New Compact VM Four-Phase Oscillator Employing Only Single Z-Copy VDTA and All Grounded Passive Elements

1Abstract—In this paper, a new compact voltage-mode fourphase oscillator employing single z-copy voltage differencing transconductance amplifier (ZC-VDTA) and only grounded passive elements is introduced. The use of only grounded capacitors and resistors makes the proposed circuit ideal for integrated circuit implementation. The condition of oscillation and the frequency of oscillation are independently adjustable. The passive and active sensitivities of the proposed circuit configuration are low. Experimental measurement results using readily available Maxim Integrated ICs MAX435 are given to prove the theory.


I. INTRODUCTION
Sinusoidal oscillators are linear electric circuits that are used in wide area of electronics and represent an important unit in many radio receivers, telecommunication, instrumentation, control and data monitoring systems [1]- [3].Recently the voltage-mode (VM) four-phase oscillators, which are special type of multiphase oscillators, have received considerable attention in the literature [4]- [13].In Table I the available circuits are listed and compared based on relevant criterions.The given survey shows that these oscillator structures are based on operational amplifiers (Op-Amps) [4], [7], differential difference current conveyors (DDCCs) [5], second-generation current conveyors (CCIIs) [6], [8], [9], differential output-current inverter buffered amplifier (DO-CIBA) [10], voltage differencing inverting buffered amplifiers (VDIBAs) [12], or dual-output controlled gain current follower buffered amplifiers (DO- CG-CFBAs) and current amplifier (CA) [13].In addition, the Complementary Metal-Oxide-Semiconductor (CMOS)-RC based oscillators are recently also popular [11].Considering the number of active elements in above mentioned VM four-phase oscillators it can be seen that at least two active building blocks (ABBs) are required for their realization.However, our detailed study showed that used ABBs in [10] and [12] represent an interconnection of two sub-circuits such as current inverter and differential output buffered amplifier in case of [10] or operational transconductance amplifier (OTA) [14] and unity-gain inverting voltage buffer in [12].It should be also mentioned that in [5] and [7] additional voltage followers/inverters are needed.Hence, in these circuits excessive number of ABBs is used.From the monolithic integration point of view, circuits that employ only grounded passive elements are attractive.Only circuits in [6], [8], and [9] satisfy this crucial criterion.However, the oscillator in [8] employs one additional capacitor (in total three) that significantly increases the chip area in case of integration.
In 2008, set of new ABB concepts have been introduced [14] from them recently probably the voltage differencing transconductance amplifier (VDTA) received the most of attention [15]- [19].The VDTA belongs to new group of ABBs so-called 'voltage differencing' elements and it is a 'voltage' counterpart of the well-know current differencing transconductance amplifier (CDTA) [14].
In this paper, to increase the universality of the conventional VDTA, the "z-current copy" technique is with advantage used, which was previously introduced for other circuit concepts [14].In [15]- [19] VDTA-based VM and current-mode (CM) second-and four-order filters, lossless grounded & floating inductance simulators, and CM quadrature oscillators were published.Based on CM concept from [19], this paper presents the first VM four-phase quadrature oscillator using VDTA in the literature and its practical realization including amplitude gain control (AGC) circuit.The proposed circuit employs only single z-copy VDTA.Hence, the number of ABBs against [4]- [13] The proposed realization of VM four-phase oscillator employing single ZC-VDTA, two capacitors, and three resistors, all in grounded form, is shown in Fig. 2. Using (1), routine circuit analysis yields the following characteristic equation (CE).  From (2) the condition of oscillation (CO) and the frequency of oscillation (FO) can be evaluated as: From ( 3) and ( 4) it is clear that the CO can be controlled independently of FO by means of varying the resistor R1 and the FO can be adjusted by the transconductance gm2, respectively.Thus, the proposed oscillator is an SRCO and provides independent control of the CO and the FO.

III. NON-IDEAL ANALYSIS
For a complete analysis, it is important to take into account parasitics of active element shown in Fig. 3: Furthermore, it must be also mentioned that in the same node the parasitic resistances Rv-and Rx+ are also in shunt and in further analysis labeled as Rvx. At nodes 3, 4 the parasitic resistances Rzc-, Rx-are absorbed into external resistors R2 and R3, respectively, as they appear in shunt with them and labeled as R2 and R3.Thus, the non-ideal effects of parasitic impedance at 1 st , 3 rd , and 4 th nodes of the proposed oscillator are reduced, if not completely eliminated.At the node 2 the parasitic capacitance can also be absorbed in the external capacitor, but the presence of parasitic resistance Rvx at this node would change the type of the impedance, which should be of a purely capacitive character.A possible solution is to make the operating frequency f0 > 1/(2RvxC2).Taking into account the aforementioned non-idealities, except for the parasitic capacitances Czc-and Cx-, the CE in (2) becomes which by neglecting the parasitic resistance Rvx turns to a form that only by non-ideal transconductance gains 1 and 1 differs from the ideal CE in (2) and subsequently from the ideal CO and FO in (3) and ( 4).Hence, in practice a precise design of the ZC-VDTA should be considered to alleviate the non-ideal effects.

IV. MEASUREMENT RESULTS
In order to confirm the theoretical study, the behavior of the proposed VM four-phase oscillator has been verified by experimental measurements.The complete circuit configuration of the proposed oscillator supplemented by AGC circuit including specific values of passive elements is shown in Fig. 4. In measurements the ZC-VDTA was implemented using commercially available ICs MAX435 by Maxim Integrated.The DC power supply voltages were equal to ±5 V. Generated voltages in all nodes are available through additional voltage buffers.For this purpose operational amplifier LT1364 was used.The AGC circuit contains cascade diode doubler and BS250 FET transistor.Experimental measurements were carried out using RIGOL DS1204B four-channel oscilloscope and HP4395A network-spectrum analyzer.The spectrum analyzer requires impedance matching (50 ).Therefore, the voltage buffers LT1364 have been very important.
Measurement results are shown in Fig. 5-Fig.7. Figure 5 shows all four transient responses together.Experimentally measured oscillation frequency was f0  4 MHz, which matches well with theory.The frequency spectrum for Vo2 is depicted in Fig. 6.THD value obtained from measurements for output amplitudes Vo2 at f0  4 MHz was 0.58 %.Tunability of f0 via gm2 and output voltage levels and THD vs. f0 during the tuning process are shown in Fig. 7. Ideal frequency range of FO tuning was calculated from 2.18 to 14.49 MHz.However, this calculation does not take into account the main real features of active elements used.Therefore, expected range of FO = {1.65 -11} MHz was obtained by more accurate calculation, which includes mainly parasitic capacitances and low values of resistance in high-impedance nodes (outputs of MAX435).Measured frequency range corresponds with expected calculations, since FO was in range from 1.36 MHz-10 MHz.Adjustment of FO was realized by changes of transconductance gm2 from 0.4 mA/V to 18.3 mA/V.For Vo1,3 output amplitudes reached values from 0.5 V to 1 V and for Vo2,4 from 1.1 V to 2.2 V, respectively.THD values fluctuate between 0.4 %-1.4 % and 2.3 %-3.1 % for outputs Vo1,3 and Vo2,4, respectively.In addition, the amplitude of Vo1,3 are almost unchangeable in range from 1.36 MHz to 7 MHz.In overall, obtained results match very well with theory.

V. CONCLUSIONS
This paper presented a new compact voltage-mode fourphase oscillator employing recently introduced single z-copy voltage differencing transconductance amplifier and only grounded passive elements.The use of only grounded capacitors and resistors makes the proposed circuit ideal for integrated circuit implementation.The condition of oscillation and the frequency of oscillation are independently adjustable.Experimental results using commercially available integrated circuits confirm the feasibility of the proposed circuit.
Fig. 1.(a) Circuit symbol and (b) behavioral model of ZC-VDTA.II.CIRCUIT DESCRIPTION The circuit symbol and behavioral model of ZC-VDTA are shown in Fig. 1(a) and Fig. 1(b), respectively.The ZC-VDTA essentially consists of two balanced-output OTAs, wherein the difference of input voltages Vv+ and Vv-is transferred by the first transconductance gain gm1 to current at the terminals z and zc-(negative of z) and the voltage drop at the terminal z is transferred to current at the terminals x+ and x-(negative of x+) by second transconductance gain gm2.In practice both transconductances gm1,2 can be simultaneously electronically controlled by either external DC bias currents or voltages.All six terminals exhibit high-impedance values.Using standard notation, the terminals relationship of an ideal ZC-VDTA can be characterized by the following hybrid matrix
2gm2Vz, where Vd = (Vv+ -Vv-), i and i represent transconductance gains of the ZC-VDTA that differ from their ideal values by transconductance tracking errors 1i and 2i (|1i|, |2i| « 1), where i = 1, 2.  The parasitic resistances Rv+, Rv-and parasitic capacitances Cv+, Cv-appear between the high-impedance v+ and v-input terminals of the ZC-VDTA and ground, respectively, and their typical values in case of ZC-VDTA implementation by Maxim Integrated ICs MAX435 are 800 k ǁ 5 pF. The parasitic resistances Rz, Rzc-and parasitic capacitances Cz, Czc-appear between the high-impedance z and zc-auxiliary terminals of the ZC-VDTA and ground, k ǁ 10 pF and 3.5 k ǁ 5 pF, respectively. The parasitic resistances Rx+, Rx-and parasitic capacitances Cx+, Cx-appear between the high-impedance x+ and x-output terminals of the ZC-VDTA and ground, respectively, and their typical values are 3.5 k ǁ 5 pF.Considering the effect of aforementioned non-idealities on the proposed oscillator shown in Fig. 2, the following useful analysis can be provided:  At the node 1 the parasitic resistances Rv+, Rz and capacitances Cv+, Cz are absorbed into external resistor R1 and capacitor C1, respectively, as they appear in shunt with them and in analysis below they are labeled as R1 and C1. At the node 2 the parasitic capacitances Cv-and Cx+ are absorbed into external capacitor C2 as it appears in shunt with them and in further analysis it is labeled as C2.
Manuscript received January 30, 2013; accepted May 21, 2013.Ing.Norbert Herencsar, Ph.D. was supported by the project CZ.1.07/2.3.00/30.0039 of Brno University of Technology.Research described in this paper was also in part supported by the project SIX CZ.1.05/2.1.00/03.0072from the operational program Research and is reduced.Moreover, it employs only grounded capacitors and New Compact VM Four-Phase Oscillator Employing Only Single Z-Copy VDTA and All Grounded Passive Elements N. Herencsar 1 , R. Sotner 2 , J. Koton 1 , J. Misurec 1 , K. Vrba 1resistors that make the circuit ideal for integrated circuit implementation.Experimental measurement results on frequency of oscillation equal to 4 MHz with satisfactory total harmonic distortion are included to support the theory.