zz Available online at http://www.journalcra.com INTERNATIONAL JOURNAL OF CURRENT RESEARCH International Journal of Current Research Vol. 5, Issue, 11, pp. 3404-3407, November, 2013

ISSN: 0975-833X RESEARCH ARTICLE COMPARATIVE STUDY OF LC LADDER FILTER WITH 3-OTA SIMULATED *1Manjula V. Katageri and 2Mutsaddi, M. M.

1 Government2 First Grade College, Bagalkot, India ARTICLE INFO ABSTRACTBasaveshwar Science College, Bagalkot, India Article History: The innovative technique of realising floating using OTA’s as an active element and grounded for the realisation of the floating inductor was comparitively studied in developing four stage LC ladder low pass Received 14th September, 2013 Received in revised form filters. A comparitive study of 3 OTA’s and grounded capacitor of different configarations, as modified technique of floating inductor in ladder filter applications was studied in comparision with concept. The response of 18th September, 2013 each stage exhibits the shootng characteristics of the output voltage in respect of filtering characteristic property Accepted 26th October, 2013 with sharp roll off ratio in the modified technique of floating inductor. A comparative study on four stage LC Published online 19th November, 2013 ladder low pass filter using gyrator concept was exhibiting best performance in filtering action which has high frequency application in instrumentation. Key words: LPF-Low Pass Filter, OTA – Operational Transconductance , Si-L-Simulated inductor.

Copyright © Manjula V. Katageri and Mutsaddi, M. M. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

INTRODUCTION  gm adjustable over wide range and is linear Floating inductance simulation is one of the important  Excellent mathing between technique in analog electronic filter circuit design. Its  Linearising applications are found in active filters, oscillators and system  Controlled impedance buffers response compensation. Several methods for realization of  High output signal to noise ratio. floating inductance simulator have been reported in the literarature (Chitpol Koomgaew et al., 2009; Priyanka Soni The ideal OTA has Zin = ∞, Zout =∞, Band width =∞, Inverting et al., 2011; Neha gupta et al., 2012; Alexender J. Casson et al., input current = Non inveritng input current. The (Fig.1) Shows 2011; Hajek et al., 2006; Wandeev Petchmaneelumka et al., circuit symbol of OTA. The voltage controlled current source 2009; Ananda Mohan 1998). Since OTA is a commercially low is mathematically expressed as Iout = gm (V1 – V2 ), where gm = cost device for easy implimentation in the monolithic form. In (Ibias/2VT), VT is thermal voltage = 26mV at room temperature. this paper 3-OTA based floating inductor circuits (Chitpol (Datasheet, 2004). Koomgaew et al., 2009; Priyanka Soni et al., 2011; Neha gupta et al., 2012) of three configarations are studied. The replacement of conventional inductors by simulated one in passive LC ladder filter,which is well known method of low sensitivity high order . The LC ladder low pass filter (LPF) in respective of four stage using three different simulated inductor circuits consisting of three OTA’S and grounded capacitor as only passive element was studied. The operational transconductance amplifier is a device in which the input voltage controlls the output current. It contains Fig.1. Circuit symbol of OTA the feature of linear controlled transconductance with tunable property of biasing current. The magnitude of inductance can Circuit Discription be electronically varied by changing the external bias current The circuits shown in (Fig. 2. Chitpol Koomgaew et al., 2009) of OTA. LM13600/LM13700 consists of two current (Fig.3. Priyanka Soni et al., 2011), and (Fig.4. Neha gupta controlled transconductance amplifier with different inputs and et al., 2012) are three different 3-OTA based floating inductor push pull outputs.Which has following features simulation circuits. The equivalent impedance of (Fig.1) & *Corresponding author: Manjula V. Katageri (Fig.2) has the dimention of inductance as Government First Grade College, Bagalkot, India. 3405 Manjula V. Katageri and Mutsaddi, M. M. Comparative study of LC ladder filter with 3-OTA simulated inductors

Zin = = = = SL Vx = (4)

L = at gm1 = gm2 = gm3 = gm At Ic = I3 , input impedance can be obtained from Eq.s (1),(2),(3) & (4) at I1 = - Iin & I2 = -Iout

Zin = = = = = SL (5)

If gm1 = gm2 = gm3 = gm is set , then L =

The evalution of inductors from the known values of C and gm suits the value of L obtained from .

EXPRIMENTAL RESULTS

LC ladder simulation

The passive LC ladder Low pass filter (LPF) with 4 stage is Fig. 2. Paper (Chitpol Koomgaew et al., 2009) 3-OTA based floating shown in (Fig.5) was studied for C = C = C = C = 1nF and inductor A B c D the passive inductance was replaced with active simulated inductance at LA =LB = LC =LD = 1mH. for each three different 3-OTA circuits shown in (Fig.6), (Fig.7) & (Fig.8). Using the tunable property of of bias current of OTA the simulated inductance was 1mH at IBias=50µA and C1 = C2 = C3 = C4 =1nf. The simulated results tested through Protuse professonal 7 software. So that each LC low pass filter gives

cutoff frequency of Fc = 159KHz

√ =

input L1 out1 L2 out1 L3 out3 L4 out4

1mH 1mH 1mH 1mH

CA CB CC CD 1nF 1nF 1nF 1nF

Fig. 3. Paper (Priyanka Soni et al., 2011) 3-OTA based floating inductor

The 3-ota Gyrator type simulated inductor is shown in (Fig.4) Fig. 5. Passive LC Ladder gives best performance due its low sensitivity. The output currents of OTA1 & OTA2 are Then low pass filter characteristics at four output stages was obtained for the three stated different techniques of simulated floating inductance (Fig. 6,7 & 8). The characteristic response of the low pass filter Shown in (Fig.9) exhibits the response of LPF using three OTA based inductor shown in (Fig.2). A family of low pass filter charactristics of Si-L as shown in (Fig.3) was presented in (Fig.10) with a family of curves. Similarly 3-OTA Gyrator inductance simulator for four stage LC Ladder characteristics is shown in (Fig.11). An observation on three graphs reveals the salient features of 3 OTA Gyrator floating inductor application in the design of LPF.

Fig. 4. Gyrator type 3 OTA floating inductor The method used in (Fig.3) was found to exhibiting overshoot of voltage near cutoff frequency (Fig.10). The appearance of I1=-gm1Vx (1) this shooting was due to error signal in the design of filter with the deviation in the value of L due to its quality factor. The I2 = gm2 Vx (2) Simulated inductance is not stable near the cutoff value. As its value decreases from calculated ones. The roll off ratio output I3 = gm3 ( V1 – V2 ) (3) voltage is sharp compared to other configarations. 3406 International Journal of Current Research, Vol. 5, Issue, 11, pp. 3404-3407, November, 2013

U8:A(AMPBIAS) VALUE=150u U8:B(V-) U1:A(AMPBIAS) VALUE=150u U1:B(V-) U8:A U8:B 1 0 1 1 2 6 1 9 U1:A U1:B 1 0

1 1 2 6 1 9 3 13 input 5 12 3 13 4 14 5 12 4 14 6 7 8 1 6 5 LM13600 1 1 1 LM13600 C2 6 7 8 1 6 5 LM13600 1 1 1 LM13600 1nf C1 1nf

U7:A U8:B(V+) 1 2 2 1 1 t u U2:A U1:B(V+) o 1 1 2 1 1

t 3 u

o 5 3 4 5 4 8 7 6 LM13600 CB 8 7 6 LM13600 1nf CA 1nf

U5:A(AMPBIAS) VALUE=150u U5:B(V-) U3:A(AMPBIAS) VALUE=150u U3:B(V-) U5:A U5:B 1 0 1 1 2 6 1 9 U3:A U3:B 1 0

1 1 2 6 1 9 3 13 5 12 3 13 4 14 5 12 4 14 6 7 8 1 6 5 LM13600 1 1 1 LM13600 C4 6 7 8 1 6 5 LM13600 1 1 1 LM13600 1nf C3 1nf

U6:A U5:B(V+) 1 4 2 1 1 t u U4:A U3:B(V+) o 1 3 2 1 1

t 3 u

o 5 3 4 5 4 8 7 6 CC LM13600 1nf CD 8 7 6 LM13600 1nf

Fig.6. Active LC Ladder using Simulated L of paper (Chitpol Koomgaew et al., 2009)

U1:A(AMPBIAS) U1:B(V+) VALUE=150u U3:A(AMPBIAS) U3:B(V+) VALUE=150u

U1:A U1:B 1 5 6 1 1 1 2 1 1 1 U3:A U3:B 1 5 6 1

input 1 1 2 1 1 1 3 14 5 12 3 14 4 13 5 12 4 13 6 7 8 9 0 6 1

LM13600 LM13600 6 7 8 9 0 6 C1 LM13600 1 LM13600 1nF C2 1nF U2:A 1 1 1 2 U4:A 1 1 1 2 U1:A(V-) 3 out1 5 U3:A(V-) 3 out2 4 5 4 CA 6 7 8 CB LM13600 1nF 6 7 8 LM13600 1nF

U7:A(AMPBIAS) U7:B(V+) U5:A(AMPBIAS) U5:B(V+) VALUE=150u VALUE=150u

U7:A U7:B 1 5 6 1 U5:A U5:B 1 1 2 1 1 1 1 5 6 1 1 1 2 1 1 1 3 14 3 14 5 12 5 12 4 13 4 13 6 7 8 9 0 6 1

6 7 8 9 0 6 LM13600 LM13600 LM13600 1 LM13600 C4 C3 1nF 1nF U8:A 1 U6:A 1 1 2 1 1 1 2 U7:A(V-) 3 out4 U5:A(V-) 3 out3 5 5 4 4 CD 6 7 8 CC 1nF 6 7 8 LM13600 LM13600 1nF

Fig.7. Active LC Ladder using Simulated L of paper (Priyanka Soni et al., 2011)]

U2:A(V-) U2:A(V+) U4:A(V-) U4:A(V+)

input out1 out2 2 2

5 U1:A 4 3 U2:A 1 U1:B 5 U3:A 4 3 U4:A 1 U3:B

2 8 6 11 15 9 CA 2 8 6 11 15 9 CB 1 7 7 1 16 10 1nf 1 7 7 1 16 10 1nf 11 6 8 2 11 6 11 6 8 2 11 6 3 4 5 4 3 3 4 5 4 3

LM13600 LM13600 1 1 LM13600 LM13600 LM13600 1 1 LM13600

U1:A(AMPBIAS) U3:A(AMPBIAS) VALUE=150u VALUE=150u C1 C2 1nF 1nF

U6:A(V-) U6:A(V+) U8:A(V-) U8:A(V+)

out3 out4

U5:A U6:A 2 U5:B U7:A U8:A 2 U7:B 5 4 3 1 5 4 3 1 CD 2 8 6 11 15 9 CC 2 8 6 11 15 9 1nf 1 7 7 1 16 10 1nf 1 7 7 1 16 10 11 6 8 2 11 6 11 6 8 2 11 6 3 4 5 4 3 3 4 5 4 3

LM13600 LM13600 1 1 LM13600 LM13600 LM13600 1 1 LM13600

U5:A(AMPBIAS) U7:A(AMPBIAS) VALUE=150u VALUE=150u C3 C4 1nF 1nF

Fig.8. Active LC Ladder using gyrator type of Simulated inductance 3407 Manjula V. Katageri and Mutsaddi, M. M. Comparative study of LC ladder filter with 3-OTA simulated inductors

Conclusion A comparative study of four stage LC ladder using three different circuits of 3-OTA Simulated inductors a gyrator type circuit is one of the best method for simulating floating inductance which eliminates the noise at the passage of pass band to stop band with the roll off rate at -40dB/decade per stage. Such a characteristic property of the filter is desirable in instrumentation applications.

REFERENCES Fig.9. Chitpol Koomgaew, et al. 2009. “OTA - based Floating Inductance Simulator” ICROS_SICE INC-2009, Fukuoka International congress center, Japan, August 18-21.pp 857-860. Priyanka Soni, et al. 2011. “Design of OTA based Floating Inductor”, IEEE 978-1-4244-9190-2/11 Neha gupta et al. 2012. “ Design Using Two OTA based Floating Inductance Simulator” International Journal of VLSI & Signal Processing applications, Vol.2, Issue 1, Feb, pp 47-50. Alexender J. Casson et al. 2011: “A Review and Modern Approach to LC Ladder Synthesis”, J. Low Power Electron. Appl, I, 20-44; doi: 10.3390/jlpea 1010020, Hajek K., V. Michal et al. 2006. “A simple method of Goal – Fig.10. directed Lossy Synthesis and Network Optimization”, Advances in Electrical and , pp 249-253 Wandeev Petchmaneelumka et al. 2009. “Simple floating inductance simulators using OTAs” International instrumentation and measurement Technology conference 12MTC2009, Singapore, 5-7 May. Ananda Mohan P.V. 1998. “Grounded capacitor based grounded and floating inductor simulation using current conveyors” Electronic letters 28th May 1998 Vol.34 No.11 Datasheet- National Semiconductor Corporation, 2004. “LM13600/LM13700 Dual Operational Transconductance Amplifiers with linearising Diodes and buffers.”

Fig.11. A close observations on the three characteristics of the filter shown in (Fig.9), (Fig.10) & (Fig.11) shows that 3 OTA Gyrator technique was one of the best method for simulating floating inductor in obtaining approximate to ideal characteristics. In Successive stages of LC ladder roll off rate increases from- 40dB/decade, -80dB/decade, -120dB/decade & -170dB/decade gives low sensitive Butterworth response. *******