Active and Passive Electronic Components

Volume 2009 (2009), Article ID 835789, 5 pages

http://dx.doi.org/10.1155/2009/835789

## Electronically Tunable Dual-Input Integrator Employing a Single CDBA and a Multiplier: Voltage Controlled Quadrature Oscillator Design

^{1}Department of Electronics & Telecommunication Engineering, Jadavpur University, Kolkata-700032, India^{2}Department of Electronics & Communication Engineering, Heritage Institute of Technology, Kolkata-700107, India^{3}Department of Electronics & Communication Engineering, B.P. Poddar Institute of Management & Technology, Kolkata-700052, India

Received 23 July 2009; Revised 1 December 2009; Accepted 3 December 2009

Academic Editor: Rezaul Hasan

Copyright © 2009 R. Nandi et al. 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.

#### Abstract

A new dual-input differential input active integrator using a current differencing buffered amplifier (CDBA) is proposed. A multiplier element is appropriately used in the circuit whose control voltage () tunes the integrator time constant () electronically. The design of a voltage controlled quadrature oscillator (VCQO) based on the proposed integrator had been satisfactorily implemented. A new type of measurement for the tuning error of the oscillator based on the Nyquist plot is presented that shows an error of only 2% at 1?MHz with Total Harmonic Distortion (THD) less than 3%.

#### 1. Introduction

With the advent of the CDBA building block [1, 2], various analog signal processing/conditioning circuit realisation schemes using this element appeared in the recent literature [2–6]. The CDBA offers several advantageous features viz., high slew rate, improved bandwidth, and accurate port tracking characteristics when configured with a pair of matched current feedback amplifier (AD-844-CFA) devices [3, 4] which leads to extremely low active circuit sensitivity. We propose here a new electronically tunable differential integrator using a CDBA; the control voltage of a multiplier element, incorporated suitably in the circuit, tunes electronically.

The ICL-8013 device is a four-quadrant analog multiplier whose output is proportional to the electronic product of two input voltage signals with a transmission constant [7, 8]. The high accuracy (±1%), relatively wide bandwidth (B = 1?MHz), and improved versatility make it quite suitable for analog signal conditioning and active filter design applications.

Albeit various CDBA-based active filters/oscillators [3–6] are now available, the feature of electronic tuning in the CDBA active function circuit had not yet been reported. The design of a voltage controlled quadrature oscillator (VCQO) had then been implemented using the double integrator loop. The proposed functions had been verified by PSPICE macromodel simulation of the AD-844 based CDBA and by hardware circuit tests.

#### 2. Analysis

The proposed circuit is shown in Figure 1. The nodal equations characterizing an ideal CDBA element are [1]. Analysis with these port relations for the CDBA [1–4] and writing the multiplier [7, 8] output = where multiplier constant = 0.1 per volt [9] yield where denotes the shunt parasitic transadmittance at node of the CDBA; as per datasheet [10] mho and .

We therefore get the realisability conditions for a true differential integrator, putting ; to 4, as here we assumed . With (2) in (1), an ideal dual-input integrator function is obtained as where if then with Hence the time constant is electronically tunable for the range ?V d.c.

With a nonideal CDBA device, these design equations would alter. The device imperfections may be expressed in terms of some port mismatch ratios [2–4] given by the relations The and terminals of the CDBA however are internally grounded; hence In the literature, the mismatch ratios are postulated in terms of some low-magnitude error [2–6] quantities given by , and for an ideal device the errors vanish.

By Reanalysis assuming finite quantities, we get a modified transfer equation

The realisability conditions for a true differential integrator now modify to Here we neglect the error products since ; thus .

The active **-**sensitivity may be estimated after writing for simplicity, which gives since [4, 11, 12]. Effect of the multiplier device nonideality may be derived by expressing so that we can effectively write for sensitivity calculation, which yields

In this analysis, we neglected the parasitic series resistance (?ohm) [12] of the CDBA and noted that the -node parasitics are bypassed to ground since The integrator quality factor may be evaluated after writing and then deriving given by where

Inspection of (7) indicates the realisability of high quality integration where may be preset to a high value by , and sets the realisability while tunes electronically and independently. For example, if we assume for a desired at ?MHz with a typical set of values ?V d.c., ?nF, ?nF, and K, then from (7) we get ?K.

#### 3. VCQO Design

The quadrature oscillator finds various applications in SSB modulators and spectral phase measurements: its functional capabilities are further enhanced if electronic tuning property can be incorporated. We design a VCQO using the proposed integrator in a two integrator loop, each being used single ended, one inverting and the other in noninverting mode, that is, from (3) we designed and , thereafter cascading the two integrators in a loop.

With identical integrator, the oscillation frequency would be . The frequency stability factor is evaluated by at where is loop phase shift. After putting we obtained since we selected . A comparison of the values with some recent CDBA based oscillators is listed in Table 1.

#### 4. Simulation and Experimental Results

Both the integrator and VCQO functions have been tested with PSPICE macromodel simulation [13] and by breadboarding hardware circuit after implementing the CDBA block with a pair of AD-844 devices [3] being biased with ?V.d.c. regulated supply. The results are shown in Figure 2. The responses had been measured for a range of 150?KHz ?MHz with suitable set of RC components wherein ?V d.c. is used for the tunability range taking The ICL-8013 multiplier element is implemented through the Macromodel databook [7–9]. It may be mentioned here that one can select any of the two default values of the multiplier constant and for the ICL 8013 multiplier device [7–9, 13, 14] in order to enhance the tuning range concomitantly while keeping and as the limit.

We tested the frequency response of the integrator with antiphase input sinusoid signals and observed the phase error of about 5.5° at 1?MHz. The CMRR had been measured to be 96?dB with sinusoid excitation. It may be seen that the select-frequency was reported in the range of a maximum of 200?KHz in the earlier circuits [3, 4, 6]. Embedding the HA 2557 multiplier device [7, 8] with BW 130?MHz, in place of the ICL-8013 BW(1?MHz), it is possible to obtain an extended frequency range.

In order to examine the tuning error in we had carried out a new type of measurement using the Nyquist plot of the loop transfer function of the double-integrator loop in the vicinity of as shown in Figure 2(d). The deviation is then computed from the intersection of the function with the real axis of the plot following the Barkhaussen criterion. We obtained three such graphs corresponding to oscillation generation at the nominal frequencies of 500?KHz, 720?KHz, and 1.02?MHz. The tuning error is then derived as shown in Figure 2(e) and Table 2.

#### 5. Conclusion

A new single CDBA-based differential integrator with a multiplier element in the circuit loop is presented for obtaining electronic tunability. Subsequently, a double integrator type VCQO had been designed and tested in a frequency range of 150?KHz–1?MHz with suitable design. Albeit other electronically tuned active realisations were reported recently in relatively lower frequency-range using CFA [14], current conveyors [15, 16], or OTA-based allpass filter [17], such a function circuit using the CDBA had not yet been presented.

#### References

- C. Acar and S. Ozoguz, “A new versatile building block: current differencing buffered amplifier suitable for analog signal-processing filters,”
*Microelectronics Journal*, vol. 30, no. 2, pp. 157–160, 1999. View at Publisher · View at Google Scholar · View at Scopus - S. Özoǧuz, A. Toker, and C. Acar, “Current-mode continuous-time fully-integrated universal filter using CDBAs,”
*Electronics Letters*, vol. 35, no. 2, pp. 97–98, 1999. View at Google Scholar · View at Scopus - J.-W. Horng, “Current differencing buffered amplifiers based single resistance controlled quadrature oscillator employing grounded capacitors,”
*IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences*, vol. E85-A, no. 6, pp. 1416–1419, 2002. View at Google Scholar · View at Scopus - A. Ü. Keskin, “Voltage-mode high-Q band-pass filters and oscillators employing single CDBA and minimum number of components,”
*International Journal of Electronics*, vol. 92, no. 8, pp. 479–487, 2005. View at Publisher · View at Google Scholar · View at Scopus - M. Gülsoy and O. Cicekoglu, “Lossless and lossy synthetic inductors employing single current differencing buffered amplifier,”
*IEICE Transactions on Communications*, vol. E88-B, no. 5, pp. 2152–2155, 2005. View at Publisher · View at Google Scholar · View at Scopus - W. Tangsrirat, D. Prasertsom, T. Piyatat, and W. Surakampontorn, “Single-resistance-controlled quadrature oscillator using current differencing buffered amplifiers,”
*International Journal of Electronics*, vol. 95, no. 11, pp. 1119–1126, 2008. View at Publisher · View at Google Scholar · View at Scopus - Intersil Datasheet, file number 2477.5, September 1998.
- Intersil Datasheet, file number 2863.4, April 1999.
*Semiconductor Product Databook*, Intersil Corp., Milpitas, Calif, USA, 2000.*Analog Devices: Linear Products Databook*, Norwood, Mass, USA, 1990.- A. Zeki and H. Kuntman, “Accurate and high output impedance current mirror suitable for CMOS current output stages,”
*Electronics Letters*, vol. 33, no. 12, pp. 1042–1043, 1997. View at Google Scholar · View at Scopus - B. J. Maundy, A. R. Sarkar, and S. J. Gift, “A new design topology for low-voltage CMOS current feedback amplifiers,”
*IEEE Transactions on Circuits and Systems II*, vol. 53, no. 1, pp. 34–38, 2006. View at Publisher · View at Google Scholar · View at Scopus *Macromodel of AD844AN in PSPICE Library*, Microsim Corp., Irvine, Calif, USA, 1992.- R. K. Nagaria, A. Goswami, P. Venkateswaran, S. K. Sanyal, and R. Nandi, “Voltage controlled integrator/differentiator using current feedback amplifier,” in
*Proceedings of the International Symposium on Signals, Circuits and Systems (ISSCS '03)*, vol. 2, pp. 573–576, Iasi, Romania, 2003. - H. Sedef, M. Sagbas, and C. Acar, “Current-controllable fully-integrated inductor simulator using CCCIIs,”
*International Journal of Electronics*, vol. 95, no. 5, pp. 425–429, 2008. View at Publisher · View at Google Scholar · View at Scopus - N. Padey and S. K. Paul, “A novel electronically tunable sinusoidal oscillator based on CCCII(-IR),”
*Journal of Active & Passive Electronic Devices*, vol. 3, pp. 135–143, 2008. View at Google Scholar - A. U. Keskin, K. Pal, and E. Hancioglu, “Resistorless first-order all-pass filter with electronic tuning,”
*AEU—International Journal of Electronics and Communications*, vol. 62, no. 4, pp. 304–306, 2008. View at Publisher · View at Google Scholar · View at Scopus