Project:Sandbox

Buck Convertor
Current mode

Output Current Ripple
Output voltage ripple $$\Delta {{V}_{o}}=\Delta {{I}_{o}}\centerdot {{C}_{o\_esr}}+\frac{\Delta {{I}_{o}}}{8\centerdot {{f}_{sw\_rev}}\centerdot {{C}_{o\_rev}}\centerdot N}$$

Load step $${{I}_{o\_step\_\max }}={{I}_}\centerdot 80%$$

Response to load step $$\Delta {{V}_{o\_step}}=\frac{{{t}_{L\_response}}\centerdot ({{I}_}-{{I}_})}$$

Output rms current $${{I}_{o\_rms}}=\frac{\Delta {{I}_{o}}}{\sqrt{12}}$$

Output capacitor power dissipation $${{C}_{o\_diss}}={{I}_{o\_rms}}^{2}\centerdot {{C}_{o\_esr}}$$

Input Capacitance
Input current ripple $$m(d,n)=floor(n*d)$$, where $$n=0\ldots N$$ and $$d=0\ldots 1$$

$${{I}_{i\_rms}}(d,Io,Lo,Vo,fsw,n)=\sqrt{\left( d-\frac{m(d,n)}{n} \right)*\left( \frac{(m(d,n)+1)}{n}-d \right)*I{{o}^{2}}+\frac{n*\left( \frac{\left( \frac{Vo*(1-d)}{fsw} \right)}{Lo} \right)}{12*n*{{d}^{2}}}*\left( {{(m(d,n)+1)}^{2}}*{{\left( d-\frac{m(d,n)}{n} \right)}^{3}}+m{{(d,n)}^{2}}*{{\left( \frac{m(d,n)+1}{n}-d \right)}^{3}} \right)}$$

$$\Delta {{I}_{i}}=\sqrt{3}\centerdot {{I}_{i\_rms}}$$

Input voltage ripple (pk-pk) $$\Delta {{V}_{i}}={{D}_{nom}}\centerdot {{I}_{o}}\centerdot \left( {{C}_{i\_esr}}+\frac{1-{{D}_{nom}}}{{{C}_{i\_rev}}\centerdot {{f}_{sw\_rev}}} \right)$$

Input RMS voltage $${{V}_{i\_rms}}=\frac{2\centerdot \pi \centerdot {{f}_{sw\_rev}}\centerdot {{C}_{i\_rev}}}+{{I}_{i\_rms}}\centerdot {{C}_{i\_esr}}$$

Input capacitance power dissipation $${{C}_{i\_diss}}={{I}_{i\_rms}}^{2}\centerdot {{C}_{i\_esr}}$$

AN77, High Efficiency, High Density, PolyPhase Converters for High Current Applications, Linear Tecknology, 1999