5. Passive Components

Transcription

1 5. Passive Components

2 Inductive Elements Components - Inductors - Transformers Materials - Laminated alloys for example Silicon-steel (High poer, lo frequency, high sat ) - Iron poder (Medium poer, lo to medium frequency, medium sat ) - rrites (Lo poer, high frequency, lo sat ) Designed by poer engineering and poer electronics designers!

3 Inductive Elements - Core Losses Core losses depend both on frequency and pea flux density. - Usually specified in loss curves (one curve for certain frequencies) - lso analytical expressions lie Steinmetz s formula: a1 ˆ a p f + h ac ec f ˆ ac Steinmetz s formula includes to loss terms - Hysteresis loss - Eddy current loss Empirical expressions are provided by some core manufacturers f p + a b c + + ˆ ˆ ˆ 3 ac.3 ac 1.65 ac ( df ˆ ) ac

4 Inductor Design Inductance dψ L di i H l µ 0µ µ 0H i µ µ 0 l + H l H + l µ ψ Φ ψ l i µ 0 µ 0 l + ψ l i µ 0 µ ψ µ 0 L i l µ l >> µ 0 L l + l µ l + l Figure 5.1: asic gapped iron core inductor.

5 Inductor Core Size Selection rea product ψ ˆ Liˆ m I ˆ m For an inductor ith a single inding i ( t) i ( t) m Liˆ I P ˆ Liˆ m I P Liˆ mi P ˆ m ˆ m For an inductor ith several indings 1 P L m, m iˆ I ˆ, Figure 5.1: asic gapped iron core inductor.

6 Transformer Core Size Selection rea product For sinusoidal voltage I V S v i R v e dt d Ψ v dt d dt d Ψ V ) ω I I,,,1,,,1 K K I 1 1 P dt d S ) ω S P ) ω For pieceise constant voltage (forard converter) s dc dc D T V V dt d + 0 ˆ D I V P dc f P T D V P s s dc ˆ 1 ˆ f P P s ˆ

7 Core Configurations - Main variants Figure 5.: EE core (left) and EI core (right) ith indings (grey) and geometrical dimensions. Figure 5.3: Inductive component based on to C core halves ith indings (grey) and geometrical dimensions. ote that to indings are used. Figure 5.4: Toroid core and its geometrical dimensions. ote that the inding is not included.

8 Inductor Design Example (I) Inductor specification I Table 5.4: Inductor specification. L 0.3 mh 1 Hz 10 I 5 Hz 10 I 10 Hz 5 rea product 10 The C-core TELMG Su 150b (Figure 5.5), have geometrical properties according Table 5.5. Table 5.5: Geometry of the core Su 150b. a b c d e g 55.6 mm 150. mm 49.4 mm 76. mm mm 50.0 mm ˆ i ˆ 0.35 T Liˆ I P ˆ 379 cm 4 Figure 5.5: Inductor based on a C-core. The inding (grey) is split into to parallel connected indings.

9 Inductor Design Example (II) TELMG Su 150b cm 3.8 cm cm 77.0 cm P 4 57 cm Liˆ 48 turns ˆ l FF µ 0 L 3 mm 16 mm l e 1 + ln.65 l µ 0 l L FF 3 turns ˆ ˆ Li 0.53 T ˆ ˆ ˆ 1Hz 5 Hz 10 Hz i T 0.09 T T P P, i 157 W P, i P P P P 388dl ˆ fii,1hz,5 Hz,10 Hz i 4 W 1 W W P, i 18 W P P P,1Hz,5 Hz,10 Hz 141 W 10 W 6 W

10 Inductor Design Example (III) TELMG Su 150b MLT c+ d + g 351 mm Ψ T 4 4 ( T T ) ε s a, 10 rad R P MLT ρ 4.04 mω R I 58 W T, 4 e( c+ g) + e( d + g) + 4g( c+ g) + dg m T, 4 bc+ bd + 4cf m Ψ Ψ T T 1 e, P + P + P 78 W/m b+ e T, 1 b, P 1154 W/m b + e T, Ψ. 17F Ψ T T, conv T ΨT, rad + ΨT, conv s T a, a T s T, a T s T ΨT + α + 0 α o η ( T T ) p T o a s C C a

11 Inductor Design Example (IV) T -T [ C] s a Ψ T [W/m ] Figure 5.6: Calculated temperature rise at an ambient temperature of 40 C, based on radiated heat (blac) and an approximate method (grey). ir-gap losses not included Ψ T 1 e, P + P 1074 W/m b+ e, a T s T T, 67 o C

12 Inductor Design Example (V) Figure 5.7: Magnetic flux lines (left) of the entire inductor, and (right) of the region around one of the air gaps. ote the component of the fringing flux that is perpendicular to the surface of the steel tape.

13 Capacitors Design Metallized film polypropylene capacitors have a thin plastic film to support the metal layer of the electrodes. The plastic used for the film can for example be polyester. If the plastic film has electrodes (of the same polarity) on both sides it is referred to as double metallized film. The dielectric consists of a polypropylene film. To avoid air pocets resulting in a locally high electric field strength, the polypropylene film should be somehat porous to be able to absorb oil. Wet aluminium electrolytic capacitors contain a fluid, the electrolyte, beteen the aluminium electrodes. The electrolyte is absorbed by paper in beteen the aluminium electrodes, in order to avoid air pocets. Since the electrolyte is conductive, the aluminium electrodes are electrically close together, only separated by the dielectric of the capacitor. The dielectric constitutes of a thin aluminium oxide layer on the positive electrode.

14 Capacitors - Equivalent circuit i C R ESR R ESR tan0 ( f ) R s + πfc P ESR ( f ) R ESR ( f ) I ( f C ) L ESL C P R ESR ESR IC Figure 5.8: Capacitor simulation model.