201O International Conference on Mechanical and Electrical Technology (ICMET 2010)

Analog filters using simulated inductor

D.Susan School of Electrical & Electronics Engineering

SASTRA University, Thanjavur- 613 401, India e-mail: d _susan@ece.sastra.edu

Abstract-This paper deals with simulation of passive component the inductor and the application of the simulated inductor in analog filters. The analog filters use active component the operational Amplifiers, resistors and the simulated inductor. The design of various analog filters is based on the basic LCR resonator circuits. Various types of filters are realized and the frequency response are obtained using the analog simulator PSPICE

Keywords- Simulated inductor; operational amplifier; analog filters;

I. INTRODUCTION

The use of inductors in analog circuits has many disadvantages, mentioned in the paper [1]. One among them is that the analog filters using inductor works well at high frequencies, however, in low frequency applications that is in the frequency range (0- 20 kHz), the inductors cannot be used for the reasons [2]

• The size and weight of the inductors are large and physically bulky and the quality factor becomes very low

• Their characteristics are quite non-ideal • Inductors are impossible to fabricate in

monolithic form and are incompatible with any of the modem techniques for assembling electronic systems.

So, it is required to design the analog filters without the use of inductors. One of the possible methods is the use of inductor less filter. These analog filters are based on the op-amp-RC resonator circuit obtained by replacing the inductor L in the LCR resonator by a simulated inductor.

II. INDUCTOR REPLACEMENT CIRCUIT

The inductor simulation circuit is obtained from the Generalized Impedance Converter (GIe), which consists of two-operational amplifiers, and five impedances consisting of RC components [3]. The equivalent impedance Z of the GIC circuit is given by Z = Z\Z3Z5/ Z2 Z4. From this basic circuit the passive inductor is obtained by replacing Z\ by RJ. Z2 by R2, Z3by R3, Z4 by C4, and Z5 by R5 .The circuit will become as shown in figure. I. This is the Antoniou inductor simulator after its generator A. Antoniou [1] shown in figure.I. It uses two op amps, five resistors and a capacitor. The circuit exhibits input impedance of an ideal inductor whose input impedance is given by.

978-1-4244-8102-6/10/$26.00 © 2010 IEEE 659

S.Jayalalitha School of Electrical & Electronics Engineering

SASTRA University, Thanjavur -613 401, India : e-mail: sLinstru@eie.sastra.edu

Figure 1. Antoniou Inductor simulation circuit

ZI = V;

= sC4RIR3RS

II R2 which is an inductor L given by

L = C4RIR3RS

R2

(1)

(2)

The analysis of the circuit is done with the basic assumptions for the operational amplifier

• The op-amps are ideal • Virtual short circuit appears between the two

terminals of the op-amp • The input currents of the op-amp are zero

By selecting R\ = R2 = R3=R5 =R and C4= C, leads to L= CR

2

III. WHY INDUCTORS ARE NOT USED IN LOW

FREQUENCIES?

To design a notch filter with 60 Hz frequency and with C= 1.6uF , the value of L becomes 4.42 H. So, a large inductor is required. That is the reason why passive filters are not practical in low frequency applications. Hence the LCR resonator shown in figure. 2 can be used to realize different filter types after replacing L by the simulated inductor circuit as shown in figure. 1.

2010 International Conference on Mechanical and Electrical Technology (ICMET 2010)

IV. BASIC LCR RESONATOR CIRCUIT

The basic LCR resonator of second order shown in figure. 2 can be used to realize different filter types

L R

x

Figure 2. Basic LCR resonator circuit

The resonator is excited with a current source I connected in parallel. The response function in terms of impedance is given by

(3)

Equating the denominator

lS2 + s( (00 / Q) + (002 J

leads to

to the standard form

2 1/ (00 = ILC

flJ� _ YcR

(00 = Y.J LC and Q =

flJo CR

V. REALIZA nON OF FILTERS

(4)

(5)

(6)

(7)

Using the basic LCR resonator circuit, the nodes x, y, z can be connected in different ways to obtain all types of filters. The Table. I shows how different filters are realized. Here Vi is the supply voltage.

TABLEr.

Node x

Vr ground ground

Vi

FORMATION OF FILTERS BY CONNECTING LCR BASIC CIRCUIT IN DIFFERENT MODES

Node z Node y Resulted filter

ground ground LPF Vi ground HPF

ground Vi BPF

Vi ground Notch at COo

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A. Realization of low pass filter In the basic LCR circuit for low pass filter, L is replaced

by the Simulated Inductor [6] as shown in figure.3. The frequency response of the low pass filter thus obtained is given in the figure 4

Simulated L +

V I Vo

Figure 3. Low pass filter

The transfer function of the low pass filter circuit is given by

(8)

where K is the de gain

l'

-� : \

�. -\) �"J '\ I

, \ I \

I

\ \ \

� lDt JlIi

Figure 4. Frequency response of low pass filter

B. Realization of high pass filter Similarly for high pass filter, L is replaced by the

Simulated Inductor in the basic LCR circuit as shown in figure.5. The frequency response of the high pass filter is shown in the figure 6.

2010 International Conference on Mechanical and Electrical Technology (ICMET 2010)

Figure 5. High pass filter

The transfer function of the high pass filter is given by

(9)

where K is the high frequency gain

Thr-------------------------��----

IDt

Figure 6. Frequency response of high pass filter

C. Realization of band pass filter The same LCR is modified to get band pass filter as

shown in figure.7 The frequency response of the band pass filter which is simulated is given in figure.8.

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Figure 7. Band pass filter

The transfer function of the band pass filter is given by

11\ l 1 I I \ ; I

I \ i i i : ! \ I I I

I \ , Y I :

/1 1\ I I / \ I I I "" I ----./ i " � I I

Figure 8. Frequency response of band pass filter

D. Realization of Notch filter

(10)

The notch filter can be obtained in the same manner as shown in figure.9. The frequency response of such notch filter obtained is given in the figure.10.

2010 International Conference on Mechanical and Electrical Technology (ICMET 2010)

Simulated L

�---J r---�.--------o C +

V I

Figure 9. Notch filter.

where K is the low and high frequency gain

u�---����-,-----------�

Figure 10. Frequency response of notch filter

VI. CONCLUSION

The frequency response of analog filters for low frequency is obtained using simulated inductor. The simulated results obtained using PSPICE for low pass, high pass, band pass and notch filter are presented. This replacement of inductor using simulated inductor has the disadvantage that it is suitable only for grounded inductor [5] and not for floating inductor [4]. In such cases the use of Frequency dependant negative resistance (FDNR) gives the solution for it

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REFERENCES

[I] Umesh Kumar and Sushil Kumar Shukla, "Analytical study of inductor simulation circuit"active and passive Elec.comp 1989, vol. 13, pp 211-227

[2] Dutta Roy, S.C. , "A High Q Inductance Transistor Ckt and a tuned oscillator for Microminiature applications", Int. J. Electronics 1963, 18, pp. 1-16.

[3] Sedra and Smith, Microelectronic Circuits, Fourth Edition 2002, Oxford University Press.

[4] Sergio Franco, Design with operational Amplifiers and Analog Integrated circuits Second Edition, 2007, McGraw Hill International Editions

[5] Dutta Roy, S.C. , "Operational Amplifier Simulation of a Grounded Inductance: General characteristics and a critical comparison of various circuits", AEI, March 1975.

[6] R. Cuppens, H.J. De Man and W.M.C. Sansen, "Simulation of large on-chip capacitors and inductors", IEEE J. solid state circuits, vol. SC-14, no. 3, pp. 543-547, June 1979.