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Direct-Off-Line Single-Ended Forward Converters and The Right-Half-Plane Zero

Direct-Off-Line Single-Ended Forward Converters and The Right-Half-Plane Zero. Presented by: Geetpal Kaur EE136 Student. Direct-Off-Line Single-Ended Forward Converter. The power stage of a typical single-ended forward converter Ls carries a large DC current component

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Direct-Off-Line Single-Ended Forward Converters and The Right-Half-Plane Zero

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  1. Direct-Off-Line Single-Ended Forward ConvertersandThe Right-Half-Plane Zero Presented by: Geetpal Kaur EE136 Student 12/06/2003

  2. Direct-Off-Line Single-Ended Forward Converter • The power stage of a typical single-ended forward converter • Ls carries a large DC current component • The term “Choke” is used to describe this component • The general appearance of the power stage is similar to the flyback unit 12/06/2003

  3. Forward converter with energy recovery winding 12/06/2003

  4. Operating Principles • When transistor Q1 turns on • Supply voltage Vcc is applied to the primary winding P1 • As a result a secondary voltage Vs is developed and applied to output rectifier D1 and choke Ls 12/06/2003

  5. Operating Principles • The voltage across the choke Ls will be Vs less the output voltage Vout • The current in Ls will increase linearly di / dt = (Vs – Vout) / Ls 12/06/2003

  6. Operating Principles • At the end of an on period • Q1 will turn off • Secondary voltages will reverse • Choke current IL will continue to flow in the forward direction 12/06/2003

  7. Operating Principles • As a result diode D2 will turn on • D2 allows the current to continue circulating in the loop D2, Ls, Co, and load • The voltage across the choke Ls will reverse 12/06/2003

  8. Operating Principles • The current in Ls will decrese • -di / dt = Vout / Ls 12/06/2003

  9. Output Voltage • Vout = (Vs * ton) / (ton + toff) • Vs = secondary voltage, peak V • ton = time that Q1 is conduction, µs 12/06/2003

  10. Output Voltage • toff = time that Q1 is off, µs the ratio: ton / (ton + toff) is called the duty ratio 12/06/2003

  11. Circuit Simulation 12/06/2003

  12. The Right-Half-Plane Zero • The difficulty of obtaining a good stability margin and high-frequency transient performance from the continuous-inductor-mode flyback and boost converters 12/06/2003

  13. Causes of the RHP Zero • A negative zero in the small-signal duty cycle control to output transfer function • The negative sign locates this zero in the right half of the complex frequency plane 12/06/2003

  14. The RHP ZeroA simplified Explanation • The right-half-plane (RHP) zero has the same 20dB/decade rising gain magnitude as a conventional zero, but with 90º phase lag instead of lead 12/06/2003

  15. Effects of Increasing Duty Ratio • The peak inductor current increases in each switching cycle • The diode conduction time decreases • This is the circuit effect which is mathematically the RHP Zero 12/06/2003

  16. The RHP ZeroA simplified Explanation 12/06/2003

  17. Duty Raito Control Equations • The equations for the flyback circuit are developed starting with the voltage VL across the inductor: • VL = ViD–Vo (1-D) = (Vi+Va)D – Vo 12/06/2003

  18. Duty Raito Control Equations • Modulating the duty ratio D by a small AC signal d whose frequency is much smaller than the switching frequency generated an ac inductor voltage νL: • νL = (Vi + Va)d – νo(1-D) = (Vi + Vo)d 12/06/2003

  19. Duty Raito Control Equations • RHP zero frequency: • ωz = Vi / L IL 12/06/2003

  20. Current-Mode Control Equations • Io = iL (1-D) – (j ω L IL iL) / (Vi + Vo) = Vi iL / (Vi + Vo) - (j ω L IL iL) / (Vi + Vo) • The first term in equation is constant with frequency and has no phase shift. 12/06/2003

  21. Current-Mode Control Equations • This term dominates at low frequency. • It represents the small-signal inductor current, which is maintained constant by the inner current control loop, thus eliminating the inductor pole. 12/06/2003

  22. Current-Mode Control Equations • It dominates at frequencies above ωz where the magnitudes of the two terms are equal. • The RHP zero frequency ωz may be calculated by equating the two terms of equation (9.9). 12/06/2003

  23. Current-Mode Control Equations • The second term increases with frequency, yet the phase lags by 90º, characteristic of the RHP zero. 12/06/2003

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