New insensitive active ideal inductance with single resistor control using current conveyors

0026-2692/83/1402-0073 $5.00/0

short contribution New insensitive active ideal inductance with single resistor control using current conveyors by R. Nandi* and S. Nandi** * JadavpurUniversity,Calcutta, India ** The Women'sPolytechnic,Calcutta,lndia A new active-RC network for ideal inductancesimulationusing second generationcurrentconveyor (CC II) active elements is proposed. The inductance is single resistorcontrollableand is insensitive to active parametervariationsthese featuresare desirablefor microcircuitfabrication.

1. Introduction

2. Ideal inductancesimulation

Active-RC simulation of inductive driving point impedance functions has become useful with the advent of modem integratedelectronics. With the introduction of the second generation current conveyor (CC II) active elements,' renewed interest has centred on inductance simulation using this device. Recently, a number of CC IIlossy-inductance realisation schemes'v have appeared in the literature. Lately, Soliman" has proposed a single CC II ideal inductance simulation scheme in which a capacitor controls the magnitude of the simulated inductance. In integrated circuits, the fabricated capacitors are limited to picofarad ranges, and variation of resistor ratios is always preferred for tuning purposes over variation of nominal capacitance values. In thiscommunication,a new network for active ideal inductance (All) using two CC II devices, three resistors, and a capacitor is proposed. The advantage of this scheme lies in the fact that, unlike capacitance control as in ref. [6], the realisability condition and inductancecontrol are independent, yielding a single resistor control of the All. This would facilitate its application in tunable filter/oscillator designs," Moreover, following the method of sensitivity analysis suggested by the author,2-s the proposed All is shown to be stable and insensitive to active CC II parameterchanges.

The All simulating network is shown in Fig. 1. The terminal characteristicsof the CC II element are given by the hybrid matrix! as:

~] [~J'"

o o

(I)

The input impedance in Fig. 1, assuming ideal currenttrackingproperty (h32; = 1, i = 1,2.) of the CC lIs, may be expressed as: 1 Yin(w) = - - + rp

1

-.-JwL

... (2)

where rp = R!R2/(R! - R 2) L = CRoR2/2 ... (3) The condition for an All simulation is simply: R! = R z = R The lossless inductanceis then given by L, = CR o R/2

(4) (5)

Thus continuous single resistor control of the magnitude of L o is obtained by adjustment of the resistor R, without affecting the realisability condition in eqn. (4).

MICROELECTRONICS JOURNALVol 14 No 2 © 1983 Benn ElectronicsPublicationsLtd, Luton

73

New insensitive active deal inductancewith single resistorcontrol etc continuedfrompage 73

()e

·x y

tee . ]I 1

z

~

X ~

+

C~TIfiz .

+

..; ~

::~ R, u-

rn

Fig .1

Lossless inductancesimulating network.

3. Sensitivity For sensitivity analysis, the CC II elements are assumed to be nonideal on the assumption of a finite current tracking error between ports x and Z,7 characterisedby: h32j

=1-

€j ;

i = 1,2.

. .. (6)

With eqn. (6), the value of the inductance is modified to ... (7) The sensitivities ofL o are

~

=

S~ = -

~

=

~~ =

1;

€) / (I-€d S1.o

~

= 0

'"

(8)

= €21(2-€2)(1-€2) . .. (9)

The quantity € has been found to be very small and deviations in the ideal currenttrackingcharacteristics have been reported to be of the orderof2 to 4 percent of the norninal.I"The All is therefore seen to be sufficiently stable and insensitive to the active CC II parameterchanges.

4. Conclusion A new insensitive active ideal inductance simulation scheme is proposed using CC II elements. The inductance is suitable for application in a tunable filter/oscillator4 •10 because of a single resistor control.

5. Acknowledgment The authorswish to express their gratitude to Professor A. R. Sahafor sustained encouragement and interest.

74

C

j

6. References [1] Sedra, A. and Smith, K. c., "A second generationcurrentconveyor and its applications", IEEETrans. Circuit tu., CT-17, 132 (Feb. 1970). [2] Nandi, R., "Inductor simulation using a current conveyor", Proc. IEEE, 65, 1511 (Oct. 1977). [3] Soliman, A. M., "Ford-Girting equivalent circuit using CC II", Electron. Letts., 14,721 (Oct. 1978) . [4] Nandi, R., "Active inductancesusing current conveyors and their application in a simple bandpass filter realisation", Electron. Letts., 14,373 (June1978). [5] Nandi, R., "Insensitive grounded capacitor simulation of grounded inductors using current conveyors", Electron. Letts., 15,693-694 (Oct. 1979). [6] Soliman, A. M., "New active gyrator circuit using a single current conveyor", Proc. IEEE, 66, 1580-1581(Nov. 1978). [7] Black, G. G. A., Friedman,R. T. and Sedra, A. S., "Gyratorimplementation with integrable current conveyors", IEEE Jl. SolidState Circt., Sc-6, 3% (Dec. 1971). [8] Dejager W. and Smit, J., "Application, design and symbolic analysis of a current follower", IEEE Jl. Electron. Circuits & Syst., 1,79 (Jan. 1977). [9] Bel, N., "A high precision monolithiccurrent follower", IEEEJl. Solid-State Circt., SC-13, 371-373 (June1978). [10] Mitra, S. K., Active Inductorless Filters IEEEPress (1971). '