peak_rec

peak_rec - Analysis of Peak Rectifier with Resistive Load...

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-1- Analysis of Peak Rectifier with Resistive Load Consider the following Half-Wave rectifier circuit loaded by a resistance R L : v i + - D C R L + - v L i D i C i L v D where v i ( t ) = V p cos( ± t ) ; t ² 0 , and v L ( t ) = V p cos( t t 1 ² t ² t 2 V p cos( t 2 ) e ³ t R L C ; t 2 ² t ² T ³ t 1 () ´ µ · v i L v v i

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-2- Kirchoff's Current Law applied to the D,C,R L node yields i D = i C + i L (1) = C dv i dt + i L (2) If R L C>>T, then V r will be small and the load current can be approximated by i L ± I L ± V p R L ± V L R L ± V p ² 1 2 V r R L (3) where I L is the (approximate) dc component of i L . The dc component of the load voltage can be approximated by V L ± V p ² 1 2 V r (4) that is, the average of the extreme values of v L . At the onset of diode conduction, the capacitor will have discharged to V p -V r , or V p ± V r ² V p e ±³ R L C ( i.e. , since V p cos ± t 2 ± V p and T- t 1 ± T) and, again, if R L C>>T, then the exponential term can be approximated by a truncated Taylor series to yield V p ± V r ² V p 1 ± ³ R L C ´ µ · ¸ ¹ or V r ± V p ² R L C = V p fR L C (5) where f =1 /T is the frequency, in Hz, of v i ( t ). And substituting (5) back into (4) yields V L ± V p ² V p 2fR L C or V L ± V p 2fR L C-1 2fR L C ² ³ ´ µ · (6) which gives the approximate dc component of the load voltage, in terms of the peak source voltage and the time constant characterizing the "filter" function.
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This note was uploaded on 12/21/2010 for the course EECE EECE 254 taught by Professor Robinturner,purangabomasumi during the Spring '09 term at UBC.

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peak_rec - Analysis of Peak Rectifier with Resistive Load...

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