Tepe Akım Kontrol Modunda Çalışan SEPIC DA/DA Dönüştürücünün Tam Çözümlü Sembolik Zayıf Sinyal Analizi

Yıl 2020, , 121 - 133, 01.02.2020

Ekrem Cengelci

https://doi.org/10.16984/saufenbilder.585574

Öz

 Bu makalede tepe akım kontrollü izolasyonsuz SEPIC dönüştürücünün tam
çözümlü küçük sinyal analizi sürekli iletim modunda "pwm switch"
modeli vasıtasıyla sunulmuştur. Makalede sunulan analiz SEPIC dönüştürücünün
çıkış geriliminin kontrol gerilimine oranından oluşan transfer fonksiyonunun
sıfır ve kutuplarını topolojideki 4 reaktif elemanının iç dirençlerini içine
katarak sembolik formda gösterir. Analizi yapılan transfer fonksiyonu 4.
dereceden pay ve 5. dereceden paydadan ibaret olup, transfer fonksiyonun sıfır
ve kutuplarının sembolik formüllerinin elde edilmesi için belli şartlar altında
yaklaşıklık yapılması zorunludur. Sembolik formda türetilmiş olan transfer
fonksiyonunun doğruluğu gerilim yükselten ve gerilim düşüren çalışma modlarında
iki ayrı sayısal örnek üzerinde gösterilmiştir. Bu sayısal örneklerde ortalama
devre modelleri vasıtasıyla yapılan frekans domeni PSpice devre benzetimleri ve
zaman domeninde yapılan LTspice devre benzetimlerinin sonuçları
karşılaştırılmıştır. SEPIC dönüştürücünün transfer fonksiyonunun matematiksel
analizleri, PSpice ve LTspice devre benzetimleri ile laboratuvar ölçüm
sonuçları birbirlerini desteklemeleri göstermektedir ki makalede analizi
sunulan transfer fonsiyonunu başarılı bir şekilde türetilmiştir.

Anahtar Kelimeler

SEPIC, tepe akım modu kontrolü, pwm-switch, küçük sinyal analizi, sürekli iletim modu

Full Order Symbolic Small Signal Analysis of Peak-Current-Controlled SEPIC by PWM-Switch Model

Öz

Full order small signal analysis of peak-current controlled non-isolated
Single Ended Primary Inductor Converter (SEPIC) is presented by utilizing
pwm-switch model in Continuous Conduction Mode (CCM). The analysis provides
control to output voltage transfer function together with its zeros and poles
in symbolic form taking into account parasitic resistances of all four reactive
components in the SEPIC topology. The resultant transfer function is with 4th
order numerator and 5th order denominator, which necessitates approximation in
deriving formulas of zeros and poles in symbolic form. Symbolically derived
transfer function of the SEPIC is validated on two different numerical
examples, one with operating in step down mode and another operating in step up
mode, by frequency domain PSpice simulations on average circuit models and by
time domain LTspice simulations on switching models. The mathematical analysis,
PSpice and LTspice simulations, and measurement results of control to output
voltage transfer function of SEPIC agree very well proving that the symbolic
control to output voltage transfer function of SEPIC together with its zeros
and poles are successfully derived.

Anahtar Kelimeler

SEPIC, peak current-mode control, pwm-switch, small signal analysis, continuous conduction mode

Kaynakça

• [1] R. P. Massey, E.C. Snyder, “High voltage single-ended DC-DC converter,” in Proc. IEEE PESC, pp. 156-159, June 1977.
• [2] R. Ridley, “A New Small Signal Model for Current Mode Control”, Ph.D. Dissertation, ECE Dept., Virginia Institute of Tech., Blacksburg, VA, USA, 1990.
• [3] R. Redl, N. Sokal, “Current-mode control, five different types, used with the three basic classes of power converters”, in Proc. IEEE PESC, pp. 771-785, June 1985.
• [4] V. Vorperian, “Simplified analysis of PWM converters using model of PWM switch. Part I: Continuous conduction mode,” in IEEE Trans. Aerospace Electron. Syst., vol. 26, issue 3, pp. 490-496, May 1990.
• [5] V. Vorperian, “Analysis of Current-Controlled PWM Converters Using the Model of the Current-Controlled PWM Switch,” in PCIM Conference, pp. 183-195, 1990.
• [6] V. Vorperian, “Chapters 8.7 to 8.11” in Fast Analytical Techniques for Electrical and Electronic Circuits, 1st ed., Cambridge, United Kingdom, Cambridge University Press, 2002.
• [7] R. D. Middlebrook and S. Cuk, “A general unified approach to modeling switching-converter power stages,” in Proc. IEEE PESC, 1976, pp. 521–570.
• [8] W. M. Moussa, “Modeling and performance evaluation of a dc/dc SEPIC converter,” in Proc. IEEE APEC, pp. 702-706, March 1995.
• [9] W. Gu, “Small signal modeling for current mode controlled Cuk and SEPIC converters,” in Proc. IEEE APEC, pp. 906-910, March 2005.
• [10] R.W. Erickson, D. Maksimovic, “Chapter 8.1.8,” in Fundamentals of Power Electronics, 2nd ed. Boulder, CO, Kluwer Academic Publishers, 2004.
• [11] K.D.T. Ngo, “Alternate forms of the PWM switch models,” in IEEE Trans. Aerospace Electron. Syst., vol. 35, issue 4, pp. 1283-1292, Oct. 1999.
• [12] J. Chen, K.D.T. Ngo, “Alternate forms of the PWM switch model in discontinuous conduction mode,” in IEEE Trans. Aerospace Electron. Syst., vol. 37, issue 2, pp. 754-758, Apr. 2001.
• [13] V. Vorperian, “Simplified analysis of PWM converters using model of PWM switch. II. Discontinuous conduction mode,” in IEEE Trans. Aerospace Electron. Syst., vol. 26, issue 3, pp. 497-505, May 1990.
• [14] S. Ben-Yaakov, V. Vorperian “Modeling the switch of PWM convertors (comments, with reply, on 'Simplified analysis of PWM converters using models of PWM switch' by V. Vorperian),” in IEEE Trans. Aerospace Electron. Syst., vol. 28, issue 3, pp. 921-925, July 1992.