Simple Resistor-less Generator Utilizing Z-copy Controlled Gain Voltage Differencing Current Conveyor for PWM Generation

This paper deals with a very simple functional generator employing single multi-terminal advanced active device, so-called z-copy controlled gain voltage differencing current conveyor (ZC-CG-VDCC). This active element offers various inter-terminal relations and interesting possibilities of multi-parameter electronic control, which are utilized to control resulting application (triangular and square wave generator). Simple pulse width modulator (PWM) based on two ZC-CG-VDCCs is a further application example of presented generator. Verification of expected behavior was performed by simulation based on CMOS model of the ZC-CG-VDCC and also by lab measurement. DOI: http://dx.doi.org/10.5755/j01.eee.21.5.13322

many cases.Beneficial features of advanced active elements can be also used in the design of functional generators.
Electronically controllable functional (triangular and square wave) generators are widely employed in many analog and digital communication subsystems (clock generation, pulse width modulation, TTL or CMOS logic, DC-DC, AC-DC converters, etc.) [6], [7].
Operational transconductance amplifiers (OTA) [1], [8] were the first active elements that were very suitable for design of generators.

II. DISCUSSION OF RELATED RESEARCH
Siripruchyanun et al. [9] and Chung et al. [10] proposed a generator based on three adjustable OTAs and three passive elements.Three commercially available active elements were utilized in solution presented in [11], where electronic controllability of the solution was the main contribution.
Another solution employing two (indivisible to subblocks) active elements and four passive elements was reported by Janecek et al. [12].However, his work does not focuses on electronic controllability.Chien [13] proposed a generator based on two differential voltage current conveyors (DVCCs) that are multi-terminal active elements, and four passive elements.
Kumbun et al. [14] starts with utilization of electronically controllable active elements with active subsections.Their active element, referred to as multiple-output through transconductance amplifiers (MO-CTTA) employs current amplifier with special input feature (sCA) and OTA.Two MO-CTTA are required for construction of the generator.The same number of active devices is required for generators presented by Silapan et al. [15].Silapan et al. [15] used two multiple-output current controlled current differencing amplifiers (MO-CCCDTAs) which consist of current differencing unit (CDU) [1], [16], [17] and OTA subsections.A solution presented by Srisakul [18] is based on multiple-output current controlled current conveyor transconductance amplifier (MO-CCCCTA) where current controlled current conveyor of second generation (CCCII) [1], [19], [20] and OTA create subsections.
Two active elements are sufficient for construction of a functional generator presented in [21], where dual-output voltage differencing buffered amplifier (DO-VDBA) and fully balanced voltage differencing amplifier (FB-VDBA) were employed.These elements are created by internal subsections in a form of operational transconductance amplifier and voltage buffer (VB) or voltage inverter (VI).The proposed generator allows differential outputs of both generated responses.
Single active element, so-called controlled gain current and differential voltage amplifier (CG-CDVA) is sufficient for construction of the generator presented in [22].Active devices consist of adjustable current amplifier (aCA) and adjustable differential voltage amplifier (DVCA) subsections.
Therefore, a solution of generator, introduced in this paper, offers some significant improvements.Employed active element is not complex and only one element is enough in order to form the generator.Number of external passive elements is decreased to only one grounded capacitor and both signals (square and triangle wave) are available in both voltage and current form.Moreover, functions of our solution are experimentally verified in order to prove the correctness of our concept.

III. ACTIVE ELEMENT DESCRIPTION Z-copy Controlled Gain Voltage Differencing Current
Conveyor (ZC-CG-VDCC) is an active device covering high variability of terminal relations and controllable parameters itself that is highly beneficial for many applications.A detailed principle is discussed in [4] and [5], where we can find also internal CMOS structure that was used for simulations also in this paper.Therefore, we provide only brief explanation of ideal behavior of this multi-terminal active element.Simplified behavioral block model is shown in Fig. 1.In fact, ZC-CG-VDCC is interconnection of two main sub-blocks: OTA and electronically controllable current conveyor of second generation (ECCII) [1]- [3].Behavior of model in Fig. 1 is defined by: , where controllable parameters are transconductance (gm) internal resistance of current input terminal X (RX) 1 , and current gain Parameters Iset_gm, Iset_RX, Iset_B, Ib2 are values of internal bias sources of the CMOS structure, WM and LM are dimensions of used transistors and KP are transconductance parameters for used fabrication technology (for more details see [5]).

IV. FUNCTIONAL GENERATOR
The proposed generator in Fig. 2 is formed by two parts: integrator and comparator (Schmitt trigger).We can form these subparts very simply by internal sections of the ZC-CG-VDCC (integrator = capacitor + OTA section, comparator = ECCII section).Square wave is available also in form of current flowing from zc_TA terminal.A part of the comparator (input z_TA, output zp) has the following principle.The highest current gain in structure of ZC-CG-VDCC has theoretical maximum limited to Bmax ≈ 4 [4], [5] for very low DC bias current Iset_B.Voltage transfer between z_TA and zn terminals has ideal formula where transfer has character of unity gain voltage amplifier for B < 1.In case of B ≥ 1, this part of active element behaves as comparator with hysteresis [10].Direct copy of current IX (in saturation given by Ib1 = 100 A in [5]) multiplied by gain B is available at terminal zp.Voltage at this terminal is in saturation corner without load resistance.
Between zn and z_TA terminals unity gain (7) still persists, therefore threshold input voltages are equal to saturation corners Vzn/zn_sat (approximately 0.8 V to 0.9 V in our case).Due to this fact, we can obtain equal amplitudes of triangular and square wave response.This statement is valid only for B ≥ 1 in real case.Supposing equality of threshold and output level of the repeating frequency is given (for 50 % duty cycle) as where VTR_max = VSQ_max and 2 in denominator comes from current mirror ratio in CMOS structure [5].The proposed variant of the generator can also operate with different duty cycle (D) than 50 %, see Fig. 3.Only one additional DC current source is supplemented into the structure.Using routine analysis, we obtain the following expression for repeating frequency and duty cycle (Iz_TA_max = 2Iset_gm) where n = Id/2Iset_gm and represents relation between D and f0.(Id is theoretically limited to 2Iset_gm).Constant 2 is also given by multiplication of current mirrors in OTA section in frame of the ZC-CG-VDCC element (see [5]).Setting of D independently of f0 is also possible for constant ratio n = 2D−1 (Id = 2.Iset_gm(2D−1)).Accurate ratio of two DC currents is quite easily available in IC design.

A. Functional Generator
We obtained the following simulation results for parameters: C = 40 pF, Rx = 1 k (Iset_Rx = 34 A), gm = 1 mS (Iset_gm = 54 A), B = 2 (Iset_B = 58 A).Transient responses (VTR, VSQ) are given in Fig. 4 for f0 = 0.844 MHz.The repeating frequency obtained from simulation was 0.904 MHz.The triangle wave signal has inverting polarity (consequence of inverting Schmitt trigger).Tuning of the generator (Fig. 5) was verified from 109 kHz to 1479 kHz by adjusting of Iset_gm from 5 A to 99 A (ideal range of f0 control is 78 kHz−1 547 kHz).Range of the adjusting is proportional to Iset_gm.The results of exemplary f0 tuning for two different frequencies and D = 30 % or 70 % (simulated as 29.7 % and 30.8 % or 66.9 % and 69.7 %) are given in Fig. 6 and Fig. 7. Utilization of current output terminal zc_TA (resistive load at this terminal) allows to obtain differential voltage output of the square wave that is useful in low-voltage and low power applications, where voltage swing is very limited.

B. PWM Modulator
Pulse width modulator (PWM) [23] is both quite important and typical application of the functional generator.PWM modulators are frequently used in power supply sources/converters (DC-DC, AC-DC) and high-efficient audio amplifiers (D class) for example.We established the following PWM modulator (Fig. 8) as a simple example of utilization of the triangular wave output of the generator.Two ZC-CG-VDCCs are sufficient to provide simple PWM modulator employing low number of passive elements (one R and one C only).Input OTA section of the ZC-CG-VDCC2 which is directly connected to the current conveyor CCII input Y (z_TA) forms simple comparator without hysteresis.Output response is available after internal voltage buffer in frame of CCII part (at X terminal).

VI. MEASUREMENT RESULTS
Triangle and square wave generator based on ZC-CG-VDCC (Fig. 2) was implemented to be measured in lab.Behavioral model of ZC-CG-VDCC consisting of commercially available active devices was prepared for such a reason.Prepared behavioral model is depicted in Fig. 10.The subpart consisting of ECCII-1, ECCII-2, VB1, VB2 and CF/I1 (CF/I -current follower and inverter) emulates overall ECCII section in Fig. 1.The rest of blocks (VCA1, ECCII3, CF/I2) represents OTA section in Fig. 1.Three adjustable parameters [11], [24] of the basic model in Fig. 1 are defined as: RX  Rj / /VSET_Rx, B  VSET_B and gm  VSET_gm/Rk / .Our model includes also additional parameter A (voltage gain) that is suitable for further development of applications (additional degree of freedom) that is available in relation between Iz_TA (Izc_TA and Vp and Vn) as: (VpVnA)gm = Iz_TA = Izc_TA, where A  10 -2(V SET_A +1) .We used discussed behavioral model for verification of proposed generator in Fig. 2. Supposing equality of amplitudes of generated waveforms (VSQ_max = VTR_max), approximate equation for f0 has it this case form The equation ( 11) is different than previous derivations because model in Fig. 10 only emulates behavior of the ZC-CG-VDCC device and it has not exactly the same principle of operation as CMOS model of ZC-CG-VDCC in [5].

VII. CONCLUSIONS
Presented functional generator requires only one active element and really low number of external passive elements (one capacitor only) and moreover it provides outputs (square and triangle wave) in both voltage and current form.By utilizing CMOS model of the active device from [5] we obtained very large adjustability range from 109 kHz to 1479 kHz by adjusting of Iset_gm from 5 A to 99 A.For comparison with already published solutions see Table I, where a brief overview was provided.Note that our work includes also real measurement results that prove the design correctness.Behavioral model suffers from the significant parasitics that limit useful bandwidth in this case, as was discussed in previous section, therefore it was measured in 11 kHz to 110 kHz range.Proposed generator can be used for PWM modulation by a very simple way -a part of additional active device is used for comparisons of triangular wave with constant DC component to create PWM signal.All adjustable parameters (gm, RX, B) of the ZC-CG-VDCC were not necessary in the presented applications.Engagement of all controllable features is fully utilized in reconnection-less reconfigurable active filters [5] or multiphase oscillators [4] for example.Note that the generator can be obtained also if internal subsections (Fig. 1) of the ZC-CG-VDCC are interchanged (integrator is created by ECCII and comparator by OTA section) [25].However, solution presented here saves two resistors.

Fig. 3 .
Fig. 3. Triangle and square wave generator with duty cycle control based on ZC-CG-VDCC.

Fig. 5 .
Fig. 5. Dependence of the repeating frequency on DC bias current Iset_gm.

1 Fig. 8 . 9 .
Fig. 8.A simple pulse width modulator based on two ZC-CG-VDCC.Output of the PWM is terminated by load resistance 1 k and rest of terminals (ZC-CG-VDCCs) was kept unconnected or grounded.Configuration of the modulator was set as: repeating frequency 0.904 MHz, C = 40 pF.Additional parameters (bias currents) are noted in figures including simulation results (Fig.9).We tested system in two situations: a) linear sweep of DC control voltage (Vcontrol) from −0.8 V to 0.8 V and b) harmonic excitation (1.1 Vp-p, 50 kHz).

Fig. 10 .
Fig. 10.Behavioral model of ZC-CF-VDCC (concept from Fig. 1) consisting of commercially available active devices.As an example, transient responses of triangle and square wave signals with D = 50 %, and f0 = 11.1 kHz (VSET_gm = 0.04 V), f0 = 110 kHz (VSET_gm = 0.63 V) were selected (Fig. 11) were obtained for C = 1 nF.Values of other parameters and constants during tests are noted in the following Fig. 12. Dependence of f0 on VSET_gm and dependence of output levels (peak-to-peak) on f0 are shown in Fig. 12. Validity of approximate equation (11) was verified by measurement (Fig.12) up to 80 kHz (VSET_gm = 0.32 V).As obvious from the graph, further increasing of VSET_gm causes problems with linearity of transfer characteristics and problems with slew-rate.Proposed behavioral model is obviously not suitable for high frequency operation with large signal levels (it reaches supply saturation corners in our case -see square waves in the graph), due to existence of high impedance node with large parasitic capacitance (frequency dependent impedance) of node of VSQ, where terminals n and zp are interconnected.

TABLE I .
COMPARISON OF SELECTED GENERATOR SOLUTIONS.

No. of active/passive elements Abbreviation of active element or elements Internal subsections Available current and voltage output of square wave type Differential square wave outputs available Type of output signals (current or voltage)
Note: N/A -information is not available or verified