Тгапфгтег Design

ISA Over the intended range of operating frequencies, Itie frequency dependence of the eure-loss eoeffieient

fC of a certain ferrile t;ore material tan be approximated using a monotonicalty intreasing fourth-order polynomial of the form

I -t-a.

4(i4

where А !), й, tij, w, and Д are t;onstams. In atypical converter transformer applitaticm, lhe applied primary vull-seconds Я., varies diretdy with lhe swilthing period 7, = llf.ll is desired to thoose the opli-raura switthing frequenty suth lhat K, and therefore the transformer size, are minimized.

(a) Show lhat the optimum switching frequency is a root of the polynomial

1 +я,

\i-2 P

Next, a core material is thosen whose tore loss parameters are lOOkHz

Л}, = 7.0

, =-1.3

, = 5,3

= 0,075

The polynomial fits the manufacturers published data over the range 10 kHz </< 1 MHz. (b) Sketch Kj vs./

fc) Determine the value of/ that mi tiimizes iji.-

id) Stetch Kif)IK{\m kHz), over the range 100 kHz </< 1 MHz. How sensitive is the transformer size to the choite of swilching frequency?

155 Transformer design lo attain a given temperature rise. The temperature rise ATof the tenter leg of a fer-

rite tore is directly propordonal to the total power loss P of a transformer: Д7 = ithPftit lttt the thermal resistance of the transformer under given environmetital cotidiliotis. You may assume lhat this temperature rise has minimal dependence on the distribulion of losses within the transformer. Il is desired to modify the Af transformer design method, such lhat temperature rise AT replaces total power loss as a specification. You may neglect the dependence of the wire resistivity p on temperature.

(a) Modify the n-winding iransformer ff design method, as necessarj. Define a new tore geometrical constant Kf lhal includes Л,у,.

(b) Thermal resistances of ferrile EC ctires are listed in Section D.3 of Appendix D. Tabulate Alor these cores, using fi = 2.7.

(c) A 750 W single-oulpul full-bridge isolated buck dc-dc converter operates with converter switching frequency /, = 200 kHz, dt input vohage f = 400 V. and dc otuput vollage V = 48 V. The turns rario is 6:1. The core iiiss eqnalitm parameters al 100 kHz are Лд, - !0 W/Тст and fj = 2.7, Assume a fill factor of A, = 0,3, You may negletl proximity losses. LJse your design pra-cedure of parts (a) and (b) to design a transformer for this application, in which the temperature rise is limited to 20°C, Specify: EC core size, primary and secondarj turns, wire sizes, and peak ac flux denshy.

Part IV

Modern Rectifiers and Power System Harmonics

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