On practical construction of electronically controllable compact current amplifier based on commercially available elements and its application

Accepted Manuscript On Practical Construction of Electronically Controllable Compact Current Amplifier Based on Commercially Available Elements and its Application Roman Sotner, Norbert Herencsar, Jan Jerabek, Lukas Langhammer, Josef Polak PII: DOI: Reference:

S1434-8411(17)31052-X http://dx.doi.org/10.1016/j.aeue.2017.07.002 AEUE 51959

To appear in:

International Journal of Electronics and Communications

Received Date: Revised Date: Accepted Date:

29 April 2017 17 June 2017 6 July 2017

Please cite this article as: R. Sotner, N. Herencsar, J. Jerabek, L. Langhammer, J. Polak, On Practical Construction of Electronically Controllable Compact Current Amplifier Based on Commercially Available Elements and its Application, International Journal of Electronics and Communications (2017), doi: http://dx.doi.org/10.1016/ j.aeue.2017.07.002

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Title page:

On Practical Construction of Electronically Controllable Compact Current Amplifier Based on Commercially Available Elements and its Application Dr. Roman Sotnera,b Assoc. Prof. Norbert Herencsarb Assoc. Prof. Jan Jerabekb Dr. Lukas Langhammera,b, Josef Polak, M.Sc.b

a

Department of Radio Electronics, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technicka 3082/12, 61600 Brno, Czech Republic

E-mail: [email protected], [email protected]

b

Department of Telecommunications, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technicka 3082/12, 61600 Brno, Czech Republic

E-mail: [email protected], [email protected], [email protected]

1

On Practical Construction of Electronically Controllable Compact Current Amplifier Based on Commercially Available Elements and its Application Roman Sotnera,b, Norbert Herencsarb, Jan Jerabekb, Lukas Langhammera,b, Josef Polakb a

Department of Radio Electronics, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technicka 3082/12, 61600 Brno, Czech Republic b

Department of Telecommunications, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technicka 3082/12, 61600 Brno, Czech Republic Abstract: This paper presents a new concept of a current amplifier (CA) with electronically adjustable features (input resistance and current gain) implemented using commercially available devices. Several variations of basic structure are studied, described and the selected solutions verified by PSpice simulations and, moreover, also by lab experiments. Saving one discrete active device in comparison to already known similar topologies of single-input and single-output version (CA-SISO) is significant benefit whereas all other qualitative features remain very similar to previously reported ones. Simple modification of CA concept to multiple-output version (CA-SIMO), having independent adjustable current gain in each of output branches, is easily available. Experimental tests of features of discussed concepts yield adjustability range of input resistance from 100 Ω to more than 10 kΩ and current gain adjusting from 0.1 to 3.5 with bandwidth (-3 dB) of CA transfer response up to 16 MHz. As an example of application, proposed CA was successfully implemented in quadrature oscillator with a very wide tunability range from 29 kHz to 4.94 MHz. It was achieved by electronic control of several adjustable parameters of proposed CA.

Keywords: Adjustable current gain, adjustable resistance of current input terminal, current amplifier, quadrature oscillators, tunability range extension.

1. Introduction Active elements with multi-parameter control are sought especially for adjustable applications having several degrees of freedom [1], [2]. Many papers focused on achievement of several independently controllable parameters in frame of multi-terminal (multi-port) device such as electronically controllable current conveyors (ECCIIs) [3], [4], some members of family of voltage differencing current conveyors (VDCCs) [1], [2], [5]-[7], current follower transconductance amplifiers (CFTAs) [1], [2], [8]-[11], etc. These and also many other devices provide various types of inter-terminal (interport) relations. However, simpler types of active devices have been studied rarely. In fact, also simple two-port transfer function offers three degrees of freedom (input impedance, output impedance and transfer gain/attenuation). However, the first two mentioned features are often expected to be constant and as close to ideal as reasonable for requested type of processing (i.e. in ideal case: voltage mode – input impedance Zinp equal to infinity, output impedance Zout equal to zero; current mode – input impedance Z inp equal to zero, output impedance Zout equal to infinity). Nevertheless, possibility to control these impedances can be viewed as beneficial advantage in some types of circuit synthesis and design in order to reach additional degree of freedom used for adjustability and controllability of some parameter(s) of future application. We will focus on the simplest current-mode active elements that are 2

frequently used for both current-mode and voltage-mode applications. A current amplifier (CA) with controllable current gain (B) and controllable Zinp (real part) can be considered as one of the most useful active device for current-mode signal processing. The simplest theoretical approach looks at this device as having only single controllable parameter (B), however, as mentioned above, a number of controllable parameters can be increased. The initial study of adjustable current gain (B) in frame of the current conveyor was provided several decades ago by Surakampontorn et al. [12] and some of its modifications appeared in literature later [13], [14]. Similarly, the first idea of electronically controllable Rinp has been presented in frame of so-called current controlled current conveyor by Fabre et al. [15] and later in its modifications (for example [16]). However, implementation of both of these features in frame of single CA is not so old idea. Several modifications of CA, extending number of controllable parameters, have been presented recently. Works [17], [18] introduced concept of CA offering electronically controllable input resistance (R inp as real part of Zinp) together with adjustable current gain B. CAs presented in [18] employ also feedback with variable gain (A) voltage amplifiers (VGAs) in order to control value of input resistance. It is worth noting that solutions [17], [18] can still be simplified as will be shown in this paper. It could be objected that both these features can be obtained in case of active elements presented in [3], [4], just by grounding of input voltage terminal of proposed ECCIIs. Unfortunately, these concepts are simulated only at theoretical level of CMOS implementation and represent therefore only hypothetical devices; i.e. they were not fabricated and are not commercially available. Moreover, any detailed information about qualitative description (frequency features and dynamics of Rinp) are frequently not discussed [3], [4], [10], [11], [15]-[17]. Some attempts leading to practical implementation of controllable Rinp were fabricated as presented in [6], [7]. Available features of all discussed concepts regarding R inp range, frequency features, and dynamic ranges (depending on availability in referred work) are summarized in Tab. 1, together with features of proposed devices that are going to be presented within this paper.

Ratio (max/min value) [-]

Frequency performance (bandwidth) [MHz]

DC dynamics of current input [µA]*

N/A 10→150 µA 6→300 µA N/A N/A 0.1→500 µA 30→2000 µA 0.1→3 V

N/A 2.53→0.45a 2.10→0.31a N/A N/A 100→0.02a 0.3→0.01 a 2.80→0.11a

N/A 5.6 6.8 N/A N/A 5000 30 25

N/A < 100 0.1→1 N/A N/A N/A N/A N/A

N/A N/A ± 50 N/A N/A N/A N/A N/A

control voltage

0.1→3 V

2.7→0.10 a

27

0.1→2

> ± 200

a

control voltage

0.1→2 V

2.67→0.13

21

0.2→4

> ± 200

control voltage

0.5→0.98 V

0.12→0.71b

5.9

0.2→2

> ± 100

control voltage

0.5→1.35 V

b

0.12→0.55

4.6

0.5→2

> ± 1600

control voltage

0→1.5 V

1→11 b

Proposed 11 0.1→2

3

> ± 50

Verification

Range of Rinp control [kΩ]

bias current bias current bias current bias current bias current bias current bias current control voltage

Technology

Fig. 2

Range of driving parameter

[3], [4] [5] [6], [7] [10] [11] [15] [16] [17] Fig. 3 [18] Fig. 3 [18] Fig. 4a [18] Fig. 6a [18] Fig. 7a

Type of Rinp control

Reference

Tab. 1. Comparison of available approaches to Rinp control of current input

bipolar CMOS CMOS bipolar bipolar bipolar bipolar commercial devices (3 ECCIIs, 1 R) commercial devices (3 ECCIIs, 1 R) commercial devices (3 ECCIIs, 1 R) commercial devices (2 VGA+1 DT, 2 R) commercial devices (2 VGA+1 DT, 2 R)

Simulation Simulation Measured Simulated Simulated Simulated Simulated Simulated

commercial devices

Measured

Measured Measured Measured Measured

0→0.98 V

Fig. 3

control voltage

a – hyperbolic control of Rinp

0→0.98 V 0→0.99 V ∼ 1/control

(1→0.1)b **Combined: (0.1→11) 1→20 b 1→100b***

10 110**

<1

> ± 1000

(1 VGA+1 ECCII, 1 R)

20 100***

0.1→3 0.01→3

> ± 50

commercial devices (1 VGA+1 ECCII, 1 R)

Measured

b – exponential control of Rinp ∼ exp(control) or 1/exp(control) * valid for the highest available resistance value ** both polarities of voltage gain A tested; change of polarity is beneficial because it is not necessary to interchange input terminals of VGA in order to change the polarity. *** even higher value is available (> 100 kΩ) but it is not practical due to particular limitations such as very high sensitivity of this parameter due to natural character of relation for Rinp as well as very low frequency bandwidth (this is typical for any solution having such high value of Rinp).

The following conclusions can be drawn to the comparative study in Tab. 1. Simulated or fabricated active elements utilize possibility to control bias current in limited range given by functionality borders of internal topology in order to adjust Rinp as hyperbolic function of control [5]-[7], [15]-[18]. Let us now briefly discuss impact of bias current also on output impedance (resistive part), dynamics and frequency features of whole device (bandwidth of current transfer between X and Z terminal and voltage transfer between Y and X terminal [6] of the current conveyor). Some solutions from a specified list indicate really high value of Rinp (hundreds of kΩ) obtained by setting of very low values of bias current [15], [16], however, transistors in internal topology are not operating in intended regime in this case (especially in CMOS) for any level of input signal because dynamics, linearity, and frequency bandwidth of the solution become very limited (units of µA, tens of kHz). On the other hand, high value of bias current in topology causes not only intended decrease of Rinp and welcomed improvement of dynamics and frequency bandwidth [6] but also unintentional reduction of resistance of current output in typical case [5]. When implementation of CA by several commercially available devices is compared to CMOS solutions of CA based on bias current control of Rinp [5]-[7], the range of R inp adjustability is extended. However, three active devices and external resistor are required [17], [18]. Adjustability of Rinp is exponentially dependent on control quantity in several cases (possible for solutions based on commercially available devices), but the number of active devices is similar and one more resistor must be used [18]. This paper intends to introduce a new and improved concept of single-input and single-output current amplifier (CA-SISO) based on commercially available elements reducing the number of necessary active devices to two only, in which the first device is employed for control of Rinp and the second for control of current gain B. Later on, the introduced CA is extended to single-input and double-output (SIDO) or multiple-output (SIMO) version in order to extend application potential. Newly proposed CA concept offers most importantly: a) significantly reduced complexity (two active devices only, VGA and ECCII in SISO version of CA are sufficient to provide all required features including independent adjustability of Rinp and B), b) single external resistor in CA-SISO version (previously reported solutions utilized two external resistors [18] in SISO version), c) multiple-output version (SIMO) easily available (simple extension in order to obtain more outputs), d) exponential control of Rinp and linear control of B. The mentioned benefits of described arrangement of CA were verified in case of novel quadrature oscillator, where CA-SIDO ensures controllability of frequency of oscillation and independent driving of condition of oscillation. This paper is organized as follows: Section 2 focuses on specification of the newly proposed versions of CA. Section 3 highlights operation of these active devices verified by PSpice simulations and also by lab measurements. Application of CA-SIDO in simple quadrature oscillator with extended tunability features is discussed in Section 4 and the obtained results are compared to several known solutions, where possible extension of tunability range was already introduced. Section 5 summarizes the main results of this study. 4

2. Newly designed solutions of Adjustable Current Amplifiers Employing Variable Gain Voltage Amplifier and Electronically Controllable Second Generation Current Conveyor This section aims to introduce a novel and less complex structures of CA allowing identical behavior and operation as firstly appeared in [17], [18], i.e. CA with independent control of two required features, i.e. current gain B and resistance of input terminal R inp. Basic concept of this device can be viewed in Fig. 1 in form of schematic symbol. In ideal case this device performs amplification of current gain (Iout = B·Iinp), where the current gain B = f(VSET_B) and intentional control of input resistance (Rinp = f(VSET_Rinp)).

Fig. 1. Symbol of current amplifier (CA) with independent electronic control of input resistance and current gain.

Functionality of the device shown in Fig. 1 can be achieved by various methods [3]-[5], [17], [18], but the newly presented one is the simplest from those focused on practical implementation using “on the shelf” active devices [18] (see a comparison in Tab. 1), because only two active elements are sufficient to create this type of CA in SISO variant. Such approaches are welcomed by designers and researchers having no direct access to expensive fabrication of internal BJT/CMOS structures [2]-[7] or when saving time from design to production. The following subsections describe three possible conceptions of such CA device based on utilization of only single variable gain amplifier (VGA) [1] and electronically controllable current conveyor of second generation (ECCII) [1], [2], [12], [13].

2.1. Controllability based on multiplication of intrinsic resistance by electronically adjustable term This first type of novel improved solution of the CA based on negative feedback of VGA is shown in Fig. 2. The following equations are valid for ideal operation of the device:

Rinp = Rx (1 + A) ,

I out = B ⋅ I inp .

(1), (2)

By interchange of input terminals of the VGA (not shown in Fig. 2), (1) turns to: Rinp = Rx (1 − A) ,

(3)

which ensures reaching the lowest (almost zero) positive input impedance for A → 1 (Rinp_max → Rx; Rinp_min → 0). Input resistance defined by (3) can be also obtained in negative form (for A > 1). Feature of negative resistance effect can be beneficially used especially in oscillators as will be discussed in Section 3.

5

Fig. 2. The first variant of the concept of the CA based on single VGA and single ECCII.

2.2. Controllability based on division of intrinsic resistance by electronically adjustable term The second version of the CA (Fig. 3) omits negative feedback (visible in Fig. 2) and therefore, offers different form of ideal relation for Rinp as follows: Rinp =

Rx . 1− A

(4)

Similarly to (3), negative value of resistance for A > 1 is available, but there is also a possibility to reach the highest (almost infinity) positive input impedance for A → 1 (Rinp_max → inf.; Rinp_min → Rx ). Current transfer from input to output terminal has the same form as (2). VSET_B

Rx

Iinp

X

VSET_Rinp Vinp

Y

B ECCII

Iout Z Vout

VGA

A

Fig. 3. The second variant of the concept of the CA based on single VGA and single ECCII.

Simple interchange of input terminals of the VGA (+ ↔ −) results in positive character of the denominator as follows: Rinp =

Rx . 1+ A

(5)

However, the maximal value of Rinp is given by Rx in this case and minimal value depends on A by indirect proportion, which means that very large value of VSET_Rinp will be required to obtain very low Rinp value. Because of this variability, solutions in Fig. 2 and Fig. 3 and also the mentioned variants with interchanged input terminals of VGA satisfy demands for various ranges of Rinp control. Presented concept of CA can be simplified in order to be implemented in applications requiring current followers (CFs) with controllable Rinp [19]-[22]. Current follower (inverting) can be built very easily from solution in Fig. 3. The only modification of circuitry shown in Fig. 4 is the output section where ECCII is replaced by diamond transistor (DT) [2]. Current transfer is not given by (2) but has a simpler form: Iout = Iinp. Note that equations (4) and (5) and the principle of interchange of input terminals of VGA are valid also for the circuit in Fig. 4.

6

Fig. 4. Possible simplification of the concept of CA from Fig. 3 leading to the inverting CF.

2.3. Enhancement of the CA concept provided in order to obtain multiple current output terminals Additional current outputs of the CA are frequently required for current-mode applications such as summation and subtraction of currents in node. Therefore, it is very important to implement such feature also into newly proposed solutions of CA-SIMOs. Figure 5 introduces such modification of solution from Fig. 2, where additional branches of current outputs with independently settable gains are available. Ideal transfer response can be characterized by equation: I outi = Bi ⋅ Iinp ,

i = 1, 2, … n

(6)

and its input resistance can be characterized by: Rinp =

(1 + A) .

(7)

n

1 ∑ i =1 Rxi

Numerator of (7) can be also considered as (1 ± A), when change of input terminals (VGA) or polarity of A is supposed. Note that similar approach can be used also in case of modification of the solution from Fig. 3 in order to obtain multiple outputs with independent control of current gain (not presented in this paper). VSET_Bn

Rxn Bn

X

Y

ECCII

Ioutn Z Voutn

VSET_B1

Rx1

Iinp

B1

X

VSET_Rinp Vinp

Y

ECCII

Iout1 Z Vout1

VGA

A

a)

b)

Fig. 5. The CA-SIMO based on single VGA and multiple ECCIIs having outputs with independently controllable current gains B: a) symbol, b) proposed concept.

For some applications, same polarity of all outputs of CA-SIMO is not advantageous. Very simple modification of solution from Fig. 5 is possible in order to obtain both polarities of output currents as shown in Fig. 6 (additional DT was used as current mirror inverter). Resulting solution in Fig. 6 was selected as specific example of CA-SIMO from Fig. 5 b with dual current outputs (CA-SIDO).

7

VSET_B2

Rx2 X

Y

B2 ECCII

Iout2 E

Z

DT B

C Vout2

V SET_B1

Rx1

Iinp

X

V SET_Rinp Vinp

Y

VGA

B1 ECCII

Iout1 Z Vout1

A

a)

b)

Fig. 6. Example of the second variant of the CA-SIDO based on single VGA and two ECCIIs having inverting and non-inverting outputs with independently controllable gains: a) symbol, b) proposed concept.

3. Analysis of proposed solutions The printed circuit board (PCB) shown in Fig. 7 was developed for purposes of laboratory tests of proposed concepts (CA operation as well as application of CA in quadrature oscillator tunable in wide range). Variable gain amplifiers are embedded by DIL versions of VCA810 [23], ECCIIs by EL2082 [24], and diamond transistors by OPA860 [25]. The voltage gain of the VGA can be expressed as A = 102(VSET_A − 1) and the current gain of the ECCII (transfer between X and Z terminal) as B ≅ VSET_B. All practical experiments were carried out in laboratory of the SIX Research Center and performed by vector network analyzer 4395A, impedance analyzer 4294A cooperating with PC interconnected also to DC power supply sources and multimeters in order to provide precise tests in DC and AC domain.

Fig. 7. Experimental board (PCB) for detailed testing of the CA and construction of proposed application.

3.1 Analysis of features of CA with intrinsic resistance multiplied by electronically adjustable term The detailed test results of solution in Fig. 2 (with Rx = 1 kΩ) are summarized in this subsection. All results suppose existence of parasitic capacitance Cp = 10 pF in input node (approximately modeling 8

real capacity of PCB). The results of control of Rinp of CA are shown in Fig. 8. Change of input polarity of VGA allows Rinp to obtain value lower than 1 kΩ due to term (1–A) in definition of Rinp. The results of impedance magnitude in frequency domain for this configuration are included in Fig. 9. Figure 10 indicates dependence of Rinp on VSET_Rinp (A) for both cases. In case of non-interchanged polarity, the concept operates highly linearly in discussed range of Rinp (1 kΩ → 10 kΩ) with value of input current up to ± 50 µA (A > 2). Small deviation from strictly linear behavior allows to process signal with peak-to-peak value up to ± 500 µA especially for A < 5 (VSET_Rinp < 1.35 V). Interchanged polarity of input terminals of VGA in frame of solution based on topology in Fig. 2 offers Rinp operation below 1 kΩ (1 kΩ → 100 Ω). Frequency domain characteristics of Rinp are given by Cp in input node and actual Rinp value. Hence, useful bandwidth (flat region) falls into 100 kHz for the highest values of Rinp (tens of kΩ) and 1 MHz (the lowest values of Rinp). Transfer features of CA are mainly given by limitations of ECCII. The results given in Fig. 11 focus on AC and DC transfer responses by varying current gain B (VSET_B). Adjusting of VSET_B in range 0 → 4.1 V provides gain (B) control from 0 to 3.5. Smooth operation of the device in this range of gain is ensured almost up to ± 1 mA with bandwidth (−3 dB) about 16 MHz. In simulations we achieved wider bandwidth up to 23 MHz due to some not included real effects of PCB. Note that almost the identical results were obtained for all CA concepts presented within this work and using this arrangement of ECCII (these results are not presented in this paper).

a)

b)

Fig. 8. a) Dependence of input impedance (positive character) on frequency and A (VSET_Rinp) in AC domain, b) results in DC domain (dependence of Vinp on Iinp ).

Fig. 9. Dependence of input impedance (positive character, inputs of VGA interchanged + ↔ −) on frequency and VSET_Rinp (AC domain).

9

a)

b)

Fig. 10. Dependence of Rinp on control voltage VSET_Rinp for solution in Fig. 2: a) Rinp = Rx(1+A), b) Rinp = Rx(1−A).

a)

b)

c) Fig. 11. Dependence of characteristics of the CA on VSET_B in a) AC domain, b) DC domain. c) Dependence of value of B on VSET_B.

3.2 Analysis of CA with intrinsic resistance divided by electronically adjustable term Solution in Fig. 3 was also tested in order to verify larger range of Rinp control given by beneficial form of R inp = Rx/(1−A). Simulation and measurement results of input impedance are compared in Fig. 12. Tested range of Rinp (1 kΩ → 20 kΩ) was obtained for VSET_Rinp adjusted from 0 to 0.98 V. 10

Note that sensitivity of R inp to values of VSET_Rinp close to 1 V is very high and Rinp value is significantly increased (103 kΩ was obtained experimentally for A = 0.992). However, useful bandwidth of impedance drastically decreases below 10 kHz for the highest Rinp values. Therefore, in general due to frequency limitations it is not recommended to use any of designed CA with larger Rinp than several tens of kΩ above audio bandwidth. Achievement of negative value of Rinp is beneficial for application in oscillators and undamped resonators [26]. Negative values were reached for A > 1 (VSET_Rinp > 1 V). The results in Fig. 12 b compare phase responses of input impedance for positive Rinp = 2 kΩ (VSET_Rinp = 0.85 V) and negative Rinp = -1 kΩ (VSET_Rinp = 1.15 V). Dependence of Rinp on VSET_Rinp is shown in Fig. 12 c. Note that DC dependence of Vinp on Iinp (positive Rinp) is very similar to Fig. 8 b as well as DC dependence of Iout on Iinp (identical to Fig. 11 b). Therefore, these characteristics achieved for variant of CA from Fig. 3 are not shown.

a)

b)

c) Fig. 12. a) Dependence of input impedance on A (VSET_Rinp) for A = 0 → 1 in AC domain, b) change of polarity of Rinp for A = 0.5 and 2, c) dependence of Rinp on VSET_Rinp.

4. Application of designed CA-SIDO in Quadrature Oscillator with Extended Tunability Feature 4.1 Theoretical principle of operation Proposed oscillator shown in Fig. 13 utilizes CA from Fig. 5, particularly in dual-output variant (CA-SIDO). This oscillator consists of a lossless (compiled from ECCII, VGA, Ra and C1 ) and 11

lossy (created by CA and C2) current-mode integrators. An additional feedback from second output of CA to C2 is required in order to control condition of oscillation (CO) independently. The lossless integrator subpart allows the same type of control as provided by CA in Fig. 5, i.e. exponential control of auxiliary resistance Raux and linear control of current gain B (B1b). Two parameters serve for linear control of oscillation frequency (VSET_B1a, VSET_B1b) and two parameters (V SET_Rinp, VSET_Raux) for nonlinear control of the same frequency. Utilization of VGA with exponential control of gain A1 (providing: Raux = Ra(1+A1) ≅ Ra(1 + 102(VSET_Raux − 1))) is necessary due to requirement of an electronically adjustable time constants in the structure having both the same dependence on driving voltage (exponential control of Rinp and Raux). Therefore, coordination of parameters of the CA and rest of the circuit brings significant extension of adjustability of frequency of oscillation (FO) including simple and independent control of CO. The characteristic equation of the circuit in Fig. 13 has form (basic form shown as (8a), extended form including DC driving voltages shown as (8b)): s2 +

s2 +

(

2 − VSET _ B 2

Rx 1 + 10

2 (V SET _ Rinp −1)

s+

)C

1

2 − B2 B1a B1b s+ =0, C1Rinp Rinp RauxC 1C2

V

(

Rx 1 + 10

(8a)

V

SET _ B1 a SET _ B1b 2 (V SET _ Rinp −1) 2 (V SET _ Raux −1 a

)R (1 + 10

)C C 1

= 0,

(8b)

2

where FO is:

ω0 =

VSET _ B1aVSET _ B1b B1a B1b , ≅ 2 (VSET _ Rinp −1) 2 (V −1 RinpRauxC1C2 Rx 1 + 10 Ra 1 + 10 SET _ Raux C1C2

)

(9)

B2 ≥ 2 ⇒ VSET _ B 2 ≥ 2 V .

(10)

(

) (

and CO is:

tunability of FO extended (Rctrl and B)

V SET_Ra ux

AGC control B1a

CA

linear control of FO by B (VSE T_B)

VSET_B1b

VSET_Rinp V SET_B1a V SET_B2

nonlinear control of FO by Rctrl (VSE T_R)

Y

VC1

C1

Rinp

B2

X

ECCII

Z

B1b

Ra VGA

A1

Raux VC2

C2

Fig. 13. Proposed quadrature oscillator with extended tunability utilizing proposed CA-SIDO.

Routine analysis of amplitude and phase relations between generated waveforms yields the following result: VSET _ B1a VC1 B1a . = ≅ VC 2 sC1Rinp sC1Rx 1 + 102 (VSET _ Rinp −1)

(

12

)

(11)

Supposing equality of B1a = B1b = B (VSET_B1a = VSET_B1b = VSET_B), Rinp = Raux = Rctrl (in fact Rx = Ra = Rr and VSET_Rinp = VSET_Raux = VSET_R) and C1 = C2 = C, then (9) and (11) significantly reduce to the following forms:

ω0 =

B RctrlC

≅

(

VSET _ B 2(VSET _ R −1)

Rr 1 + 10

)C

VC1 =−j ⇒ VC 2

,

VC1  π  = exp − j  . VC 2  2 

(12), (13)

Note than dependence of FO on VSET_B is linear whereas dependence of FO on VSET_R has indirect proportion to exponential character. However, combination of both methods may help to significantly extend adjustability of FO as will be explained later.

4.2 Experimental tests of nonlinear FO tuning by VSET_R All theoretical calculations suppose C1 = C2 = (100 + 10) pF (parasitic value of 10 pF is added as effect of real PCB affecting high-impedance nodes of C1 and C2 are expected). Rest of parameters was selected as follows: Rx = 1005 Ω (consisting of 910 Ω + 95 Ω parasitic intrinsic resistance of EL2082 in CA-SIDO), Ra = 1 kΩ. Control voltage VSET_R was changed as noted in the results presented graphically whereas VSET_B was constantly equal to 1 V during tests of nonlinear tuning. Operation of the oscillator requires precise amplitude gain control circuit (AGC) for amplitude stabilization (input taken from node of VC1, output is connected to VSET_B2 terminal directly). Slight modification of AGC solution from [27] was established for these purposes and therefore it is not presented within this paper. Analyzed non-linear way of control (Rctrl by VSET_R) can be observed in Fig. 14 a showing the dependence of FO on VSET_R. Tunability of FO was experimentally verified from 1.42 MHz to 216 kHz (decreasing slope) by adjusting VSET_R from 0 to 1.5 V (meaning that Rinp and Raux are controlled simultaneously from 1 kΩ to 10 kΩ). FO of 1.43 MHz → 131 kHz was expected theoretically, and range 1.39 MHz → 135 kHz was obtained from simulations, therefore, there is very good agreement of theory, simulation and real measurement. Measured dependences of output levels of VC1 and VC2 on FO are shown in Fig. 14 b. The high-impedance nodes were separated by voltage buffers. Measured dependences of total harmonic distortion (THD) and phase shift between generated signals on FO are shown in Figs. 14 c and 14 d, respectively. Figure 15 shows an example of output quadrature waveforms and spectral analysis of selected waveform VC2.

a)

b)

13

c)

d)

Fig. 14. Detailed analysis of proposed oscillator with non-linear control of FO (controlled by adjustable resistances): a) dependence of FO on VSET_R, b) dependence of output levels on FO, c) dependence of THD on FO, d) dependence of phase shift between generated signals on FO.

a)

b)

Fig. 15. Example measurement results of the oscillator in configuration with non-linear control of FO (VSET_R = 0.85 V, VSET_B = 1 V): a) transient responses, b) spectrum for VC2 .

4.3 Experimental tests of extended FO tuning by VSET_R and VSET_B The proposed solution of the oscillator from Fig. 13 offers beneficial feature of extension of FO tuning range by utilization of all parameters influencing both time constants. It is possible due to implementation of CA (with controllable parameters Rinp, B1a) and ECCII with external adjustable resistance connected to X terminal and controllable current gain (i.e. Raux, B1b). Dependence of FO on VSET_R for several values of VSET_B allows to achieve several-times higher tunability range of FO than in case of the previous method, see Fig. 16 a. Overall adjustability can be observed from Fig. 16 b, where different view on extended adjustability of FO is provided. A comparison of available methods of control is given in Tab. 2, where also linear type of control of FO (that was not presented in detail in the paper) is shown for comparison. Maximal range of FO tuning was theoretically expected as 24 → 5 067 kHz, when simulations yield 59 → 4 730 kHz and range 29 → 4 940 kHz was obtained by experimental measurements.

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a)

b)

Fig. 16. Extended adjustability of FO illustrated by two different dependences: a) dependence of FO on VSET_R, b) dependence of FO on VSET_B.

Tab. 2. Comparison of operation of both methods of FO control with conjunctive method. Method of control VSET_B [V] VSET_R [V]

Nonlinear 0.1 1.35→0.1

f0min [kHz] f0max [kHz] ∆f0 [kHz] ratio [-]

24 143 118 6.0

f0min [kHz] f0max [kHz] ∆f0 [kHz] ratio [-]

59 138 79 2.3

f0min [kHz] f0max [kHz] ∆f0 [kHz] ratio [-]

29 153 124 5.3

Linear 0.1→4.1 0.01

Both 0.1; 4.1 1.35; 0.1

143 5 067 4 924 35.4

24 5 067 5 043 212.4

138 4 730 4 592 34.3

59 4 730 4 671 78.9

153 4 940 4 787 32.3

29 4 940 4 911 171.2

Theory

Simulation

Measurement

4.4 Discussion Proposed oscillator in Fig. 13 is quite unique, because only the limited number of solutions providing similar features has been reported in open literature. The first realization worth mentioning employs so-called Double Current Controlled Current Feedback Amplifier (DCC-CFA) [28]. This active device includes two independently controllable parameters. However, it cannot sufficiently replace herein proposed CA-SIDO in presented application (Fig. 13) due to unavailability of independently adjustable gain B in each current output. However, DCC-CFA was employed in another circuit topology of second-order quadrature oscillator [29], where tunability ratio 14.6:1 has been obtained by combination of both methods of FO control. Drawback of circuit in [29] lies in the fact of dependence of generated waveforms on tuning process. An attempt to extend tunability of FO was presented also in [27]. However, extension of FO range is not given by combined control of several parameters and their simultaneous change, but by suitable form of equation of FO, where variable voltage gain (A) may reach both polarities (voltage-mode multiplier implemented in VGA solution). However, multiphase features of topology in [27] are limited since the circuit does not generate quadrature signals. Therefore, a newly presented solution (Fig. 13) brings important improvements as also obvious from the following Tab. 3, where the main features of these oscillators are summarized.

Tab. 3. Comparison of relevant solutions of oscillators with intentionally extended tunability range of FO

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control voltages

Range of f0 control (combined method) [MHz]

Maximal f0 ratio (max/min value) [-]

Amplitudes independent on tuning process

3.7→27.1

7.3

N/A

Rinp , B Rctrl, B

0.24→3.48 14.6 Proposed 0.029→4.94 171.2

No Yes

Verification

Fig. 13

A

Realization

[29]

control voltages bias currents

Controllable parameters (for FO control)

Type of FO control

Reference [27]

commercial devices bipolar/CMOS

Measurement

commercial devices

Measurement

Simulation

5. Conclusion The active element CA-SISO is two-port device having single input and single output terminal and providing availability of electronic control of input resistance (Rinp) and current gain (B). Dependence of Rinp on DC control voltage has nonlinear character due to nonlinear character of control of VGA whereas dependence of B on DC control voltage is mostly linear similarly to as presented in our experiments. Several specific variants of CA differing by type of VGA interconnection were shown. The first one employs single resistor, single VGA with direct negative feedback, and single ECCII. Such arrangement offers adjusting of Rinp by multiplicative term consisting variable voltage gain A as adjustable parameter. Input resistance Rinp can theoretically achieve only positive (A ≥ 0) value (1), (5) or positive value (1 ≥ A ≥ 0) and negative value (A > 1) in case of (3), (4) after appropriate interchange of VGA inputs (+ ↔ −) in Fig. 2 and 3 as described in the paper. Adjustability of R inp was tested from 100 Ω to 10 kΩ (1 kΩ → 10 kΩ and 1 kΩ → 100 Ω). The second solution (Fig. 3) operates without any feedback in frame of VGA part, i.e one from two differential input terminals of VGA is always grounded. Division of external resistance value by term containing adjustable parameter allows adjustment of Rinp in this case. Negative value of Rinp can be reached for the same theoretical values of A as in previous case. Control of Rinp was tested and proved to be most beneficial in range from 1 kΩ to 20 kΩ. Proposed CA brings advantage of extended controllability into the synthesis of applications. These advantages were proven in case of quadrature oscillator with extended tunability of frequency of oscillation. Despite voltage form of output waveforms, proposed circuit topology utilizes currentmode signal operations [2], [26], [30], [31] provided by CA (dual current outputs for summation/subtraction of currents in nodes, control of nodal resistance) that allow to simplify overall complexity. Readjustment ratio of 171.2:1 (f0max/f0min ) was obtained experimentally in case of combination of both methods of electronic control. Presented features of the newly introduced CA can be useful for implementation of electronic tunability in topologies of classical (integer-order) oscillators (for example [32]), multiphase oscillators [33], special fractional-order square-wave generators [34] and as well as for special operations with output amplitudes [35] due to increased degree of freedom in multi-parameter controllability.

6. Acknowledgement Research described in this paper was financed by Czech Ministry of Education in frame of National Sustainability Program under grant LO1401. For research, infrastructure of the SIX Center was used. 16

Research described in the paper was supported by Czech Science Foundation projects under No. 1611460Y.

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