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AN021 Datasheet(PDF) 4 Page - Analog Intergrations Corporation |
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AN021 Datasheet(HTML) 4 Page - Analog Intergrations Corporation |
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4 / 7 page  AN021 October, 2001 4 ) ( ) ( 3 2 1 2 2 C C R C R s G C + = … ..(Constant) gain at high frequency: 3 1 1 ) ( C sR s G C = β is the gain of the feedback resistor divider. Note that due to the origin pole, the phase at low frequency is -90 ° and the gain curve is at -20dB/ decade. When the frequency approaches to zero, the phase increases toward 0 ° with a flat gain curve. When it moves toward the second pole, the frequency will be towards -90 ° and the gain curve goes back to -20dB/ decade again. Control Strategy The loop transfer function of Fig.1 is shown as below: ] LC 1 )s L r r R CR 1 ( L[s ) C r 1 (s r V V 1 ß ) //C (C R 1 )(s //C (C )R C (C sR ) C R 1 (s C R (s) G PWM (s) G T(s) L C L 2 C C IN M 3 2 s 3 2 2 3 2 1 2 2 2 2 P C + + + + + + × × × × + + + = × × = .……… (5) After meeting the power circuit requirement, we start to design the control loop. Therefore the LC poles and output capacitor zero are already allocated. What we can do is to distribute the location of pole and zero of compensation network to achieve the desired response demand. To obtain high gain at low frequency, the origin pole is already set. Then here comes the strategy for the location of the zero and the second pole. For the reason of stability, the zero of compensation network must be set lower than the zero of Buck converter. Without compensation zero, the zero of Buck converter would face three poles before it. The phase of the loop transfer function falls down toward -270 ° and passes through -180° between the poles of LC and the zero of Buck converter. This situation can lead to an unstable condition. To avoid that, the compensation circuit zero is advised to be lower than that of Buck converter. However the location of the compensation zero will affect the phase margin around the crossover frequency. To improve the phase margin of the loop transfer function and keep high gain at low frequency, the compensation zero is suggested between ωn and × 1 . 0 ωn. (ωn= LC 1 ). The second pole of compensation network is suggested far from the zero of Buck converter. In this way, we can obtain the –20dB/decade slope around the crossover frequency. According to the sampling theorem, the second pole of compensation network is suggested to be under one fifth of switching frequency of Buck converter ( Switching f 5 1 ) to reduce the noise at high frequency. Gc(s) PWM Gp(s) dVOUT(s) dVOUT(s)=0 + _ dVc(s) dD(s) Fig. 8 The Unity Feedback Control Loop for Buck Converter |
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Similar Description - AN021 |
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