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Hindawi Publishing CorporationJournal of EngineeringVolume 2013, Article ID 309124, 6 pageshttp://dx.doi.org/10.1155/2013/309124

Research ArticleVoltageMode PulseWidthModulator UsingSingle ��erational �ransresistance ��li�er

Rajeshwari Pandey,1 Neeta Pandey,1 and Sajal K. Paul2

1 Department of Electronics and Communication, Delhi Technological University, Bawana Road, Delhi 110042, India2Department of Electronics Engineering, Indian School of Mines, Dhanbad, Jharkhand 826004, India

Correspondence should be addressed to Neeta Pandey; [email protected]

Received 31 August 2012; Revised 2 December 2012; Accepted 10 December 2012

Academic Editor: Kyoung Kwan Ahn

Copyright © 2013 Rajeshwari Pandey et al. is is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properlycited.

is paper presents a voltage mode pulse width modulator (PWM) using single operational transresistance ampli�er (OTRA).eproposed PWM consists of a relaxation oscillator output which is modulated using modulating signal. PSPICE simulation resultsand experimental results have been included to verify the theoretical analysis.

1. Introduction

Pulse width modulation (PWM) scheme is widely used incommunication systems, DC motor speed controller, powerconversion control circuits [1–3], and instrumentation. InPWM, the width of pulses of a pulse train is changed inaccordance to voltage level of modulating signal. e PWMgenerators are available in Integrated Circuits (ICs) form;however, the internal circuitry is somewhat complex andtypically consists of current sources, �ip-�op, comparators,and analog switches [4]. Apart from these readily availableICs, the PWM signal can most commonly be generated bycomparing a modulating signal with a sawtooth or trian-gular waveform. Alternatively, information signal can �rstbe combined with a sawtooth or triangular waveform andthereaer comparing the combined signal with a referencelevel to generate PWM signal.is can be implemented usinga Schmitt trigger with an RC circuit in feedback loop [5].Extensive literature review reveals that PWMs based on thisconcept are available using different active analog buildingblocks such as op-amps [6], current conveyor II (CCII)[4], and operational transconductance ampli�er (OTA) [7,8]. High-frequency performance of PWMs employing op-amps is limited due to lower slew rate and constant gain-bandwidth product of the op-amps. e CCII-based PWMhas the advantage of generating accurate PWM signal with

high operating frequencies [4], and the output amplitudeand frequency of the PWMs based on OTAs can be inde-pendently/electronically tuned [7]. Despite these advantages,the circuits proposed in [4, 7] suffer a drawback of usingexcessive number of active elements. Reference [8] presentsanother OTA-based PWM which uses derivative method. Inderivative method, the duty cycle of PWM signal dependson a differentiated result of the modulating signal. ismethod is not suitable for applications where the changes inmodulating signal are rare, such as in power converters [7].e open literature suggests that a PWM pulse train can alsobe producedwith the use of voltage-controlled delay lines [9],current-controlled delay cells [10], and voltage-controlledphase shier [11] wherein the underlying concept is not thesame as used in [4–8]; that is, the comparison of modulatingsignal with reference triangular/sawtooth waveform [9] usestwo voltage-controlled delay lines, a �xed delay element, tworising edge detectors, along with an RS latch to generate a0%–50% duty cycle at the output of the latch. Two 0%–50%modulators are connected in parallel to extend the duty cycleto 100%. Current-controlled delay cell-based duty oscillatorand pseudohyperbola charge current generator are used in[10] for generating PWM. Yet, another PWM is proposed in[11] which employs a voltage-controlled phase shier, a two-input logic AND gate, a network of logic inverters, and FET

2 Journal of Engineering

switches.is circuit generates a 0% to 50% pulse width usingthe phase shier and anANDgate and then extends the rangeto 0%–100% using the inverters.

is paper aims at presenting an operational transre-sistance ampli�er (OTRA) based PWM, using a relativelysimpler scheme, wherein the modulating signal is combinedwith an exponential carrier waveform and compared witha reference. is paper is organized as follows. In Section2, the function of an OTRA is brie�y described, followedby the operation principle of the proposed PWM circuit.e feasibility of the presented circuits is veri�ed throughcircuit simulations and experimental results in Section 3.It is observed that the simulation and experimental resultsare in close agreements with theoretical propositions. ecomparison of the proposed circuit with earlier reportedstructures is presented in Section 4. Section 5 concludes thepaper.

2. Circuit Descriptions

OTRA is a high gain current input voltage output device.e input terminals of OTRA are internally grounded,thereby eliminating response limitations due to parasiticcapacitances and resistances and, hence, are appropriate forhigh-frequency operation. e circuit symbol of OTRA isshown in Figure 1, and the port characteristics are given by(1), where 𝑅𝑅𝑚𝑚 is transresistance gain of OTRA. For idealoperations, the 𝑅𝑅𝑚𝑚 of OTRA approaches in�nity and forcesthe input currents to be equal. us, OTRA must be used ina negative feedback con�guration. Consider

𝑉𝑉𝑝𝑝𝑉𝑉𝑛𝑛𝑉𝑉𝑜𝑜

=

0 0 00 0 0𝑅𝑅𝑚𝑚 −𝑅𝑅𝑚𝑚 0

𝐼𝐼𝑝𝑝𝐼𝐼𝑛𝑛𝐼𝐼𝑜𝑜

. (1)

e general scheme of PWM is depicted in Figure 2. emodulating signal and carrier signal are �rst summed up,and then PWM output signal is generated by comparing thesummation signal and reference level.

e proposed PWM circuit is shown in Figure 3. ecircuit consisting of OTRA, resistors 𝑅𝑅𝐹𝐹 and 𝑅𝑅𝐿𝐿, and capac-itor C serves as square wave generator. Exponential voltagewaveform across capacitor C serves as carrier waveform.emodulating signal 𝑣𝑣𝑖𝑖 and the carrier wave are summed upat node 𝑝𝑝 through resistor 𝑅𝑅𝑠𝑠. us, the voltage across thecapacitorwill be summation of carrier andmodulating signal,and the PWM output is available at 𝑣𝑣𝑜𝑜.

e resistor 𝑅𝑅𝐹𝐹 and capacitor C form a positive feedbackloop. 𝑉𝑉+sat and 𝑉𝑉

−sat are the two possible saturation levels of

output 𝑣𝑣0. Assume initially that 𝑣𝑣0 switches to saturationlevel 𝑉𝑉+sat at 𝑡𝑡 = 0, as shown in Figure 4. is results incharging of the capacitor present in the feedback loop, andthe voltage across the capacitor reaches𝑉𝑉TH, a value at which𝐼𝐼𝑝𝑝, the current through 𝑝𝑝 terminal, becomes slightly less thanthe current through 𝑛𝑛 terminal, 𝐼𝐼𝑛𝑛. As a result, the outputvoltage switches to 𝑉𝑉−sat, and the capacitor starts charging inthe opposite direction. Now, as capacitor voltage approaches𝑉𝑉TL, the output once again switches back to 𝑉𝑉

+sat.

��

�n

��

�n

�

��

F 1: OTRA circuit symbol.

PWM output

Carrier waveform generator

ComparatorModulating

input

Reference

level

∑

F 2: e scheme of PWM [4].

e𝑉𝑉TH and𝑉𝑉TL values can be obtained from the routineanalysis of this PWM circuit and are expressed by (2) and (3),respectively. Consider

𝑉𝑉TH = 𝑉𝑉+sat 1 −

𝑅𝑅𝐹𝐹𝑅𝑅𝐿𝐿

+ 𝑣𝑣𝑖𝑖 (𝑡𝑡)𝑅𝑅𝐹𝐹𝑅𝑅𝑆𝑆

, (2)

𝑉𝑉TL = 𝑉𝑉−sat 1 −

𝑅𝑅𝐹𝐹𝑅𝑅𝐿𝐿

+ 𝑣𝑣𝑖𝑖 (𝑡𝑡)𝑅𝑅𝐹𝐹𝑅𝑅𝑆𝑆

. (3)

ese values of 𝑉𝑉TH and 𝑉𝑉TL result in 𝑇𝑇on and 𝑇𝑇off asfollows:

𝑇𝑇on = 𝑅𝑅𝐹𝐹C ln2𝑅𝑅𝐿𝐿/𝑅𝑅𝐹𝐹 − 1 − 𝑣𝑣𝑖𝑖 (𝑡𝑡) 𝑅𝑅𝐿𝐿/𝑉𝑉

+sat𝑅𝑅𝑆𝑆

1 − 𝑣𝑣𝑖𝑖 (𝑡𝑡) 𝑅𝑅𝐿𝐿/𝑉𝑉+sat𝑅𝑅𝑆𝑆,

𝑇𝑇off = 𝑅𝑅𝐹𝐹C ln2𝑅𝑅𝐿𝐿/𝑅𝑅𝐹𝐹 − 1 − 𝑣𝑣𝑖𝑖 (𝑡𝑡) 𝑅𝑅𝐿𝐿/𝑉𝑉

−sat𝑅𝑅𝑆𝑆

1 − 𝑣𝑣𝑖𝑖 (𝑡𝑡) 𝑅𝑅𝐿𝐿/𝑉𝑉−sat𝑅𝑅𝑆𝑆.

(4)

e overall period of the modulated output is given by

𝑇𝑇 = 𝑇𝑇on + 𝑇𝑇off, (5)

and the duty factor (𝐷𝐷) can be computed as

𝐷𝐷 =𝑇𝑇on𝑇𝑇

× 100%. (6)

Equation (4) shows that the duty cycle of the output canbe controlled with the help of modulating signal 𝑣𝑣𝑖𝑖(𝑡𝑡).

3. Realizing an OTRA and Nonideality Analysis

For the proposed PWM circuit, the OTRAwas realized usingAD844 CFOA IC as shown in Figure 5 [12]. e equivalentcircuit of Figure 5 for nonideal analysis [13] is presentedin Figure 6. e CFOAs have been replaced with currentconveyors having �nite input resistances (𝑅𝑅𝑋𝑋) and �nite

Journal of Engineering 3

𝑉𝑖(𝑡)𝑅𝑆

𝐶

𝑅𝐿

𝑝

𝑛

𝑅𝐹

𝑉𝑜

F 3: e OTRA PWM circuit.

𝑉TH

𝑉TL

𝑉−

𝑡

𝑉𝑜(𝑡)

𝑉𝑐(𝑡)

𝑉+sat

sat

𝑇on 𝑇off

F 4: Output of the square wave generator of Figure 3.

resistance at its 𝑍𝑍 terminal (𝑅𝑅𝑍𝑍). Ideally, the input resistanceat the𝑋𝑋 terminal is �ero and is in�nite at the𝑍𝑍 terminal. Forthe AD844 CFOA, the input resistance 𝑅𝑅𝑋𝑋 is around 50Ω,and 𝑅𝑅𝑍𝑍 is around 3MΩ [14].

From Figure 6, various currents can be calculated asfollows:

𝐼𝐼𝑍𝑍𝑍 = 𝐼𝐼+,

𝐼𝐼𝐷𝐷 = 𝐼𝐼𝑍𝑍𝑍 𝑅𝑅𝑍𝑍

𝑅𝑅𝑋𝑋 + 𝑅𝑅𝑍𝑍 ,

𝐼𝐼𝑋𝑋𝑋 = 𝐼𝐼− − 𝐼𝐼𝐷𝐷,

𝐼𝐼𝑍𝑍𝑋 = 𝐼𝐼𝑋𝑋𝑋.

(7)

Ideally, 𝐼𝐼𝐷𝐷 should be equal to 𝐼𝐼𝑍𝑍𝑍, which can be approx-imated only if 𝑅𝑅𝑍𝑍 ≫ 𝑅𝑅𝑋𝑋, which is true for AD844. Also,

+

−

+

−

AD844

1

AD844

2𝐼𝑛

𝐼𝑝𝑉𝑂1

𝑉𝑂2𝑉𝑂

𝐼𝑍1

𝐼𝑍2

𝑇𝑍1

𝑇𝑍2𝐼2

𝑅𝑚

𝑉𝑝 𝑝

𝑉𝑛 𝑛

F 5: OTRA constructed with AD844.

CCII

1

1

1

2

RZ

CCII

𝐼𝑛

𝑝

𝑛

𝑅𝑋

𝑅𝑋

𝐼𝑋2

𝑋𝑌

𝑍

𝑋𝑌

𝑍

𝐼𝐷

𝐼𝑍1

𝐼𝑍2

𝑅𝑍

𝑊

𝑊 𝑉𝑂

𝐼𝑝

F 6: Equivalent circuit of OTRA constructed with AD844.

the approximation that the input terminals are virtuallygrounded will be true only if the external resistance at theinput terminal of the OTRA is much larger than 𝑅𝑅𝑋𝑋. If thesetwo conditions are satis�ed, the OTRA constructed withAD844 closely approximates an ideal OTRA.

From (7), the output voltage 𝑉𝑉𝑂𝑂, taking into account thepreviously mentioned approximations, can be calculated as

𝑉𝑉𝑂𝑂 = 𝐼𝐼+ − 𝐼𝐼− 𝑅𝑅𝑍𝑍, (8)

where 𝑅𝑅𝑍𝑍 is the transimpedance gain of the OTRA.If in PWMcircuit shown in Figure 3 the equivalent circuit

of OTRA constructed with AD844 is used, then the thresholdlimits of the output get modi�ed to

𝑉𝑉TH = 𝑉𝑉+sat 𝑍 −

𝑅𝑅𝐹𝐹 + 𝑅𝑅𝑥𝑥𝑅𝑅𝐿𝐿 + 𝑅𝑅𝑋𝑋//𝑅𝑅𝑍𝑍

+ 𝑣𝑣𝑖𝑖 (𝑡𝑡)𝑅𝑅𝐹𝐹 + 𝑅𝑅𝑥𝑥𝑅𝑅𝑆𝑆 + 𝑅𝑅𝑥𝑥

, (9)

𝑉𝑉TL = 𝑉𝑉−sat 𝑍 −

𝑅𝑅𝐹𝐹 + 𝑅𝑅𝑥𝑥𝑅𝑅𝐿𝐿 + 𝑅𝑅𝑋𝑋//𝑅𝑅𝑍𝑍

+ 𝑣𝑣𝑖𝑖 (𝑡𝑡)𝑅𝑅𝐹𝐹 + 𝑅𝑅𝑥𝑥𝑅𝑅𝑆𝑆 + 𝑅𝑅𝑥𝑥

. (10)


250 300 350 400−10

0

10

𝑉 0(V

)

Times (𝜇s)

F 7: PWM output without modulating signal.

0 0.5 1

−10

0

10

Time (ms)

𝑉 𝑜(V

)

(a) Modulating signal and PWM output signal

Time (ms)

0 0.5 1−10

0

10

𝑉 𝑜(V

)

(b) Summed up modulating and carrier signals

F 8: PWMoutput for 5V, 1 KHz sinusoidal modulating signal.

e external resistance at the input of the OTRA shouldbe much larger than R𝑋𝑋 so that the feedback current canbe absorbed into the input terminals. Since 𝑅𝑅𝐿𝐿, 𝑅𝑅𝐹𝐹, 𝑅𝑅𝑆𝑆, and𝑅𝑅𝑍𝑍 ≫ 𝑅𝑅𝑋𝑋, Equations (9) and (10) reduce to (2) and (3),respectively.

4. Simulation and Experimental Results

e proposed circuit is simulated using PSPICE. OTRAis realized using current feedback operational ampli�ers(CFOAs) IC AD844 as shown in Figure 5. Macro model ofAD844 is used for simulations. Figure 7 shows the outputvoltage of the PWM when modulating signal is not applied,for 𝑅𝑅𝐹𝐹 = 20KΩ, 𝑅𝑅𝐿𝐿 = 70KΩ, 𝑅𝑅𝑆𝑆 = 80KΩ, and C =200 pF, and corresponds to a 50% duty cycle. e observedoutput frequency is 66.7 KHz as against the calculated valueof 69.7 KHz.

Simulated output of pulse width modulator, with samecomponent values as used in Figure 7, is shown in Figure

0 400 800

−10

0

10

𝑉 𝑜(V

)

Time (𝜇s)


0 400 800−10

0

10

𝑉 𝑜(V

)Time (𝜇s)


F 9: PWM output of for 8V, 2.2 KHz modulating signal.

8 for a 5V, 1KHz sinusoidal modulating signal. Figure 8(a)shows the modulating signal and the PWM output, andsummation of modulating and carrier wave is depicted inFigure 8(b). Figures 9 and 10 show the output of pulsewidth modulator for an 8V, 2.2 KHz modulating signal and5V, 40KHz modulating signal, respectively, for same set ofcomponent values. Frequency spectrum of the pulse widthmodulator for 8V, 2.2 KHz modulating signal is shown inFigure 11 which consists of modulating component andcarrier signal. us, the modulating signal can be recoveredwith the help of appropriate low pass �lter.

Figure 12 shows the variation of theoretically computedand simulated%duty factor of themodulatorwith the appliedinput signals. is shows that the two results closely matchwith each other.

e functionality of the proposed pulse width modulatorcircuits is veri�ed through hardware as well.

e commercial IC AD844AN is used to implement anOTRA. Supply voltages used are±5V. Figure 13 shows typicalexperimental results of the circuit for two different mod-ulating signals. Figure 13(a) depicts output for componentvalues 𝑅𝑅𝐹𝐹 = 20KΩ, 𝑅𝑅𝐿𝐿 = 70KΩ, 𝑅𝑅𝑆𝑆 = 80KΩ andC = 200 pF and for an 8V, 2.2 KHz modulating signal.Another screen shot of oscilloscope is shown in Figure 13(b)for a high-frequency modulating signal of 40KHz with 5Vamplitude.ese experimental results are in close agreementto simulated results.

Journal of Engineering 5

T 1: Comparison between the proposed and the previously reported works.

References no. of active components No. of passive components Carrier signal type Electronictunability[4] Single CC-II, two op-amps Single capacitor, three resistors Triangular No[6] Single op-amp Single capacitor, three resistors Exponential No

[7] (i) Two OTAs, an inverter, and a MOS switch (i) Single capacitor, single resistor (i) Sawtooth Yes(ii) Four OTAs and an inverter (ii) Single capacitor, single resistor (ii) Triangular Yes

[8] ree OTAs Single capacitor, two resistors Triangular YesProposed Single OTRA Single capacitor, three resistors Exponential No

0 100 200−10

0

10

𝑉 𝑜(V

)

Time (𝜇s)


0 100 200

−10

0

10

𝑉 𝑜(V

)

Time (𝜇s)


F 10: PWM output for 5V, 40KHz modulating signal.

5. Comparison

In this section, a comparison of the proposed work withthe previously reported analog PWM circuits [4, 6–8] ispresented, which are all based on the concept of comparinga modulating signal with a reference sawtooth or trian-gular waveform to generate PWM signal. Table 1 showsthe detailed comparison. e study of Table 1 reveals thattopologies presented in [4, 7, 8] use more number ofactive components as compared to the proposed work. eproposed circuit is simpler as compared to the topologiesof [4, 7, 8], since it uses the exponential voltage wave-form across the capacitor of the square wave generatoras carrier wave and, hence, does not require additionalcircuitry needed for triangular/sawtooth waves. oughexponential carrier wave being a nonlinear signal yields

Frequency (KHz)

0 50 100 1500

5

10

� �(V

)

(a) Frequency spectrum of modulating signal

Frequency (KHz)

0 50 100 150 0

5

10

� �(V

)

(b) Frequency spectrum of modulated signal

F 11: Frequency spectrum of the PWM.

relatively inaccurate PWM signal at lower carrier frequenciesas compared to the triangular/sawtooth wave, yet one cantrade off accuracy for simplicity depending upon the appli-cation.

e PWM topology of [6], which is a classical opamp-based design, uses same number of active and passivecomponents as in proposed circuit. However, the opamp-based circuits show limited high-frequency performance dueto lower slew rate and constant gain-bandwidth product ofthe op-amps. Additionally, the input terminals of OTRAbeing virtually grounded, the proposed circuit is free fromparasitic effects.

6. Conclusion

In this paper, single OTRA-based PWM generator, a nonlin-ear application ofOTRA, is proposed.is circuit can be usedfor speed control of DC motors and for DC-DC converters.


0

10

20

30

40

50

60

70

80

90

100

−7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7

Du

ty f

acto

r (%

)

Simulated

Ideal

𝑉𝑖 (V)

F 12: Variation of duty factor with applied input signal.

(a) PWM output for an 8V, 2.2 KHz modulating signal

(b) PWM output for a 5V, 40KHz modulating signal

F 13: Experimental results of the proposed PWM.

PSPICE simulation results using AD844 macromodel andexperimental results have been included for veri�cation of thetheoretical propositions which are found in close agreement.

References

[1] W. Mathis, “Nonlinear systems and communications systems,”in Proceedings of the International Conference on Telecommu-nication in Modern Satellite, Cable and Broadcasting Services(TELSIKS ’01), vol. 1, pp. 293–296, September 2001.

[2] M. S. Roden, Analog and Digital Communication Systems,Prentice-Hall, Englewood Cliffs, NJ, USA, 4th edition, 1996.

[3] D. Maksimovic and S. Cuk, “A uni�ed analysis of PWMconverters in discontinuous modes,” IEEE Transactions onPower Electronics, vol. 6, pp. 476–490, 1991.

[4] M. Siripruchyanun, P. Wardkein, and W. Sangpisit, “Simplepulse width modulator using current conveyor,” in Proceedingsof the TENCON ’00), vol. 1, pp. 452–457, September 2000.

[5] A. S. Sedra and K. C. Smith, Microelectronic Circuits, OxfordUniversity, 2004.

[6] APEXMicrotechnology, “PWMBasics, PulseWidthModulatorAmpli�er,” Application Note 30.

[7] H. Kim, H. J. Kim, and W. S. Chung, “Pulsewidth modulationcircuits using CMOS OTAs,” IEEE Transactions on Circuits andSystems I, vol. 54, no. 9, pp. 1869–1878, 2007.

[8] M. Siripruchyanun and P. Wardkein, “A fully independentlyadjustable, integrable simple current controlled oscillator andderivative PWM signal generator,” IEICE Transactions onFundamentals of Electronics, Communications and ComputerSciences, vol. 86, no. 12, pp. 3119–3126, 2003.

[9] A.Djemouai,M. Sawan, andM. Slamai, “NewCMOS integratedpulse width modulator for voltage conversion applications,” inProceedings of the IEEE International Conference on Electronics,Circuits and Systems (ICECS ’00), vol. 1, pp. 116–119, December2000.

[10] J.-J. Chen, H.-Y. Lin, Y.-T. Lin, and W.-Y. Chung, “Integratedpulse-width-modulation circuit using CMOS processes,” inProceedings of the Power Electronics Specialists (IEEE PESC ’04),pp. 1356–1358, June 2004.

[11] Y. Zheng and C. E. Saavedra, “Pulse width modulator using aphase-locked loop variable phase shier,” in IEEE InternationalSymposium on Circuits and Systems (ISCAS ’05), pp. 3639–3642,May 2005.

[12] C. L. Hou, H. C. Chien, and Y. K. Lo, “Squarewave generatorsemploying OTRAs,” IEE Proceedings Circuits, Devices andSystems, vol. 152, no. 6, pp. 718–722, 2005.

[13] Y. K. Lo, H. C. Chien, and H. J. Chiu, “Switch-controllableOTRA-based bistable multivibrators,” IET Circuits, Devices andSystems, vol. 2, no. 4, pp. 373–382, 2008.

[14] AD 844 Datasheet, Analog Devices Inc.

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3FTFBSDI SUJDMF 7PMUBHF.PEF1VMTF8JEUI ...UP MPXFS TMFX SBUF BOE DPOTUBOU HBJO CBOEXJEUI QSPEVDU PG UIF PQ BNQT "EEJUJPOBMMZ UIF JOQVU UFSNJOBMT PG 053" CFJOH WJSUVBMMZ HSPVOEFE …