Novel current-mode quadrature oscillators with explicit-current-outputs using CCCDTA Abhirup Lahiri 1 , Abhinav Misra 2 , Kinshuk Gupta 3 1

2 3

Department of Electronics and Communications, Netaji Subhas Institute of Technology, University of Delhi, New Delhi, India. Department of Electronics and Communication Engineering, University Institute of Engineering and Technology, Panjab University, Chandigarh, India. [email protected], [email protected], [email protected]

Abstract. The paper presents novel current-mode (CM) quadrature oscillators (QOs) created using the recently proposed active building block (ABB), namely the current controlled current differencing transconductance amplifier (CCCDTA). Two circuits have been proposed and both of them employ minimum components, namely one multipleoutput CCCDTA (MO-CCCDTA) and two grounded capacitors. One of the proposed circuits is suitable to be used as a very low frequency oscillator (VLFO) and the other circuit provides non-interactive CO and FO control and could be used as a variable frequency oscillator (VFO). Both the circuits provide explicit quadrature current outputs. Non-ideal analysis, sensitivity study are provided and PSPICE simulations have been included which verify the workability of the circuit.

Keywords Current-mode (CM), active building block (ABB), multiple-output current controlled current differencing transconductance amplifier (MO-CCCDTA).

1. Introduction In the last decade, current-mode (CM) active building blocks (ABBs) have received considerable attention owing to their higher bandwidth, larger dynamic range and low power consumption. The most recent addition to the list of CM ABBs is the current controlled current differencing transconductance amplifier (CCCDTA), first proposed in [1] by Siripruchyanun and Jaikla. Although recently proposed, it has been found to be versatile for CM signal processing and its use has reportedly provided several circuit solutions [2]-[9]. In this paper it is used to create CM quadrature oscillators (QOs). QOs are important for communications systems wherein there is a requirement of multiple sinusoids which are 90◦ phase shifted [10], e.g. quadrature mixers and single single-sideband modulators [11]-[12].

Several QOs using CCCDTAs have been reported in the literature [4]-[6]. An oscillator circuit providing explicit current outputs ECOs can be truly classified as a CM oscillator. Although the authors in [4]-[6] argue that their proposed circuits are CM QOs, but the availability of explicit current outputs (ECOs) had not been investigated. A problem which, however, requires more attention is the output currents flowing into working impedances. In Fig. 3 of [4], the quadrature currents Io1 and Io2 flow through the working capacitor C1 and C2 , respectively and are not available explicitly. The current Io2 can be sensed if the CCCDTA is modified to have a copy of z1 terminal but providing Io1 as an ECO is not very direct and it cannot be directly sensed for explicit utilization without disturbing the circuit parameters. A common method is to reconstruct all the currents that add up to give Io1 . This method has been dealt in detail in [13] and requires copies of all the currents (through z1 , z2 , x1 and x2 terminals) which shall add up to give the desired explicit current output. Using this method Io1 could be made available explicitly, but the error in creating it depends on the concordance rate and the parasitic current gains associated with the copies of the currents. In this paper, two novel realizations of QOs using CCCDTA have been proposed and have the following advantageous features: (i) The circuits easily provide ECOs by means of either z or x copy terminals and no addition/subtraction of the currents is required to generate the ECOs. (ii) One of the proposed circuits can generate low frequency sinusoids and hence, is suitable to be used as a very low frequency oscillator (VLFO). No CCCDTA based VLFO has been reported till date. (iii) The second proposed QO provides noninteractive/independent control of condition of oscillation (CO) and frequency of oscillation (FO) and hence, is suitable to be used as a variable frequency oscillator (VFO). (iv) Both the QOs are ”resistor-less” and employ minimum components, namely one multiple-output CCCDTA (MO-CCCDTA) and two grounded capacitors. The use of grounded capacitors further makes the circuit suitable for monolithic integration as grounded capacitor circuits

can compensate for the stray capacitances at their nodes [14]-[15].

2. Proposed Circuits A multiple-output CCCDTA (MO-CCCDTA) with multiple z and x terminals, has been used to create the QO. The characterizing equation of this ABB is given as      Ip Rp 0 0 0 0 Vp            Vn   0 Rn 0 0 0   In             Iz , Izc  =  1 −1 0 0 0   Vx 1             Ix1   0 0 0 0 gm1   Vx2       Vz 0 0 0 0 gm2 Ix2 (1) IB2 IB3 T where Rp = Rn = 2IVB1 and gm1 = 2V and g = . m 2 2V T T IB1 ,IB2 and IB3 are the DC bias currents and VT is the thermal voltage whose value is approximately 26mV at 27◦ C. The detailed bipolar implementation of CCCDTA could be found in [1]-[2] and MOSFET implementation could be found in [6].

2.1 QO with ECOs The CCCDTA based QO with both the quadrature currents available for direct utilization, is shown in Fig. 1. Using (1) and doing routine circuit analysis yields the following characteristic equation s2 (C1 C2 Rp ) + s(C2 − C1 gm1 Rp ) + gm2 − gm1 = 0 (2)

(3)

and frequency of oscillation (FO) is s 1 gm2 − gm1 fo = 2π C1 C2 Rp

Clearly, for k1 = k2 = 1 the quadrature currents have equal amplitudes.

2.2 QO with non-interactive CO and FO control The circuit in Fig. 1 does not offer an independent CO control, since all the terms in the CO are also present in the FO. However, with a simple modification in the circuit, non-interactive/independent CO and FO control could be achieved. The modified circuit is shown in Fig. 2 and the CO and the FO for this circuit are given as CO : FO :

Hence, the required condition for oscillation (CO) is C1 = C2 gm1 Rp

Figure 1: The proposed QO with ECOs

(4)

C1 = C2 gm1 Rp fo =

1 2π

r

gm2 C1 C2 Rp

k1 =

where

ωo C1 k2 = gm2

and Io1 = jk2 Io3

ωo C1 gm1

where

(5)

(6)

(8)

It is evident from (5) and (6), that gm2 term does not appear in CO and gm1 does not appear in FO and thus, CO and FO could be independently controlled by bias currents IB2 and IB3 , respectively. The circuit provides ECOs, which are also related according to (5) and (6).

It is evident from (3) and (4) that both the CO and the FO are bias current controllable. Since, gm2 term does not appear in CO, therefore the FO can be independently controlled by the bias currents IB3 . A unique feature in this circuit is that a difference term is present in the numerator of the FO. This makes the circuit suitable for producing very low frequency sinusoidal waves and hence, it could be used as a very low frequency oscillator (VLFO) [14]. Care, however, should be taken such that IB2 > IB3 . The explicit quadrature current outputs have been marked in the circuit diagram (Fig. 1) and are related as Io1 = jk1 Io2

(7)

Figure 2: The proposed QO with independent CO and FO control

2.3 Non-Ideal analysis For a complete analysis of the circuit, it is necessary to take into account the following non-idealities of MOCCCDTA, 1. Iz = αp Ip − αn In , Izc = βIz , Ix0 (−) Ix (−) = 1 = gm1 Vz , Ix1 (+) = 1 γ1 γ2 Ix (−) Ix2 (+) = 2 = gm2 Vz (9) γ3 where αp , αn and β are the parasitic current transfer gains from p, n and zc terminals to z terminal, respectively. γ1 , γ2 and γ3 are the parasitic current gains associated with copies of the currents from x1 and x2 terminals. All these gains slightly differ from their ideal values of unity by current tracking errors. 2. The parasitic resistances and capacitances appear between the high-impedance z, x1 and x2 terminals of the CCCDTA and ground. The stray/parasitic capacitance at terminal z and x2 (−) can be absorbed into the external grounded capacitors as they appear in shunt with them. But, the parasitic resistances appearing at terminal z and x2 (−) would change the type of the impedance which should be of a purely capacitive character. A good design of CCCDTA should be considered to alleviate the non-ideal effects of the parasitic impedances.

Hence, fo active and passive sensitivities are less than unity and the circuit exhibits good sensitivity performance.

3. Simulation Results The proposed oscillator circuits are simulated in PSPICE using the bipolar implementation of MO-CCCDTA as provided in [2]. The process parameters for the PR100N and NR100N bipolar transistors of ALA400 transistor array from AT & T [16] have been used with ±2.5V voltage supply. The QO shown in Fig. 2 is taken as the design example and has been designed with C1 = C2 = 1nF and with the following bias currents values: IB1 = 25uA, IB2 = 100uA and IB3 = 100uA. The time domain waveforms of quadrature currents Io1 , Io2 and Io3 , in steady-state is shown in Fig. 4. The variation of the FO with the bias current IB3 is shown in Fig. 5 and simulated values have close correspondence with theoretical values. The FO is found to vary from 95KHz at IB3 = 10µA to 939KHz at IB3 = 1000µA, which shows a ten fold variation in FO for a two decade variation in IB3 . The measured total harmonic distortion (THD) at both the outputs are smaller than 3% . Due to the non-availability of the required resources, the experimental results could not be carried out. However, it is expected that the experimental results would agree well with the theoretical and simulated results.

Considering the first non-ideal effect, the CO and FO for the QO shown in Fig. 2, get modified to

FO :

CO : C1 = C2 αn γ1 gm1 Rp (10) s 1 αp γ3 gm2 + gm1 (αp γ2 − αn γ1 ) fo = (11) 2π C1 C2 Rp

It is evident from (10) and (11) that both CO and FO are affected by the non-idealities. With a more careful design of the CCCDTA such that αp = αn and γ1 = γ2 , the CO and FO can be approximated as CO :

C1 = C2 αn γ1 gm1 Rp

FO :

1 fo = 2π

and

r

αp γ3 gm2 C1 C2 Rp

(12)

(13)

and then independent control of CO and FO via bias currents IB2 and IB3 could be achieved as before in the ideal case. It should also be noted that although, the FO would vary with the change in operating temperature, but this, however, should not be considered as a drawback, as the designer has an electronic control over the FO through the bias current. Using (13) as the final result for the oscillation frequency, the sensitivity study indicates that fo |SR p ,gm

2 ,C1 ,C2 ,αp ,γ3

|=

1 2

Figure 3: Time Domain Waveforms of Quadrature Currents

(14)

4. Conclusions Two new current-mode sinusoidal oscillators using multiple-output current controlled current differencing transconductance amplifier (MO-CCCDTA) have been proposed. No external resistors are used and employment of two grounded capacitors makes the circuit suitable for monolithic integration. One of the circuits is suitable for producing low frequency waves and the other circuit enjoys non-interactive control of condition of oscillation (CO) and frequency of oscillation (FO) by means of bias currents. Both the circuits provide explicit quadrature current outputs and hence, are true current-mode oscillators.

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[10] LAHIRI, A. Novel voltage/current-mode quadrature oscillator using current differencing transconductance amplifier. Analog Integrated Circuts and Signal Processing, doi: 10.1007/s10470-009-9291-0

Theoretical Simulated

Frequency (Khz)

[11] HOROWITZ, P., HILL, W. The Art of Electronics. Cambridge University Press, U.K. [12] KHAN, I.A., KHAWAJA, S. An integrable gm-C quadrature oscillator. International Journal of Electronics, 2000, vol. 87, no. 1, pp. 1353-1357.

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[13] BIOLEK, D., SENANI, R., BIOLKOVA, V., KOLKA, V., Active Elements for Analog Signal Processing: Classification, Review, and New Proposals. Radioengineeing, 2008, vol. 17, no. 4, pp. 15-32. 1

10 1 10

2

10 Bias Current Ib3 (uA)

Figure 4: Variation of FO with bias current IB3

The workability of the circuits has been verified by PSPICE simulations.

5. Acknowledgement The authors would like to thank Prof. Raj Senani, the Director, Netaji Subhas Institute of Technology and Prof. Renu Vig, University Institute of Engineering and Technology, Panjab University for their support and guidance.

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