12/06/2003 1 direct-off-line single-ended forward converters and the right-half-plane zero presented...

12/06/200312/06/2003 11

Direct-Off-Line Single-Ended Direct-Off-Line Single-Ended Forward ConvertersForward Converters

andandThe Right-Half-Plane ZeroThe Right-Half-Plane Zero

Presented by:Presented by:

Geetpal KaurGeetpal Kaur

EE136 StudentEE136 Student

12/06/200312/06/2003 22

Direct-Off-Line Single-Ended Direct-Off-Line Single-Ended Forward ConverterForward Converter

The power stage of a typical The power stage of a typical single-ended forward convertersingle-ended forward converter

Ls carries a large DC current Ls carries a large DC current componentcomponent

The term “Choke” is used to The term “Choke” is used to describe this componentdescribe this component

The general appearance of the The general appearance of the power stage is similar to the power stage is similar to the flyback unitflyback unit

12/06/200312/06/2003 33

Forward converter with energy Forward converter with energy recovery windingrecovery winding

12/06/200312/06/2003 44

Operating PrinciplesOperating Principles

When transistor Q1 turns onWhen transistor Q1 turns on

Supply voltage Vcc is applied to Supply voltage Vcc is applied to the primary winding P1the primary winding P1

As a result a secondary voltage As a result a secondary voltage Vs is developed and applied to Vs is developed and applied to output rectifier D1 and choke Lsoutput rectifier D1 and choke Ls

12/06/200312/06/2003 55


The voltage across the choke Ls The voltage across the choke Ls will be Vs less the output voltage will be Vs less the output voltage VoutVout

The current in Ls will increase The current in Ls will increase linearly linearly

di / dt = (Vs – Vout) / Lsdi / dt = (Vs – Vout) / Ls

12/06/200312/06/2003 66


At the end of an on periodAt the end of an on period

Q1 will turn offQ1 will turn off

Secondary voltages will reverseSecondary voltages will reverse

Choke current IChoke current ILL will continue to will continue to flow in the forward directionflow in the forward direction

12/06/200312/06/2003 77


As a result diode D2 will turn onAs a result diode D2 will turn on

D2 allows the current to D2 allows the current to continue circulating in the loop continue circulating in the loop D2, Ls, Co, and loadD2, Ls, Co, and load

The voltage across the choke Ls The voltage across the choke Ls will reversewill reverse

12/06/200312/06/2003 88


The current in Ls will decreseThe current in Ls will decrese -di / dt = Vout / Ls-di / dt = Vout / Ls

12/06/200312/06/2003 99

Output VoltageOutput Voltage

VVoutout = (V = (Vss * t * tonon) / (t) / (tonon + t + toffoff))

Vs = secondary voltage, peak VVs = secondary voltage, peak V

ton = time that Q1 is conduction, ton = time that Q1 is conduction, µsµs

12/06/200312/06/2003 1010

Output VoltageOutput Voltage

toff = time that Q1 is off, µstoff = time that Q1 is off, µs

the ratio:the ratio:

ton / (ton + toff)ton / (ton + toff)

is called the duty ratiois called the duty ratio

12/06/200312/06/2003 1111

Circuit SimulationCircuit Simulation

12/06/200312/06/2003 1212

The Right-Half-Plane ZeroThe Right-Half-Plane Zero

The difficulty of obtaining a The difficulty of obtaining a good stability margin and good stability margin and high-frequency transient high-frequency transient performance from the performance from the continuous-inductor-mode continuous-inductor-mode flyback and boost convertersflyback and boost converters

12/06/200312/06/2003 1313

Causes of the RHP ZeroCauses of the RHP Zero

A negative zero in the small-A negative zero in the small-signal duty cycle control to signal duty cycle control to output transfer functionoutput transfer function

The negative sign locates this The negative sign locates this zero in the right half of the zero in the right half of the complex frequency planecomplex frequency plane

12/06/200312/06/2003 1414

The RHP ZeroThe RHP ZeroA simplified ExplanationA simplified Explanation

The right-half-plane (RHP) zero The right-half-plane (RHP) zero has the same 20dB/decade rising has the same 20dB/decade rising gain magnitude as a gain magnitude as a conventional zero, but with 90º conventional zero, but with 90º phase lag instead of lead phase lag instead of lead

12/06/200312/06/2003 1515

Effects of Increasing Duty RatioEffects of Increasing Duty Ratio

The peak inductor current The peak inductor current increases in each switching cycleincreases in each switching cycle

The diode conduction time The diode conduction time decreasesdecreases

This is the circuit effect which is This is the circuit effect which is mathematically the RHP Zeromathematically the RHP Zero

12/06/200312/06/2003 1616

The RHP ZeroThe RHP ZeroA simplified ExplanationA simplified Explanation

12/06/200312/06/2003 1717

Duty Raito Control EquationsDuty Raito Control Equations

The equations for the flyback The equations for the flyback circuit are developed starting circuit are developed starting with the voltage VL across the with the voltage VL across the inductor:inductor:

VVLL = V = ViiD–VD–Vo o (1-D) = (V(1-D) = (Vii+V+Vaa)D – V)D – Voo

12/06/200312/06/2003 1818


Modulating the duty ratio D by a Modulating the duty ratio D by a small AC signal d whose small AC signal d whose frequency is much smaller than frequency is much smaller than the switching frequency the switching frequency generated an ac inductor voltage generated an ac inductor voltage ννLL::

ννLL = (Vi + Va)d – = (Vi + Va)d – ννo(1-D) =o(1-D) =

(Vi + Vo)d (Vi + Vo)d

12/06/200312/06/2003 1919


RHP zero frequency:RHP zero frequency:

ωωz z = Vi / L IL= Vi / L IL

12/06/200312/06/2003 2020

Current-Mode Control EquationsCurrent-Mode Control Equations

Io = iL (1-D) – (j Io = iL (1-D) – (j ωω L IL iL) / (Vi + L IL iL) / (Vi + Vo) = Vi iL / (Vi + Vo) - (j Vo) = Vi iL / (Vi + Vo) - (j ωω L IL L IL iL) / (Vi + Vo)iL) / (Vi + Vo)

The first term in equation is The first term in equation is constant with frequency and has constant with frequency and has no phase shift.no phase shift.

12/06/200312/06/2003 2121


This term dominates at low This term dominates at low frequency. frequency.

It represents the small-signal It represents the small-signal inductor current, which is inductor current, which is maintained constant by the inner maintained constant by the inner current control loop, thus current control loop, thus eliminating the inductor pole.eliminating the inductor pole.

12/06/200312/06/2003 2222


It dominates at frequencies It dominates at frequencies above ωz where the magnitudes above ωz where the magnitudes of the two terms are equal. of the two terms are equal.

The RHP zero frequency ωz may The RHP zero frequency ωz may be calculated by equating the be calculated by equating the two terms of equation (9.9). two terms of equation (9.9).

12/06/200312/06/2003 2323


The second term increases with The second term increases with frequency, yet the phase lags by frequency, yet the phase lags by 90º, characteristic of the RHP 90º, characteristic of the RHP zero. zero.

12/06/2003 1 direct-off-line single-ended forward converters and the right-half-plane zero presented...

Documents