Transfer Function of the LC Filter

In a buck, there is a post-LC filter present. Therefore this filter stage can easily be treated as a cascaded stage following the switch. The overall transfer function is then very easy to compute as per the rules mentioned in the previous section. However, when we come to the boost and buck-boost, we don t have a post-LC filter — there is a switch/diode connected between the two reactive components that alters the dynamics. However, it can be shown, that even the boost and buck-boost can be manipulated into a canonical model in which an effective post-LC filter appears at the output — thus making them as easy to treat as a buck. The only difference is that the original inductance L (of the boost and buck-boost) gets replaced by an equivalent (or effective) inductance equal to L/(l—D)2. The C remains the same in the canonical model. 

From the equations for Q and resonant frequency, we can conclude that if L is increased, Q tends to decrease, and if C is increased, Q increases. 

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Finally, note also that the following relations are very useful when trying to manipulate the transfer function of the LC filter into different forms... 

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