Project:Sandbox

= Buck Convertor = Among the most common topologies, the buck converter offers a practical and efficient means of power distribution.

Continuous Conduction Mode (CCM)

 * Fixed frequency and high current

Discontinuous Conduction Mode (DCM)

 * During low current operation, causes the voltage / current aplied to switch to be reversed
 * Violates assumptions made in realizing converter equations
 * If controller is not in forced continuous mode, designer must consider both modes of operation.

Inductor Ripple Current
$$m(d,n)=floor(n*d)$$, where $$n=0\ldots N$$ and $$d=0\ldots 1$$ $$\Delta {{I}_{o}}(d,n)=\frac{{{V}_{o}}+\frac{N}\centerdot \left( TFE{{T}_{rds\_on\_no{{m}_{nom}}}}+{{L}_{o\_dcr}} \right)}{{{f}_{s{{w}_{nom}}}}\centerdot {{L}_{o\_rev}}}\centerdot \frac{n\centerdot \left( d-\frac{m(d,n)+1}{n} \right)\centerdot \left( \frac{m(d,n)}{n}-d \right)}{d\centerdot n}$$

Peak Inductor Current
$${{I}_{L\_pk}}=\frac{N}+\frac{\Delta {{I}_{L}}}{2}$$

Ripple current as a percentage of max load
$$\Delta {{I}_{L\_per}}=\frac{\Delta {{I}_{L}}}$$

Output Inductor Response Time
$${{t}_{L\_response}}=\frac{{{L}_{o}}\centerdot {{I}_{o}}}{N\centerdot ({{V}_{i\_rev}}-{{V}_{o}})}$$

Output Inductor Power Dissipation
$$E{{T}_{ckt}}=\left( \frac\centerdot (1-{{D}_{rev}})\centerdot {{10}^{6}} \right)$$ $${{B}_{pk}}=\frac{E{{T}_{ckt}}}{E{{T}_{100}}}\centerdot 100$$ $${{f}_{e}}=\frac{2\centerdot \pi \centerdot ({{D}_{rev}}-{{D}^{2}})}$$ $${{V}_{e}}={{f}_{sw}}\centerdot {{10}^{-14}}$$ $${{P}_{core}}={{K}_{0}}\centerdot {{f}_}^{x}\centerdot {{B}_{p{{k}_{nom}}}}^{y}\centerdot {{V}_{e}}$$

$${{R}_{oper}}={{L}_{o\_dc{{r}_{nom}}}}\centerdot \frac{\left( Temp \right)}{259.5}$$ $${{P}_{dc}}={{\left( \frac{{{I}_{o}}}{N} \right)}^{2}}\centerdot {{R}_{oper}}$$

$${{P}_{ac}}={{K}_{1}}\centerdot \Delta {{I}_}^{2}\centerdot \sqrt\centerdot {{R}_{ope{{r}_{\max }}}}$$

$${{P}_{Lo}}={{P}_{core}}+{{P}_{dc}}+{{P}_{ac}}$$

Output Current Ripple

 * Given a constant load current, the output capacitor current ripple must equal the output inductor 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 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