Translinear Circuit - The Translinear Principle

The Translinear Principle

The translinear principle is that in a closed loop containing an even number of translinear elements (TEs) with an equal number of them arranged clockwise and counter-clockwise, the product of the currents through the clockwise TEs equals the product of the currents through the counter-clockwise TEs or

The TLP is dependent on the exponential current-voltage relationship of a circuit element. Thus, an ideal TE follows the relationship

where is a pre-exponential scaling current, is a dimensionless multiplier to, is a dimensionless multiplier to the gate-emitter voltage and is the thermal voltage .

In a circuit, TEs are described as either clockwise (CW) or counterclockwise (CCW). If the arrow on the emitter point clockwise, it's considered a CW TE, if it points counterclockwise, it's considered a CCW TE. Consider an example:

By Kirchhoff's Voltage Law, the voltage around the loop that goes from to must be 0. In other words, the voltage drops must equal the voltage increases. When a loop that only goes through the emitter-gate connections of TEs exists, we call it a translinear loop. Mathematically, this becomes

Because of the exponential current-voltage relationship, this implies TLP:

this is effectively because current is used as the signal. Because of this, voltage is the log of the signal and addition in the log domain is like multiplication of the original signal (i.e. ). This rule, that the product of the current through CW TEs is equal to the current through CCW TEs in a translinear loop is known as the translinear principle.

For a detailed derivation of the TLP, and physical interpretations of the parameters in the ideal TE law, please refer to or.

A derivation of the TLP based on graph theory concepts has been given by Rafael Vargas-Bernal et al. in 2000. In this work, it is illustrated as a graphical representation can be used for the future development of a verification tool that plays an important and fundamental role in the structured design of translinear circuits.