Transfer Functions of Switching Converters...Copto = 2 nF CTR = 0.3 FB This is a fixed-frequency current-mode-controlled flyback converter delivering 19 V 3 A from a 120-V source.

Hi everyone, my name is Christophe Basso and I am releasing a new book on small-signal modeling (available fall2020). I have derived the control-to-output transfer functions of many converters, starting from simple dc-dc cells(buck, buck-boost or boost) to isolated versions like flyback or forward converters operated in voltage mode (VM),current mode (CM), quasi-resonance (QR), constant on-time (COT), constant off-time (FOT) with various operatingmodes like continuous conduction (CCM) or discontinuous conduction (DCM) and borderline conduction (BCM orCrM) for power-factor-corrected converters for instance. Many simulation hours mainly in SIMPLIS® using the freedemonstration version Elements. Over the proposed 61 files, less than 6 require the full professional version tooperate (such as the PFCs for instance) the rest is 100% operating on Elements which is an excellent news. Allapplication circuits come with an automated calculation window in which you enter the wanted design goalsextracted from the power stage response and the program calculates the compensation elements for you. Thevalues are available in the netlist and easily accessed from the development environment. If you are a powersupply designer, you can’t miss these ready-made templates for your engineering job. Enjoy these files and let meknow what you think of these examples. Thank you – Christophe Basso, May 2020.

https://www.simplistechnologies.com/product/elements

Transfer Functions of Switching ConvertersFast Analytical Techniques at Work with Small-Signal Analysis

If you like these circuits and want to support my modestcontribution to the technical community, a small amountsent to my Paypal account will behighly appreciated! Thank you.

Version 1.1

The Template – it is a ready-to-simulate circuit. Load it, press F9 and there you go:

Copto = 2 nFCTR = 0.3

FB

This is a fixed-frequency current-mode-controlled flyback converterdelivering 19 V 3 A from a 120-V source. Enable the 6-ohm load for acanalysis and disable the PWL source (right-click after selection) tosee the transient response. Check Simulator>Edit Netlist (after preprocess)

to see the calculated component values.

This is a typical converter for an ac-dc notebook adapter.

- Christophe Basso - Transfer Functions of Switching Converters -

1-V clamped divide-by-3 block

R29250m

VOUT

VCS

R1{Rload}

Vdrain

IN OUT

=OUT/IN

IN OUT

=OUT/IN

R15{Rr}

R219k

FB

L2600u IC=0

R2130m

R33.3k

IC=1R31

VOUT

VOUT

FB

OPIN

+C1100p IC=0

C131.36m IC=0

C2

{C1a} IC=10

OPIN

+

C3{Ccol} IC=0

DRVC847p IC=0

D3

MBR20200CTP

DRV

FB

FB

VOUT

FB

Isec

Iout

G1

-100u

I2

Idrain

R5{Rupper}

R7{Rpullup}

Vmod

AC 1 0

R4{RLED}

IC=1R8

P1

TX1

S1

V2

V3

5

Vin

120

TL431_CB

U2

S1

Vramp R6{Rlower}

Q

QN

R

S

U35

S2

U4

OptocouplerU1

X1

Transient response

Compensated loop gain

Enable ordisable witha right-click.

The Compensation – display the power stage response at the selected operating point and extract parameters

Extract data at the selected crossover frequency. Here, it is 2 kHz with a 60° phase margin as a goal.

Magnitude

Phase

Power Stage

Magnitude at fc

Phase at fc

The Compensation – find all calculated values in the Edit Netlist submenu

Magnitude

Phase

Compensated loop gain

Loop Gain

fc

PM

The Template – change the load from a fixed resistance to a current source for the step load response

1. Right click on the resistance2. Enable it - Enable Selected3. Right click on the current source4. Disable it – Disable Selected5. Press F86. Choose ac analysis

Step load: disable the loading resistance, press F8 then check transient Ac sweep or steady-state: disable the current source, press F8 then check

ac analysis. The POP delivers the ac response and the operating waveforms.

SIMPLIS® starts the ac analysis when the so-called periodic operating point or POP is found.The engine finds the exact point at which theconverter is in a stable operating point alsocalled steady-state operation. In this mode, theaverage current in any capacitor is extremelysmall (0 A in theory) while the average voltageacross any inductor is also an extremely smallvalue (0 V in theory). It happens that SIMPLIS®cannot find its POP and you have to help himconverge. It can happen if you have selected awrong target for a crossover frequency, a tooaggressive phase margin or the converter cansimply not be stabilized. Check the computedelements in the netlist to make sure there areno negative values. This is generally a sign of awrong goal set for instance or a bad position ofthe double zeroes in the type 3 compensator.Running a transient analysis with a loadresistance usually helps identify what is wrong.

You have 61 ready-to-simulate switching converters to play with!