Control to output transfer function of offline Flyback SMPS

[treez]

Hi,
This is about SMPS feedback loop theory of offline flyback ...
Page 9 of the following application note offers us to find the "control-to-output-transfer function" [CtO]. Is that regarded as being the power stage transfer function in cascade with the modulator transfer function?...or just the power stage transfer function on its own?

I ask because the modulator transfer function is the parameter "K" on page 9....
In expression (33), the parameter "K" is included, and this is for CtO for the CCM flyback. In expression (34), the parameter "K" is not included, and this is the expression for CtO for the DCM flyback.

Why is "K" not included for the DCM flyback?

Application Note:

https://www.all-electronics.de/wp-content/uploads/migrated/document/167525/46fbe8c82a6.pdf

 

[Easy peasy]

control to o/p, would be the FB pin to output, i.e open loop ....

--- Updated Jun 1, 2021 ---

fig. 16 shows the combined quite nicely ...

 

[treez]

Thanks, yes, and page 3 (in the below) of the actual flyback controller datasheet (the one concerning the app note in top post) shows a 3.5:1 divider in the feedback signal path, yet somehow, this doesnt appear to be accounted for in the feedback loop equations of the application note in post #1.
..Though i guess that equation (32) in the App Note takes account of this divide down.

The point is, why is expression 32 in the App Note not applied to the DCM flyback case? Expression (32) is the modulator transfer function, and without it, surely that DCM flyback open loop transfer function is incomplete?

FSCM0465 flyback controller datasheet

https://media.digikey.com/pdf/Data%20Sheets/Fairchild%20PDFs/FSCM0465R.pdf

 

[Easy peasy]

DCM and CCM are different, CCM has the RH plane zero

 

[treez]

Thanks, yes, and i am also wondering why the DCM small signal feedback open loop transfer function does not incorporate the modulator gain?

 

[treez]

Would you agree that the expression for Control-to-output transfer function for DCM flyback, given on page 9 (equn 34) of the below App Note cannot possibly be correct?

App Note (AN-4137 by onsemi)

http://educypedia.karadimov.info/library/AN-4137.pdf

....this expression implies that the modulator gain is "Vo1/VFB".

this could not possibly be right. The modulator gain should be "Ipk/VFB"...as per equn (32) also on page 9.
Would you agree?

 

[treez]

Another thing about equation (34) is that the output capacitor and load are not referred back to the primary side....so surely you agree that equn (34) is
totally incorrect?

 

[treez]

Also, the power stage transfer function is zero dB at zero Hz (DC condition)
This is because the capacitors and load resistor and any inductors etc have no gain at DC
Would you agree with this.

The only time a power stage transfer function has gain and goes above 0dB is when there is an LC resonance peak? Would you agree? -Eg the voltage mode , CCM resonance of eg a Buck converter power stage.

So in other words, if someone gives you a control-to-output transfer function, and it is above zero dB at DC, then it must incorporate the modulator transfer function? Would you agree?

......................................---------------------------........................................---------------------------..........................
On a similar note, may I just speak about the FSCQxxxx series of Quasi-Resonant Flyback controllers?.... Its interesting that the App Note (AN-4146) for the FSCQxxxx series has vanished from the onsemi.com website…its now only available from the Chinese version of onsemi website. Page 10 of AN-4146 gives the control-to-output transfer function of an FSCQxxxx based Flyback…..(equation 39)….but that equation is for a CCM Flyback, and this is totally irrelevant to a Quasi Resonant flyback converter…would you agree?

FSCQxxxx QR flyback controller datasheet

http://www.onsemi.com/pdf/datasheet/fscq1565rt-d.pdf

AN-4146 App Note by onsemi (Chinese website)

http://www.onsemi.cn/pub/Collateral/AN-4146CN.pdf

......................................---------------------------........................................---------------------------..........................

--- Updated Jun 5, 2021 ---

.....................................-------------------------------.....................................................-------------------
On a similar note…
The FSDMxxxx series of flyback controllers, and the FSCQxxxx series of QR Flyback controllers, have an effective feedback loop primary side pullup resistor of value 2.8k.
..Considering the FAN6300 QR Flyback controller, would you agree that its “equivalent” pullup resistor value is 5k?
The FAN6300 datasheet and App note (below) don’t say.

FSCQxxxx datasheet:

http://www.onsemi.com/pdf/datasheet/fscq1565rt-d.pdf

FSDMxxxx datasheet:

http://www.onsemi.com/pdf/datasheet/fsdm0465rb-d.pdf

FAN6300 datasheet
http://www.onsemi.com/pdf/datasheet/fan6300-d.pdf

FSCQxxxx series App Note:

http://www.onsemi.cn/pub/Collateral/AN-4146CN.pdf

FSDMxxxx series App Note:

http://educypedia.karadimov.info/library/AN-4137.pdf

FAN6300 App Note:

http://www.onsemi.com/pub/collateral/an-6300.pdf

.....................................-------------------------------.....................................................-------------------

--- Updated Jun 5, 2021 ---

(My sincere apologies for the doubled up links, i am not sure how this happened, i thought all i did was delete the space that was there)

--- Updated Jun 5, 2021 ---

...oh...woops sorry, the doubled up links now are gone i notice

 

[Easy peasy]

It depends how you define 0dB, a boost converter will have a high gain at very light loads if you increase the pwm marginally, if the gain is defined as change in Vout / change in PWM, then for the boost mentioned >1 is possible, hence > 0dB

 

[treez]

Thanks,
In a TL431/OPTO isolated UCC28C43 based flyback, with opto collector to COMP pin (common emitter connection) , what is the effective value of the pullup resistor?...ie the one needed for the error amplifier small signal transfer function.

 

[Easy peasy]

you need a value of pull up resistor that the opto can overcome, i.e pull the volts down, for a reasonable current in the opto led, say 8mA max ( don't forget allowance for aging ) given the CTR spread, i.e the lowest CTR ....

 

[treez]

Thanks, yes i appreciate that, the thing is, when doing opto feedback with UCC28C43, as you will know, one sets up the internal error amplifier as a 1mA current source, by grounding its FB pin....one then connects the opto in common emitter connection, with collector to COMP pin.........so there won't actually be a pullup resistor, but an "effective pullup resistor value" is needed for the feedback loop equation. What is the value of that "effective pullup resistor" in this case?

Post #8 above shows that for the FSCQxxxx and FSDMxxxx controllers. that "effective pullup resistor" is 2k8. What is it for the described UCC28C43 situation?

UCC28C43

https://www.ti.com/lit/ds/symlink/ucc28c43.pdf?ts=1622976093696&ref_url=https%253A%252F%252Fwww.ti.com%252Fproduct%252FUCC28C43%253Futm_source%253Dgoogle%2526utm_medium%253Dcpc%2526utm_campaign%253Dapp-null-null-GPN_EN-cpc-pf-google-eu%2526utm_content%253DUCC28C43%2526ds_k%253DUCC28C43%2526DCM%253Dyes%2526gclid%253DCj0KCQjw5PGFBhC2ARIsAIFIMNeqL7X8FcCMmC5198WTuOtTl05vlZjPQmIj_nsSK6PzfrWPWi5XskQaApO-EALw_wcB%2526gclsrc%253Daw.ds

 

[treez]

....................................---------------------........................------------------------
On a similar note...
The attached is a LTspice simulation of an LT1243 based offline flyback with common emitter opto connection feedback. The error amp in the LT1243 is set up as a ~1mA current source by grounding the FB pin. (the LT1243 is pin-for-pin like the UCC28C43)

Also attached is the small signal open loop feedback loop calculation document in excel (for this converter).
This shows that the “effective pullup resistor” at the COMP pin of the LT1243 must be ~10k.

{this was asserted because setting the pullup resistor to 10k in the excel doc revealed a crossover frequency exactly correspondent to what is shown in the LTspice simulation (attached). The simulation demonstrates the feedback loop crossover frequency by way of its vout deviation following a sudden load transient}.

The question is, the “effective pullup resistor” value of 10k is correct….but how is it calculated?

As an estimation, I would say that the fact that the error amp is outputting a current, means that in actual fact the “effective pullup resistor” value will vary with the load on the converter? Would you agree that it is pertinent to simply calculate the “effective pullup resistor” value by dividing the voltage at the output of the error amp (ie at the COMP pin) by the current value that it is outputting?…and do this for the case of maximum load?

...you then end up with the highest value that the "effective pullup resistor" could be. This is a good value to take because it will give the least phase margin, and so represents a conservative calculation. Would you agree?
................................................-----------------------------------........................................................

 

[treez]

-----------------------............................-----------------------............................------------------
On a similar note....
Supposing a 150W DCM flyback has a 4mF “local” output capacitor, (C1) then at the end of a cable of resistance 0.5R, (Rs), has the 150W load (RL) and a 22mF output capacitor (C2)


C1 has ESR of Re Ohms
…So, would the power stage poles and zeros be as follows…

Load pole = 1/(C1.(RL+Rs) )
Output cap zero = 1/(Re.C1)
Output pole = 1/(Rs.C2)

…Is that all?.....any more zeros and poles?
-----------------------............................-----------------------............................------------------

 

[Easy peasy]

4mF - 0.004F ?

22mF = 0.022F ?

 

[Easy peasy]

if you have a Vcc on the opto collector side of 5v say and at nominal load the opto pulls the pin down to 2v5 say, then, for small signals, a 2k5 pull up resistor is the same as a 1mA current source ( very similar to Vcc =15v and a 15k res )

For large signals and low Vcc, there is no direct equivalent, only approximations.

 

[treez]

4mF - 0.004F ?

22mF = 0.022F ?

Thanks, yes, milliFarads...i know why you're asking.....it sounds as if it might be a bit high, the 22mF.

--- Updated Jun 7, 2021 ---

For large signals and low Vcc, there is no direct equivalent, only approximations

Thanks, it does seem surprising that no-one has done a feedback loop expression which accomodates this use of a current source fromt the FB pin, as many of the newer controllers use this method......calcuating the equivalent" pullup resistor seems a bit hit and miss. Ive got Basso's books so i am going to look again and harder through them to see if he address's this.