Novel Oscillator Based on Voltage and Current-Gain Adjusting Used for Control of Oscillation Frequency and Oscillation Condition

The paper deals with novel controllable oscillator where two types of electronic control are used. Proposed second-order circuit contains current follower, adjustable current amplifier, adjustable voltage amplifier, two resistors and two grounded capacitors. Oscillation frequency is tuned by voltage gain of used voltage amplifier that is represented by high-frequency voltage-mode multiplier. Oscillation condition is automatically regulated by current gain of the adjustable current amplifier which is based on current-mode multiplier. Experimental results confirmed workability of the circuit . DOI: http://dx.doi.org/10.5755/j01.eee.19.6.4567


I. INTRODUCTION
Many active elements which are suitable for electronic control could be found in open literature [1].Several ways how to control parameters of applications have been described [2]- [9].Surakamponton et al. [2] and Fabre et al. [3] 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 [1], [4], [5].Another way of control is change of transconductance [1], [6] by bias current.Geiger were used by Tangsrirat et al. in [20].Solutions of third order oscillators were also investigated.Horng [21], [22] built oscillator with three grounded capacitors.Prasad et al. [23] utilized novel approach in oscillator with one multipleoutput current controlled current differencing transconductance amplifier (MO-CCCDTA).The second group consists of oscillators which are controllable by adjustable intrinsic resistance of current input (R X ) in novel modified active elements.Current conveyor transconductance amplifier (CCTA) introduced by Prokop et al. [24] was also frequently used in adjustable oscillators.Siripruchyanun et al. [25] introduced possibility of R X control and its usefulness in applications together with g m adjusting.The CDTA element was also extended and controllable R X and g m parameters were determined for control of resistor-less oscillator by Jaikla et al. [26].Similar oscillator was proposed also by Sakul et al. in [27].The third group contains solutions employing adjusting of the current gain (B G ) in order to control the application.Kumngern et al. implemented combination of two methods, i.e. control of R X and current gain (B G ) for adjusting of FO and CO in [28].Biolek et al. [29] 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 [30]- [33].Herencsar et al. [34] introduced programmable current amplifier (PCA, DACA) [35] and its application in oscillator.
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 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 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 1 .The MO-CF/I produces identical copies of its input current (inverting or non-inverting output).Negative output is connected to C 2 , where current is changed to voltage (node 2).This voltage is amplified or attenuated by adjustable voltage amplifier (VA) with voltage gain A G .Finally, the output voltage of the VA is transferred through divider (R 1 , R 2 ) with capacitive load (C 1 ).The second loop Analysis of the SFG in Fig. 2 (by Mason rule [36], [37]) yields to following characteristic equation

( )
. 0 We can determine CO and FO as follows: It is obvious that CO is controllable by B G and FO by A G and they are mutually independent.The relative sensitivities of FO on values of passive elements and gains, that are evident from (3), are:

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 [38] current mode multiplier.The current amplifier (CA) with adjustable current gain is represented by EL2082 [39] current mode multiplier.We constructed adjustable voltage amplifier from high frequency voltage mode multiplier AD834 [40] and high speed opamp AD8045 [41].Additional (separation) buffers were BUF634 types [42].We selected values of passive elements as follows: The main problem is in the node 2, because input resistance of VA (AD834) is only 25 kΩ i.e.
We can include parasitic capacitances to "working" values as Analysis of parasites in circuit in Fig. 3 leads to more real forms of CO and FO: The term A G R p1 R p2 in (7) has more than hundred times higher value than term B G / R p1 R 2 for B G = 2 and A G > 1.Therefore, its influence on FO is insignificant.Nevertheless, significant effects appear for lower A G (<< 1).This drawback increases with lower value of R p2 (R p1 >> R 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 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 1 is quite low (about 100 mV 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 A G is depicted in Fig. 6.Ideal range (when only R 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 A G adjusted from 1.2 to 4. THD was evaluated as 0.3 to 2% (Fig. 7).Measured prototype is shown in Fig. 8.

IV. CONCLUSIONS
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 m ) [10]- [23], intrinsic resistance [7], [8], [25] or their combination [26], [27] for example.Researchers try to find alternative methods of control of FO and CO (as we can see in [29]- [35]).Such methods may avoid using some not-generally advantageous ways of direct electronic control of parameters (control of intrinsic resistance R X for example).Presented solution is also an attempt, which shows how to avoid necessity of R X control in mixed-mode applications utilizing current-mode active elements (compared to [26]- [28]).
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 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 highfrequency 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.

Fig. 1 .
Fig. 1.Active elements applied in proposed oscillator: a) adjustable voltage amplifier, b) current distributor c) adjustable current amplifier.

(S 2 ) 2 .
contains current amplifier (CA) with the current gain B G and it is connected directly to positive output of the MO-CF/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 1 , R 2 and C 1 .Proposed oscillator: a) SFG for explanation; b) circuit representation.

5 .
168 pF.However, estimation of parasitic features given by printed circuit board (PCB) is very problematic.Experimental results for f0 = 25.5 MHz, AG = 4: a) all transient responses, b) spectrum of VC1, c) spectrum of VC2, d) spectrum of VVA.

TABLE I .
COMPARISON OF IMPORTANT PREVIOUSLY REPORTED CONTROLLABLE OSCILLATORS Notes (parameters and abbreviations which are not explained in text of the introductory section): Ib -bias current (type of control) gm / gm -two different transconductances are used for independent FO and CO control gm / R -transconductance suitable for FO