Direct-Off-Line Single-Ended Forward Converters and The Right-Half-Plane Zero Presented by: Geetpal Kaur EE136 Student 12/06/2003

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

Forward converter with energy recovery winding 12/06/2003

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

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

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

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

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

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

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

Circuit Simulation 12/06/2003

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

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

The RHP Zero A 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

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

The RHP Zero A simplified Explanation 12/06/2003

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

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

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

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

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

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

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