Novel oscillator based on voltage and current-gain adjusting used for control of oscillation frequency and oscillation condition.
Many active elements which are suitable for electronic control could be found in open literature . Several ways how to control parameters of applications have been described -. Surakamponton et al.  and Fabre et al.  introduced active elements with possibility of current gain control. This active element is referred to as electronically controllable current conveyor of second generation (ECCII) and it allows adjusting of current transfer between current input and current output of the current conveyor , , . Another way of control is change of transconductance ,  by bias current. Geiger et al.  described several basic applications of transconductors (OTAs) and formulated background of knowledge in this topic. Fabre et al.  presented active element with different possibility of control. The biasing current in internal structure of the current conveyor was used for control of intrinsic resistance of current input. Minaei et al.  proposed ECCII with combination of two methods of control in one device (intrinsic resistance and current gain). Marcellis et al.  implemented control of the current and voltage gains. Digital potentiometers are popular solutions for control of applications with standard voltage opamps at low frequencies (hundreds of kHz maximally) because their frequency features are not satisfactory in this particular case. Methods how to control frequency of oscillation (FO) and condition of oscillation (CO), that were sketched out, are discussed in more detail in the following text. All discussed ways of control suppose direct electronic adjusting in frame of parameter of active element. Other ways which use passive elements (resistors in many cases) and their replacements (FETs, digital potentiometers, ...) belong to group of indirect methods.
The first group of oscillator solutions employs controllable tranconductances ([g.sub.m]). In the past, only simple transconductors (voltage controlled current sources) with differential input and single output were used. Rodriguez-Vazques et al. , Linarez-Barranco et al. , , Senani , Abuelmaatti  and many others presented simple and flexible solutions using at least two transconductors. Over the years, transconductor conceptions have been improved and also novel modified types were developed. Biolek ,  introduced so-called current differencing transconductance amplifier (CDTA), where current differencing unit at the input of transconductor is used. Lahiri  proposed controllable oscillator with two CDTAs and two grounded capacitors or oscillator employing only one active element , . Three CDTAs were used by Tangsrirat et al. in . Solutions of third order oscillators were also investigated. Horng ,  built oscillator with three grounded capacitors. Prasad et al.
The second group consists of oscillators which are controllable by adjustable intrinsic resistance of current input ([R.sub.X]) in novel modified active elements. Current conveyor transconductance amplifier (CCTA) introduced by Prokop et al.  was also frequently used in adjustable oscillators. Siripruchyanun et al.  introduced possibility of [R.sub.X] control and its usefulness in applications together with gm adjusting. The CDTA element was also extended and controllable [R.sub.X] and [g.sub.m] parameters were determined for control of resistor-less oscillator by Jaikla et al. . Similar oscillator was proposed also by Sakul et al. in . The third group contains solutions employing adjusting of the current gain ([B.sub.G]) in order to control the application. Kumngern et al. implemented combination of two methods, i.e. control of [R.sub.X] and current gain ([B.sub.G]) for adjusting of FO and CO in . Biolek et al.  proposed oscillator with so-called z-copy controlled-gain current differencing buffered amplifier (ZC-CG-CDBA) where they also implemented possibility of current gain adjusting. Several applications of adjustable current gain were also discussed in -. Herencsar et al.  introduced programmable current amplifier (PCA, DACA)  and its application in  utilized novel approach in oscillator with one multiple-output current controlled current differencing transconductance amplifier (MO-CCCDTA). oscillator.
Several solutions of the controllable oscillators based on above discussed methods are compared in Table I. Following problems of the discussed results are evident: I. some solutions require larger number of passive elements , , , , ; II. only few works deal with applications that operate in frequency range above 10 MHz , , ; III. many solutions were designed as tunable (or have these abilities), but their verification was not provided , , , , ; IV. some variants suffer from high total harmonic distortion (THD) , , , ; V. automatic gain control (AGC) for amplitude stabilization was proposed in minimum conceptions , , , , ; VI. additional conversion of DC control voltage to bias current (controlling [g.sub.m] for example) is required -, ; VII. in some cases equations for FO or CO are complicated--matching of several parameters (equality of several C or [g.sub.m]) required for electronic control , , ; VIII. intrinsic resistance ([R.sub.X]) is generally nonlinear temperature dependent parameter and intended control by [R.sub.X] - may cause problems for higher amplitudes of processed signals in some applications; IX. some solutions require controllable replacement of passive resistor to control of CO , , , , -.
We prepared a solution that solves several above discussed problems simultaneously. Independent direct electronic control of FO and CO by adjustable voltage and current gain that was not discussed in hitherto published works is used in our approach. Advantages (fulfilled together) of proposed circuit are: I. direct electronic DC voltage control of FO allows comfortable driving from digital systems; II. simple oscillation condition suitable for direct electronic control; III. approach based on high-speed voltage- and current-mode multipliers (used as behavioral representation of active elements) allows operation range in tens of MHz; IV. precise AGC allows sufficient THD in adjusted frequency range; V. we avoid the [R.sub.X] control (for adjustable purposes) in this work; VI. CO is directly controllable by parameters of active element (no replacement of resistor is required). When on-chip implementation is performed, one resistor with low value is "absorbable" to the current input intrinsic resistance. Of course, other simpler circuits (Table I), controlled by several different ways exist, but above listed features are not fulfilled simultaneously in many of discussed solutions.
II. PROPOSED OSCILLATOR
The basic principle of active elements (adjustable voltage amplifier, adjustable current amplifier and current distributor --current follower/inverter) is explained in Fig. 1.
We implemented two integrator loops with controllable current feedback in order to design simple type of the adjustable oscillator with minimum passive elements and grounded capacitors. Possibility of current and voltage gain control is very useful for tuning of FO and control of CO in our solution that is shown in Fig. 2. Basic component of the signal flow graph (SFG) is the current follower and inverter (MO-CF/I). Combined arrows substitute voltage to current (open-closed) and current to voltage (closed-open) conversion in Fig. 2(a).
We can briefly explain principle of the circuit in Fig. 2(b). The node 1, where three passive elements are connected together, is the most important part. These elements form significant impedance (conversion constant between current and voltage). Voltage in node 1 is transformed to the current through [R.sub.1]. The MO-CF/I produces identical copies of its input current (inverting or non-inverting output). Negative output is connected to [C.sub.2], where current is changed to voltage (node 2). This voltage is amplified or attenuated by adjustable voltage amplifier (VA) with voltage gain [A.sub.G]. Finally, the output voltage of the VA is transferred through divider ([R.sub.1], [R.sub.2]) with capacitive load ([C.sub.1]). The second loop ([S.sub.2]) contains current amplifier (CA) with the current gain [B.sub.G] and it is connected directly to positive output of the MOCF/I. The CA represents the feedback path which is connected back to the node 1. Output current of the CA is transformed from current to voltage at the impedance formed by [R.sub.1], [R.sub.2] and [C.sub.1].
Analysis of the SFG in Fig. 2 (by Mason rule , ) yields to following characteristic equation
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (1)
We can determine CO and FO as follows:
[B.sub.G] [greater than or equal to] 1 + [[R.sub.1]/[R.sub.2]], (2)
[[omega].sub.0] = [square root of [A.sub.G]/[R.sub.1][R.sub.2][C.sub.1][C.sub.2]]. (3)
It is obvious that CO is controllable by [B.sub.G] and FO by [A.sub.G] and they are mutually independent. The relative sensitivities of FO on values of passive elements and gains, that are evident from (3), are:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (4)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (5)
III. REAL IMPLEMENTATION AND EXPERIMENTAL VERIFICATION
We created non-ideal model of the proposed circuit from Fig. 2(b). Additional nodal impedances that are caused by real active elements and additional voltage buffers for impedance separation were added. Complete model is shown in Fig. 3. We implemented commercially available active elements for experimental verifications. The MO-CF/I element was implemented by EL4083  current mode multiplier. The current amplifier (CA) with adjustable current gain is represented by EL2082  current mode multiplier. We constructed adjustable voltage amplifier from high frequency voltage mode multiplier AD834  and high speed opamp AD8045 .
Additional (separation) buffers were BUF634 types . We selected values of passive elements as follows: [R.sub.1] = 39 [ohm] (real input resistance of MO-CF/I is considered), [R.sub.2] = 78 [ohm], [C.sub.1] = [C.sub.2] = C = 150 pF, [B.sub.G] = 2. Important parameters of the MO-CF/I (EL4083 ) are output impedances, both are characterized by [R.sub.out_MO-CF] [approximately equal to] 1 M[ohm]/ [C.sub.out_MO-CF] [approximately equal to] 5 pF and also input resistance, [R.sub.inp_MO-CF] [approximately equal to] 40 [ohm]. Producer of EL2082 (modeling CA) indicates output properties as follows: [R.sub.out_CA] [approximately equal to] 1 M[ohm]/[C.sub.out_CA] [approximately equal to] 5 pF, [R.sub.inp_CA] [approximately equal to] 95 [ohm]. We suppose that influence of [R.sub.inp_CA] is negligible because [R.sub.tap_CA] [much less than] [R.sub.out_MO-CF]. The voltage amplifier (VA) is characterized by input resistance [R.sub.inp_VA] [approximately equal to] 25 k[ohm] (AD834). High speed VA was built in accordance with recommendations in . Output resistance of VA is negligible (datasheet of AD8045 shows value < 4 [ohm] up to 100 MHz). Input impedance of additional separation voltage buffer is [R.sub.inp_VB] [approximately equal to] 8 M[ohm]/[C.sub.inp_VB] [approximately equal to] 8 pF (BUF634). Outputs of the MO-CF/I are dominant in the node 1 where [R.sub.p1] [approximately equal to] [R.sub.out_CA] [parallel] [R.sub.inp_VB] [approximately equal to] 890 k[ohm] and [C.sub.p1] [approximately equal to] [C.sub.out_CA] + [C.sub.inp_VB] [approximately equal to] 13 pF.
The main problem is in the node 2, because input resistance of VA (AD834) is only 25 k[ohm] i.e. [R.sub.p2] [approximately equal to] [R.sub.inp_VA] [parallel] [R.sub.out_MO-CF] [parallel] [R.sub.inp_VB] [approximately equal to] 24 k[ohm]. Capacitances in the node 2 have overall values [C.sub.p2] [approximately equal to] [C.sub.inp_VA] + [C.sub.out_MO-CF] + [C.sub.inp_VB] [approximately equal to] 18 pF. Value of R1 is also influenced by [R.sub.inp_MO-CF] [approximately equal to] 40 [ohm], i.e. real [R.sub.1.sup./] [approximately equal to] [R.sub.1] + [R.sub.inp_MO-CF] [approximately equal to] 79 [ohm]. We can include parasitic capacitances to "working" values as [C.sub.1.sup./]' [approximately equal to] [C.sub.1] + [C.sub.p1] [approximately equal to] 163 pF, [C.sub.2.sup./] [approximately equal to] [C.sub.2] + [C.sub.p2] [approximately equal to] 168 pF. However, estimation of parasitic features given by printed circuit board (PCB) is very problematic.
Analysis of parasites in circuit in Fig. 3 leads to more real forms of CO and FO:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (6)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (7)
The term [A.sub.G][R.sub.p1][R.sub.p2] in (7) has more than hundred times higher value than term [B.sub.G.sup./][R.sub.p1][R.sub.2] for [B.sub.G] = 2 and [A.sub.G] > 1.
Therefore, its influence on FO is insignificant. Nevertheless, significant effects appear for lower [A.sub.G] ([much less than] 1). This drawback increases with lower value of [R.sub.p2] ([R.sub.p1] [much greater than] [R.sub.p2] in our equivalent circuit model). It is caused by specific feature of used VA. The next important problem is quite high value of [C.sub.p2].
We tested proposed circuit in laboratory and find out the following results. The oscillator was modified (supplemented by automatic gain control circuit--AGC for amplitude stabilization, impedance matching) and carefully adjusted for adequate operation. The tested device was connected to measuring installation included in Fig. 4. Additional opamp in the AGC loop (pre-amplification) was necessary because output level of [VB.sub.1] is quite low (about 100 [mV.sub.P-P]) for sufficient THD (AD834 has restricted linear dynamical range of input voltage) and does not reach threshold voltage of the diode in the rectifier. Time domain results and spectral analyses for the highest achieved FO are shown in Fig. 5.
The dependence of FO on Ag is depicted in Fig. 6. Ideal range (when only [R.sub.inp_MO-CF] is included) of FO tuning was calculated between 14.81 and 27.05 MHz. Expected range (calculation from (7)) of FO control is from 13.43 to 24.52 MHz. Measurements provided range from 12.01 to 25.50 MHz. All results were obtained for Ag adjusted from 1.2 to 4. THD was evaluated as 0.3 to 2% (Fig. 7). Measured prototype is shown in Fig. 8.
Presented work shows that two different ways of control (voltage and current gain) are also possible for tunable oscillator in comparison to classical method based on change of resistor(s) value or standard methods of electronic control by transconductance ([g.sub.m]) -, intrinsic resistance , ,  or their combination ,  for example. Researchers try to find alternative methods of control of FO and CO (as we can see in -). Such methods may avoid using some not-generally advantageous ways of direct electronic control of parameters (control of intrinsic resistance [R.sub.X] for example). Presented solution is also an attempt, which shows how to avoid necessity of [R.sub.X] control in mixed-mode applications utilizing current-mode active elements (compared to -).
Presented solution has several conveniences that are not fulfilled in many above compared solutions (Table I) simultaneously. Main advantages of the proposed solution are: I. direct simple DC voltage control of FO; II. simple and specially established CO--easy implementation of AGC by DC control voltage (no replacement of passive resistor is required); III. proposal of precise AGC system, which ensures sufficient THD level (0.3-2%) in intended frequency range; IV. additional simplification for on-chip implementation--one resistor ([R.sub.1]) is "absorbable" to fixed value of intrinsic resistance of current input; V. no additional conversion of control voltages to bias current etc. is required --DC voltage is directly available to adjust the oscillator from control part or other device; VI. due to the high-frequency devices and low values of passive elements, operational range of FO adjusting was at frequencies of several tens of MHz (between 12-25.5 MHz). In real case, an attention to sufficient values of nodal impedances (resistances and capacitances) and undesirable couplings must be given.
Active elements were modeled by commercially available current multipliers, voltage amplifiers and buffers. This approach allows preliminary laboratory tests. The authors believe that if the circuit built from discrete commercially available elements works well, then appropriate and future on-chip implementation will work even better.
Manuscript received January 27, 2013; accepted April 9, 2013.
Research described in the paper was supported by Czech Science Foundation projects No. 102/11/P489, 102/09/1681 by internal grant FEKT-S-11-15 and project Electronic-biomedical co-operation ELBIC M00176. Dr. Herencsar was supported by the project CZ.1.07/2.3.00/30.0039 of Brno University of Technology. 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.
We would like to thank to Pavel Kopecek, M.Sc. for his help with experimental work and measurements.
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R. Sotner (1), J. Jerabek (2), W. Jaikla (3), N. Herencsar (2), K. Vrba (2), T. Dostal (1,4)
(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 Engineering Education, Faculty of Industrial Education, King Mongkut's Institute of Technology Ladkrabag, Ladkrabag, Bangkok 105 20, Thailand
(4) Department of Electrical Engineering and Computer Science, College of Polytechnics Jihlava, Tolsteho 16, Jihlava 586 01, Czech Republic
TABLE I. COMPARISON OF IMPORTANT PREVIOUSLY REPORTED CONTROLLABLE OSCILLATORS Work Active element No. of Simple active/passive equations elements for FO/CO  OTA 4/3 YES/YES  OTA 2-4/2-4 NO/NO  OTA 3/2 YES/YES  OTA 2/3 YES/YES  CDTA 2/6 YES/YES  CDTA 2/3 YES/YES  CCTA 1/4 YES/YES  DVCCTA 1/4 YES/YES  CDTA 3/2 YES/YES  CDTA 3/3 YES/NO  CDTA 3/3 YES/YES  MO-CCCDTA 1/3 YES/YES  CCCDTA 2/2 YES/YES  CCCDTA 2/2 YES/YES  CCCII 2/2 YES/YES  ZC-CG-CDBA 2/5 YES/YES  CCTA 1/4 YES/YES  DT, CA 3/4 YES/NO  ECCII-, CCII+ 3/5 YES/YES  CG-CIBA/CFBA 2/5 YES/YES  PCA 3/4 YES/YES Prop. VA, CA, MO-CF/I 3/4 YES/YES Work AGC FO range THD proposed  YES 3-10.3 MHz 0.2 %  YES 12-56 MHz 2.5 %  N/A N/A N/A  N/A N/A (300 kHz) * N/A  N/A N/A (1 MHz) * N/A  N/A N/A (10 MHz) * N/A  N/A 21-682 kHz N/A  N/A 20-700 kHz 4.6 %  N/A 0.2-1.8 MHz 2.5 %  N/A 3-9 kHz 1-2.6 %  N/A 0.4-0.8 MHz 10 %  N/A N/A (114 kHz) * 0.6 %  N/A 0.1-5 MHz N/A  YES 1-4 MHz 1.6 %  N/A 0.1-1.7 MHz 1-7 %  YES 0.25-2.75 MHz 0.2 %  N/A 0.25-1.23 MHz 0.6-4 %  N/A 0.6-2.2 MHz 0.4-0.9 %  N/A 0.26-1.25 MHz 0.2-1.5 %  YES 0.1-1.26 MHz 0.6-1.3 %  N/A 50-300 kHz N/A Prop. YES 12-25.5 MHz 0.3-2 % Work Type of FO DC voltage /CO control control of FO  [g.sub.m]/[g.sub.m] NO ([I.sub.b])  [g.sub.m]/[g.sub.m] NO ([I.sub.b])  [g.sub.m]/[g.sub.m] NO ([I.sub.b])  [g.sub.m]/R NO ([I.sub.b])  R/R, [g.sub.m] NO  [g.sub.m]/R, [g.sub.m] NO ([I.sub.b])  [g.sub.m]/R NO ([I.sub.b])  [g.sub.m]/R NO ([I.sub.b])  [g.sub.m]/[g.sub.m] NO ([I.sub.b])  [g.sub.m]/[g.sub.m] NO ([I.sub.b])  [g.sub.m]/[g.sub.m] NO ([I.sub.b])  [g.sub.m]/R NO ([I.sub.b])  [g.sub.m]/[R.sub.X] NO ([I.sub.b])  [g.sub.m]/[R.sub.X] NO ([I.sub.b])  [R.sub.X]/B NO ([I.sub.b])  [B.sub.G]/R NO (digital)  [B.sub.G]/R YES  [B.sub.G]/R YES  [B.sub.G]/[B.sub.G] YES  [B.sub.G]/[B.sub.G] YES  [B.sub.G]/[B.sub.G] NO ([I.sub.b]) Prop. [A.sub.G]/[B.sub.G] YES Notes (parameters and abbreviations which are not explained in text of the introductory section): [I.sub.b]--bias current (type of control) [g.sub.m]/[g.sub.m]--two different transconductances are used for independent FO and CO control [g.sub.m]/R--transconductance suitable for FO and resistance value for CO control R/R, [g.sub.m]--resistance value(s) suitable for FO control and resistance or/and transconductance suitable for CO control [g.sub.m]/R, [g.sub.m]--two different transconductances and also one transconductance and resistance are suitable for independent FO and CO control [g.sub.m]/[R.sub.X]--transconductance suitable for FO and electronically controllable intrinsic resistance suitable for CO control [B.sub.G]/R--current gain suitable for FO and resistor value for CO control [B.sub.G]/[B.sub.G]--two different current gains are used for independent FO and CO control [A.sub.G]/[B.sub.G]--voltage gain suitable for FO and current gain for CO control CCCDTA--current controlled CDTA; DVCCTA--differential voltage CCTA; CCCII--current controlled (translinear) current conveyor of second generation; CA--current amplifier (controllable); VA--voltage amplifier (controllable); MO-CF/I--multi-output current follower/inverter; DT--diamond transistor; CG-CIBA/CFBA--controlled gain current inverted buffered amplifier/current follower buffered amplifier N/A--not possible, not available or not verified * verified only at stable FO (discrete value sets)
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|Author:||Sotner, R.; Jerabek, J.; Jaikla, W.; Herencsar, N.; Vrba, K.; Dostal, T.|
|Publication:||Elektronika ir Elektrotechnika|
|Date:||Jun 1, 2013|
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