1. Direct-Off-Line Single-Ended Forward Converters and The 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
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3. Forward converter with energy recovery winding
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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
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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
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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
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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
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8. Operating Principles The current in Ls will decrese
-di / dt = Vout / Ls
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9. Vout = (Vs * ton) / (ton + toff)
Output Voltage
Vout = (Vs * ton) / (ton + toff)
Vs = secondary voltage, peak V
ton = time that Q1 is conduction, µs
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10. Output Voltage toff = time that Q1 is off, µs the ratio:
ton / (ton + toff)
is called the duty ratio
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11. Circuit Simulation
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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
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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
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14. 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
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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
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16. The RHP Zero A simplified Explanation
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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
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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
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19. Duty Raito Control Equations
RHP zero frequency:
ωz = Vi / L IL
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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.
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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.
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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).
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23. Current-Mode Control Equations
The second term increases with frequency, yet the phase lags by 90º, characteristic of the RHP zero.
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