LM3488 Flyback-Mathcad Example

SWITCHING POWER SUPPLY DESIGN:DISCONTINUOUS MODE FLYBACK CONVERTER

Written by Michele [email protected]

Application EngineerNational Semiconductor

Typical Flyback 3 output power supply:

Notes: Write down the power supply requirements on :Xxx

Get the results on:Rsultsxx

This Mathcad file helps the calculation of the external components of a typical discontinuous mode switching power supply.

Input voltage:

-Minimum input voltage: Vimin 30 volt

Maximum input voltage: Vimax 50 volt

Output:

Nominal output voltage, maximum output ripple, minimum output current, maximum output current

Vo1 5 volt Vrp1 10 mV Io1min 0.250amp Io1max 5 amp



(negative)

Vdfw 0.6 volt ( diode's forward drop voltage)

Pomin Vo1 Vdfw Io1min Vo2 Vdfw Io2min Vo3 Vdfw Io3min Pomin 7.7watt

Pomax Vo1 Vdfw Io1max Vo2 Vdfw Io2max Vo3 Vdfw Io3max Pomax 53.2watt

Switching Frequency: fsw 150 kHz

T1

fsw T 6.667sec

Transformer's Efficiency: 0.95

1) Maximum Stress on the switching mosfet :

- Define the flyback voltage across the mutual inductance: Vfm

Kfb 0.8 (Kfb is a value between 1 to 0.5)

Vfm Kfb Vimin Vfm 24volt

Nps1Vfm

Vo1 Vdfw Nps1 4.286

-Maximum Switching voltage on the switching-mosfet:Fspike 0.4

Vdsmax Fspike 1 Vimax Vfm Vdsmax 103.6volt

Safe factor (assume spikes of 30% of Vdc )

-The leakage inductance coefficient: Klk 0.95(Klk =0.95 means that the leakage inductance is 5% of the primary inductance)

-The total energy stored in the transformer: Wfly (Energy delivered to the outputs plus the Energy lost due to the leakage inductance)

Wlptot1

Klk Wlptot 1.053

WflyWlptot Pomax

fsw Wfly 3.73333 10 4 joule

2) Maximum and minimum duty cycle : Dmax and Dmin

To maintain the discontinuous mode of operation the maximum on-time has to be < 0.5 :

Ton+Tr+Tdt = T (On time+ reset time+ dead time = 1/ switching frequency )

-Choose minimum dead time duty cycle: Ddt 0.1

-Maximum drop voltage across the switching mosfet during the on time:On resistance of the Mosfet:Rdson 0.06 ohm

Vdson

Pomax

ViminRdson Vdson 0.112volt

Vfb Nps1 Vo1 Vdfw

Tonmax

Vfb 1 Ddt T

Vimin Vdson Klk Vfb Tonmax 2.748sec

Tonmin

Vfb 1 Ddt T

Vimax Vdson Klk Vfb Tonmin 2.017sec

-Maximum duty cycle

Dmax

Tonmax

T Dmax 0.412

-Minimum duty cycle

Dmin

Tonmin

T Dmin 0.303

3) Primary current:

- Primary peak current:

Ippk2 Wfly fsw

Vimin Dmax Ippk 9.056amp

- Primary RMS current:

Iprms

Ippk

3

Tonmax

T Iprms 3.357amp

- Primary DC current:

Ipdc

Pomax

Vimin Ipdc 1.867amp

- Primary AC current:

Ipac Iprms2 Ipdc

2 Ipac 2.79amp

4) Primary inductance:

The energy stored is: ELp Ip2

2 = Po T and Ip

Vomin Tonmax

Lp

Edt Vimin Tonmax Edt 8.245 10 5 volt sec

- Primary inductance:

Lp2 Wfly

Ippk2

Lp 9.105H

5) Secondary currents and turns ratios (secondary/primary) : Nsp1 & Nsp2

Nsp1Vo1 Vdfw

Vfb Nsp1 0.233

Nsp2Vo2 Vdfw

Vfb Nsp2 0.525

Nsp3Vo3 Vdfw

Vfb Nsp3 0.525

1

Nsp14.286

1

Nsp21.905

1

Nsp21.905

-Master output:

- Secondary peak current:

Is1pk

Io1max 2

1 Dmax Ddt Is1pk 20.503amp

- Secondary RMS current:

Is1rms

Is1pk

31 Dmax Ddt Is1rms 8.267amp

- Secondary AC current:

Is1ac Is1rms2 Io1max

2 Is1ac 6.584amp

- Secondary inductance :

Ls1 Nsp12 Lp Ls1 0.496H

-First slave output:


Is2pk

Io2max 2



Is2rms

Is2pk




2 Is2ac 1.317amp

- Secondary inductance :


-Second slave output:


Is3pk

Io3max 2



Is3rms

Is3pk




2 Is3ac 1.317amp

- Secondary inductance:


6) Maximum Stress across the output diodes: VdiodeMaximum voltage present on the cathode of diodes

Vdiode1max Vimax Nsp1 Vo1 Vdiode1max 16.667volt



Select a diode with Va-c>> Vdiode.max, and ultra-fast switching diode

7-a) Output ripple Specifications : Output Capacitors- Secondary inductance :


To meet the output ripple specifications without using an external LC filter, the output capacitors have to meet two criteria:- satisfy the standard capacitance definition: I=C*dV/dt where t is the Ton time, V is 25% of the allowable output ripple.- The Equivalent Series Resistance (ESR) of the capacitor has to provide less than 75% of the maximum output ripple. (Vripple=Ipeak*ESR)-Maximum output ripple:

Vrp1 10mV Vrp2 20mV Vrp3 20mV

-Minimum output capacitance:

Co1 Is1pk

Tonmax Vrp1 0.25

Co1 2.254 104 F

-Maximum ESR value:

ESR1Vrp1 0.75

Is1pk

ESR1 3.658 10 4 ohm


Co2 Io2max

Tonmax Vrp2 0.25

Co2 549.685F

-Maximum ESR value:

ESR20.75 Vrp2

Io2max

ESR2 0.015ohm


Co3 Io3max

Tonmax Vrp3 0.25

Co3 549.685F

-Maximum ESR value:

ESR30.75 Vrp3

Io3max

ESR2 0.015ohm

7-b) Output ripple Specifications with external LC filter :In some cases to meet the output ripple specifications, it is more convenient to add a second order LC filter and therefore reduce the size and cost of the output capacitors:Att 20 dBLC filter attenuation:

Co1a Is1pk

Tonmax Vrp1 0.25 Att

Co1a 1.127 103 F

ESR1a1 Vrp1 Att 0.75

Is1pk

ESR1a 7.316 10 3 ohm

-Second order filter:Filter order loss per octave*1 62 123 184 24

k 1000Attenuation required (in dB): Db 10

Loss per Octave for filter: 12

Frequency at needed att. : (switching frequency)fx fswRequired cutoff frequency:

fcfx

2

Db

fc 84.185kHz

One of the critical factor of a filter design is the attenuating character at the corner frequency.The damping factor ( zeta) describes the gain at the corner frequency and the time response of the filter. As the damping factor becomes smaller, the gain at the corner frequency becomes larger.For many filters, a damping factor of 1 and a cutoff frequency within about an octave of the calculated ideal should provide suitable filtering.Damping factor much greater than 1 may cause unacceptably high attenuation of lower frequencies and a damping factor much less than .707 may cause undesired ringing and the filter may itself produce noise. (* octave= interval that has the frequency ratio 2:1 )-For each output:-Output load resistance:

Ro1Vo1

Io1max

-Desired damping factor: .7

c 2 fc c 5.289 105rad

sec

-Inductance calculated:

L1 2 Ro1

c L1 2.647H

-Capacitance calculated:

Co1b1

L1 c2 Co1b 1.35F

-Inductance used: L1used 10H

-Capacitance used: Co1bused 50F

i 1 5000

cu1

2 L1used Co1bused

fi 100

i 500( )

250

wi fi 2 rad

sec si j wi

n1

L1used Co1bused nc

1

L1 Co1b

1L1used

2 Ro1 L1used Co1bused 1 0.224

1cL1

2 Ro1 L1 Co1b 1c 0.7

As1i1

1 i 2 1wi

cu

wi

n

2

As1ci1

1 i 2 1cwi

c

wi

nc

2

Mags1i 20 log As1i Magsc1i 20 log As1ci

100 1 103

1 104

1 105

1 106

40

30

20

10

0

10

20

used-valuescalculated values

Second Order output filter

Frequency

Ma

gn

itud

e,

dB

-Capacitor Selection:The performance of a filter critically depends on the capacitor used. Besides the basic voltage and capacity requirements, select capacitors with low ESL, for high frequency attenuation, and low ESR, for mid band attenuation and/or high ripple current capability.-Choke Design:Filter chokes should be designed to reduce parasitic capacity as much as possible:-the input and output should be as far as possible. -singular layer or Banked windings.

-use thicker than usual inter-layer insulation. 6 9 3 5 8 1 2 4 7(Banked windings)8) Input capacitor: The input capacitor has to meet the maximum ripple current rating Ip(rms) and the maximum input voltage ripple ESR value.

9) Snubber Circuit:The basic intent of a snubber is to absorb energy from the leakage inductance in the circuit.The leakage inductance is part of the primary inductance that is not mutually coupled with the secondary inductance. It is important to keep the leakage inductance as low as possible because it reduces the efficiency of the transformer and it causes spikes on the drain of the switching device. A capacitor placed in parallel with other circuit elements will control the voltage across those elements.Usually the leakage inductance is 2-5% of the inductance of the primary winding:

Lleakage 0.03 Lp Lleakage 0.273H

Total energy: 1/2LI^2

Esnubber1

2Lleakage Ippk

2 Esnubber 1.12 10 5 joule

Esnubber fsw 1.68watt

There are different ways to dissipate this energy and reduce the spikes on the drain of the switching mosfet.A typical snubber circuit is a resistance and a capacitor connected in series between the input voltage and the drain of the mosfet.(approximately half of this energy has to be dissipated on the snubber circuit)A good starting point for the snubber capacitance could be:

Csnubber

Esnubber

2 Fspike Vimax Vfm 2 Csnubber 2.557 10 3 F

The RC time has to be larger than the on time switching period: 1/RC<Ton

Rsnubber

Tonmin

4Csnubber

Rsnubber 197.233

Prsnubber Vimax2 Csnubber fsw Prsnubber 0.959watt

For low output power applications, a clamp zener or a transient suppressor can be used as shown on the flyback application of the LM3488 datasheet.

9) Switching Mosfet: Power DissipationThe Mosfet is chosen based on maximum Stress voltage (section1), maximum peak input current (section 3), total power losses, maximum allowed operating temperature, and driver capability of the LM3488. -The drain to source Breakdown of the mosfet (Vdss) has to be greater than:Vdsmax 103.6volt

-Continuous Drain current of the mosfet (Id) has to be greater than:

Ippk 9.056amp

- Maximum drive voltage: The voltage on the drive pin of the LM3488, Vdr is equal to the input voltage when input voltage is less than 7.2V, and Vdr is equal to 7.2V when the input voltage is greater than 7.2V Vdr 7.2 voltRdron 7 ohm

-Total Mosfet losses and maximum junction temperature:The goal in selecting a Mosfet is to minimize junction temperature rise by minimizing the power loss while being cost effective. Besides maximum voltage rating, and maximum current rating, the other three important parameters of a Mosfet are Rds(on), gate threshold voltage, and gate capacitance.The switching Mosfet has three types of losses, conduction loss, switching loss, and gate charge loss:-Conduction losses are equal to: I^2*R losses, therefore the total resistance between the source and drain during the on state, Rds(on) has to be as low as possible.-Switching losses are equal to: Switching-time*Vds*I*frequecy. The switching time, rise time and fall time is a function of the gate to drain Miller-charge of the Mosfet, Qgd, the internal resistance of the driver and the Threshold Voltage, Vgs(th), the minimum gate voltage which enables the current through drain source of the Mosfet. -Gate charge losses are caused by charging up the gate capacitance and then dumping the charge to ground every cycle. The gate charge losses are equal to: frequency • Qg(tot) • VdrUnfortunately, the lowest on resistance devices tend to have higher gate capacitance.Because this loss is frequency dependent, in very high current supplies with very large FETs, with large gate capacitance, a more optimal design may result from reducing the operating frequency.Switching losses are also effected by gate capacitance. If the gate driver has to charge a larger capacitance, then the time the Mosfet spends in the linear region increases and the losses increase. The faster the rise time, the lower the switching loss. Unfortunately this causes high frequency noise.

n 10 9Mosfet: Fairchild FQB10N20L- D2PAKRdson 0.3 ohm

(Total resistance between the source and drain during the on state)Coss 95 pF(Output capacitance)Qgtot 13 n coul

(Total gate charge)Qgdmiller 6.1 n coul

(Gate drain Miller charge)Vgsth 2 volt

(Threshold voltage)-Conduction losses: Pcond

Pcond Rdson Iprms2 Dmax

Pcond 1.394watt-Switching losses: Psw(max)Turn On time:

tsw Qgdmiller

Rdron

Vdr Vgsth tsw 8.212 10 9 sec

Pswmax tsw Vdsmax Ippk fsw Coss Vdsmax

2 fsw

2 Pswmax 1.232watt

- Gate charge losses: Pgate

The average current required to drive the gate capacitor of the Mosfet:

Igateawg fsw Qgtot Igateawg 1.95 10 3 amp

Pgate Igateawg Vdr Pgate 0.014watt

-Total losses: Ptot(max)

Ptotmax Pcond Pswmax Pgate Ptotmax 2.64watt

-Maximum junction temperature and heat sink requirement: -Maximum junction temperature desired:Tjmax 130 Celsius

-Maximum ambient temperature: Tamax 50 Celsius

-Thermal resistance junction to ambient temperature:

jaTjmax Tamax

Ptotmax

ja 30.3051

watt Celsius

If the thermal resistance calculated is lower than that one specified on the Mosfet's data sheet a heat sink or higher copper area is needed.For Example for a T0-263 (D2pak) package the Tja of the Mosfet versus copper plane area is:

10) Current limit:

The LM3488 uses a current mode control scheme. The main advantages of current mode control are inherent cycle-by-cycle current limit for the switch, and simple control loop characteristics.Since the LM3488 has a maximum duty cycle of 100%, and the power supply is designed to work in discontinuous mode with a 50% maximum duty cycle, the current limit should be designed so that the peak short circuit current limit is reached just before the 50% boundary is reached.

Rsense160mV

Ippk 1.1 Rsense 0.016

11) Transformer Design:

The inductor- transformer should be designed to minimize the leakage inductance, ac winding losses, and core losses.When the transformer is designed to operate in discontinuous mode the total inductance is lower than in continuous mode, and the size of the transformer may be smaller. But the peak currents will be at least twice the average current, therefore ac winding losses and core losses are the predominant factors rather than the dc losses and core saturation. The total losses are minimized when core losses and winding losses are approximately the same value.

-Core selection:To reduce the core losses, ferrite-P material is usually the preferred material for discontinuous flyback transformers with operating switching frequencies higher than 100Khz. (TDK PC40, Philips 3C85)The window shape of the core should be as wide as possible to minimize the number of layers and therefore minimize the the ac winding losses and the leakage inductance.E-type cores with an internal air-gap are the best choice for low cost and lower leakage inductance.

- Winding techniques to minimize leakage inductance, ac losses and EMI noise:To minimize the ac losses, leakage inductance and the EMI noise, particular attention has to be paid to the design of the primary and secondary windings of the transformer.The primary winding should be designed for less than three layers, thus minimizing the winding capacitance and the leakage inductance of the transformer. In high switching frequency applications an additional insulating layer between windings is usually used.If the transformer has multiple secondary windings, the highest power secondary should be closest to the primary of the transformer.For high power applications, a split primary construction is typically used to reduce the leakage inductance. To avoid high ac winding losses due to the skin effect (at high frequency currents tend to flow close to the surface of the conductor), Litz wire or Foil windings are typically used.Litz wire for power applications is usually made with a few small diameter wires twisted together in a strand, and few of these strands twisted into bigger strands.Shielding tape or an additional winding between primary and secondaries is typically used to reduce the capacitive coupling of common mode noise between primary and secondary. The end of this additional winding has to be connected to ground or to the high input voltage of the transformer.

To assist in the design of the transformer any application note from the transformer core manufacturers can be used, or the "Transformer and Inductor Design Hadbook" written by Colonel Wm. T. McLyman" or the "Magnetics Designer Software" from Intusoft may be used. The required parameters for the flyback inductor-transformer design are:

-Core type and material: (TDK E core ferrite with internal air-gap)

-Switching frequency:

fsw 150kHz

-Edt: volt-seconds

Edt 8.245 10 5 sec volt

-Primary and secondaries currents:

Ippk 9.056amp Ipdc 1.867amp Ipac 2.79amp

Is1pk 20.503amp Io1max 5amp Is1ac 6.584amp



-Primary and secondary’s inductance:

Lp 9.105H Ls1 0.496H Ls2 2.51H Ls3 2.51H

Documents

LM3488 Flyback-Mathcad Example