or 1000-to-1 purely through area scaling means either an enormous output transistor or an impractically tiny one, both of which create real layout and matching headaches on a die; the Widlar technique sidesteps that entirely by using a resistor (which is comparatively cheap and precise in area) to do the heavy lifting that device-area scaling alone would struggle with.

The emitter resistor adds a genuine stabilizing side benefit beyond just setting the current ratio — it's the same degeneration mechanism used throughout analog design. Because the resistor sits in series with the emitter, any transient increase in the output transistor's current increases the voltage drop across that resistor, which reduces the effective VBE driving that current and self-corrects — the same local negative feedback mechanism as an emitter-degenerated common-emitter stage — which is why Widlar-biased outputs tend to be somewhat less sensitive to transistor-to-transistor variation and supply noise than a bare mirrored output would be, a bonus that comes along with the current-scaling benefit rather than requiring separate design effort.

Bob Widlar's invention at Fairchild Semiconductor became foundational specifically because early integrated op-amps needed small bias currents from circuits that otherwise only had larger currents available. The technique first appeared in the µA702 and became a standard building block in the µA741 and essentially every bipolar op-amp and voltage reference that followed, because IC designers routinely need microamp-level bias currents for low-power stages while a design's primary reference current is set in the milliamp range for other reasons (supply regulation, noise performance) — Widlar's resistor-based trick solved exactly that mismatch, and the topology remains a standard teaching example specifically because it demonstrates how a single well-placed resistor can exploit device physics rather than fight it.

Read a Widlar current mirror through a *logarithm-as-leverage* lens rather than a *resistor-trick* lens: it works because a transistor's exponential current-voltage relationship means a huge current ratio only costs a modest voltage difference to produce, and a modest voltage difference only costs a small, practical resistor — the circuit succeeds specifically by routing around linear scaling limits through a device physics relationship that happens to be logarithmic instead.