2. Contents
• History
• What is Translinear?
• Translinear Cells
• Modern usage of the word
• General Principles
• Translinear Loop/Network
• Translinear Principle
• Application of Translinear Principle
• Extended Translinear Theory
• Effect of Device non idealities
• Conclusion
3. History
• The word translinear (TL) was
invented by Barrie Gilbert in
1975 to describe circuits that used
the exponential current-voltage
relation of BJTs
• Concept arose within the con-
text of ‘gain cells’ for use in
oscilloscopes.
4. What is Translinear?
• Used of those cells invoking
exponential device behaviour
• Applies to all BJTs, and MOS
transistor operating in sub
threshold region
• Everyday use in analog
multipliers, variable-gain cells,
filters, RMS converters and
many other nonlinear circuits.
• Strictly TL(just TL) in BJTs and
Voltage Translinear in MOS
Transistors
5. Translinear Circuit Types
• Translinear Cells are categorised as TL cells and
TN cells on the basis of network topology
• TL Cells are Translinear Loops
• TN Cells are characterized by having multiple
emitters tied to a common node and biased by one
current
• TN Cells are the Translinear cell network
• A TL Cell can be an integral part of TN Cell
6. TN Cells Vs. TL Cells
A Translinear Network but not a Translinear
Loop
7. Characteristics of TL Cell
• Use of monolithically integrated bipolar junction
transistors (BJTs)
• Simple and elegant, being largely comprised of DC-
coupled BJTs and current sources
• Arranged in closed loops, each containing at least
two base-emitter junctions
• Variables-the cell inputs, outputs and control biases
are all in current-mode form.
• Operation at very low supply voltages was possible
• squaring; square-rooting; multiplication and
division; multi-dimensional vector addition and
subtraction;
8. Modern Usage of the Word
• Seevinck and Wiegerink have stretched the idea
of translinearity even further
• JFETs and MOSFETs in strong inversion exhibit
a Voltage Translinearity
• Transconductance is a linear function of the
gate-source bias Vgs, starting with the
popularly-assumed quadratic relationship
9. General Principles
• The basic starting point is the
exponential relationship of BJT’s
collector current and base emitter
voltage
• And also
• The collector current will vary
enormously even for fixed base
emitter voltage
• A TL circuit is quite immune to
this immense variation in current
10. Translinear Loops
• Function depends primarily on the use of
current as signals
• Arranged in one or more closed loops
• Augmented by various biasing means.
• Nevertheless, such circuits can be quickly
understood when the Translinear Principle is
applied
• Example- A simple Current Mirror
11. Translinear Network
• BJT circuits such as LNAs, differential pairs,
CML and ECL logic gates, multi-tanh
transductors
• These circuits have no closed loop junctions
• But transconductance (or transresistance) of the
transistors is of crucial importance
• A differential pair is general example of a
translinear network.
13. Application of TL Principle
• Using translinear
Principle
the vector sum can
be shown to be
achieved easily
14. Extended TL Theory
• In basic TL circuits, this ratiometric behaviour
arises from setting the net loop voltage to zero.
• However, it is certainly possible, and
occasionally even useful, to include one or more
voltage sources in a loop, when the governing
equation becomes
• A practical use of such a voltage is to null out
the 'VBE mismatch' in a TL loop
15. The Ratiometric Viewpoint
• The advantage of this viewpoint is that one
does not need to worry about the absolute
value of the currents
16. Effect of Device nonidealities
• There are various nonidealities in the BJT
operation
• The value of base emitter voltage used in (2.1b)
assumes a base collector voltage of zero which is
not such
• The current gets modified by a factor of
• There are no general solutions to dilemmas of
this sort, but they usually can be worked around
17. Conclusion
• The 'voltage- controlled current-source' view of
the BJT, which is captured in the notion of
'translinearity', is a more useful one than the
older idea of a 'current-controlled current
source' (the 'beta view') in a modern monolithic
context.
• Largest utilization of translinear concepts has
been in the area of analog multiplication.
• 'MOS-translinear' (MTL) circuits are Voltage
translinear circuits.
