L1_2 - DC LOAD VOLTAGE Some circuit arrangement effectively...

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Unformatted text preview: DC LOAD VOLTAGE Some circuit arrangement effectively place a DC voltage in the circuit as part of the load. This might result from capacitor voltage, another source may be the back electromotive force (EMF) of DC motor. As shown, if the inductor is ideal (no resistance), then the circuit equations impose the constraint that d v E = d C R i i i = + The average value of the capacitor current is zero for steady operation, d R E I I R = = , If the load inductance is smaller than some critical value then the average load is significantly different from the values predicted by the previous equations. 7 Determination of Critical Inductance 8 d d di X v E d ϑ =- , where 2 X L fL ϖ π = = ( 29 ( 29 ( 29 ( 29 1 1 sin cos cos ; d d m m i v E d V E d X X V E X X ϑ ϑ α α ϑ ϑ ϑ α ϑ ϑ α =- =- = ∫ ∫ =--- 9 The average value of d i is determined by integration: ( 29 ( 29 2 2 2 1 cos cos m d d V E I i d d T X X ϑ ϑ α α ϑ α ϑ ϑ α ϑ π ∫ ∫ = =--- ( 29 2 2 2 2 2 2 2 2 cos cos cos ( ) (sin sin ) cos 2cos sin 2 2 cos 2cos 2 cos 2sin d ϑ α α ϑ ϑ α ϑ α ϑ α ϑ α ϑ α π α ϑ α π α ϑ α π ϑ π α π α α ∫- =--- = +- =- = ÷ ÷ + =- = ÷ =- = ⇒ = + = + ( 29 2...
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L1_2 - DC LOAD VOLTAGE Some circuit arrangement effectively...

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