OTRA-based Grounded-FDNR and Grounded-Inductance Simulators and Their Applications

Circuits Syst Signal Process (2012) 31:489–499DOI 10.1007/s00034-011-9345-2

OTRA-based Grounded-FDNRand Grounded-Inductance Simulatorsand Their Applications

Ashish Gupta · Raj Senani · D.R. Bhaskar ·A.K. Singh

Received: 5 December 2010 / Revised: 14 July 2011 / Published online: 24 August 2011© Springer Science+Business Media, LLC 2011

Abstract New grounded frequency-dependent negative-resistance (FDNR) andgrounded inductance simulation circuits, employing an operational trans-resistanceamplifier (OTRA) along with two capacitors, two resistors and a voltage followerhave been introduced. The application of the new simulators in the realization of asingle-resistance controlled oscillator (SRCO) and a single-capacitance controlledoscillator (SCCO) has been demonstrated and the effect of parasitic capacitanceand input and output resistances of the OTRA on the performance of these circuitshas been evaluated. The workability of the application circuits has been confirmedby experimental results using an OTRA-implemented from commercially availableAD844-type current-feedback operational amplifiers (CFOAs).

A. Gupta · A.K. SinghDepartment of Electronics and Communication Engineering, ITS Engineering College, 46, KP-III,Greater Noida, UP, India

A. Guptae-mail: [email protected]

A.K. Singhe-mail: [email protected]

R. Senani (�)Division of Electronics and Communication Engineering, Netaji Subhas Institute of Technology,Sector-3, Dwarka, New Delhi 110078, Indiae-mail: [email protected]

R. Senanie-mail: [email protected]

D.R. BhaskarDepartment of Electronics and Communication Engineering, Faculty of Engineering andTechnology, Jamia Millia Islamia, New Delhi, 110025, Indiae-mail: [email protected]

mailto:[email protected]





490 Circuits Syst Signal Process (2012) 31:489–499

Keywords Inductance simulation · Frequency-dependent-negative-resistance ·Sinusoidal oscillators · Operational transresistance amplifier

1 Introduction

Although a large number of analog circuit building blocks have been considered asalternatives to the classical voltage-mode operational amplifier (VOA) which suf-fers from the limitations caused by the finite gain-bandwidth product and limitedslew rates, the operational trans-resistance amplifiers (OTRA) [6, 7, 9] have beenfound to be particularly attractive in various analog signal processing/signal genera-tion applications [1–5, 8, 10–17, 19–24] due to their following advantageous features:(i) transmission properties similar to the current-feedback op-amp (CFOA), (ii) elim-ination of slew rate limitations as encountered in VOAs and (iii) availability of twolow-impedance inputs and one low-impedance output, which are advantageous forfacilitating easy cascadability of OTRA-based circuits.

The OTRA [6, 9] is a three terminal analog building block characterized by thematrix equation [

V1V2VO

]=

[ 0 0 00 0 0

Rm −Rm 0

][I1I2IO

](1)

The circuit symbol of the OTRA is shown in Fig. 1.In an OTRA, both the input terminals are virtually grounded and the output voltage

is the difference of the two input currents multiplied by the trans-resistance gain Rm,such that

Vo = Rm(I1 − I2) (2)

Since both the input and output terminals are characterized by low impedance, thiseliminates the response limitations incurred by capacitive time constants leading tocircuits that are insensitive to the stray capacitances at the input terminals. For idealoperation, the trans-resistance gain Rm approaches infinity thereby forcing the twoinput currents to be equal. Thus, the OTRA must be used in a negative feedbackconfiguration in a way similar to VOAs.

For discrete designs, the OTRA can be implemented using two Current-feedbackOperational Amplifiers (CFOAs) [2, 5, 19] as shown in Fig. 2. On the otherhand, from the viewpoint of analog VLSI implementation, several high-performanceCMOS OTRA realizations have also been introduced in the current literature for in-stance, see [7, 17, 21] and references cited therein.

Fig. 1 Circuit symbol of theOTRA

Circuits Syst Signal Process (2012) 31:489–499 491

Fig. 2 Implementation of anOTRA using two CFOAs

Fig. 3 The proposed generalconfiguration for groundedadmittance simulation

2 The Proposed Configurations

The use of OTRAs has been widely investigated in a number of applications such asimmittance simulators [18], filters [22] and oscillators [23, 24], to name a few.

The proposed simulators evolve from the general schematic of Fig. 3, an analysisof which yields

Yin = Iin

Vin= Y0

(1 − Y1

Y3

)+ Y2Y0

Y3(3)

2.1 Grounded FDNR

The proposed circuit for simulating FDNR is obtained by choosing Y0 and Y2 ascapacitors and Y1 and Y3 as resistors and is as shown in Fig. 4.

The input admittance Yin of the circuit is given by

Yin = Iin

Vin= sC2

(1 − R1

R2

)+ s2C1C2R1 (4)

In the above expression, if the condition R1 = R2 is taken, then the above expressionbecomes

Yin = s2C1C2R1 (5)

Thus, the circuit realizes a FDNR whose value is given by

D = C1C2R1 (6)


Fig. 4 Grounded FDNRsimulator

Fig. 5 Lossless groundedinductor simulation

2.2 Grounded Inductor

The proposed simulated inductor is obtained by choosing Y1 and Y3 as capacitors andY0 and Y2 as resistors and is shown in Fig. 5, which can be considered to be a RC:CR transformed version of the circuit of Fig. 4.

The input admittance Yin of the circuit is given by

Yin = 1

R2

(1 − C2

C1

)+ 1

sC1R1R2(7)

If C2 = C1, then the above expression becomes

Yin = 1

sC1R1R2(8)

Thus, the circuit realizes a lossless grounded inductor whose value is given by

Leq = C1R1R2 (9)

3 Oscillator Realizations Using the Proposed Circuits

3.1 SRCO

In the circuit of Fig. 4 if a grounded resistor R3 is placed across the input terminals,we obtain a single-resistance controlled oscillator (SRCO), which is shown in Fig. 6.


Fig. 6 A single-resistancecontrolled oscillator

For the circuit of Fig. 6, a routine analysis gives the value of input admittance Yi

as

Yi = 1

R3+ sC2

(1 − R1

R2

)+ s2C1C2R1 (10)

Thus, the circuit realizes an oscillator with frequency of oscillation (FO) given by

fo = 1

2π

1√R1R3C1C2

(11)

and the condition of oscillation (CO) is given by

R2 ≤ R1 (12)

From the above two expressions we can conclude that the frequency of oscillation canbe controlled independently through resistance R3 while the condition of oscillationcan be controlled independently through resistance R2.

3.2 SCCO

By placing a grounded capacitor C3 across the input terminals in the circuit of Fig. 5,we obtain a single-capacitor controlled oscillator (SCCO), which is shown in Fig. 7.

For the circuit of Fig. 7 the input admittance Yi is given by

Yi = sC3 + 1

R2

(1 − C2

C1

)+ 1

sC1R1R2(13)

so that the circuit realizes an oscillator with FO given by

fo = 1

2π

1√C1C3R1R2

(14)

and CO given by

C2 ≤ C1 (15)


Fig. 7 A single-capacitorcontrolled oscillator

From the above two expressions we can conclude that the frequency of oscillation canbe controlled independently through capacitance C3 (and also through the resistancesR1 and/or R2) while the condition of oscillation can be controlled independentlythrough capacitance C2. Thus, although the circuit has been synthesized as a SCCO,due to offering independent frequency control through the resistances R1 and/or R2,it can also be considered to be a SRCO.

4 Non-ideal Analysis of the Proposed SRCO and SCCO

Practically, the trans-resistance gain is finite and therefore its effect should be consid-ered. The frequency limitations associated with the OTRA should also be considered.Considering a single-pole model the trans-resistance gain, Rm, can be expressed as

Rm(s) = Ro

1 + sωo

= Roωo

s + ωo

= 1s

Roωo+ 1

Ro

(16)

for

Ro → ∞, Rm(s) ∼= 1

sCp

(17)

where Ro is the dc transresistance gain and CP is the parasitic capacitance.For the circuit of Fig. 6, a non-ideal analysis gives the following results for FO

and the CO.The FO is given by

fo = 1

2π

√√√√ 1

C1C2R1R3(1 + Cp

C1)

(18)

whereas the CO is given by

R2

R1+ CpR2

C2R3≤ 1 (19)


Fig. 8 A typical waveformgenerated by the SRCO circuitof Fig. 6 V0(pp) = 0.38 Volt andf0 = 424.3 kHz

Similarly, for the circuit of Fig. 7, a non-ideal analysis gives the following expressionsfor FO and the CO:

fo = 1

2π

√√√√ 1

C3R1R2C1(1 + Cp

C1)

(20)

C1 + Cp ≤ C2 (21)

From the above non-ideal analysis, it can be concluded that the effect of parasitic ca-pacitance although disturbs the independent tunability in the case of SRCO of Fig. 6,it does not alter these properties in case of SCCO/SRCO of Fig. 7, where C2 can stillbe used to adjust CO without affecting FO, which is also independently adjustable byC3, R1 and R2.

It is shown in Appendix that if the effect of non-zero input and output impedancesof the OTRA are also considered, then the errors in the oscillation frequencies of theoscillators of Figs. 6 and 7 are found to be less than 3%.

5 Experimental Results

The circuits of Figs. 6 and 7 were experimentally tested by constructing OTRA usingtwo CFOAs (AD844s). The voltage follower has been implemented using a CFOA.The DC bias supply of the CFOAs AD844 was chosen as ±5 Volts DC and the com-ponent values chosen were for the circuit of Fig. 6, C1 = C2 = 100 pF, R1 = 1 k�,R2 = 1 k� (fixed) +10 k� (variable), R3 = 10 k�. A typical waveform observed onthe oscilloscope is shown in Fig. 8, while the variation of fo with respect to R3 isshown in Fig. 9. For the circuit of Fig. 7, C1 = 600 pF, C2 = 100 pF–1200 pF (vari-able), C3 = 100 pF, R1 = 1 k�, R2 = 15 k�. A typical waveform observed on theoscilloscope is shown in Fig. 10 while the variation of fo with respect to R1 shownin Fig. 11.


Fig. 9 Variation of frequency of oscillation w.r.t. resistance (R3)

Fig. 10 A typical waveformgenerated by the SCCO circuitof Fig. 7 V0(pp) = 7.8 Volt andf0 = 150 kHz

6 Concluding Remarks

New circuits have been proposed for simulating a grounded inductor and groundedFDNR using a single OTRA, two capacitors and two resistors along with a volt-age follower. The proposed circuits are shown to be useful in realizing a SRCO andSCCO/SRCO, respectively. A non-ideal analysis has been presented, which showsthat in the SCCO/SRCO oscillator circuit, the independent controls of CO and FOremain available even under the influence of parasitic capacitance of the OTRA.The workability of the proposed SRCO and SCCO/SRCO circuits has been veri-fied in hardware using OTRA implemented from commercially available AD844-


Fig. 11 Variation of frequency of oscillation with respect to resistance (R1)

type CFOAs. The proposed circuits thus add new and useful results to the existingrepertoire of OTRA-based circuits [1–24].

Acknowledgements This work was performed partly at ASP Research Lab of the Division of ECE,NSIT, New Delhi and partly at Advanced Analog Signal Processing Lab, Department of ECE, Jamia MilliaIslamia, New Delhi, India. The authors thank the anonymous reviewers for their constructive suggestions.

Appendix: Effect of Non-ideal Input and Output Impedances of the OTRA

Considering the non-zero input impedances of the OTRA as Rp and Rn and the non-zero output impedance as Ro, by a lengthy but routine analysis, the non-ideal fre-quency of oscillation (FO) for the SRCO of Fig. 6 is found to be

∧ωo

∼= 1

C1C2R1R3

√√√√ 1

1 + Cp

C1{1 + (Ro+Rn

R1) + C2Ro+C1Rn

C2R3}

(22)

whereas the non-ideal condition of oscillation (CO) is found to be

R2

R1+ CpR2

C2R3≤ 1 +

CpR2Rn

C2R3(1 + Ro

R3)

1 + Cp

C1{1 + (Ro+Rn

R1) + C2Ro+C1Rn

C2R3}

(23)

It can be readily seen that with Rp → 0, Rn → 0, and Ro → 0 (22) and (23) reduceto their ideal forms as shown in (18) and (19), respectively.


Similarly, for the SCCO of Fig. 7, the non-ideal FO is found to be

∧ωo

∼= 1

C1C3R1R2

√√√√ 1

1 + Cp

C1{1 + C2Rp

C3R2+ C1(Ro+Rn)

C3R2}

(24)

whereas the non-ideal CO is found to be

C1 + Cp

(1 + Rn

R1

)≤ C2

[1 +

C2Rp

R1{1 + CpRo

C1R2+ CpRn

C1R1+ Cp(Ro+Rn)

C3R2}

1 + Cp

C1{1 + C2Rp

C3R2+ C1(Ro+Rn)

C3R2}

](25)

It can be readily seen that with Rp → 0, Rn → 0, and Ro → 0, (24) and (25) reduceto their ideal forms as in (20) and (21), respectively.

From the above, it is seen that the CO for both the cases gets modified. However,in case of SRCO of Fig. 6 the non-ideal CO is still independently controllable by R2(because R2 does not feature in FO). On the other hand, the non-ideal FO for SCCOof Fig. 7 is affected by the non-ideal input and output impedances; however, by anumerical check the percentage error in the frequency of oscillation it is found to be–2.82% for the SRCO of Fig. 6 and –2.78% for the SCCO of Fig. 7.

In conclusion, the errors caused by the finite input and output impedances of theOTRA are well within the acceptable limits.

References

1. C. Cakir, U. Cam, O. Cicekoglu, Novel all pass filter configuration employing single OTRA. IEEETrans. Circuits Syst. II 52, 122–125 (2005)

2. U. Çam, A novel single-resistance-controlled sinusoidal oscillator employing single operational tran-sresistance amplifier. Analog Integr. Circuits Signal Process. 32, 183–186 (2002)

3. U. Çam, F. Kacar, O. Çicekoglu, H. Kuntman, A. Kuntman, Novel grounded parallel immittancesimulator topologies employing single OTRA. AEÜ, Int. J. Electron. Commun. 57, 287–290 (2003)

4. U. Cam, C. Cakir, O. Cicekoglu, Novel transimpedance type first-order all pass filter employing singleOTRA. Int. J. Electron. Commun. 58, 296–298 (2004)

5. U. Çam, F. Kacar, O. Çicekoglu, H. Kuntman, A. Kuntman, Novel two OTRA-based grounded im-mittance simulator topologies. Analog Integr. Circuits Signal Process. 39, 169–175 (2004)

6. J.-J. Chen, H.-W. Tsao, C.-C. Chen, Operational trans-resistance amplifier using CMOS technology.Electron. Lett. 28, 2087–2088 (1992)

7. J.-J. Chen, H.-W. Tsao, S.-I. Liu, W. Chiu, Parasitic capacitance insensitive current-mode filters usingoperational transresistance amplifier. IEE Proc., Circuits Devices Syst. 142, 186–192 (1995)

8. J.-J. Chen, H.-W. Tsao, S.-I. Liu, Voltage-mode MOSFET-C filter using operational transresistanceamplifiers (OTRAs) with reduced parasitic capacitance effect. IEE Proc., Circuits Devices Syst. 148,242–249 (2001)

9. W. Chiu, J.-H. Tsay, S.-I. Liu, H.-W. Tsao, J.-J. Chen, Single capacitor MOSFET-C integrator usingOTRA. Electron. Lett. 31, 1796–1797 (1995)

10. C.L. Hou, H.C. Chien, Y.K. Lo, Square wave generators employing OTRAs. IEE Proc. Circuits De-vices Syst. 152, 718–722 (2005)

11. Y.S. Hwang, D.-S. Wu, J.J. Chen, C.C. Shih, W.S. Chou, Realisation of higher-order MOSFET-Cactive filters using OTRA. Circuits Syst. Signal Process. 26, 281–291 (2007)

12. S. Kilinc, U. Cam, Realization of n-th order voltage transfer function using a single operational tran-sresistance amplifier. ETRI J. 27, 647–650 (2005)

13. S. Kilinc, U. Cam, Transimpedance type fully integrated biquadratic filters using operational transre-sistance amplifiers. Analog Integr. Circuits Signal Process. 47, 193–198 (2006)


14. S. Kilinc, K.N. Salama, U. Cam, Realisation of fully controllable negative inductance with singleoperational transresistance amplifier. Circuits Syst. Signal Process. 35, 47–57 (2006)

15. S. Kilinc, A.U. Keskin, U. Cam, Cascadable voltage-mode multifunction biquad employing OTRA.Frequenz 61, 84–86 (2007)

16. Y.K. Lo, H.C. Chien, Current mode monostable multivibrators using OTRA. IEEE Trans. CircuitsSyst. II, 53, 1274–1278 (2005)

17. H. Mostafa, A.M. Soliman, A modified CMOS realization of the operational transresistance amplifier(OTRA). Frequenz 60, 70–76 (2006)

18. R. Pandey, M. Bothra, Multiphase sinusoidal oscillators using operational transresistance amplifier,in IEEE Symposium on Industrial Electronics and Applications, pp. 371–376 (2009)

19. K.N. Salama, A.M. Soliman, CMOS operational transresistance amplifier for analog signal process-ing. Microelectron. J. 30, 235–245 (1999)

20. K.N. Salama, A.M. Soliman, Novel oscillators using operational transresistance amplifier. Microelec-tron. J. 31, 39–47 (2000)

21. K.N. Salama, A.M. Soliman, Active RC applications of the operational transresistance amplifiers.Frequenz 54, 171–176 (2000)

22. A.M. Soliman, History and progress of the Tow-Thomas biquadratic filter part-II using OTRA, CCII,and DVCC realizations. J. Circuits Syst. Comput. 17, 797–826 (2008)

23. A.M. Soliman, A.H. Madian, MOS-C Tow-Thomas filter using voltage op-amp, current feedbackop-amp and operational transresistance amplifier. J. Circuits Syst. Comput. 18, 151–179 (2009)

24. A.M. Soliman, A.H. Madian, MOS-C KHN filter using voltage op-amp, current feedback op-amp,operational transresistance amplifier and DCVC. J. Circuits Syst. Comput. 18, 733–769 (2009)

Documents

OTRA-based Grounded-FDNR and Grounded-Inductance Simulators and Their Applications