The document summarizes a research paper that proposes a new current-mode logarithmic and anti-logarithmic amplifier circuit based on a Current Differencing Transconductance Amplifier (CDTA). The proposed log amplifier circuit uses one CDTA and two diodes. The anti-log amplifier circuit uses one switched capacitor, one diode, and one CDTA. Simulation results confirm the logarithmic and exponential behavior with low error. The circuit provides advantages over operational amplifier-based designs such as current-mode operation, reduced power consumption, and improved stability.

1. International Journal of Electronics and JOURNALEngineering & Technology (IJECET), ISSN 0976 –
INTERNATIONAL Communication OF ELECTRONICS AND
6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 6, November-December (2013), © IAEME
COMMUNICATION ENGINEERING & TECHNOLOGY (IJECET)
ISSN 0976 – 6464(Print)
ISSN 0976 – 6472(Online)
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SWITCHED CAPACITOR BASED LOG – ANTILOG AMPLIFIER USING
CDTA (A CURRENT MODE IMPLEMENTATION)
Indu Prabha Singh1, Meeti Dehran2, Kalyan Singh3
1, 2
3
Deptt. of Electronics and Comm. Engg. SRMGPC, Lucknow-227105, India
Deptt. of Physics and Electronics Engg. , Dr. RML Avadh University, India
ABSTRACT
The paper presents Log and Antilog Amplifier using Current Differencing Transconductance
Amplifier (CDTA).The proposed circuit configuration consists of a single CDTA. Owing to its
current mode operation it consumes less power. Furthermore, the instability problem found in OpAmp based log-antilog amplifiers due to the presence of an active element in the feedback loop is
absent in the CDTA log-antilog amplifier. It provides the advantage of using switched capacitor
instead of a resistor that is beneficial to IC implementation in terms of space consideration. The
simulation results confirm the logarithmic and anti-logarithmic behavior with very low-error.
Keywords: Logarithmic Function, Current Mode Circuits, CDTA, Logarithmic Amplifier,
Anti-Log Amplifier and Analog Signal Processing.
1. INTRODUCTION
Log and Antilog Amplifiers are non-linear circuits in which the output voltage is proportional
to the logarithmic and exponential value of the input respectively [1-3]. They have numerous
applications in medical equipments, electronic communication, instrumentation and control systems
such as amplitude modulation, frequency multiplier, frequency divider, automatic gain control, phase
lock loop, adaptive filtering, powers and roots compression and decompression, true RMS detection
and process control. Logarithmic circuits need to have high input dynamic range to compress the
large amplitude of the signals in the radar receivers input, high accuracy for arithmetical operation
functions and low power consumption.
Log-antilog amplifiers use the exponential property of a forward bias p-n junction, using
either a diode or bipolar transistor, to provide the necessary log and antilog function [4]. Typically,
conventional log-antilog multipliers could be realized using Operational Amplifiers, bipolar
transistors and resistors for its multiplication function [5]. However, using Operational Amplifiers as
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2. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –
6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 6, November-December (2013), © IAEME
building blocks to synthesize the multiplication function will limit the high frequency operation of
the multiplier. Moreover, it will also increase the cost, power consumption, and chip areas. For these
reasons, it is useful to apply the translinear log-antilog multipliers/dividers avoiding Operational
Amplifiers and introducing current-mode signal processing [6, 7]. However, log-antilog
multiplier/divider configurations in [6, 7] are only suitable for bipolar technology. The current-mode
techniques provide large benefits in practical circuits and systems, and give elegant solutions for
many above discussed problems [8].
Current Differencing Transconductance Amplifier (CDTA) introduced in 2003, has been
acknowledged to be a versatile current-mode active building block in designing analog circuits [9].
This device with two current inputs and two kinds of current output provides an easy implementation
of current-mode log – antilog amplifier. It also exhibits the ability of electronic tuning by the help of
its transconductance gain (gm). All these advantages together with its current-mode operation nature
make the CDTA a promising choice for realizing the current-mode log – antilog amplifier. As a
result, a variety of CDTA applications has also been considered by various researchers [10-14].
In this paper, a new current-mode log-antilog amplifier based on CDTA is proposed. The
circuit employs one CDTA and two diodes for log amplifier and one switched capacitor, one diode
and one CDTA for antilog amplifier. This circuit enjoys excellent temperature stability and is very
suitable for implementation in CMOS technology. The theoretical results are verified by PSPICE
simulations.
2. CURRENT DIFFERENCING TRANSCONDUCTANCE AMPLIFIER (CDTA)
Although many types of signal processing have indeed moved to digital domain, analog
circuits are fundamentally necessary in many of today’s complex, high performance systems. This is
caused by the reality that naturally occurring signals are analog. Therefore analog circuits act as a
bridge between the real world and digital systems. In the beginning, Operational Amplifiers were the
main building blocks for analog circuit design. Unfortunately, their limited performance such as
bandwidth, slew-rate etc. led the analog designer to search for other possibilities and other building
blocks. As a result, new current-mode active building blocks receive considerable attention due to
their larger dynamic range and wider bandwidth.
The proposed circuits are based on CDTA. The CDTA is composed of translinear elements,
mixed loops and complementary current mirrors. The electrical symbol of the CDTA is shown in
Fig.1. The terminal relation of the CDTA can be characterized by the given matrix.
Fig.1: CDTA electrical symbol
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3. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –
6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 6, November-December (2013), © IAEME
ܸ
0
௣
‫ۍ ې ۍ‬
‫0 ێ ۑ ܸێ‬
௡
‫ۑ ێ‬ൌ‫ێ‬
‫ܫ ێ‬௭ ‫1 ێ ۑ‬
‫ێ ۑ ێ‬
‫ܫ ۏ‬௫ ‫0 ۏ ے‬
0
0
െ1
0
0
0
0
േ݃௠
0
‫ې‬
0‫ۑ‬
‫ۑ‬
0‫ۑ‬
‫ۑ‬
0‫ے‬
‫ܫ‬௣
‫ې ۍ‬
‫ܫ ێ‬௡ ‫ۑ‬
‫ۑ ێ‬
௭
‫ۑ ܸێ‬
‫ے0 ۏ‬
ሺ1ሻ
Where
p and n are input terminals,
z and ±x are output terminals,
gm is the transconductance gain,
And
Vz is the voltage produced due to external impedance connected at the terminal z.
According to above equation, the current flowing out of the terminal z (iz) is a difference (ipin) between the currents through the terminals p and n. The voltage drop at the terminal z is
transferred to a current at the terminal x (ix) by a transconductance gain (gm), which is electronically
controllable by an external bias current (IB). Hence the product of transconductance (gm) and the
voltage at the z terminal gives the magnitudes of output currents. These currents, which are copied to
a general number of output current terminals x, are equal in magnitude but may flow in opposite
directions.
Figure 2 shows a CMOS realization of the CDTA element [15]. The transistors M1 to M16
form the input difference current controlled current source stage and M21 to M28 form the dualoutput transconductor stage. Quiescent current of the circuit flowing over MOSFET MB is chosen as
40µA. Aspect ratios of the transistors in the Figure 2 are given in Table 2.
Table 2. Aspect ratios of the transistors
M1= 70µm/0.7µm
M15= 35µm/0.7µm
M2= 70µm/0.7µm
M16= 35µm/0.7µm
M3= 70µm/0.7µm
M17= 35µm/0.7µm
M4= 28µm/0.7µm
M21= 28µm/0.7µm
M5= 28µm/0.7µm
M22= 16µm/0.7µm
M6= 28µm/0.7µm
M23= 28µm/0.7µm
M7= 42µm/0.7µm
M24= 16µm/0.7µm
M8= 10.5µm/0.7µm
M25= 56µm/0.7µm
M9= 10.5µm/0.7µm
M26= 59µm/0.7µm
M10= 42µm/0.7µm
M27= 56µm/0.7µm
M11=10.5µm/0.7µm
M28= 56µm/0.7µm
M12= 98µm/0.7µm
MB= 7µm/0.7µm
M13= 10.5µm/0.7µm
M30= 50µm/0.7µm
M14= 10.5µm/0.7µm
M31= 50µm/0.7µm
3. PROPOSED CIRCUIT
The proposed current-mode log amplifier employing CDTA and two diodes is shown in
Fig.3. In this circuit, the input applied is a current source connected directly to the p-terminal.
The I-V relationship of the diode is approximated by:
‫ ܫ‬ൌ ‫ܫ‬ୱ ݁‫ ݌ݔ‬ቀܸൗܸ ቁ
(2)
்
Where Is is the reverse saturation current and VT is the thermal voltage.
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4. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –
6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 6, November-December (2013), © IAEME
Vdd
M12
M08
M06
M11
M04
M09
M26
M27
M05
M07
M21
M10
P
M03 M01
n
x+
x–
M02
M17
M23
M15
M16
z
M22
M24
IB
VSS
M14
M13
M28
M25
MB
VSS
Fig.2. CDTA CMOS implementation from [15]
Routine analysis of the circuit shown in Fig. 3 leads to the following expression of Vz (with In set to
zero):
‫ܫ‬
ܸ ൌ ்ܸ ݈݊ ൭ ௉ൗ‫ ܫ‬൱
௭
(3)
ௌ
And hence,
‫ܫ‬
‫ܫ‬଴ ൌ ݃௠ ்ܸ ݈݊ ൭ ௉ൗ‫ ܫ‬൱
(4)
ௌ
Fig. 3: Proposed current-mode Log-Amplifier
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5. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –
6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 6, November-December (2013), © IAEME
If Input current Ip is DC in nature, only diode D1 is required. In case of AC input, both
diodes D1 and D2 are needed for the logarithmic amplification. If the input is a voltage instead of
current, it can be applied to the p-terminal of CDTA through a resistor. Consequently, (3) and (4)
will contain Vi/R in place of Ip. If a voltage output is required then it may be taken at z-terminal.
However, as z-terminal is a high impedance node, a buffer will be required to avoid loading effect.
Fig. 4 shows the circuit of Antilog amplifier. For antilog amplifier, input voltage is applied to
the p-terminal through a diode and a switched capacitor is required at Z terminal.
The switched capacitor (SC) functions as a resistor and reduces the required space for the
fabrication. The SC is compatible with CMOS technology. The value of the capacitor C1 used in
switched capacitor is calculated using the formula given as:
‫ܥ‬ଵ ൌ 1ൗܴ ݂
ሺ5ሻ
Where, R is the equivalent resistance value of the switched capacitor and f is the frequency of
clock signal (Φ1) and (Φ2), applied at two MOSFETs (M30, M31) of switched capacitor.A routine
analysis shows that output current is given by
ܸ
‫ܫ‬଴ ൌ ݃௠ ܴ ‫ܫ‬௦ ݁‫ ݌ݔ‬൭ ௜ൗܸ ൱
்
ሺ6ሻ
Ip
Vi
I in
Io
X+
P
CDTA
N
Z
IZ
ɸ
ɸ
ɸ
ɸ
1
C1
ɸ
2
Fig. 4: Proposed switched capacitor Antilog-Amplifier
4. SIMULATION RESULTS
The performance of the proposed log-antilog amplifier is verified using the simulation in
PSpice. The CDTA model from [15] is used; employing the n-well CMOS process TSMC 0.35mm.
The transconductance was set to 888mS via a bias current of 40mA.
Fig. 5 shows the simulated DC transfer characteristics of the log amplifier circuit. Here Ip is
varied from 0 to 100µA and In is kept at 0. Response of log amplifier for AC signal applied at P
terminal is shown in Fig.6
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6. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –
6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 6, November-December (2013), © IAEME
240uA
200uA
I(X+)
160uA
120uA
80uA
40uA
0
A0
A
10uA
20uA
30uA
40uA
50uA
60uA
70uA
80uA
90uA
100uA
IP
Fig. 5: Simulated DC transfer characteristics of the Log Amplifier for In = 0
200uA
I(X+)
IP
100uA
0A
-100uA
-200uA
5u
0
10u
15u
20u
25u
s
30u
35u
40u
45u
50u
Time
Fig. 6: Simulated logarithmic output for AC signal input
40uA
I(X+)
0A
-40uA
-80uA
-120uA
-160uA
-200uA
0
10uA
20uA
30uA
40uA
50uA
60uA
70uA
80uA
IN
90uA 100uA
Fig. 7: Simulated DC transfer characteristics of the Log Amplifier for Ip = 0
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7. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –
6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 6, November-December (2013), © IAEME
200uA
I(X+)
IN
100uA
0A
-100uA
-200uA
0
5us
10u
15u
20u
25u
30us
35u
40u
45u
50u
Time
Fig. 8: Simulated logarithmic output for AC signal at n input terminal
The amplified output current corresponding to the DC and AC input current signal at n
terminal is shown in Fig. 7 and Fig. 8 respectively.
The transfer characteristic of the antilog amplifier is shown in Fig. 9. In this figure, the
current Ip is also swept from 0 to 200µA. Default value of temperature is assumed at 260C (room
temperature). The results are obtained with Vdd = – Vss = 1.8V, and bias current IB = 40 µA.
150µA
I0
100µA
50µA
0µA
20µA
60µA
140µA
100µA
180µA
200µA
IP
Fig.9: Simulated antilog output
5. CONCLUSION
A new log-antilog current amplifier has been presented. The proposed circuit employs single
CDTA, diodes and a switched capacitor, which is very much suitable for implementation in CMOS
technology. The switched capacitor (SC) reduces the required space in IC implementation. This
circuit will be a useful sub circuit for analog signal processing system. As there is no feedback in
both circuits, it is free from well recognized problem of instability found in op-amp based
logarithmic amplifiers.
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