INTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, VOL. 16, 93-96 (1988)

LETTERS TO EDITOR

ELECTRONICALLY CONTROLLED OTA-C FILTER WITH FOLLOW-THE-LEADER-FEEDBACK STRUCTURE

RAINER NAWROCKI

Institut fur Allgemeine Elektrotechnik, TU Braunsch weig, 3300 Braunsch weig, RFA

INTRODUCTION

An important design method ‘Follow-the-Leader-Feedback’ (FLF) for the synthesis of active filters starts with easily realizable and adjustable blocks with a voltage transfer function of the second-order (biquads). In contrast to cascade filters, whose biquad blocks are connected in series, FLF filters contain additional feedback branches in order to improve their sensitivity. Up to now only the operational amplifier has been regarded as the active element in the FLF design method. ’*’

Since 1969 the Operational Transconductance Amplifier (OTA) is available as an integrated device. The OTA is a differential voltage-controlled current source, whose transductance can be controlled by an external bias current.

For filters, which are built with OTAs and capacitors only, it is possible to tune the characteristic of the voltage transfer function over a wide range (cut-off frequency up to 200 kHz) with this external control variable.

In the following letter it is shown that FLF structures can also be realized with OTAs as the active elements. The special merit of filters designed in this way are-besides their tunability-their simple struc- ture, the small number of necessary components and in general the exclusive employment of grounded capacitors.

FLF FILTER ONLY WITH OTAS AND CAPACITORS

Figure 1 shows the structure of an FLF filter with a simple feedback structure. If such a filter is built with operational amplifiers as active elements, the feedback branches ( B ) together

with the addition node (C), are realized by a voltage adder. The biquad blocks (here F;*H;(s)) produce a voltage-to-voltage transfer function and have an infinitely small output resistance.

This principle cannot be transferred to OTA-capacitor circuits, since OTAs as a controlled current source have finite output resistances. Therefore the coupling of the different parts of the network has to be done in a different way.

In the design principle newly developed for OTA-C circuits, the feedback branches ( B ) and the amplifiers ( F ) represent yoltage-@Current converters (V-to-C converters), while the biquad blocks (H;(s)) work as C-to-V converters. The summation (C) is realized by several currents flowing into a com- mon current node. By this procedure arbitrary FLF structures with OTA-C components can be realized. As an example for this, an arbitrary allpole bandpass with the feedback structure pictured in Figure 1, will be explained below. A simple method for the dimensioning of a bandpass filter proceeds from a lowpass voltage transfer function, which results from an approximation process or has been drawn from a filter design catalogue. The centre frequency and the bandwidth of the requested bandpass must also

0098-9886/88/010093-04$05 .OO 0 1988 by John Wiley & Sons, Ltd.

Received 6 January 1987 Revised 5 May 1987

94 LETTERS TO EDITOR

I

HN-I hl . . . H t l s J F2 H2 1‘5) F3 H3 151

Figure 1. Structure of a simple allpole FLF filter

be known for the lowpass-band pass-transformation:

From these values the corresponding values for the feedback and amplifier branches and the bandpass- biquads can be calculated by the following equations (see also Reference 2):

F2, F3 ... Fn free choice

(n - P Y I 1 - 1

__I_

an-1 n! _ _ _ k‘ ( n - i ) ! i ! ( n - i ) ! 22 Bp ( i - p ) ! B; =

I

II Fj j = 2

k“ Fi i = 2

The amplification factors ( F ; ) , which are free of choice, can be used to optimize the dynamic behaviour of the filter. The optimization must assure that, for the relevant frequency range, none of the differential inputs of the OTAs are overdriven. For this calculation, the used biquad circuits and the desired voltage transfer function must be known.

BIQUADS WITH CURRENT-TO-VOLTAGE TRANSFER FUNCTION

For a complete description of the presented design principle, the realization of all components has to be given. The V-to-C converter is realized by a n OTA as a voltage controlled current source. The adjustable transductances are set to the values calculated for the feedback respective amplifier branches (B , F ) .

For V-to-V biquads, realizations are given in, References 4 and 5 , but in this case C-to-V biquads (band-

LETTERS TO EDITOR 95

Figure 2. Bandpasses with current-to-voltage transfer function

passes) are needed. In Figure 2, four C-to-V circuits are presented. (The conductances shown in Figure 2 could be replaced by feedback OTAs as explained in Reference 1. With the circuits in Figure 2c and d, a maximum quality of 0.7 can be obtained).

TUNABILITY

One of the eminent properties of OTA-C filters is the possibility to tune the voltage transfer characteritic on the frequency axis proportional to the values of the transductances.

If in a network all transductances are set to the same value, a number of adjustable current sources with the same value according to the number of transductances are required for tunability. But if in the net- work described above all transductances are of the same value, then-corresponding the above explanations-all feedback coefficients are of the same value too, so that'the required dimensioning cannot be obtained. A solution to this problem can be achieved by inserting an additional stage of a resistor (as a C-to-V converter for the summation of the currents) and a multiplier (as V-to-C converter, to match the input of the following biquad) between the summation node and the first biquad.

PRACTICAL RESULTS

To demonstrate the quality of an FLF filter designed with the presented method, a Chebyshev filter of the sixth-order will be used, which is derived from a lowpass catalogue filter of the third-order (maximal pass- band attenuation of 0.1 dB; break attenuation of 24 dB; coefficients: a3 = 1, a2 = 2-848, a1 = 4.805, a0 = 3.954, rn = 1). A centre frequency WOBP = 2a5O kHz and a bandwidth BBP = 2x10 kHz for the band- pass are chosen. The circuit of Figure 2b is chosen for the bandpasses.

In Figure 3 the corresponding network is given. The transductances g2 to 810 are set to the same value g for tunability. As a consequence F2 = F3 = 1 results.

R = 1 kQ and g = 19 mmhO (the largest possible value for the transductance of a real OTA) are arbitrarily selected.

As a result the value for the three other transductances are:

B2 B3 Fo R R R

8 1 2 = - = 2.332 mmhO, gll = - = 1 e291 mmhO, gl = - = 4.624 mmhO

The capacities are calculated by comparison of the bandpass functions (Cl =.ll.48 nF, CZ = 318.6 nF). Figure 4 shows on one hand the ideal filter curve, and on the other hand the curves that were measured

in the filter described above with a centre frequency of 50 kHz or with a centre frequency of 5 kHz (after a tuning of the transductances g2 to g lo ) respectively. (To clarify this figure, all curves are scaled to a centre frequency of unity.)

It can be seen that the concrete realization of the bandpass FLF filter corresponding well with the theoretical frequency characteristic. (The deviation of the theoretical and the measured curves can be explained by the finite input impedance of the OTA device. The curves can be adjusted by increasing the input transductance gl . )

96 LETTERS TO EDITOR

I

I

v,

- - . . . I- - 4--J- - - -qJ-

F, I HI (5) FZ Hz(s) Fj H3 IS)

Figure 3. FLF filter of the sixth-order with OTA-C-components

ideal measured Ifgpg=SkHz/

- 30

-40 1.2 1.4 1.6 - 2

frequency 0.5 0.6 0.7 0.8 1

Figure 4. Voltage transfer functions of a Chebychev bandpass filter 0.1 dB/24 dB ideal/foBp = 5 kHZ/foBp = 50 kHz

CONCLUSION

It was shown the bandpass filters with infinite transmission zeros can be realized with the FLF design method using OTAs and capacitors only. Measurements verify these theoretical considerations.

The same principle can also be used for more complex FLF structures, e.g. for bandpasses with finite transmission zeros.

A special advantage of the so designed filters is the possiblity of tuning the voltage transfer function by the externally controlled transductances of the OTAs. An additional advantage can be found in the method described above that only grounded capacitors and no resistors are used, which allows an inte- gration in monolithic as well as in hybrid IC fabrication techniques.

REFERENCES

1 . G. Hurtig, ‘Filter network having negative feedback loops’, U.S. patent B, 720, 881 (1973). 2. A. S. Sedra and P. 0. Brackett, Filter Theory and Design: Active and Passive, Pitman, 1978. 3 . C. F. Wheatley and H. A. Wittlinger, IOTA obsoletes op amp’, Proc. Nat. Electron. Cony. 152-157 (1969). 4. R. L. Geiger, ‘Voltage controlled filter design using operational transconductance amplifiers’, IEEE 83, Int. Sympos. on Circuits

5 . H. S. Malvar, ‘Electronically controlled active-C filters and equalizers with operational transconductance amplifiers’, IEEE Tran-

6. R. L. Geiger and E. Sanchez-Sinencio, ‘Active filter design using operational transconductance amplifiers: A tutorial’, IEEE Cir-

and Systems. 2 , Newport Beach, USA, 494-597 (1983).

sactions on Circuits and Systems CAS-31, 645-469 (1984).

cuits and Devices Magazine, 1 , 20-32 (1985).