Design of a compact 200 W DC/DC converter

Introduction

• Simplified model of a complete power supply:
• Only the DC/DC-Converter without any control is build in this project
• Design Parameters:

  output voltage	19.5 V
  output power	200 W
  input voltage	380 V DC
  switching frequency	200 kHz
  maximum power loss	10 W in the complete device - maybe 6 W in this DC/DC-Converter
  topology	Series Resonant Converter (SRC)

• New GaN-EHEMT devices are used for the primary side

Analysis

• SRC tank circuit with ideal switches and parasitic capacitances:
• Real transformer model assumed
• Ideal full-bridge rectifier assumed instead of centre-tap circuit
• Output voltage assumed to be constant during one period
• Analytic determination of signals without Fourier-transformation
• Differe two general cases (Q₁ on):
• D open
• Simple LC-resonant circuit:
  $\begin{array}{rcl} i_\mathrm{1} = i_\mathrm{h} & = & a \cdot \mathrm{sin} \left (\omega t \right ) + b \cdot \mathrm{cos} \left (\omega t \right ) \\ i_\mathrm{2} & = & 0 \\ \end{array}$     where     $\begin{array}{rcl} \omega & = & \frac{1}{\sqrt{C_\mathrm{res} \cdot (L_\mathrm{\sigma 1} + L_\mathrm{h})}}\\ a & = & (V_\mathrm{in} - V_\mathrm{Cres,0}) \cdot \sqrt{\frac{C_\mathrm{res}}{L_\mathrm{\sigma 1} + L_\mathrm{h}}}\\ b & = & i_\mathrm{h,0} \end{array}$
• D conducting
• The currents are given with the following differential equation system:
  $\begin{array}{rcl} L_\mathrm{h} \cdot \frac{\mathrm{\delta} i_\mathrm{h}}{\mathrm{\delta} t} & = & V_\mathrm{C'out} + i_2 \cdot R'_2 + L'_\mathrm{\sigma 2} \cdot \frac{\mathrm{\delta} i_2}{\mathrm{\delta} t} \\ V_\mathrm{in} & = & L_\mathrm{h} \cdot \frac{\mathrm{\delta} i_\mathrm{h}}{\mathrm{\delta} t} + L_{\mathrm{\sigma} 1} \frac{\mathrm{\delta} (i_\mathrm{h} + i_2)}{\mathrm{\delta} t} + \int \frac{i_\mathrm{h} + i_2}{C_\mathrm{res}} \mathrm{\delta} t \end{array}$
• All currents i₁, i_h, i₂ have the scheme
  $i_* = a_* \cdot e^{\beta_1 t} + \left ( b_* \cdot sin(\omega t) + c_* \cdot cos(\omega t) \right ) \cdot e^{\beta_2 t} + d_*$
  where
  $\begin{array}{lcl} \omega & = & \frac{\sqrt{3}}{2} (u + v)\\ \beta_1 & = & u + v - \frac{B}{3 A}\\ \beta_2 & = & - \frac{B}{3 A} - \frac{1}{2} (u + v)\\ \end{array}$ $\begin{array}{lcl} u & = & \sqrt[3]{-\frac{q}{2} + \sqrt{\frac{q^2}{4} + \frac{p^3}{27}}}\\ v & = & \sqrt[3]{-\frac{q}{2} - \sqrt{\frac{q^2}{4} + \frac{p^3}{27}}} \end{array}$ $\begin{array}{lcl} p & = & \frac{9 A C - 3 B^2}{9 A}\\ q & = & \frac{2 B^3 - 9 A B C + 27 A^2 D}{27 A^3} \end{array}$ $\begin{array}{rcl} A & = & C_\mathrm{res} \cdot (L_\mathrm{h} L_\mathrm{\sigma 1} + L_\mathrm{h} L'_\mathrm{\sigma 2} + L_\mathrm{\sigma 1} L'_\mathrm{\sigma 2})\\ B & = & C_\mathrm{res} R'_2 \cdot (L_\mathrm{h} + L_\mathrm{\sigma 1})\\ C & = & L_\mathrm{h} + L'_\mathrm{\sigma 2}\\ D & = & R'_2 \end{array}$
• The constants a_*, b_*, c_*, d_* are different for each current [...]
• Same differential equations for all Q_{1 / 2} switching states
• During the dead time, C_res and C_Q1 + C_Q2 are in series
• When Q₂ is on, V_in = 0
• The times of the diode switching actions have to be approximated
• 
• Download program

Program

Transformer

• Used core type: EFD 30/15/9
• 31 primary + 2x 3.2 secondary windings

GeckoMAGNETICS calculation

PCB

Rectification circuit

Measurements

Compare simulation and mesaurement

Ifrared

Conclusion

• Primary side works with high efficiency
• Secondary rectification is challenging
• Transformer efficiency is not perfect
• Better fitting litz wires/foils
• Flat design: extra coil former / paralleled cores / planar transformer
• Higher frequency
• Control strategy has to be found
• Analytic program can be improved to find control functions
• PFC