Systematic realisation of quadrature oscillators using ... - IEEE Xplore

www.ietdl.org Published in IET Circuits, Devices & Systems Received on 10th April 2010 Revised on 13th October 2010 doi: 10.1049/iet-cds.2010.0227

ISSN 1751-858X

Systematic realisation of quadrature oscillators using current differencing buffered amplifiers J.K. Pathak1 A.K. Singh2 R. Senani3 1

Department of Electronics and Communication Engineering, Institute of Technology and Management, HUDA Sector 23 A, Gurgaon 122 017, India 2 Department of Electronics and Communication Engineering, ITS Engineering College, KP-III, Greater Noida, UP, India 3 Division of Electronics and Communication Engineering, Netaji Subhas Institute of Technology, Sector-3, Dwarka, New Delhi 110078, India E-mail: [email protected]; [email protected]

Abstract: A systematic approach is presented to realise quadrature oscillators using current differencing buffered amplifiers (CDBAs). Based on a general scheme employing a cascade of a special type of low-pass filter and an integrator in a closed loop, a general configuration is formulated that yields 12 single-resistor-controlled-quadrature oscillator circuits using CDBAs an active elements. All the oscillator circuits enjoy fully uncoupled independent control of condition of oscillation and frequency of oscillation using a minimum possible number of active components, grounded/virtually grounded capacitors and grounded/virtually grounded resistors. PSPICE simulation results along with hardware experimental results, based on commercially available AD844 ICs to construct the CDBAs, are included which confirm the practical workability of the new quadrature oscillator configurations.

1

Introduction

Quadrature oscillators (QOs) find numerous applications in signal processing, communication (such as in quadrature mixers and single-side band generators [1]) and measurement (such as in vector generators and selective voltmeters [2]). Several methods of designing of quadrature sinusoidal oscillators are known in the literature [1 – 15] out of which those using a cascade of two all-pass filters circuits [5, 10] or those using a cascade of an all-pass filter circuit along with a non-inverting integrator circuit in a closed loop [6] are quite well known. Recently, a lot of emphasis has been given on designing QOs [9– 15] employing a relatively new active building block named current differencing buffered amplifier (CDBA) [7] as compared to current feedback operational amplifier (CFOA) and current conveyor-II (CCII) because of the superior terminal characteristics of CDBAs over the CFOAs/CCIIs. Using CDBA, QOs have been developed earlier by using a cascade of two all-pass filters as in [10] and cascade of an all-pass filter and an integrator as in [12]. While the approach in [10] requires four resistors and four capacitors as passive components and has the disadvantage of not providing independent control of frequency of oscillation (FO) and condition of oscillation (CO), on the other hand, the approach used in [12] although provides independent control of CO and FO but requires three resistors and three capacitors and hence, the circuits therein are ‘non-canonic’. By contrast, the proposed approach requires only four resistors and two IET Circuits Devices Syst., 2011, Vol. 5, Iss. 3, pp. 203– 211 doi: 10.1049/iet-cds.2010.0227

capacitors as passive components and hence, results in circuits which are ‘canonic’ and also provide fully uncoupled independent control of FO and CO through separate resistors. It is well known that the performance of CFOA- and CCII-based oscillators is affected because of the presence of internal parasitic capacitances at the input terminals of these building blocks while these capacitances do not exist in CDBA as its input terminals are internally (virtually) grounded [9]. Apart from this, CDBA is particularly attractive as it provides two current input terminals with a virtual ground at both the inputs as well as a voltage mode output at a terminal having very low output impedance, which is very useful for easy cascading. Moreover, a CDBA is also quite suitable for current mode operation and can operate in frequency range of more than tens of MHz [8]. The aim of this paper is to present a systematic approach to realise QOs based on a general configuration employing CDBA-based sub-circuits thereby resulting in a family of 12 QO circuits. The workability of the proposed circuits is verified through PSPICE simulations along with hardware experimental results.

2 Proposed systematic approach to realise QO circuits A general scheme to realise sinusoidal QO circuits, consisting of a first-order low-pass filter (LPF) block and an integrator block, is shown in Fig. 1. 203

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Fig. 2 Symbolic notation of the CDBA

VX K1 = Vin s + (a − b)

(1)

The CDBA can be implemented in a number of ways; however, a popular realisation based on the use of two commercially available CFOAs [16] is shown here in Fig. 3. Fig. 4 shows the proposed general configuration to realise single-resistance-controlled-quadrature oscillator (SRCQO) circuits using two CDBAs. From a straightforward circuit analysis, the general transfer functions of the two blocks of the proposed configuration are found to be

VO K2 = VX s

(2)

VX (Y5 − Y3 ) = Vin (Y1 + 2Y6 + Y4 − Y2 )

(9)

VO Y9 − Y8 = VX Y10

(10)

Fig. 1 General realisation scheme for QOs

The voltage transfer functions of the first-order LPF T1(s) and integrator T2(s) are assumed to be of the type T1 (s) =

T2 (s) =

where K1 and K2 are the gain constants and (a 2 b) is the pole frequency of the LPF. The loop gain of the oscillator circuit can be expressed as VO K1 K2 = T1 (s) T2 (s) = Vin s[s + (a − b)]

(3)

The current in Y7 (which is VxY7) adds up to ip and since (ip 2 in) constitutes iz that also has one component of current same as VxY7; hence, it is obvious that Y7 will not appear in the expression for (VX/Vin) and is, thus, redundant.

There are two possibilities to obtain the desired type of characteristic equation of the QO circuit resulting from the above. Case 1: K1 is negative and K2 is positive. Case 2: K1 is positive and K2 is negative. In either of the above two cases, we obtain VO −K1 K2 = T1 (s) T2 (s) = 2 Vin [s + s(a − b)]

(4)

which gives the closed-loop characteristic equation as s2 + s(a − b) + K1 K2 = 0

(5)

Fig. 3 Implementation of CDBA using commercially available CFOAs

Therefore the CO is given by a=b

(6)

whereas, the FO is found to be  K1 K2 fO = 2p

(7)

(In the above equation, only magnitudes of K1 and K2 are considered).

3 Generation of various QO configurations using CDBAs The circuit symbol of the CDBA is shown in Fig. 2. The terminal characteristics of the CDBA are given by Vp = Vn = 0,

Iz = I p − In ,

VW = VZ

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(8)

Fig. 4 Proposed general configuration to realise SRCQO circuits a General configuration for realising the LPF b General configuration for realising the integrator IET Circuits Devices Syst., 2011, Vol. 5, Iss. 3, pp. 203 –211 doi: 10.1049/iet-cds.2010.0227

www.ietdl.org In the above, Y1 – Y6 have been chosen to realise the transfer function T1(s) ¼ (VX/Vin) ¼ (K1/s + (a 2 b)) whereas Y8 – Y10 have been chosen to derive the transfer function of either a positive or a negative integrator, that is, T2(s) ¼ (VO/ VX) ¼ (K2/s). Various LPF circuits realising T2(s) of (9) and integrator circuit T2(s) of (10), which yield the required kind of QOs are given in Table 1. The circuits resulting from the choices detailed in Table 1 are shown in Fig. 5. It may be mentioned that based on the proposed realisation scheme and general configuration of Fig. 4, a total of only 12

Table 1

circuits have been possible to be derived which are shown in Fig. 5. CO and FO of the 12 circuits are given in Table 2. From the last two columns of Table 2, it may be seen that in all the 12 circuits, the two resistances (e.g. R2 and R4 in QO circuit 1) appearing in the CO do not appear in the FO and the remaining two resistors that appear in the FO (e.g. R3 and R9 in QO circuit 1) are not appearing in the CO. Since this feature is available in all the 12 circuits, fully uncoupled independent control of CO and FO is available in all cases (e.g. CO by R2 or R4 and FO by R3 and/or R9 as in QO circuit 1).

Various LPF realising T1(s) of (9) and integrator T2(s) of (10), which yield the required QOs

LPF

Low pass filter circuits Y1

Y2

Y3

Y4

Y5

Y6

1

sC1

1 R2

1 R3

1 R4

0

0

2

sC1

1 R2

1 R3

0

0

3

sC1

1 R2

0

1 R4

4

sC1

1 R2

0

5

1 R1

1 R2

6

1 R1

7

Integrator circuits Y8

Y9

Y10

T2(s)

−1    1 1 1 C1 R3 s + − C1 R4 R2

0

1 R9

sC10

1 sC10 R9

1 R6

−1    1 2 1 C1 R3 s + − C1 R6 R2

0

1 R9

sC10

1 sC10 R9

1 R5

0

1    1 1 1 C1 R 5 s + − C1 R4 R2

1 R8

0

sC10

−1 sC10 R8

0

1 R5

1 R6

1    1 2 1 C1 R 5 s + − C1 R6 R2

1 R8

0

sC10

−1 sC10 R8

1 R3

sC4

0

0

−1    1 1 1 C4 R3 s + − C4 R1 R2

0

1 R9

sC10

1 sC10 R9

1 R2

0

sC4

1 R5

0

1    1 1 1 C4 R 5 s + − C4 R1 R2

1 R8

0

sC10

−1 sC10 R8

1 R1

1 R2

1 R3

0

0

sC6

−1    1 1 1 2C6 R3 s + − 2C6 R1 R2

0

1 R9

sC10

1 sC10 R9

8

1 R1

1 R2

0

0

1 R5

sC6

1    1 1 1 2C6 R5 s + − 2C6 R1 R2

1 R8

0

sC10

−1 sC10 R8

9

0

1 R2

1 R3

1 R4

0

sC6

−1    1 1 1 2C6 R3 s + − 2C6 R4 R2

0

1 R9

sC10

1 sC10 R9

10

0

1 R2

0

1 R4

1 R5

sC6

1    1 1 1 2C6 R5 s + − 2C6 R4 R2

1 R8

0

sC10

−1 sC10 R8

11

0

1 R2

1 R3

sC4

0

1 R6

−1    1 2 1 C4 R3 s + − C4 R6 R2

0

1 R9

sC10

1 sC10 R9

12

0

1 R2

0

sC4

1 R5

1 R6

1    1 2 1 C4 R 5 s + − C4 R6 R2

1 R8

0

sC10

−1 sC10 R8

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T1(s)

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Fig. 5 Various CDBA-based QO circuits

From the configurations of Fig. 5, the relationship between V01 and V02 can be expressed as V02 = +sC10 Rk V01

(11)

(where k ¼ 8 for oscillators 3, 4, 6, 8, 10, 12 and k ¼ 9 for oscillator 1, 2, 5, 7, 9, 11) which indicates that in all cases, V01 and V02 have a phase shift of F ¼ +908, that is, V01 and V02 are in quadrature. It may be mentioned that out of the 12 circuits generated here, only circuit 3 has been known earlier (as reported by Horng [13]); however, to the best of the authors’ knowledge, all the remaining circuits are new. It may also be mentioned that since the QOs derived here have no mechanism for automatic amplitude control, non-linear effects owing to the limited output dynamic swing of the CDBAs will limit the amplitude of oscillations; hence, the linear oscillation condition could be inaccurate and quadrature condition can worsen. Although this situation can be improved by incorporating an appropriate additional amplitude controlling circuitry; however, devising the required additional circuitry was considered to be outside the scope of the present work whose main object was to present a general method of deriving new CDBA-based QOs and therefore additional circuitry for amplitude control has not been attempted here. To demonstrate that the proposed approach is, indeed, general, we show in Appendix 1 how one can generate QO circuits using conventional op-amps and a new active 206 & The Institution of Engineering and Technology 2011

building block known as CDTA (current differencing transconductance amplifier) employing the presented approach. To the best of the authors’ knowledge, both the resulting circuits too are new. It is, thus, clear that one can apply the presented approach to derive new QO circuits employing a variety of other building blocks also.

4

Effects of CDBA non-idealities

A non-ideal CDBA can be described by the following terminal relationships: Vp = Vn = 0,

Iz = bp Ip − bn In ,

VW = a VZ

(12)

where bp ¼ 1 2 1p and 1p (|1p| ≪ 1) is the current tracking error from p-terminal to z-terminal, bn ¼ 1 2 1n and 1n (|1n| ≪ 1) is the current tracking error from n-terminal to z-terminal, and a ¼ 1 2 1v and 1v (|1v| ≪ 1) is the voltagetracking error from z-terminal to w-terminal of the CDBA. The results of the non-ideal analysis of the CDBA-based oscillator circuits of Fig. 5 taking non-ideal effects of CDBA into account are shown in Table 3. From the non-ideal expressions of the oscillation frequency, given in the last column of Table 3, the various sensitivity coefficients of the proposed circuits with respect to various active parameters and passive elements are found to be 0 ≤ |SXY | ≤

1 2

(13)

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www.ietdl.org Table 2 QO circuit

Details of the parameters of the various QO circuits CO [a ≤ b]

 K1 K2 2p

LPF

Integrator

K1

K2

a

b

1

LPF 1

NI

−1 C1 R3

1 C10 R9

1 C1 R4

1 C1 R2

R2 ≤ R4

1  2p C1 C10 R3 R9

2

LPF 2

NI

−1 C1 R3

1 C10 R9

2 C1 R6

1 C1 R2

2R2 ≤ R6

1  2p C1 C10 R3 R9

3

LPF 3

I

1 C1 R5

−1 C10 R8

1 C1 R4

1 C1 R2

R2 ≤ R4

1  2p C1 C10 R5 R8

4

LPF 4

I

1 C1 R5

−1 C10 R8

2 C1 R6

1 C1 R2

2R2 ≤ R6

1  2p C1 C10 R5 R8

5

LPF 5

NI

−1 C4 R3

1 C10 R9

1 C4 R1

1 C4 R2

R1 ≤ R2

1  2p C4 C10 R3 R9

6

LPF 6

I

1 C4 R5

−1 C10 R8

1 C4 R1

1 C4 R2

R2 ≤ R1

1  2p C4 C10 R5 R8

7

LPF 7

NI

−1 2C6 R3

1 C10 R9

1 2C6 R1

1 2C6 R2

R2 ≤ R1

1  2p 2C6 C10 R3 R9

8

LPF 8

I

1 2C6 R5

−1 C10 R8

1 2C6 R1

1 2C6 R2

R2 ≤ R1

1  2p 2C6 C10 R5 R8

9

LPF 9

NI

−1 2C6 R3

1 C10 R9

1 2C6 R4

1 2C6 R2

R2 ≤ R1

1  2p 2C6 C10 R3 R9

10

LPF 10

I

1 2C6 R5

−1 C10 R8

1 2C6 R4

1 2C6 R2

R2 ≤ R1

1  2p 2C6 C10 R5 R8

11

LPF 11

NI

−1 C4 R3

1 C10 R9

2 C4 R6

1 C4 R2

2R2 ≤ R6

1  2p C4 C10 R3 R9

12

LPF 12

I

1 C4 R5

−1 C10 R8

2 C4 R6

1 C4 R2

2R2 ≤ R6

1  2p C4 C10 R5 R8

FO

Notes: NI, non-inverting; I, inverting

where Y ¼ v0 and X represents any of the active parameters or passive parameters with respect to which the sensitivities have been evaluated. Thus, the proposed QO circuits enjoy very low passive and active sensitivities.

5 PSPICE simulation and experimental results 5.1

PSPICE simulation

To verify the theoretical results, all proposed CDBA-based SRCQO circuits of Fig. 5 have been simulated in PSPICE using macro model of commercially available AD844 ICs employed to construct the CDBAs as shown in Fig. 3 with supply voltages of +12 V. The results of all these circuits are summarised in Table 4. The difference between FOs determined from simulations and the corresponding theoretical value, as shown in Table 1, is attributed to the parasitic impedances of AD844. Using IET Circuits Devices Syst., 2011, Vol. 5, Iss. 3, pp. 203– 211 doi: 10.1049/iet-cds.2010.0227

PSPICE, the values of the parasitic elements and non-ideal gain parameters of CDBA (Fig. 9, Appendix 2) were determined that are found to be: Rp ¼ 50.13 V, Rn ¼ 50.13 V, R0 ¼ 12 V, Rz ¼ 2.999 MV, Cz ¼ 5.399 pF, b1 ¼ b2 ¼ 1, a1 ¼ 0.983 and a2 ¼ 0.984. Taking the above values and C1 ¼ C10 ¼ 100 pF, R2 ¼ 5 kV, R6 ¼ 11 kV, R5 ¼ 700 V, R8 ¼ 700 V for QO circuit 4 yields theoretically an oscillation of 2.028 MHz, whereas the oscillation frequency determined from simulation turns out to be 2.039 MHz that is seen to be closer to the theoretical value. A typical waveform generated by circuit 2 is shown here in Fig. 6a, which confirms the practical realisation of quadrature outputs. The output waveforms of the oscillator showing the build-up of the oscillations is shown in Fig. 6b, whereas, Fig. 6c represents the frequency spectrum of the outputs V01 and V02 . The total harmonic distortion (THD) of V01 and V02 were found to be 1.9 and 1.7%, respectively. From the simulation results, the phase shift between the two outputs has been found to be between 89.27 and 93.208. 207

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www.ietdl.org Table 3

Effects of CDBA non-idealities

QO circuit

Modified Characteristic equation 2

s C1 C10 R2 R3 R4 R9 + s a1 C10 R3 R9 (bn1 R2 − bp1 R4 )

1

+ a1 a2 bn1 bp2 R2 R4 = 0 s 2 C1 C10 R2 R3 R6 R9 + sC10 R3 R9 [(1 + bn1 )R2 − a1 bp1 R6 ]

2

+ a1 a2 bn1 bp2 R2 R6 = 0 s 2 C1 C10 R2 R4 R5 R8 + s a1 C10 R5 R8 (bn1 R2 − bp1 R4 )

3

+ a1 a2 bp1 bn2 R2 R4 = 0 s 2 C1 C10 R2 R5 R6 R8 + sC10 R5 R8 [(1 + bn1 )R2 − a1 bp1 R6 ]

4

+ a1 a2 bp1 bn2 R2 R6 = 0

CO

bn1 R2 ≤ bp1 R4

(1 + bn1 )R2 ≤ a1 bp1 R6

(1 + bn1 )R2 ≤ a1 bp1 R6

s 2 a1 bn1 C4 C10 R1 R2 R5 R8 + sC10 R5 R8 (R2 − a1 bP 1 R1 ) + a1 a2 bp1 bn2 R1 R2 = 0

6

s 2 (1 + bn1 )C6 C10 R1 R2 R5 R8 + sC10 R5 R8 [R2 − a1 bp1 R1 ]

s 2 (1 + bn1 )C6 C10 R2 R3 R4 R9 + s a1 C10 R3 R9 [bn1 R2 − bp1 R4 ] + a1 a2 bn1 bp2 R2 R4 = 0 s 2 (1 + bn1 )C6 C10 R2 R4 R5 R8 + s a1 C10 R5 R8 [bn1 R2 − bp1 R4 ]

10

+ a1 a2 bp1 bn2 R2 R4 = 0 s 2 C4 C10 R2 R3 R6 R9 + sC10 R3 R9 [(1 + bn1 )R2 − a1 bp1 R6 ]

11

+ a1 a2 bp2 bn1 R2 R6 = 0 s 2 a1 bn1 C4 C10 R2 R5 R6 R8 + sC10 R8 R5 [(1 + bn1 )R2 − a1 bp1 R6 ]

12

+ a1 a2 bp1 bn2 R2 R6 = 0

 a1 a2 bn1 bp1 1 2p (1 + bn1 )C6 C10 R5 R8

R2 ≤ a1 bp1 R1

+ a1 a2 bn1 bp1 R1 R2 = 0 9

 a1 a2 bn1 bp2 1 2p (1 + bn1 )C6 C10 R3 R9

R2 ≤ a1 bp1 R1

+ a1 a2 bn1 bp2 R1 R2 = 0 8

 a2 bp1 bn2 1 2p bn1 C4 C10 R5 R8

R2 ≤ a1 bP 1 R1

s 2 (1 + bn1 )C6 C10 R1 R2 R3 R9 + sC10 R3 R9 [R2 − a1 bp1 R1 ]

7

 1 a1 a2 bp1 bn2 2p C1 C10 R5 R8

 a2 bp2 1 2p C4 C10 R3 R9

R2 ≤ a1 bP 1 R1

+ a1 a2 bn1 bp2 R1 R2 = 0

 1 a1 a2 bn1 bp2 2p C1 C10 R3 R9

 1 a1 a2 bp1 bn2 2p C1 C10 R5 R8

bn1 R2 ≤ bp1 R4

s 2 a1 bn1 C4 C10 R1 R2 R3 R9 + sC10 R3 R9 (R2 − a1 bP 1 R1 )

5

FO

 1 a1 a2 bn1 bp2 2p C1 C10 R3 R9

 a1 a2 bn1 bp2 1 2p (1 + bn1 )C6 C10 R3 R9

bn1 R2 ≤ bp1 R4

 a1 a2 bp1 bn2 1 2p (1 + bn1 )C6 C10 R5 R8

bn1 R2 ≤ bp1 R4

(1 + bn1 )R2 ≤ a1 bp1 R6

(1 + bn1 )R2 ≤ a1 bp1 R6

 1 a1 a2 bn1 bp2 2p C4 C10 R3 R9

 a2 bp1 bn2 1 2p bn1 C4 C10 R5 R8

Notes: bpi , bni and ai are the parameters bp , bn and a of the ith CDBA (i ¼ 1, 2), respectively

Table 4

Details of PSPICE simulation results for the circuits of Fig. 5, all designed to generator f0 ¼ 2.26 MHz

Oscillator circuit

01 02 03 04 05 06 07 08 09 10 11 12

Components used and their values

Frequency

C1 ¼ C10 ¼ 100 pF, R2 ¼ 4 K, R4 ¼ 5 K, R3 ¼ 700 V, R9 ¼ 700 V C1 ¼ C10 ¼ 100 pF, R2 ¼ 5 K, R6 ¼ 11 K, R3 ¼ 700 V, R9 ¼ 700 V C1¼ C10 ¼ 100 pF, R2 ¼ 4 K, R4 ¼ 5 K, R5 ¼ 700 V, R8 ¼ 700 V C1 ¼ C10 ¼ 100 pF, R2 ¼ 5 K, R6 ¼ 11 K, R5 ¼ 700 V, R8 ¼ 700 V C4 ¼ C10 ¼ 100 pF, R2 ¼ 4 K, R1 ¼ 5 K, R3 ¼ 700 V, R9 ¼ 700 V C4 ¼ C10 ¼ 100 pF, R2 ¼ 4 K, R1 ¼ 5 K, R5 ¼ 700 V, R8 ¼ 700 V C6 ¼ C10 ¼ 100 pF, R2 ¼ 4 K, R1 ¼ 5 K, R3 ¼ 350 V, R9 ¼ 700 V C6 ¼ C10 ¼ 100 pF, R1 ¼ 5 K, R2 ¼ 4 K, R5 ¼ 700 V, R8 ¼ 350 V C6 ¼ C10 ¼ 100 pF, R4 ¼ 5 K, R2 ¼ 4 K, R3 ¼ 350 V, R9 ¼ 700 V C6 ¼ C10 ¼ 100 pF, R4 ¼ 5 K, R2 ¼ 4 K, R5 ¼ 700 V, R8 ¼ 350 V C4 ¼ C10 ¼ 100 pF, R2 ¼ 4 K, R6 ¼ 8 K, R3 ¼ 700 V, R9 ¼ 700 V C4 ¼ C10 ¼ 100 pF, R2 ¼ 4 K, R6 ¼ 8 K, R5 ¼ 700 V, R8 ¼ 700 V

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THD, %

Simulated, MHz

V01

V02

2.03 2.04 2.02 2.02 2.03 2.00 2.03 1.97 2.04 1.97 2.05 2.00

1.8 1.9 2.0 1.5 1.8 2.4 1.7 1.7 1.7 1.4 1.2 0.8

1.7 1.7 1.6 1.9 1.7 2.4 1.9 4.1 1.9 4.3 1.5 1.4

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Fig. 6 PSPICE simulation results of the proposed oscillator circuit 2 a Steady-state output waveforms b Transient waveforms c Output spectrum

Fig. 7 Experimental results of oscillator circuit 4 a Typical wave form ( fO ¼ 1.64 MHz) b Variation of fO with respect to R5

5.2 Hardware implementation and experimental results All the derived oscillator circuits have also been checked through hardware implementation of CDBAs using IET Circuits Devices Syst., 2011, Vol. 5, Iss. 3, pp. 203– 211 doi: 10.1049/iet-cds.2010.0227

commercially available AD844 CFOAs and have been found to work satisfactorily. However, to conserve space, we present here, a typical waveform generated by QO circuit 4 in Fig. 7a, whereas the experimentally observed variation of frequency as a 209

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www.ietdl.org function of the controlling resistance R5 is shown in Fig. 7b. These results confirm the practical validity of the proposed QO circuits.

10 11

6

Concluding remarks

A systematic approach of synthesising SRCQOs has been presented that has been shown to yield a family of 12 QO circuits using CDBAs. The workability of the proposed circuits has been verified by PSPICE simulation results along with hardware experimental results. The attractive features of the QO circuits derived here are: (i) employment of a minimum possible number of passive components without requiring any component matching; (ii) very low active and passive sensitivities; (iii) low harmonic distortion; (iv) fully uncoupled controls of CO and FO through separate resistors and (v) the use of only grounded/virtual grounded resistors and capacitors as preferable from integrated circuit implementation point of view. Lastly, it must be mentioned that since the CBDA is not yet commercially available, it has been implemented by commercially available CFOAs (AD844 from Analog Devices Inc.) because the CDBA implementation using CFOAs requires the use of Z-terminals of the CFOAs and AD844 appears to be the only choice (since most of the other CFOAs from other manufacturers such as CLC-400/401 from National Semiconductors and MAX 4223-4228 from MAX corporation do not provide this Z-terminal as an externally accessible pin). Although, this is a limitation of the proposed circuits at present, once CDBA becomes commercially available as an off-the-shelf IC, the same can be used directly to implement the proposed QO circuits.

12 13

14 15

16

9

differencing buffered amplifier’, Microelectron. J., 2000, 31, (3), pp. 169–174 Keskin, A.U., Aydin, C., Hancioglu, E., Acar, C.: ‘Quadrature oscillator using CDBA’, Frequenz, 2005, 60, (3– 4), pp. 21–23 Tangsrirat, W., Pukkalanun, T., Surakampontorn, W.: ‘CDBA-based universal biquad filter and quadrature oscillator’, Act. Passive Electron. Compon., 2007, 2008, Article ID 24171, p. 6 Tangsrirat, W., Pisitchalermpong, S.: ‘CDBA-based quadrature sinusoidal oscillator’, Frequenz, 2007, 61, (3–4), pp. 102–104 Horng, J.W.: ‘CDBA-based single resistance controlled quadrature oscillator employing grounded capacitors’, IEICE Trans. Fundam. Electron. Commun. Comput. Sci., 2002, E-85A, (6), pp. 1416– 1419 Maheshwari, S., Khan, I.A.: ‘Novel single resistance controlled quadrature oscillator using two CDBAs’, J. Act. Passive Electron. Devices, 2007, 2, pp. 137–142 Tangsrirat, W., Preasertsom, D., Piyatat, T., Surakampontom, W.: ‘Single resistance controlled quadrature oscillator using current differencing buffered amplifiers’, Int. J. Electron., 2008, 95, (11), pp. 1119– 1126 Salama, K.N., Soliman, A.M.: ‘Voltage mode Kerwin– Huelsman– Newcomb circuit using CDBAs’, Frequenz – J. Telecommun., 2000, 54, (3–4), pp. 90– 93

Appendix 1

9.1 Derivation of exemplary op-amp-based and CDTA-based QOs using the proposed general approach Here, we show that by implementing the required sub-circuits of the scheme of Fig. 1 by appropriate implementations using different active elements, other QO circuits can be obtained. Fig. 8 shows two such exemplary circuits using op-amps and CDTAs, respectively. For circuit 1, the voltage transfer function of the first-order LPF T1(s) and integrator T2(s) are of type T1 (s) =

7

(14)

VO K2 = VX s

(15)

Acknowledgments

The first author (JKP) is very grateful to ITM, Gurgaon for their support and encouragement. This research work was performed partly at ITM, Gurgaon and partly at Analog Signal Processing Research Laboratory, NSIT, New Delhi. The authors wish to thank the anonymous reviewers for their thoughtful comments and constructive feedback.

8

VX K1 = Vin s + (a − b)

T2 (s) =

References

1 Horowitz, P., Hill, W.: ‘The art of electronics’ (Cambridge University Press, Cambridge, UK, 1991) 2 Tietze, U., Schnek, C.K.: ‘Electronics circuits: design and applications’ (Springer, Berlin, Germany, 1991), pp. 795– 796 3 Holzel, R.: ‘A simple wide band sine wave quadrature oscillator’, IEEE Trans. Instrum. Meas., 1993, 42, pp. 758–760 4 Khan, I.A., Khwaja, S.: ‘An integrable gm-C quadrature oscillator’, Int. J. Electron., 1997, 83, (2), pp. 201–207 5 Comer, D.J.: ‘The utility of all pass filters’, IEEE Trans. Instrum. Meas., 1979, IM-28, (2), pp. 164– 167 6 Ahmed, M.T., Khan, I.A., Minhaj, N.: ‘On transconductance-C quadrature oscillators’, IEEE Trans. Instrum. Meas., 1991, 40, (4), pp. 777–779 7 Acar, C., Ozoguz, S.: ‘A new versatile building block: current differencing buffered amplifier suitable for analog signal processing filters’, Microelectron. J., 1999, 30, (2), pp. 157 –160 8 O¨zoguz, S., Toker, A., Acar, C.: ‘Current-mode continuous-time fullyintegrated universal filter using CDBAs’, Electron. Lett., 1999, 35, (2), pp. 97–98 9 Ozcan, S., Toker, A., Acar, C., Kuntman, H., Cicekoglu, O.: ‘Single resistance controlled sinusoidal oscillators employing current 210 & The Institution of Engineering and Technology 2011

Fig. 8 New op-amp-based and CDTA-based QOs using the proposed general approach IET Circuits Devices Syst., 2011, Vol. 5, Iss. 3, pp. 203 –211 doi: 10.1049/iet-cds.2010.0227

www.ietdl.org where −1 K1 = C1 R1 (1 − a)

a=

1 C1 R2 (1 − a)

a(R1 + R2 ) b= C1 R1 R2 (1 − a) 2 K2 = C2 R

a=

R4 R3 + R4

(17)

(20)

(21)

b=

R2 R3 R1 R2 + R1 R3 + R2 R3

(31)

g=

R1 R2 R1 R2 + R1 R3 + R2 R3

(32)

Using (27), (28), (30) – (32), CO is given by

(23)

(24)

IO K 2 = IX s

(25)

−gm1 g C1

(26)

a=

gm1 b C1

(27)

b=

gm1 a C1

(28)

(33)

whereas FO is found to be 1 fO = 2p

(22)

IX K1 = Iin s + (a − b)

T2 (s) =

(30)

R1 = R2 = R(say)

It may be noted that FO is independently controllable by R whereas CO is independently controllable by R2 . For circuit 2, the current transfer function of the first-order LPF T1(s) and integrator T2(s) are of type T1 (s) =

R1 R3 R1 R2 + R1 R3 + R2 R3

(19)

whereas, the FO is given by

 1 2(R3 + R4 ) fO = 2p C1 C2 RR1 R3

a=

(18)

Using (17), (18) and (21), CO is found to be R1 R3 = R2 R4

(29)

(16)

For CO a=b

gm2 C2

K2 =

 gm1 gm2 R C1 C2 (R + 2R3 )

(34)

Note that in this circuit the CO can be adjusted without affecting FO, by R1 and/or R2 while FO is independently adjustable through gm1 and/or gm2 (electronically by external DC bias currents used to set gm1 and/or gm2).

10

Appendix 2

The various parasitic impedances of a non-ideal CDBA can be represented as shown in the non-ideal CBDA model of Fig. 9.

where K1 =

IET Circuits Devices Syst., 2011, Vol. 5, Iss. 3, pp. 203– 211 doi: 10.1049/iet-cds.2010.0227

Fig. 9 Non-ideal CDBA showing various parasitic components

211

& The Institution of Engineering and Technology 2011