Translinear

Translinear refers to a class of analog circuit design techniques that exploit the exponential current–voltage relation of bipolar junction transistors to perform mathematical operations in the current domain. Translinear circuits are built from translinear elements—typically BJTs or BJT-based matched pairs—arranged in loops so that input currents control output currents without large voltage swings.

The translinear principle states that in a closed loop of translinear elements operating in forward-active region, the product of the currents flowing in one set of branches equals the product in the opposite set. Equivalently, the sum of the natural logarithms of the branch currents around the loop is constant. This yields algebraic relations that implement multiplication, division, exponentiation, and logarithms using simple current sums.

Implementations are common in bipolar or BiCMOS processes; circuits are frequently designed for current-mode operation, benefiting bandwidth, matching, and linearity in certain ranges. A typical translinear circuit uses emitter-coupled pairs whose collector currents follow I_C = I_S exp(V_BE/V_T), with V_T = kT/q. By steering currents through different branches, designers realize functions such as log amplifiers, exp converters, multipliers, and square-law devices.

History and scope: The translinear concept was formalized in the 1980s by Carver Mead and Lynn Conway as part of analog VLSI design. It remains a foundational technique for log-domain signal processing, practical exponential converters, and current-mode analog computation. In CMOS technology, subthreshold MOSFETs exhibit similar exponential behavior, enabling translinear-like circuits in low-power CMOS designs and neuromorphic applications.