Study of impact of voltage gain of comparator on performance of newly designed functional generator

Study of impact of voltage gain of comparator on performance of newly designed functional generator ŠOTNER, R.; JEŘÁBEK, J.; HERENCSÁR, N. Optik 2018, vol. 172, November 2018, pp. 203-219 ISSN: 0030-4026 DOI: https://doi.org/10.1016/j.ijleo.2018.06.140 Accepted manuscript © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license (http://creativecommons.org/licenses/by-nc-nd/4.0/), doi: https://doi.org/10.1016/j.ijleo.2018.06.140 Final version available from https://www.sciencedirect.com/science/article/pii/S0030402618309501 dspace.vutbr.cz Accepted Manuscript Title: Study of impact of voltage gain of comparator on performance of newly designed functional generator Authors: Roman Sotner, Jan Jerabek, Norbert Herencsar PII: S0030-4026(18)30950-1 DOI: https://doi.org/10.1016/j.ijleo.2018.06.140 Reference: IJLEO 61143 To appear in: Received date: 4-5-2018 Accepted date: 28-6-2018 Please cite this article as: Sotner R, Jerabek J, Herencsar N, Study of impact of voltage gain of comparator on performance of newly designed functional generator, Optik (2018), https://doi.org/10.1016/j.ijleo.2018.06.140 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Study of impact of voltage gain of comparator on performance of newly designed functional generator Roman Sotner1,2, Jan Jerabek2, Norbert Herencsar2 1Dept. of Radio Electronics, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technicka 3082/12, Brno, Czech Republic 2Dept. of Telecommunications, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technicka 3082/12, Brno, Czech Republic Abstract This paper focuses on analysis of impact of voltage gain of comparator on features of designed triangular and sine wave generator. Newly designed generator employs minimal number of passive and active components based on simple voltage controllable amplifier and electronically controllable current conveyor or adjustable current amplifier. The generator has simple structure with easily available electronic control of repeating frequency and duty cycle. Detailed PSpice analyses of the modified generator are provided and relevant results of experimental measurements are shown. Discussion of non-ideal effects of voltage gain (A) of controllable amplifier used as comparator on generated amplitudes, on repeating frequency and on duty cycle as well as effects of statistical dispersion of important parameters are given. Observed behavior was analyzed not only by simulations but also by experimental measurements. Keywords: Controllable current gain, electronic control, electronically controllable current conveyor, gain adjusting, voltage controllable amplifier, triangle and square wave generator. 1. Introduction Electronic control of parameters in frame of active element [1] is very important for applications that require variable features. Applications that we discuss in this paper focus on triangle and square wave generators based on well-known solution [2] that is formed by loop connection of lossy integrator and comparator with two thresholds/hysteresis (so-called Schmitt trigger) [2]-[4]. Classical approaches employing operational amplifiers [2] are not very feasible because their controllable features are very restricted (only replacement of resistor in integrator by controllable equivalent) and complexity (number of passive elements - at least 3 resistor and floating capacitor) is higher in comparison to solutions utilizing other active devices as will be discussed in further text. Using of other active elements [1] allow us to obtain applications with simple control of their parameter(s). Many solutions of generators in simple form based on modern active elements are available in recent literature [1]-[24]. The following text represents brief discussion of their complexity and building active elements used. Single current differencing transconductance amplifier (CDTA) and three resistors together with grounded capacitor create simple solution presented by Biolek et al. [5]. De Marcelis et al. [6] used two current conveyors of second generation (CCIIs) and six resistors together with floating capacitor in their topology. Two differential voltage current conveyors (DDCCs) complemented by three resistors and grounded capacitor are typical for solution introduced by Chien et al. [7]. Almashary et al. [8] contributed by simplified topology employing two CCIIs, three resistors and two grounded capacitors. Further simplification (also based on two CCIIs, three resistors and only one floating capacitor) was proposed by Pal et al. [9]. Circuit based on two current feedback operational amplifier (CFOAs) including four resistors and floating capacitor that was developed by Haque et al. [10] bring another benefit (low-impedance outputs). Two operational transresistance amplifiers (OTRAs) also offer features for design of generators as shown by Lo et al. [11] in topology utilizing three floating resistors and capacitor. Minaei et al. [12] tested combination of CFOAs and DVCCs in these constructions. All already discussed works ACCEPTED MANUSCRIPT have limited availability of direct electronic tuning of repeating frequency (f0). The adjusting of parameters of previously reported generators is not possible by control of internal parameters of active elements. The only way is intentional change of resistance value. Therefore, electronically adjustable solutions of generators were also introduced. Operational transconductance amplifiers (OTAs) offer simple direct electronic control of its internal parameter (transconductance) by DC bias current as shown for instance by Chung et al. [13] in topology implementing three OTAs, two grounded resistors and capacitor. Similar solution was presented by Siripruchyanun et al. [14]. Kumbun et al. [15] brought circuit based on two advanced active elements so-called multiple-output current through transconductance amplifiers (MO-CTTAs) where only one grounded capacitor is sufficient to create generator. Similarly, Silapan et al. [16] and Sristakul et al. [17] employ only two multipleoutput current controlled current differencing amplifiers (MO-CCCDTAs) and grounded capacitor in their design. Universal current conveyor (UCC), CCII and eight passive (majority of them grounded) elements including four diodes were used by Janecek et al. [18]. Unfortunately, topologies introduced in [15]-[17] generate responses in form of current only and additional I→V transformation is necessary. The work [19] represents another approach into design of generators where differential output and fully balanced voltage differencing buffered amplifier (DOVDBA, FB-VDBA) together with three grounded passive elements are used in order to obtain differential output waveforms. Solution presented in [20] focuses on application of so-called voltage differencing current conveyor (VDCC) with various methods of electronic controllability of parameters of generator. The topology may generate also differential-mode square-wave voltage but requires at least three passive elements incl. grounded capacitor. Generator introduced in [21] represents example of one of the simplest topologies (only single capacitor required as external subpart). However, active device used in [20], [21] itself is not commercially available and its emulation by accessible active subparts leads to very extensive circuitry [21]. Reference [22] deals with reconfigurability of the generator between exponential and linear charging/discharging. Special topology of electronically reconfigurable lossy/lossless integrator allows these features. Nevertheless, necessity of three active elements and four passive elements puts this circuit into the group of rather complex solutions. Detailed parameters of all discussed solutions are compared and summarized in Table 1. Table 1. Comparison of discussed solutions. Reference No. of passive elements No. of active elements Grounded capacitor Electronically tunable f0 Trend of f0 tuning (dep. of f0 on driving force – resistance or active parameter) Type of f0 control (PEpassive elements; DC V - DC bias voltage; DC I - DC bias current) f0 tunable electronically without impact on duty cycle ≠ 50% f0 control without impact on duty cycle having no matching condition Duty cycle control available (N/A – information not available) Electronically controllable duty cycle Duty cycle adjusted without additional circuity (controlled DC current source) Type of D control (PEpassive elements; DC V - DC bias voltage; DC I - DC bias current) Type of output signals (current or voltage) [5] 4 1 Yes No inversely proportional PE N/A N/A N/A No N/A - Voltages [6] 7 2 No No inversely proportional PE N/A N/A N/A No N/A - Voltages [7] 4 2 Yes No inversely proportional PE Yes Yes Yes Yes Yes DC V Voltages [8] 5 2 Yes No inversely proportional PE N/A N/A N/A No N/A - Voltages [9] 5(6) 2 No No inversely proportional PE N/A N/A N/A No N/A - Voltages [10] 5 2 No No inversely proportional PE N/A N/A N/A No N/A - Voltages [11] 4 2 No No inversely proportional PE N/A N/A N/A No N/A - Voltages [12] 4 2 Yes No inversely proportional PE N/A N/A N/A No N/A - Voltages [13] 3 3 Yes Yes linear DC I N/A N/A Yes Yes No DC I Voltages [14] 3 3 Yes Yes linear DC I N/A N/A Yes Yes Yes DC I Voltages [15] 1 2 Yes Yes linear DC I Yes Yes Yes Yes Yes DC I Currents [16] 1 2 Yes Yes linear DC I N/A N/A N/A No N/A - Currents [17] 1 2 Yes Yes linear DC I N/A N/A N/A No N/A - Currents [18] 4 2 Yes Yes linear DC V N/A N/A N/A No N/A - Voltages [19] 3 2 Yes Yes linear DC I Yes No Yes Yes No DC I Voltages [20] 3 1 Yes Yes linear DC I Yes No Yes Yes No DC I Voltages [21] 1 1 Yes Yes linear DC I Yes No Yes Yes No DC I Voltages [22] 4 3 Yes Yes linear DC V N/A N/A No No N/A - Voltages [23] 2 2 Yes Yes linear DC V Yes Yes Yes Yes No DC I Voltages [24] 2 3 Yes Yes linear DC V Yes No Yes Yes Yes DC V Voltages proposed 2 2 Yes Yes linear DC V Yes Yes Yes Yes Yes DC V Voltages N/A – not available, not solved or not shown As we can see from Table 1, circuit presented in this paper has really beneficial features because it provides all required features: a) low number of passive and active elements; b) electronic control of repeating frequency; c) electronic control of duty cycle (D); d) voltage signal at outputs. Both parameters (f0, D) are controllably by DC voltage. Table 1 indicates existence of even simpler solutions [15]-[17], [21] than those presented in this paper. However, duty cycle control is not allowed/studied in [16]-[17] and circuits provide output signals in form of current (additional conversion to voltage necessary). Simple topology utilizing single active device in [21] solves these drawbacks. Unfortunately, duty cycle control requires additional circuitry, i.e. additional specifically controlled DC current source (as in many cases included in Tab. 1) and proposed behavioral model of the active device is extremely complex. The most similar performance of the solution with low number of circuit components ACCEPTED MANUSCRIPT has been achieved in [15]. Unfortunately, the circuit produces responses in form of currents. It requires additional conversion to voltage (by resistors) and buffering (low-impedance outputs) in comparison to our solution. Adjusting of parameters (repeating frequency, duty cycle) via DC driving voltage prepares solutions proposed in this paper for immediate implementation in analog/mixed systems without additional accessories or limitations. The solution presented in this paper is easily available by of-the-shelf active devices (no expensive IC fabrication of topology is required) and consist of acceptable amount of active and passive elements in comparison to other circuits listed in Tab. 1. Goals of our design are to obtain very simple solutions with minimal number of external passive components. Experimental construction are based on commercially available devices. Research presented in this paper brings new beneficial structure including evaluation of practical impacts of real parameters of the generator. Presented circuit utilizes voltage controllable amplifier(s) for construction of Schmitt comparator [2]-[4] and electronically controllable current conveyor of second generation forming controllable loss-less integrators. Some practical/real properties are quite hidden if only brief and superficial study is done, but these features are important for estimation of expected behavior of application. Simulations and real experiments confirm operability that highly depends on real features of active elements, especially in case of very simple circuits. This was found as the most important disadvantage and was deeply investigated in this paper. Paper is organized as follows: Section 1 briefly summarizes recent progress in the field of adjustable generators. Section 2 explains theoretical behavior of generator based on well-known structure (comparatorintegrator) and modern electronically adjustable active elements. In this paper, we present interesting solution of simple triangular and square wave generator overcoming features of the most similar previously reported solutions [23]-[24] with useful controllable parameters that are analyzed in section 3. Section 4 investigates features by PSpice simulations and studies practical impacts of most influencing features of active elements (comparator especially) on generator performance. Section 5 deals with experimental results of laboratory tests in order to confirm behavior expected from simulations. Conclusion and summarization is given in section 6. 2. Construction details of the generator Block diagram of the generator is shown in Fig. 1. Unfortunately, classical structure employing loss-less integrator and Schmitt trigger (comparator) [2]-[4] based on operational amplifiers does not allow direct electronic control of parameters of generated signal and it is therefore outdated by modern solutions. comparator (hysteresis) loss-less integrator k.1/s triangular wave Schmitt trigger square wave Figure 1. Basic block diagram of the triangular and square wave generator. Our effort focuses on electronic control of parameters of application. Therefore, we prefer active elements that allow adjusting of their important parameters electronically (by external control force, in our case DC voltage). Voltage controllable (variable gain) amplifiers (VCAs) are very important for design of modern analog systems. They offer wide range of gain control (-40 dB to 40 dB for example [25]), high slew rate and bandwidth and they are available commercially (many types are digitally controllable – it gives direct control of application from microcontroller for example). There are also some types of current amplifiers (CA) [26], [27] and simple controllable current conveyors [28], [29] available and they allow synthesis and design of interesting and simple integrator circuits. We selected useful examples of discussed active elements for further design of generator, namely: voltage controllable amplifier VCA810 [25], and current-mode multiplier EL2082 [30] as electronically ACCEPTED MANUSCRIPT controllable current conveyor (ECCII) [31]-[33]. Gains of voltage controllable amplifier (A) and electronically controllable current conveyor (B) are controlled by DC voltage. The loss-less inverting integrators are the key parts of generators. Loss-less inverting integrator based on discussed adjustable-gain devices is shown in Fig. 2. C RVo ECCIIZ Y X VSETB IC Vi Figure 2. Controllable loss-less inverting integrators used in proposed generator using ECCII. Ideal voltage transfer of the integrator shown in Fig. 2 has very simple form: int () SETB V B Ks sRC sRC     . (1) The DC control voltage VSETB shown in (1) is set in accordance to [30] (approximately valid B  VSETB for VSETB ≤ 2 V). Construction of the simplest solution of comparator (Schmitt trigger) [2]-[4], which is required for these types of generators, is shown in Fig. 3, where VCA element is utilized with full positive feedback without any additional resistors. The output voltage (Vo) reaches two saturation levels (Vsat_VCA) as clear from Fig. 4. These levels can by defined by catalogue parameters [25] or also experimentally [23], [24]. Vo VSETA VCA A Vi Figure 3. The simplest solution of comparator employing VCA with positive feedback. Vo Vi +Vi_HL -Vi_LH -Vi_LH = (A -1)/A.(+Vsat_VC A) +Vi_LH = (A -1)/A.(-Vsat_VC A) +Vsat_VC A -Vsat_VC A Figure 4. DC transfer characteristics of the Schmitt comparator with hysteresis based on VCA. Output voltages Vsat_VCA of the comparator are determined by both input threshold voltages (Vi = +Vi_HL = −Vi_LH) as:         i V V iVCAsat VV A A VSETA SETA  110 10 112 12 _      . (2) ACCEPTED MANUSCRIPT The reference voltages (input thresholds – crossing of these values causes turnover of output voltage from positive to negative saturation respectively) increase for higher value of gain A and are equal to Vsat_VCA for A → -∞. 3. The generator analysis In accordance to general topology presented in Fig. 1, we proposed and tested three suitable solutions based on components described above that offer electronic control of repeating frequency (f0) and possibility of duty cycle (D) adjusting. The circuit shown in Fig. 5 uses inverting integrator from Fig. 3, comparator from Fig. 4 and requires only two passive elements. The duty cycle is now controlled by DC voltage at Y terminal of ECCII, which decreases the complexity in comparison to the similar solutions [23], [24]. The diagram of parameters of output waveforms and time sections for following analysis and derivation is given in Fig. 6. VTR C R VSQ VSETA VCA A VDUTY VC ECCIIZ Y X VSETB IC IX Figure 5. The second solution of the generator employing also ECCII and VCA active elements. ∆VC = ∆Vinp_VCA VSQ VTR T1T2 ∆VSQ +VC_max (+Vinp_VCA) IC_max/C -IC_max/C +Vsat_VCA = A/(A -1).(-Vinp_VCA) -Vsat_VCA = A/(A -1).(+Vinp_VCA) -VC_max (-Vinp_VCA) B R VV IDUTYVCAsat C         _ max_ B R VV IDUTYVCAsat C         _ max_ Figure 6. Diagram of parameters of output waveforms, time sections and thresholds. The maximum of current flowing through capacitor is limited by 1/R to value derived from VSQ and current gain B of current amplifier section. The linear dynamic range of current amplifier is supposed as sufficient for this operation. The current limitation occurs for higher input level than saturation limit represented by Vo (VCA in Fig. 3). Current gain is low and dynamics/linearity of current amplifier is favorable. Therefore, saturation of the ECCII (current amplifier part) influences charging of capacitor C minimally. Based on principle of current/voltage transformation between Y and X terminals of ECCIIin Fig. 5, the following relation: X DUTY SQ RI V V , (3) ACCEPTED MANUSCRIPT results into: CZDUTYSQ I B R I B R VV  , (4) when definition of current transfer between X and Z terminal of ECCIIis considered. Then, the maximal current levels through C can be expressed as: B R VV IDUTYVCAsat C         _ max_ , (5) B R VV IDUTYVCAsat C         _ max_ , (6) where limitation of VSQ (Vsat_VCA) is given by saturation level of VCA [25] and, therefore, also threshold voltages highly depend on gain A (2). The linear change of voltage across the capacitor from VC_max to +VC_max (thresholds of the comparator) can be expressed as: _max _max _max ( ) 2 TR C C C C V V V V V        . (7) Voltage change of VSQ (Vsat_VCA) can be achieved analogously as: _ _ _ ( ) 2 SQ sat VCA sat VCA sat VCA V V V V      . (8) We can use equation (2) to obtain the following form for relation between ΔVTR and ΔVSQ as: 1 TR SQ A VV A        . (9) Because VTR = 2VC_max, VSQ = 2Vsat_VCA, it can be rewritten also as:   _max _ 1 C sat VCA A VV A        , (10)   _max _ 1 C sat VCA A VV A        , (11) _max _ 1 22 C sat VCA A VV A     . (12) The equation for repeating frequency can be easily derived from linear voltage increase or decrease across capacitor (between ±VC_max) by help of (5), (6), (12) as: _max _1 1 2C sat VCA I A VT AC      , (13) _max _2 1 2C sat VCA I A VT AC      , (14) resulting into:   1 _ _1 2T RC BVV A A VDUTYVCAsat VCAsat         , (15)   2 _ _1 2T RC BVV A A VDUTYVCAsat VCAsat         , (16) ACCEPTED MANUSCRIPT Then both intervals are given by:   BVV RC A A V T DUTYVCAsat VCAsat         _ _ 1 1 2 , (17)   BVV RC A A V T DUTYVCAsat VCAsat         _ _ 2 1 2 . (18) The repeating frequency (f0 = 1/(T1+T2)) and duty cycle (D = T1/T, period T = T1 + T2) can be expressed as:           _ _ _ _ 022 __ 11 44 sat VCA DUTY sat VCA DUTY SETB sat VCA DUTY sat VCA DUTY sat VCA sat VCA B V V V V V V V V V fAA RC V RC V AA                   , (19) 1 _ 11 2 DUTY sat VCA V T DTV        . (20) The VDUTY voltage may influence repeating frequency. However, when D is set to specific value the parameter suitable for f0 control (B, VSETB respectively) cannot have impact on D that is significant advantage. 4. Detailed PSpice analysis of the solution Macromodels of EL2082 [30] and VCA810 [25] devices are used in the following analyses. Selected parameters (expected as design constants) are as follows: R = 390 + 95 Ω (intrinsic resistance of current input of EL2082 is 95 Ω [34]), C = 100 pF + 6 pF (parallel combination of parasitic capacitance of EL2082 output and parasitic capacitance of input of VCA610 is 6 pF [34], [28]). Adjustable parameters were initially set to: B = 0.2 (VSETB = 0.2 V), A = 5 (VSETA = -1.35 V), term A/(A-1) = 1.25, D = 50% (VDUTY = 0 V). Expected f0 (including 6 pF parasitic capacitance) has value 1.216 MHz. We have tested features of the comparator (VCA) in detail. Simulated DC characteristic of the VCAbased comparator for our initial values (A = 5) is presented in Fig. 7. Gain A has direct impact on threshold voltages and saturation corners as we have already discussed in previous text. Stepping of A (VSETA) and its influence on threshold and saturation levels is documented in Fig. 8. This behavior affects accuracy of f0 as well as D because both parameters depend on Vsat_VCA, see (19) and (20). Figure 7. Simulated DC transfer characteristic of Schmitt comparator based on single VCA. ACCEPTED MANUSCRIPT a) b) Figure 31. Dependences of measured output levels on f0 for various values VSETA: a) triangular waveform output, b) square wave output. 6. Concluding remarks Solution employing ECCII and VCA with adjustable duty cycle and repeating frequency was investigated in detail by simulations and laboratory experiments. Some of the results are summarized in Tab. 2. Detailed experimental results given for different operational conditions of comparator (VCA - different VSETA) are summarized in Tab. 3. It can be seen that variation and inaccuracy of A (VSETA) has significant effect on f0 and output levels due to setting of threshold of the comparator. Nonlinearity when processing large signals and at high frequencies causes important differences in comparison to simulations and theoretical expectations (datasheet is showing only smallsignal results). Table 2. Comparison of the most important ideal, simulated and best fitting measured results. ideal simulated measured* f0 range [MHz] (VSETB = 0.1→1.5 V) 0.64→9.67 0.63→7.05 0.85→6.00 D range [%] (VDUTY = -0.9→+0.9 V) 5→95 8→93 26→75** VSQ [VP-P] N/A 2 3.0→2.8 VTR [VP-P] N/A 1.6→1.9 1.3→2.2 * measured values for the best fitting setting (VSETA = -1.20 V) with simulation results (VSETA = -1.35 V) ** range 5→95 % is available for VDUTY = -1.5→+1.5 V due to VCA non-idealities and nonlinearities Table 3. Obtained laboratory results for different setting of VSETA (different operational conditions) when changing gain B of integrator VSETA [V] -1.15 -1.20 -1.25 -1.35 A [-] 2 2.5 3.2 5 VSETB [V] 0.1→1.5 B [-] 0.1→1.5 f0 [MHz] 1.16→6.70 0.85→6.00 0.76→5.35 0.55→4.65 f0max : f0min 5.8:1 7.1:1 7.0:1 8.5:1 VSQ [VP-P] 2.6→2.5 3.0→2.8 3→2.9 3.1 VTR [VP-P] 0.8→1.7 1.3→2.2 1.5→2.5 2.1→3.1 Statistical results of A dispersion show substantial influence on f0 and D accuracy. The way how to move the frequency range to higher value is to reduce the gain A (as shown in Tab. 3, Fig. 26) at the expense of its worse accuracy and possible dispersion with fabrication tolerances or aging of components. Lower A allows to obtain quite high value of f0 for relatively very low gain B (VSETB) in the integrator (in values below 1). Low value of A also means advantageous frequency response of the VCA (because magnitude of A falls with –20 dB/dec). On the other hand, we can see that readjustability ratio of f0 decreases with lower gain A, i.e. ratio f0max : f0min decreases for decreasing A. New solution of the generator based on ECCII and VCA presented in Fig. 2 has benefits and improved features in comparison to previous works (Tab. 1) as follows: a) minimal number of active and passive elements; b) voltage control of f0 without impact on D; c) simple duty control by DC voltage VDUTY and substantially lower ACCEPTED MANUSCRIPT complexity of resulting circuits (additional circuit for V→I conversion to control D is not necessary as in works [13], [19]-[23] for example); d) presented circuit also does not suffer from practical limitation of dynamical features of integrator construction as indicated in [24] for example. Despite inaccuracy between simulation and experimental results, both analyses confirmed expected impact of VCA gain (A) on the generator performance. Acknowledgements 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. ACCEPTED MANUSCRIPT References [1] D. Biolek, R. Senani, V. Biolkova, Z. Kolka, “Active elements for analog signal processing: Classification, Review and New Proposals Title of the paper,” Radioengineering, vol. 17, no. 4, pp. 15-32, 2008. [2] J. M. Jacob, “Analog Integrated Circuits Applications”, New Jersey: Pretice-Hall, 2000. [3] K. Kim, H-W. Cha, W-S. Chung, “OTA-R Schmitt trigger with independently controllable threshold and output voltage levels,” Electronics Letters, vol. 33, no. 13, pp. 1103-1105, 1997. [4] J. Misurec and J. Koton, “Schmitt Trigger with Controllable Hysteresis Using Current Conveyors,” International Journal of Advances in Telecommunications Electrotechnics, Signals and Systems, vol. 1, no. 1, pp. 1-5, 2012. [5] D. Biolek and V. 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