# Second-order simple multiphase oscillator using z-copy controlled-gain voltage differencing current conveyor.

I. INTRODUCTIONApplications of more than one type of controllable parameter in frame of one active device have increasing attention of many researchers. Several interesting solutions of active element with these features were reported in literature. For example, Minaei et al. [1], Marcellis et al. [2], Kumngern et al. [3] and others presented interesting conceptions. Extended version of the current conveyor introduced in [1] allows adjustable current gain (B) between x and z terminals and adjustable intrinsic resistance ([R.sub.x]) of the current input terminal x. Modified current conveyor introduced in [2] disposes controllable features of current gain between x and z terminals and voltage gain between y and x terminals. Combination of [R.sub.x] and B control is available in interesting version of translinear current conveyor [3]. Typical examples of active elements with two-parameter control are also modifications of the current differencing transconductance amplifier (CDTA) [4], [5]. DC bias currents are also used for control of [R.sub.x] and transconductance [g.sub.m] [6], [7]. Transconductance section [4], [8] combined with current conveyor of second generation [4], [9], [10] are common subparts in so-called current conveyor transconductance amplifier (CCTA) [4], [11], where independent [R.sub.x] and [g.sub.m] control is also possible [12]. Some modifications of CCTA provide also adjustable current gain control [13].

Active element presented in this paper and used in proposed application offers possibility of control of three independent parameters. In case of oscillator, it is fully utilized for control of oscillation condition and linear tuning of oscillation frequency.

The reasons for utilization of active elements employing several types of electronic control came from requirements for comfortable electronic control in applications. The important applications in the field of signal generation are oscillators. Therefore, we provided detailed study of several oscillator solutions and found following drawbacks concerning mainly lack of electronically controllable features of proposed circuits:

1. too many passive elements (for example [14]-[17]),

2. condition of oscillation given by equality of capacitors only (for example [18]-[22]),

3. matching of two controllable parameters or values of passive elements required in order to fulfill oscillation condition, and tuning of oscillation frequency is required simultaneously [18]-[22],

4. linear control of oscillation frequency is not possible especially in simple solutions having minimal number of active elements [23]-[28],

5. none of discussed simple second-order solution allow four-phase outputs with [pi]/4 shift i.e. 45, 90, 135, and 180 degree of phase shifts.

Of course, there are many multiphase solutions based on cascades (chains) of lossy blocks in one loop (for example [29] and references cited therein) that allow various phase shifts, but circuit realization is very extensive (many active and passive elements) and tunability complicated in some cases [30]. Therefore, we focused our attention on simple (minimal number of active element) electronically adjustable solutions. Despite of fact that several second-order multiphase and tunable oscillators were introduced [6], [31]-[36], any solution from them does not allow to realize phase shift between produced signals different than [pi]/2. Detailed comparison is shown in Table I. Our solution produces phase shift [pi]/4 between generated signals. The same feature is available in [37], [38], but discussed solutions do not have capability of electronic control (or any other method) of oscillation frequency or they do not have independent control of oscillation frequency (element suitable for frequency control influences oscillation condition). Therefore, oscillator presented in this paper provides significant advantages (electronic control of oscillation frequency independently on oscillation condition and minimal number of active elements) in comparison to previous works that realizes phase shift in multiples of [pi]/4 [37], [38].

II. SECOND-ORDER MULTIPHASE OSCILLATOR USING Z-COPY CONTROLLED-GAIN VOLTAGE DIFFERENCING CURRENT CONVEYOR

Presented second-order multiphase oscillator utilizes active element referred as z-copy controlled gain voltage differencing current conveyor (ZC-CG-VDCC). Detailed description of the active element and its parameters are discussed in [39]. Therefore, only very brief introduction is given here. ZC-CG-VDCC is multi-terminal mixed-mode active device that provides three independent types of controllable parameters ([R.sub.x], [g.sub.m], B). These parameters are adjustable by DC bias currents. Difference of voltages [V.sub.p] and [V.sub.n] at high-impedance input terminals is transformed to current [I.sub.z_ta] by transconductance section ([g.sub.m]). The identical copy is provided for auxiliary purposes (high-impedance terminal zc_TA). Voltage at low-impedance current input terminal x is directly given by intrinsic resistance [R.sub.x] and [V.sub.z_ta]. Current [I.sub.x] = ([V.sub.x] - [V.sub.z_ta])/[R.sub.x] is amplified by adjustable gain B to positive and negative output (high-impedance terminals [Z.sub.p], [Z.sub.n]). Symbol, including internal behavioral model, is shown in Fig. 1. Outgoing current (arrow in direction out of the device) is meant as positive. Interterminal relations are also included in Fig. 1. Possible CMOS implementation and its features are shown in [39].

Circuit structure of the multiphase voltage-mode oscillator is given in Fig. 2. Here it is worth to note that the circuit can also work in current-mode if the load resistances [R.sub.L1] and [R.sub.L2] are omitted. In this case current responses are taken from terminals zp and zc_TA. Characteristic equation of the oscillator in Fig. 2 has very favorable form

[s.sup.2] + [C.sub.2] - [C.sub.1]B/[R.sub.x][C.sub.1][C.sub.2] s + [g.sub.m]/[R.sub.x][C.sub.1][C.sub.2] = 0, (1)

where condition of oscillation (CO) and frequency of oscillation (FO) are:

B [greater than or equal to] [C.sub.2]/[C.sub.1] (2)

[[omega].sub.0] = [square root of ([g.sub.m]/[R.sub.x][C.sub.1][C.sub.2])]. (3)

The relation between outputs [V.sub.OUT2] and [V.sub.OUT1] is represented by following expression

[V.sub.OUT2]/[V.sub.OUT1] = B + [R.sub.x][g.sub.m]/B - s[C.sub.2][R.sub.x]. (4)

If CO (B = 1) is fulfilled and [g.sub.m] = 1/[R.sub.x], [C.sub.1] = [C.sub.2] = C, (4) can be simplified to

[V.sub.OUT2]/[V.sub.OUT1] = 1 + j (5)

that gives

[V.sub.OUT2] = [square root of 2] exp {j[pi]/ 4) [V.sub.OUT1]. (6)

Relation for [V.sub.OUT4] and [V.sub.OUT1] has a form

[V.sub.OUT4]/[V.sub.OUT1] = [R.sub.L2]B s[C.sub.2] + [g.sub.m]/s[C.sub.2] + [R.sub.x] - B (7)

Simplified relation ([g.sub.m] = 1/[R.sub.x], [C.sub.1] = [C.sub.2] = C, B = 1), valid at FO, has a form:

[V.sub.OUT4]/[V.sub.OUT1] = - [R.sub.L2][g.sub.m]j = - [R.sub.L2]/[R.sub.x] j, (8)

[V.sub.OUT4] = [R.sub.L2][g.sub.m] exp(-j[pi]/2)[V.sub.OUT1] (9)

Between [V.sub.OUT3] and [V.sub.OUT1] we achieve very simple relation (for discussed simplification):

[V.sub.OUT3]/[V.sub.OUT1] = - [R.sub.L1]/[R.sub.x] = - [R.sub.L1][g.sub.m], (10)

[V.sub.OUT3] = [R.sub.L1][g.sub.m] exp{j[pi])[V.sub.OUT1]. (11)

Detailed evaluation of above noted relations shows that phase shifts keep preserved during the tuning process if considered conditions ([g.sub.m] = l/[R.sub.x], [C.sub.1] = [C.sub.2] = C) are ensured. However, as we can see, amplitudes of two of produced signals ([V.sub.OUT3], [V.sub.OUT4]) vary during the tuning process. Oscillation frequency can be adjusted linearly by [g.sub.m] and [R.sub.x] simultaneously while their ratio is kept constant.

III. SIMULATION RESULTS

We used CMOS model of the ZC-CG-VDCC introduced in [39] for verification and analysis of proposed circuit. Controllability of discussed parameters ([R.sub.x], [g.sub.m], B) of the ZC-CG-VDCC CMOS model from [39] is documented in Fig. 3. Ideal traces are determined from theoretical equations for [R.sub.x], [g.sub.m], and B in accordance with the CMOS model specifications [39]. Adjusting of the DC bias current [I.sub.set_Rx] between 5.9 [micro]A and 80 [micro]A allows control of [R.sub.x] in approximate range from 4 k[OMEGA] to 0.67 k[OMEGA]. Transconductance control is in case of this proposed oscillator sufficient from 250 [micro]S to 1500 [micro]S by [I.sub.set_gm] between 9.7 [micro]A and 99 [micro]A. Current gain control B is in range 0.4 to 4 ([I.sub.set_B] from 100 [micro]A to 10 [micro]A).

The oscillator in Fig. 4 (including circuit for amplitude stabilization) was designed with following parameters: [C.sub.1] = [C.sub.2] = 30 pF, [R.sub.x] = 2 k[OMEGA] ([I.sub.set_Rx] =13.3 [micro]A), [g.sub.m] = 500 [micro]S ([I.sub.set_gm] = 22 [micro]A), B [approximately equal to] 1 (control current had to be varied in range [I.sub.set_B] [approximately equal to] 79 [micro]A-81 [micro]A). Supply voltage was [+ or -] 1 V. Values of load resistance are [R.sub.L1] = [R.sub.L2] = 2 k[OMEGA]. Ideal oscillation frequency has value 2.654 MHz.

Ideal phase and amplitude relations based on analysis in (4)-(11) for these initial parameters and discrete frequency are given in Fig. 5. Dots at the ends of lines of the constant vectors mean constant unchangeable positions (obvious at single FO value). Nonlinear tuning process based on fixed [R.sub.x] and adjusted [g.sub.m] is possible. However, amplitude ([V.sub.OUT3] and [V.sub.OUT4]) and also additional amplitude and phase changes between [V.sub.OUT1] and [V.sub.OUT2] occur, see Fig. 6 for further information, where dynamical output vectors in polar plot are shown (arrows signalize trends of amplitude changes with increasing [g.sub.m] from 100 [micro]S to 1 mS). Voltage [V.sub.OUT1] has always constant value. Simultaneous control of both parameters ([g.sub.m] = 1/[R.sub.x]) is the best choice for the operation of proposed system. Figure 7 shows that [V.sub.OUT2] keeps constant for [g.sub.m] = 1/[R.sub.x] control of FO. Amplitudes of [V.sub.OUT1] and [V.sub.OUT2] are not equal but their ratio keeps invariant in process of tuning and levels are constant (dot at the end of line of the vectors). Unfortunately, [V.sub.OUT3] and [V.sub.OUT4] are still dependent on FO control.

Value of FO, obtained from simulation, achieved 2.566 MHz. Simulation results are shown in Fig. 8, where transient responses for all four outputs are available. Simulated phase shifts were 44 degrees ([V.sub.OUT1]-[V.sub.OUT2]), 86 degrees ([V.sub.OUT1]-[V.sub.OUT4]), 181 degrees ([V.sub.OUT1]-[V.sub.OUT3]) and 139 degrees ([V.sub.OUT2]-[V.sub.OUT4]).

The FO control supposes simultaneous change of [g.sub.m] and [R.sub.x]. Theoretical range of FO control allows control in between 1.327 MHz-7.960 MHz ([g.sub.m] = 1/[R.sub.x] = <0.25; 1.5> mS). Simulations provided adjusting from 1.331 MHz to 7.391 MHz. Corresponding results are in Fig. 9. Amplitudes of [V.sub.OUT3] and [V.sub.OUT4] still changes in accordance to discussed theoretical relations ([V.sub.OUT1] and [V.sub.OUT2] are unchangeable if equality [g.sub.m] = 1/[R.sub.x] is ensured).

Frequency spectrum of [V.sub.OUT1] for four discrete frequencies is shown in Fig. 10. Figure 11 shows dependence of output levels on tuning process. It confirms theoretical relations (4)-(15). Total harmonic distortion (THD) results obtained at all available outputs are shown in Fig. 12 and reach 0.45 %-3.8 % ([V.sub.OUT1]: 0.45%-1.48%; [V.sub.OUT2] 0.45 %-2.28%; [V.sub.OUT3] 0.58 %-3.81 %; [V.sub.OUT4] 1.17 %-3.15 %) in whole range of oscillation frequency tuning. Last plot shows power consumption of the oscillator that has very slight dependence on tuning process (Fig. 13).

IV. CONCLUSIONS

The proposed simple second-order sinusoidal oscillator fulfils multiphase requirements (produces 45, 90, 135 and 180 degree phase shifts simultaneously) and can work also as the quadrature type. The matching of two parameters is required for linear electronic control of the oscillation frequency. Nevertheless, this matching is easily accessible by adjusting of both parameters (transconductance [g.sub.m] and intrinsic resistance of the current input [R.sub.x]). The third parameter (current gain B) controls the condition of oscillation. All parameters are controlled electronically. Verification of tuning was provided from 1.331 to 7.391 MHz.

http://dx.doi.Org/10.5755/j01.eee.20.9.8709

Manuscript received April 8, 2014; accepted September 14, 2014.

Research described in the paper was supported by Czech Science Foundation project under No. 14-24186P and by internal grant No. FEKTS-14-2281 and project Electronic-biomedical co-operation ELBIC M00176. The support of the project CZ.1.07/2.3.00/20.0007 WICOMT, financed from the operational program Education for competitiveness, is gratefully acknowledged. The described research was performed in laboratories supported by the SIX project; the registration number CZ.1.05/2.1.00/03.0072, the operational program Research and Development for Innovation. Dr. Herencsar was supported by the project CZ.1.07/2.3.00/30.0039 of the Brno University of Technology.

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R. Sotner (1), J. Jerabek (2), J. Petrzela (1), N. Herencsar (2), R. Prokop (3), K. Vrba (2)

(1) Department of Radio Electronics, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technicka 12, Brno, 616 00, Czech Republic

(2) Department of Telecommunications, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technicka 12, Brno, 616 00, Czech Republic

(3) Department of Microelectronics, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technicka 10, Brno, 616 00, Czech Republic

sotner@feec.vutbr.cz

TABLE 1. SOME OF RECENTLY REPORTED SOLUTIONS OF SIMPLE SECOND-ORDER MULTIPHASE OSCILLATORS. Reference Year No. No. Type of active of passive of active elements elements element [6] 2012 2 2 CCCDTA [31] 2011 2 5 or 6 DO-CIBA [32] 2013 2 3 VDIBA [33] in 3 5 DO-CG-CFBA press [34] 2014 2 5 CG-CFDOBA, CG-BCVA [35] 2012 1 3 VDTA [36] 2013 1 5 VDTA [37] 2012 2 6 CCII+. ECCII- [38] * 2013 2 3; 5 DO-VDBA, FB-VDBA proposed 1 4 ZC-CG-VDCC Reference Tunable Grounded C Mutual type dependence of oscillation frequency and condition [6] Yes Yes No [31] Yes Yes No [32] No No Yes [33] Yes Yes No [34] Yes Yes No [35] Yes Yes No [36] Yes Yes No [37] No Yes No [38] * No Yes No; Yes proposed Yes Yes No Reference Electronic Electronic Type of control control of control of (PE--passive oscillation oscillation elements-resistor; frequency condition DC V--DC bias voltage; DC I--DC bias current) [6] Yes ([g.sub.m]) Yes ([g.sub.m]) DC I [31] No (R) No (R) PE [32] Yes ([g.sub.m]) Yes ([g.sub.m]) DC I [33] Yes (B) Yes (B) DC V [34] Yes (B) Yes (A) DC V [35] Yes ([g.sub.m]) No (R) DC I [36] Yes ([g.sub.m]) No (R) DC I [37] No Yes (B) DC V [38] * Yes([g.sub.m]); No Yes ([g.sub.m]) DC I proposed Yes([g.sub.m], Yes (B) DC I [R.sub.x]); No Reference Type of the Type of phase shift output (multiplicand) signals (current or voltage) [6] k[pi]/2 current [31] k[pi]/2 voltage [32] k[pi]/2 voltage [33] k[pi]/2 voltage [34] k[pi]/2 voltage [35] k[pi]/2 current [36] k[pi]/2 voltage [37] k[pi]/4 voltage [38] * k[pi]/4 voltage proposed k[pi]/4 voltage Notes: A--voltage gain; B--current gain; [g.sub.m]--transconductance; R--resistor value * ref. [38] deals with two types of the oscillator with phase shift k[pi]/4

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Author: | Sotner, R.; Jerabek, J.; Petrzela, J.; Herencsar, N.; Prokop, R.; Vrba, K. |
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Publication: | Elektronika ir Elektrotechnika |

Article Type: | Abstract |

Geographic Code: | 4EUIT |

Date: | Sep 1, 2014 |

Words: | 4049 |

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