20120140504017

International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –
6480(Print), ISSN 0976 – 6499(Online) Volume 5, Issue 4, April (2014), pp. 160-168 © IAEME
160
A STUDY OF MULTIPLE OTA-C ACTIVE LOW PASS FILTER
Dr. Rajeshwari .S. Mathad
Department of Electronics, Basaveshwar Science College, BAGALKOT, India
ABSTRACT
A review paper on comparative study on single structure OTA-C low pass filter and multiple
structure OTA-C low pass filter. OTA single structure LC filter has a limitation in obtaining -3dB cut
off frequency in the range from KHz to MHz. The variation in the frequency with the bias current is
inconsistent, because fine tuning is not possible in obtaining -3dB frequency. In order to eliminate
inconsistency, and to obtain fine tuning the LC filter is developed using multiple OTAs representing
the transconductances gm 1=gm= 1=gm 2 > gm. Under the stated relation a sharp variation in -3dB cut off
frequency is observed by tuning the respective transconductances of the system of OTAs in respect
of the inequality. The -3dB frequency obtained are linearly related with bias current which is due to
the suited value of floating inductance of the filter. Such types of filters are useful in high frequency
applications and in instrumentation such as channel analyser.
Keywords: OTA-C Operational Transconductance Amplifier-Capacitor.
I. INTRODUCTION
In recent years Operational Transconductance Amplifier based high frequency integrated
circuits, filters and systems were widely investigated. Currently, high frequency, high linearity, and
low power are the three main concerns of OTAs. With many efforts, researchers have made
significant progress in these three aspects of OTAs. The usefulness of OTAs in comparison with
conventional Op-Amps in the design of both first order and second order active filters are well
documented. Electronically tuneable circuits attracted considerable attention in the design of analog
integrated circuits because different values of resistance, inductance or capacitance can be obtained
by the same device. Electronic tuning is one the most attractive feature of the Operational
Transconductance Amplifier (OTA), since this makes it possible to tune analog devices in
applications such as, filters, oscillators etc. OTA is a differential voltage controlled current source
INTERNATIONAL JOURNAL OF ADVANCED RESEARCH IN ENGINEERING
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ISSN 0976 - 6480 (Print)
ISSN 0976 - 6499 (Online)
Volume 5, Issue 4, April (2014), pp. 160-168
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161
(VCCS) where the output current is controlled by an applied input voltage. Tune ability of a device
can be obtained by varying the transconductance (gm) of the OTA which is controlled by the bias
current or voltage.
Analog designs are viewed as a voltage dominated form of signal processing. But current-
mode signal processing circuits are preferred over the voltage-mode signal processing circuits, due to
their advantages such as higher signal bandwidth, larger dynamic range, greater linearity, low power
consumption, and simple circuitry. Designs for active realizations of passive elements using high
performance active devices are a rich area of research.
OTA applications were extended in a variety of analog circuits, from simple components as
variable resistors and active inductors, to more complicated circuits such as filters and oscillators.
The OTA can be connected to create active element, simulating the property of an inductance in
order to be an alternative choice of an on-chip inductor instead of a passive spiral inductor which
usually has low Q-factor. Low Q factors degrade circuit performance, such as phase noise and gain.
On-chip inductors also consume much larger IC areas compared to the active devices. Compared to
the on-chip spiral inductors, an active inductor has a higher Q factor and occupies a smaller IC area
due to its composition of only active devices and capacitors, and thus is attractive to researchers.
This proposed scheme possesses many advantages. Firstly, the structure is very simple and easy to
design. No external resistor is required, which can save the area in case of fabricating on a silicon
chip. Moreover, the cut off frequency can be easily tuned electronically by adjusting the bias current
of OTA, changing the system’s configuration is also very easy and comfortable. This will be useful
in abiding when the values of passive devices are deviated.
In this paper there is a comparison between single structure OTA-C low pass filter and
multiple OTA-C low pass filter. It has been proved that the fine variation of cut off frequency can be
achieved in multiple OTA-C low pass filter by simulating the floating inductance.
OTAs are manufactured by various manufacturers which are given by different numbers. But
with the use of LM13600 and CA3080 OTA’s, it is possible to achieve extremely linear
transconductance characteristics with respect to amplifier bias current. In this paper for
experimentation, LM13600 OTA is used, which consists of two current controlled transconductance
amplifiers each with differential inputs & push pull outputs. The two amplifiers shares common
supplies but operate independently. Linearalizing diodes are provided at the inputs to reduce
distortion and allow higher levels of signals. Controlled impedance buffers which are especially
designed to complement the dynamic range of the amplifier are provided.
In the ideal OTA, the output current is a linear function of the differential input voltage,
which can be expressed as follows,
Iout= (Vin+
− Vin−
) gm .
The transconductances gm is given by,
gm = Ibias/ 2VT
Where VT: thermal voltage = 26 mV at room temperature
Ibias : bias current of OTA. [1-7]

162
Figure 1: Circuit symbol of OTA
1.1 Derivation of first order OTA-C Filter
Consider a first order OTA-C low pass filter as shown in Figure 2.
From Figure 2 we get
I1 = gm (Vin - V0)
From above equation, the transfer function for first order OTA-C low pass filter is given by,
gm/ C
T(s) = --------------
S + gm/ C
Figure 2: First order active low pass filter using single OTA
1.2 Realizations of first order low pass filter using multiple OTAs.
First order active low pass filter using multiple OTAs is shown in figure 3 in which the series
arm is a simulated floating inductance using three OTAs. From figure 3 it can be inferred that,
V3 = I2/SC
I2 = (Vin - V0 ) (Vin - Vo) gm2
Solving above equations we have V3 = -------------------------
SC
I4 = -gm Vo
I3 = -V3gm1 , But we see that I3 + I4 = 0
Therefore transfer function of the designed filter is [8]
V0 = T(s) = gm1gm2 / Cgm
Vin S + (gm1gm2/Cgm)

163
Figure 3: First order active low pass filter using multiple OTA
1.3 Floating Inductor
Lot of active elements have been used to simulate the inductance. To achieve any required
cut-off frequency in passive filter, we require different values of resistors & inductors as calculated
from mathematical expression; which may or may not be available. To solve this problem, we can
use OTAs to simulate the inductance to achieve the required inductance values by varying its gm.
An active inductor has an impedance inverter that “inverts” a real capacitor into a virtual
inductor. Its input emulates a real inductor’s voltage and current. Fig. 3 illustrate diagram of a
floating active inductor using three OTAs. Floating inductance simulation using Op amp is very
difficult, but using OTA it is easy, just by varying the bias current inductance value can be changed.
Figure 4: Three- OTA based floating active inductor
We infer that the inductance can be electronically tuned by varying the external bias current
IB of the three OTAs [9].

164
II. EXPERIMENTAL SETUP
The stated circuits of “Fig 2” and “Fig 3” are simulated using Proteus professional 7 shown in
“Fig 5” and “Fig 6”. Same circuits are arranged on bread board using usual method, the output of the
filter is measured. In first order low pass filter using single OTA bias current of the device is varied
to vary the transconductance gm , of the device to obtain different cut off frequencies. For a first order
low pass filter using four OTAs with transconductance gm1 gm1, gm2 and gm, by adjusting proper
values of bias current of gm1 gm1, gm2 and gm low pass filter action can be obtained and fine
variation of cut off frequencies can also be obtained.
Figure 5: Circuit diagram of OTA- C Low Pass filter
Figure 6: Circuit diagram multiple OTA- C Low Pass filter

165
III. RESULTS AND DISCUSSION
In OTA-C low pass filter shown in “Fig-5” bias current can be varied from 1 µA to 2mA
and the cut off frequencies obtained are from 147KHz to 267MHz respectively. Observations are
presented in the table 1.
Table 1
Bias Current
IB
Maximum gain in dB Frequency at
-3dB
1µA 0dB 147 KHz
10µA 0dB 1.48MHz
100µA 0dB 14.5 MHz
500µA 0dB 72.8 MHz
1mA 0dB 142 MHz
2mA 0dB 267 MHz
Now for single OTA-C filter structure, by varying the bias current with the difference of
10µA, that is from 50µA to 100µA the cut off frequencies obtained are from 7.47MHz to 14.5MHz.
For every change in 10µA of bias current there is change in cut off frequency approximately of order
1.5MHz, corresponding observations are given in table 2.
Table 2
Bias Current
IB
Maximum gain in dB Frequency at
-3dB
50µA 0dB 7.47 MHz
60µA 0dB 9.00 MHz
70µA 0dB 10.5MHz
80µA 0dB 11.6 MHz
90µA 0dB 13 MHz
100µA 0dB 14.5 MHz
Figure 7: Frequency response of Proteus professional 7 simulated OTA-C low pass filter circuit,
with pass band from 7.47MHz at -3dB gain. Maximum gain is 0dB. The bias current is 50µA

166
In case of multiple OTA-C structure the transconductances of all the three OTAs i,e gm 1
gm 1 and gm 2 are kept constant. The bias current of three OTAs is kept at 2mA each. But by
varying the bias current of gm from 1µA to 100µA the cut off frequencies obtained are from 412
KHz to 11.2MHz. For every change in 10µA of bias current from 50µA to 100µA the difference
between cut off frequencies are of order of 0.2MHz or 200 KHz. Where as in case of single OTA-
C structure this difference is 1.5MHz. Therefore multiple OTA-C structure is more advantageous
compared to single OTA-C structure. The required cut off frequency can be obtained just by
varying the bias current. The corresponding observations are given in table 3.
Table 3
Figure 8: Frequency response of Proteus professional 7.5simulated multiple OTA-C low pass filter
circuit, with gm 1=gm 1 = gm 2= 2mA gm = 50µ A with maximum gain 0 dB and frequency of 10
MHz at - 3dB
Bias current of
gm 1 =gm 1
Bias current of
gm 2
Bias current of
gm
Maximum gain
in dB
Frequency at
-3dB
2mA 2mA 1µA 0dB 412KHz
2mA 2mA 10µA 0dB 3.8MHz
2mA 2mA 50µA 0dB 10 MHz
2mA 2mA 90µA 0dB 11MHz

167
IV CONCLUSIONS
The discussion of observations concludes that we can achieve a tuneable range of cut off
frequencies of a filter with change in bias current in respect of the relation stated. The consistency in
gain and increase in -3dB frequency is observed with increase in bias current.
The advantage of using single OTA and multiple OTAs can be summarized as follows:
1. In case of first method, by using single OTA, we can change cut-off frequency by changing
gm but the degree of freedom for changing gm is only one ie bias current of single OTA. Fine
variation in cut off frequency is not observed.
2. In case of second method, by using multiple OTAs cut-off frequency can be changed by tuning
gm 1gm 1 or gm gm 2 separately or in combination. So we have larger tuneable parameters than
the first method. By this method fine variation in cut off frequencies can be obtained. Gain roll
off rate is at -20dB per decade.
The Low Pass filter structure using OTA has a several advantages in high frequency
applications. The structure is very simple and easy to design. No external resistor is required, which
can save the area in case of fabricating on a silicon chip. Moreover, the cut off frequency can be
tuned electronically by adjusting the bias current of OTAs in combination for specific application.
These filters are used in high frequency mixtures and in medical applications where conventional op-
amp filters can’t be used [10].
V. ACKNOWLEDGEMENTS
I am very much thankful to Prasant K. Mahapatra and et al for the design idea which has been
taken from the paper “Realization of Active Filters Using Operational Transconductance Amplifier
(OTA)” J. Instrum. Soc. India 35(1) 1-9 and encouraged for further work.
VI. REFERENCES
[1] Sergio Franco “Design with operational amplifiers and analog integrated circuits”, 3rd
ed,
pp 133-141.
[2] Randall L. Geiger and Edgar Sanchez- Sinencio, “Active Filter Design Using Operational
Transconductance Amplifiers: A Tutorial”, IEEE Circuits and Devices Magazine, Vol.1,
[1985], pp 20-32
[3] Deliyannis, Theodore L. et al "Single Operational Transconductance Amplifier (OTA)
Filters" Continuous-Time Active Filter Design Boca Raton: CRC Press LLC, 1999.
[4] Achim Gratz “Operational Transconductance Amplifiers”
http://Synth.Stromeko.net/diy/OTA.pdf
[5] Datasheet- National semiconductor Corporation, “LM13600/LM13700 Dual Operational
Transconductance Amplifiers with linearing Diodes and Buffers.” 2004.
[6] D.Prasad, D.R.Bhaskar, A.K.Singh “New Grounded and Floating simulted inductance
Circuits using Current Differencing Transconductance Amplifiers” April 2010, Radio
engineering, VOL.19, NO.1.
[7] Neha Gupta, Meenakshi Suthar, Sapna Singh, Priyanka Soni, “Active Filter Design Using
Two OTA based Floating Inductance Simulator”, International Journal of VLSI & Signal
Processing Applications, Vol.2,Issue 1, Feb 2012, (47-50), ISSN 2231-3133.

168
[8] Prashant K. Mahapatra, Manjeet Singh and Neelesh Kumar, “Realisation of active filters
using operational Transconductance Amplifier (OTA),” Journal of Instrumentation Soc. of
India, 1999, 35(1), pp 1-9.
[9] You Zheng “Operational transconductance amplifier for Giga Hertz Applications”, A thesis
submitted to the, Department of Electrical and Computer Engineering, Queen’s University
Kingston, Ontario, Canada (September, 2008).
[10] Rajeshwari S. Mathad, M. M. Mutsaddi, S. V. Halse, “Design of OTA-C Active Low pass
Filter using multiple OTAs ” IOSR Journal of Applied Physics (IOSRJAP) ISSN – 2278-
4861 Volume 1, Issue 4 (July-Aug. 2012), PP 08-12.
[11] Dr. K. Ravi Chandrudu, “Voltage Profile Improvement using Series Hybrid Active Filters”,
International Journal of Advanced Research in Engineering & Technology (IJARET),
Volume 5, Issue 1, 2014, pp. 59 - 72, ISSN Print: 0976-6480, ISSN Online: 0976-6499.
[12] Mohammed Arifuddin Sohel, Dr. K. Chennakeshava Reddy and Dr. Syed Abdul Sattar,
“Linearity Enhancement of Operational Transconductance Amplifier using Source
Degeneration”, International Journal of Advanced Research in Engineering & Technology
(IJARET), Volume 4, Issue 3, 2013, pp. 257 - 263, ISSN Print: 0976-6480, ISSN Online:
0976-6499.

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