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OTA-Based Logarithmic Circuit for Arbitrary Input
Signal and Its Application
Abstract:
In this paper, a new design procedure has been proposed for realization of logarithmic function
via three phases: 1) differentiation; 2) division; and 3) integration for any arbitrary analog signal.
All the basic building blocks, i.e., differentiator, divider, and integrator, are realized by
operational transconductance amplifier, a current mode device. Realization of exponential,
power law and hyperbolic function as the design examples claims that the proposed synthesis
procedure has the potential to design a log-based nonlinear system in a systematic and
hierarchical manner. The proposed architecture of this paper area and power consumption
analysis using tanner tool.
Enhancement of the project:
To change the parameter of the architecture for reduces the noise and power.
Existing System:
Logarithmic and exponential functions, having a wide application in communication and signal
processing, are generally implemented using bipolar junction transistors (BJTs) or MOS
transistor in weak inversion using their exponential characteristics. In this paper, a thorough
understanding of a mathematical model combined with hardware compatibility has been
exploited to realize logarithmic and exponential functions for various analog signals, which leads
to an improved design. A low-cost, high-speed architecture for binary logarithm approximation
has been proposed by many researchers. Mitchell’s method with a correction stage composed of
piecewise linear interpolation and a lookup-table correction is used to compute binary logarithm.
Both the architectures are implemented in an FPGA. Voltage–current relationships of a p-n

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junction diode and Taylor’s series expansion have been used to realize logarithmic and
exponential function. Significant efforts have been invested in using MOS transistors in
saturation region for the implementation of exponential functions. Liu and Liu proposed a
compact, low-power, and CMOS exponential function generator with a wide dynamic range. A
CMOS pseudo exponential function circuit based on Taylor series approximation using MOS
transistor operating at saturation region is presented. Chang and Liu proposed a voltage-mode
and a current-mode pseudo exponential function circuit. A low-voltage CMOS current mode
exponential circuit has been described using MOS transistors in weak inversion. Translinear
principle is used to implement the approximation to cancel the temperature effect. Maundy et al.
[9] introduced a pseudo exponential and pseudo logarithmic circuit using operational amplifier
(op-amp).
Disadvantages:
 High noise in the circuit
 High power
Proposed System:
OTA-Based Building Blocks
Differentiator: Fig. 1(a) shows the OTA-based differentiator. Uniformity has been maintained in
numbering the active and passive components of the building blocks in all the figures in this
paper. For example, in Fig. 1(a), the differentiator circuit is demonstrated with the active and
passive components marked as O(1), O(2), O(3), and C1 and this configuration has been
followed for all the blocks.

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Fig. 1. OTA-based differentiator.
Divider
Different techniques have been developed to implement multiplier using MOS transistor, op-
amp, BJT, subthreshold MOS OTAs, and so on.
Fig. 2 OTA-based divider

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Integrator
Fig. 3 OTA-based integrator

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Fig. 4. Realization of ln [f (t)] based on (1).

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TRANSISTOR LEVEL SCHEMATIC OF OTA
Advantages:
 Better tenability
 Better programmability
Software implementation:
 Tanner tools

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