**Application of Fourier Series Expansion to Electrical Power Conversion** Application of Fourier Series Expansion to Electrical

### Irina Dolguntseva Irina Dolguntseva

[2] Borzenko A. Language processing in human brain. In: Proceedings of the First AGI

[5] Williams RS, Strukov DB, Snider GS, Stewart DR. The missing memristor found. Nature.

[6] Joglekar YN, Wolf SJ. The elusive memristor: properties of basic electrical circuits.

[7] Kim H, Sah MP, Yang C, Chua LO. Memristor‐based multilevel memory. In: 12th International Workshop on Cellular Nanoscale Networks and their Applications (CNNA

[8] Manem H, Rose GS, He X, Wang W. Design considerations for variation tolerant multi‐ level CMOS/Nano memristor memory. In: Proceedings of the 20th symposium on Great

[9] Laiho M, Lehtonen E. Arithmetic operations within memristor‐based analog memory. In: 12th International Workshop on Cellular Nanoscale Networks and their Applications

[10] Xia Q, Robinett W, Cumbie MW, Banerjee N, Cardinali TJ, Yang JJ, Wu W, Li X, Tong WM, Strukov DB, Snider GS. Memristor—CMOS hybrid integrated circuits for recon‐

[11] James AP, Francis LR, Kumar DS. Resistive threshold logic. IEEE Transactions on Very

[12] Maan AK, Jayadevi DA, James AP. A survey of memristive threshold logic circuits. IEEE Transactions on Neural Networks and Learning Systems. 2016;**99:**1–13**.**DOI: 10.1109/

[13] James AP, Dimitrijev S. Cognitive memory network. Electronics Letters. 2010;**46**

[14] Petrick, S.R. A direct determination of the irredundant forms of a Boolean function from the set of prime implicants. Air Force Cambridge research Center, Cambridge. Techn.

[15] McGeer PC, Sanghavi JV, Brayton RK, Sangiovanni‐Vicentelli AL. ESPRESSO‐ SIGNATURE: a new exact minimizer for logic functions. IEEE Transactions on Very

[16] James AP, Kumar DS, Ajayan A. Threshold logic computing: memristive‐CMOS circuits for fast Fourier transform and vedic multiplication. IEEE Transactions on Very Large

[3] Chua LO. The missing circuit element. IEEE Tans. Circuit Theory. 1971;**18**:507–519. [4] Williams RS. How we found the missing memristor. IEEE Spectrum. 2008;**45**:28–35.

Conference; March 1–3; Memphis. IOS Press; 2008.

118 Fourier Transforms - High-tech Application and Current Trends

European Journal of Physics. 2009;**30**:661–675.

2010); February 3–5; Berkeley, CA. pp. 1–6; 2010.

(CNNA 2010); Feb 3; IEEE; 2010. pp. 1–4.

TNNLS.2016.2547842

Rep. AFCRC‐TR‐56–110, 10 (1956).

(10):677–678.

figurable logic. Nano Letters. 2009;**9**(10):3640–3645.

Large Scale Integration (VLSI) Systems. 2014 ;**22**(1):190–195.

Large Scale Integration (VLSI) Systems. 1993;**1**(4):432–440.

Scale Integration (VLSI) Systems. 2015;**23**(11):2690–2694.

lakes symposium on VLSI; May 16; ACM; 2010. pp. 287–292.

2008;**453**:80–83.

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/66581

Power Conversion

### Abstract

Many power electronic applications demand generation of voltage of a rather good sinusoidal waveform. In particular, dc-to-ac voltage conversion could be done by multilevel inverters (MLI). A number of various inverter topologies have been suggested so far: diode-clamped (DC) MLI, capacitor-clamped (CC) MLI, cascaded H-bridge (CHB) MLI, and others. Fourier series expansions have been used to investigate and to form a basis of different topologies comparison, to discover their advantages and disadvantages, and to determine their control. In this chapter, we discuss modulation strategies of DCMLI and CHBMLI, solve their harmonics spectra analytically, and compare them using harmonic distortion indices.

Keywords: Fourier series, multilevel inverters, pulse width modulation, harmonics, THD
