Translinear circuit
Translinearity, in a broad sense, is linear dependence of transconductance on current, which occurs in components with exponential current-voltage relationship.
The word translinear (TL) was invented by Barrie Gilbert in 1975[1] to describe circuits that used the exponential current-voltage relation of BJTs.
When Barrie Gilbert described this class of circuits he also described the translinear principle (TLP) which made the analysis of these circuits possible in a way that the simplified view of BJTs as linear current amplifiers did not allow.
TLP was later extended to include other elements that obey an exponential current-voltage relationship (such as CMOS transistors in weak inversion).
[4][5] The translinear principle (TLP) 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.
In a circuit, TEs are described as either clockwise (CW) or counterclockwise (CCW).
If the arrow on the emitter points clockwise, it is considered a CW TE, if it points counterclockwise, it is considered a CCW TE.
Because of the exponential current-voltage relationship, this implies TLP:
The translinear principle is the rule that, in a translinear loop, the product of the currents through the CW TEs is equal to the product of the currents through the CCW TEs.
For a detailed derivation of the TLP, and physical interpretations of the parameters in the ideal TE law, please refer to[2] or.
is the unit scaling current (i.e. the definition of unity for the circuit).
The same equation applies to this circuit as to the alternating topology according to TLP.
In realizing the principle the difficulty is that it is current based.
For Type B the nodes are the connected bases of the upper BJT and the emitters of the lower.
For type A (alternating), with two emitter connected pairs, the voltage relates to the ratio between the currents within each base coupled pair.
For type B (stacked/balanced), the node voltage is the sum of the two base emitter voltages in each pair and thus relates to the product of currents in each stacked base to emitter coupled pair.
Thus if the voltage is forced in either case, two currents, one in each pair, must be variable.
In the type A (alternating loop) example below, a NMOSFET allows the correct tiny voltage between the emitter nodes of the emitter coupled pairs due to negative feedback, because a higher collector/gate voltage lowers its resistance such that, the base emitter voltage of the output BJT is small enough to let it out of saturation.
The collector potential of one of the inner BJT controls both the inner BJT's current by allowing the inner two BJTs to drop their emitter currents through the low residual voltage of the NMOSFET.
As the MOSFET should not operate in reverse drain source polarity this restricts the current relations or emitter potentials that the circuit can operate at.
The first issue with this circuit is that negative values of currents need to be represented.
Plugging these values into the original equation yields
The following are the alternating loops that implement the desired equations and some biasing schemes for the circuit.
The TLP has been used in a variety of circuits including vector arithmetic circuits,[6] current conveyors, current-mode operational amplifiers, and RMS-DC converters.
[1] In the 1980s, Evert Seevinck's work helped to create a systematic process for translinear circuit design.
In 1990 Seevinck invented a circuit he called a companding current-mode integrator[8] that was effectively a first-order log-domain filter.
A version of this was generalized in 1993 by Douglas Frey and the connection between this class of filters and TL circuits was made most explicit in the late 90s work of Jan Mulder et al. where they describe the dynamic translinear principle.
More work by Seevinck led to synthesis techniques for extremely low-power TL circuits.
[9] More recent work in the field has led to the voltage-translinear principle, multiple-input translinear element networks, and field-programmable analog arrays (FPAAs).
