A Novel Dual-Mode Dual Type Hysteresis Schmitt Trigger and its Applications using Single Differential Voltage Current Conveyor Transcon-ductance Amplifier

: This paper introduces a novel Schmitt trigger circuit that can operate in two modes: voltage and trans-imped-ance mode using a sole Differential Voltage Current Conveyor Transconductance Amplifier (DVCCTA) within the same topology with external grounded resistors. The suggested designs enable dual-type hysteresis (clockwise (CW) and counter-clockwise (CCW)) simultaneously within the same circuit topology. Additionally, the proposed design includes the unique ability to control threshold levels through the transconductance parameter ( g m ) of DVCCTA via a grounded re-sistor. The proposed Schmitt trigger is extended for the application of a square/triangular waveform generator and pulse width modulator to illustrate the utility of the given Schmitt trigger circuit. All the proposed designs are appropriate for IC integration due to the available grounded passive attributes. Moreover, the design comes with a feature of independent control of oscillation frequency using a grounded capacitor eliminates the highest level of parasitics, and lessens the circuit’s sensitivity to noise immunity. The maximum absolute deviation of output amplitude is observed to be less than 0.062 % (for CW mode) and 0.038 % (for CCW mode), while for threshold voltages, it is below 0.528 % (CW) and 0.321 % (CCW), respectively against for temperature variations of 0-100 0 C. Realization of DVCCTA uses 20 MOS transistors with 0.18 µm TSMC CMOS technology parameter, which is used to authenticate the workableness of the proposed design through PSPICE. Additionally, Monte Carlo simulations, temperature-dependent variations, non-ideal analysis, schematic layout with post-layout simulation, and also experimental results using ICAD844 are presented to validate the proposed design. The simulated responses correlate with the theoretical prediction.


Nov dvonivojski histerezni Schmittov prožilec in njegova uporaba z uporabo enojnega diferencialnega napetostnega tokovnega transkonduktančnega ojačevalnika 1 Introduction
The present world of the electronics environment is augmented with filters, rectifiers, amplifiers, A/D converters, comparators, oscillators, and many more signal-processing circuits.Among these, a comparator circuit accompanied by positive feedback is named as Schmitt trigger [1] which plays a vital role in the province of both analog and digital.Schmitt trigger circuit transforms any irregularly formed input signal into a square waveform and is commonly used to improve the circuit's immunity to noise.In addition, it is an essential block used in distinct applications like a square waveform generator [2], versatile modulator [3], relaxation oscillators [4], function generators [5], monostable multivibrator [6], pulse width modulator [7], switching power supplies [8], etc.
Initially, a Schmitt trigger has been presented with a traditional Op-Amp and passive components [1] but suffers from a finite gain-bandwidth product, high power dissipation, low slew rate, lesser dynamic range, etc. [9].As an attractive strategy to waver the constraints of conventional Op-Amp [10], Various current mode analog active blocks (AAB) have been reported in the literature namely (second generation current conveyor) CCII [11] , (third generation current conveyor) CCIII [12], (operational transconductance amplifier) OTA [13], (operational trans resistance amplifier) OTRA [14], (differential voltage current conveyor) DVCC [15], (dual X current conveyors) DXCCII [16], (dual X current conveyor transconductance amplifier) DXCCTA [17] and many more.An active block namely DVCCTA is chosen from the above-cited current mode active blocks due to its prominent feature of electronically adjustable transconductance in comparison to Op-Amp.The usage of DVCCTA can be extended to the field of signal processing for designing various circuits namely analog filters [18] - [19], oscillators [20] - [21], simulator [22]and so many.
Numerous Schmitt trigger circuit implementations using distinct current mode AAB are reported in the literature .Some circuits based on CCII are discussed in [23]- [27], but these implementations require either a higher number of active or passive elements and are incapable of providing a dual-type hysteresis mode of operation.In [27], a non-inverting Schmitt trigger is demonstrated, employing only a CCII and three passive components.This circuit functions as a zero-voltage comparator and is capable of adjusting the threshold voltage levels.However, a Schmitt trigger with independent current control of amplitude and frequency using two OTA's along with two grounded resistors is cited in [28].In [29], current input dual hysteresis mode OTRA Schmitt trigger has been delivered with the possibility of changing its type of hysteresis with the help of a switch.Although, it uses a floating resistor which is not an advisable feature for IC Implementation.The improvement in circuit design using DXCCTA is also given in [30] without any passive elements.This configuration reduces the influence of temperature variation on output amplitude levels.However, it doesn't offer the capability to demonstrate both CW and CCW hysteresis.Another prominent configuration with DVCC and two grounded resistors [31] has the capability to adjust the hysteresis by varying the values of a resistor.Two more designs with (differential difference current conveyor) DDCC and (current differencing transconductance amplifier) CDTA with two resistors are demonstrated in [32] and [33] but unable to exhibit dual type hysteresis.Aside from the above mentioned circuits, dual-type hysteresis, independent and electronic control of threshold and amplitude levels are viable through (current follower differential input transconductance amplifier) CFDITA [34], (current differencing buffered amplifier) CDBA [35], (current controlled current differencing transconductance amplifier) CCCDTA [36] based designs but circuit in [34] is unable to give both type of hysteresis simultaneously.The Schmitt trigger circuit mentioned in [37] that uses a single (voltage differencing transconductance amplifier) VDTA and one resistor is unable to exhibit dual type hysteresis, but it does have the ability to independently control the output amplitude levels.Circuit cited in [38] uses single (second generation current controlled current conveyor) CCCII, a capacitor and two resistors for generating a square waveform with the maximum power consumption of 600 µW but unable to exhibit dualtype hysteresis.Square wave generators based on (second generation differential current conveyor) DCII, two resistors and a sole capacitor in [39] and [40] have the advantage of reducing noise caused by parasitics through the use of a grounded capacitor.A recent proposal introduces a Waveform generator utilizing commercially available ICs along with (extra X second generation current conveyor) EXCCII prototype [42] and five passive components.The circuit benefits from the capability of independently controlling oscillation frequency via passive elements.Also, an attempt was made to design a Schmitt trigger with (second generation voltage conveyor) VCII [43] comprising of two active blocks and five resistors exhibiting an average power consumption of 328 µW and 365 µW for transitions at non-inverting and inverting mode outputs, respectively.Table .1 demonstrates a comparative study with the earlier described Schmitt trigger circuits, which is summarized in the comparison section in great detail.
Henceforth, this paper presents a Schmitt trigger with dual-type hysteresis within the same topology available in two modes specifically voltage and trans-impedance mode with less number of grounded passive components and its application as a square/triangular wave generator and pulse width modulator.The design works with an AAB named DVCCTA for the Schmitt trigger operation.Additionally, the proposed design comes with an attractive feature of availability of both modes (voltage and transimpedance) within the same circuit topology.Notably, the topologies provide the benefit of independent control of threshold levels and oscillation frequency.The simulation results using PSPICE along with CMOS based DVCCTA and the experimental verification using IC AD844 are examined to authenticate the theory.Also, the feasibility of Schmitt trigger for different type of input voltages, temperature dependence, non-ideal analysis, and Monte Carlo analysis is illustrated.
The remaining sections of the paper are structured as follows.Section 2 discusses the circuit representation and analysis of the basic building block DVCCTA and the proposed dual mode (voltage mode and transimpedance mode) Schmitt trigger.Section 3 focuses on how the proposed circuits can be extended for the application as a square/triangular waveform generator and pulse width modulator.Section 4 gives the effect of non-ideal current and voltage transfer gains on the performance of the proposed Schmitt trigger.Section 5 presents the functional verification of the proposed circuits through simulation results.Moving on to Section 6 gives further validation of the proposed designs through experimental analysis, followed by a comparative analysis with existing models in Section 7. Finally, Section 8 addresses the conclusion.

Circuit Representation and Analysis 2.1. DVCCTA
The DVCCTA, a simple active block was first given in [44], which is a combination of DVCC [15] resides at input phase and OTA [13] remains at the output phase.Fig. 1 depicts the hierarchical block, while Fig. 2 presents the commercially available IC AD844 implementation and CMOS implementation [49] of DVCCTA, respectively.
The following characteristic equations define the analog block as: where g m can be defined as the transconductance of DVCCTA.This parameter is electronically tunable via an external biasing current (I B ) which is described by the following equation (2).

DVCCTA based Voltage mode Schmitt Trigger
The proposed voltage mode Schmitt trigger uses a single DVCCTA and only one grounded external resistor with inputs V in1 , V in2, and output V out is shown in Fig. 3.With the selection of input, we can avail dual type hysteresis operation likely CW and CCW which are clearly disclosed below.

CCW Schmitt Trigger:
Here, to enable the CCW mode of operation, the input V in1 is driven through the Y 1 terminal of DVCCTA by keeping Y 2 terminal grounded.The output V out is taken across the O-terminal of DVCCTA.Depending upon the input signal level, square wave output either saturates at (positive saturation level) +V sat or at the (negative saturation level) −V sat .
From the routine analysis of the design, Adopting the port relation of DVCCTA (V X = V Y1 − V Y2 ), and V Y2 = 0; V X = V Y1 = V in1 .Equation ( 2) can be written as Here the currents passing through the terminals Z+ and O-are equal (I Z+ = I O− ) because of the short circuit connection.From the port relations (I Z+ = I X ; I O− = −g m V Z+ ) given in equation ( 1), we can write as follows Using equations (4 and 5) and from circuit V Z+ = V out , the input voltage (V in1 ) is expressed as: Where g m is taken as 1/R m .The upper threshold voltage (V TH ) is calculated with the assumption that the initial value of output is at −V sat .
As V in1 increases from zero, V out remains at −V sat until V in1 reaches V TH .When it satisfies the condition (V in1 >V TH ), output level changes from −V sat to +V sat .Subsequently, the low threshold voltage (V TL ) is given as The output level (+V sat ) is maintained for the input V in1 >V TL .The corresponding value for the hysteresis is calculated as

CW Schmit Trigger:
This mode of operation is supervised by V in2 through the inverting Y 2 terminal of DVCCTA since V in1 is grounded.The O terminal comprises for output V out , as shown in Fig. 3.The circuit analysis is as same as CCW mode and the voltage V in2 can be expressed as The hysteresis operation is observed to be adverse of CCW operation with the assumption that the initial value of output is at +V sat .Therefore, V TH and V TL are observed to be same as in equations ( 7) and ( 8) respectively.

Transimpedance mode Schmitt Trigger:
The transimpedance mode Schmitt trigger circuit is realized using the same topology as in Fig. 3 by adding an external grounded resistors at Y terminals with a current input (I in ).Dual-type hysteresis is available within same topology with the selection of input as either I in1 or I in2 within the same design and is clearly disclosed in this section.CCW transimpedance mode Schmitt trigger is enabled through the input I in1 at Y 1 terminal of DVCCTA when Y 2 terminal is grounded and the output V out is observed at O terminal of DVCCTA which is shown in Fig. 4. The principle operation is same as the voltage mode Schmitt trigger by considering the initial value of output is at −V sat .By considering the ideal characteristics from equation ( 1), the simple calculations can be obtained below: The input current (I in1 ) is expressed as Where g m is taken as 1/R m .
The upper and lower threshold currents (I TH , I TL ) can be expressed to be CW transimpedance mode Schmitt trigger is enabled through the input I in2 at Y 2 terminal of DVCCTA while the other input terminal Y 1 is grounded.The O terminal incorporates the output V out where the operation of hysteresis is observed to be adverse of CCW type.Likewise, the input current (I in2 ) is given in equation ( 14) and I TH , I TL are the same as of CW type since the initial assumption of output is settled at +V sat .To illustrate the usefulness and practical application of the introduced work, Schmitt trigger-based square/triangular waveform generator is depicted in Fig. 5.The waveform generator incorporates the proposed voltage mode Schmitt trigger design along with an integrator using CFOA, a resistor, and a capacitor.The proposed scheme adopts only grounded passive components.Mostly, the grounded capacitor reduces the level of parasitics during fabrication.It is expanded to the waveform generator as a square wave at V out1 and triangular wave at V out2 output terminals, that can be mathematically characterized as: The Schmitt trigger either saturates at +V sat or −V sat .Initially, by assuming that the output V square is at +V sat , this voltage makes the capacitor C 0 to charge with current I Z initiating V out2 to linearly increase with a positive slope until V TH .Subsequently, the square waveform output changes to -V sat which makes the capacitor C 0 to discharge V out2 decreases linearly with a negative slope until it reaches V TL of V out1 .The succeeding relationships provide charging and discharging intervals of the capacitor.
Whereas V TH and V TL are originated from Equations ( 7) and ( 8), the time period (T = T 1 + T 2 ) of the waveform and subsequently the frequency can be computed as

3.2.Pulse Width Modulator (PWM):
PWM scheme is extensively used in voltage regulation, communication systems, power conversion control circuits, ADC, Instrumentation systems, and digital audio [45]- [48].In this technique, the pulse width of the modulated output is altered according to the voltage level of input modulating signal.PWM output signal can be more oftenly produced by comparing a modulating signal and a carrier waveform like triangular or sawtooth waveform.The proposed design is adequately suited for designing the Pulse Width Modulator (PWM) displayed in Fig. 6 consists of single DVCCTA which acts as a comparator and a resistor.The modulating signal V in is given through input terminal Y 2 , the voltage across Y 1 terminal V C operate as a carrier signal and the required PWM output V out is taken over the Z terminal of DVCCTA.The feasible saturation levels of V out are +V sat and −V sat .As the V C increases from zero and moves towards the input modulating signal V in , the PWM output voltage abides at −V sat and once V C reaches V in and satisfies the condition (V C > V in ), V out changes its state from −V sat to +V sat .It is maintained until the carrier voltage decreases and satisfies the condition of (V C < V in ), then the PWM output state changes to −V sat .
Employing the terminal characteristics given in equation ( 1), the mathematical analysis is given below The current through X terminal can be written as As we know that, from equation ( 1), I Z+ = I X and I O− = −g m V Z .Therefore, by equating I Z+ and I O− because of the short circuit connection.
Where g m is considered as 1/R m .
By making use of equations (22,23), the output voltage V out of PWM is determined as

Non ideal Analysis
To determine the non-ideal response of the proposed Schmitt Trigger, including various non-idealities of DVCCTA.The tracking errors in the matrix below show the deviation from the ideal DVCCTA's properties. ( Here, α represents the current transfer gain, while  1 and  2 denote the voltage transfer gains, and γ represents the transconductance gain.The numerical relation between α and the current tracking error (ξ i ), as well as β and the voltage tracking error (ξ v ), can be expressed as: Further analysis of the proposed circuits using equation ( 25) is as follows: For CCW operation, By taking, V X = β 1 V in1 and V Y2 = 0, equation ( 3) can be written as Also considering, (I Z+ = αI X ; I O− = −γg m V Z+ ), equation ( 5) can be written as From equations (27 & 28), the input voltage V in1 is expressed as However, for CW mode, the circuit analysis is similar to CCW mode, and voltage V in2 can be expressed according to equation (10) .

Simulation Results
The proposed voltage mode Schmitt trigger design illustrated in Fig. 3  The aspect ratios of MOS transistor are provided in Table .2. Besides, the input and output characteristics for the proposed transimpedance mode schmitt trigger with a 50 Hz sinusoidal current input (I in ) of ±2 mA amplitude and R = R 1 = R 2 = 1 kΩ, R m = 10 kΩ is shown in Fig. 9 and Fig. 10.Furthermore, to check the proposed design's workability at higher frequencies, a 5 MHz sinusoidal voltage waveform with amplitude ±8 V is applied to voltage mode Schmitt trigger design.Fig. 11 depicts that the amplitude levels are not distorted at higher frequencies which further confirms the capability of Schmitt trigger circuits over a wide range of frequency.The CCW Schmitt trigger exhibits a -3 dB bandwidth at approximately 12.86 MHz, while the CW mode shows at around 10.82 MHZ.In order to evaluate the temperature stability of the proposed Schmitt triggers, the output (V out ) is observed at different temperature values specifically (27 °C, 50 °C, 75 °C and 100 °C).As a result, as shown in Fig. 12, it is observed that the amplitude and the threshold levels of a square wave are not adversely affected due to temperature variations.To further quantify the extent of deviation in amplitude and threshold levels, it is checked for temperature variations of 0-100 °C.Notably, the findings from Figs. 13 and 14 reveals that the maximum absolute deviation in output amplitude remains below 0.0625 % (for CW Schmitt trigger) and 0.0381 % (for CCW Schmitt trigger), while for threshold voltages magnitude is less than 0.5 % (for both CW and CCW modes).Moreover, the stability of output amplitude levels through Monte Carlo analysis at temperatures 27, 50, 75 and 100 °C, considering over 200 random points with a 5 % tolerance in resistor values is depicted in Fig. 15         Finally, the circuit in Fig. 6 is used for the generation of PWM, and its output is depicted in Fig. 24 with the selection of R = 1 kΩ and R m = 10 kΩ and input voltage V in of 50 Hz sinusoidal with an amplitude of 8V pp .The carrier waveform V C of about 500 Hz is set to be a triangular wave.It is obvious that the pulse width of V out is modulated according to the input-modulating sinusoidal signal.

Conclusion
Novel dual-mode Schmitt trigger employing a single DVCCTA and its application to square/triangular wave generator constructed using an additional CFOA, a grounded capacitor, and a grounded resistor which comprises an integrator and pulse width modulator (PWM) within the same topology is presented.The proposed design avails of two modes specifically voltage and transimpedance modes where the CW and CCW type of operation is acquired within the same topology on the basis of the selection of input.It uses only grounded passive elements and also a single CMOS-based DVCCTA, which is suitable for IC integration.Additionally, independent control of threshold levels is available.Tunability of grounded components is the prominent of the design where the operating frequency can be made adjustable using a grounded capacitor and reduces the level of parasitics which sets the proposed design insensitive to noise.The highest absolute deviation of output amplitude and threshold voltage is less than 0.062 % and 0.528 %, respectively, over temperature variations ranging from 0-100 0 C. The design brings dual-mode dualtype hysteresis operation, an excellent operational frequency range, and also insensitivity to temperature variations.Monte Carlo simulations, non-ideal analysis, and experimental results as well as the schematic layout with post-layout simulation results are depicted to justify the considered structure.The unique characteristics of the proposed designs make them applicable for bio-medical and other signal processing applications and can be extended for designing relaxation oscillators, versatile modulators, monostable multivibrators, etc.

Figure 3 :
Figure 3: Proposed voltage mode Schmitt trigger circuit

Figure 5 :Figure 6 :
Figure 5: Square/triangular wave generator is examined with both CMOS and IC AD844 based DVCCTA using PSPICE with 0.18 µm CMOS technology parameter from TSMC.The passive attributes are selected as R=500 Ω and R m =1 kΩ with 50 Hz sinusoidal input voltage of amplitude ±8 V. Fig. 7 depicts the simulation responses of input and output characteristics for the (current feedback operational amplifier) CFOA based implementation of the proposed design.In addition, the transient response of a proposed Schmitt trigger circuit utilizing CMOS implementation is illustrated in Fig. 8.The CMOS-based DVCCTA is biased with a supply voltage of V DD = -V SS = 1.4V,VB = -0.4Vand I B = 60 µA (g m = 0.9961 mS), with R = 500 Ω.Here, gm is calculated to according to equation (2).

Figure 16 :
Monte Carlo simulations of output amplitude for CW mode Schmitt Trigger (a) 27 °C (b) 50 °C (c) 75 °C (d) 100 °C.Fig.17depicts the simulated responses of both the CW and CCW structures of the proposed voltage mode circuit for a triangular wave input with a frequency of 50 Hz and an amplitude of ± 4 V. Subsequently, the output is observed to be a square wave, regardless of the input waveform type.This key characteristic demonstrates the versatility and feasibility of the circuit, as it can effectively process and convert different types of input signals.

Figure 17 :
Triangular wave V in and V out waveform (a) CW (b) CCW From Figs. 18 and 19, it is observed that the threshold levels of the proposed ICAD844 based voltage and transimpedance mode Schmitt trigger circuits can be electronically controlled by adjusting the transconductance parameter (g m ) through the relationship g m = 1 R m , without disturbing the output's amplitude.Figs.20 and 21 interprets the illustration for theoretical and simulated threshold voltages against R m variation of dual type voltage mode Schmitt trigger, respectively.It is observed that the simulated threshold values concur well with the theoretical anticipation.Overall, the analysis highlights the controllability of threshold levels through R m .

Figure 18 :
Figure 18: DC transfer characteristic of voltage mode Schmitt trigger for different R m

Figure 19 :Figure 20 :Figure 21 :
Figure 19: DC transfer characteristic of transimpedance mode Schmitt trigger for different R m 3.

Figure 22 :Figure 23 :
Figure 22: The operating frequency variations with changes in C o

Figure 27 :Figure 29 :
Figure 27: Modulating input V in and PWM output waveform

Table 3 :
summary of key attributes of proposed Schmitt trigger circuits.