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TPS40210: TPS40210 Compensation Network Equation Question

Robert Alkire
Prodigy 60 points

Part Number: TPS40210
Other Parts Discussed in Thread: LM5155

I am doing a design with TPS40210 with 15VIN(min), 19.2VINNOM), 22.8VIN(MAX) with VOUT = 24V IOUT = 3A. When I start a PMIC design I usually bring the equations into a CAS (Computer Algebra System) like MathCAD and use WebBench for a sanity check.

I don’t understand equation 22 in the TPS40210 datasheet and wonder if you could help me with that.

gM is conductance in units of siemens (S) alternatively A/V or 1/Ω but the equation doesn’t seem to match that and there is no background information on how the equation was arrived at.

In the numerator, we have product L x fSW this will result in impedance which divided by resistance ROUT and this becomes a unitless ratio. The denominator has ohms squared multiplied by the sum of a scaled resistance and another impedance. The units for the denominator is in resistance in ohms cubed.

There is an example, eq 59, in the datasheet that shows a result 19.2A/V (or 19.2S or 19.2 1/Ω).

The numerator solves to a unitless 0.020555 and the denominator as 1.071x10-3Ω3 .

This would make the solution 0.020555/1.071x10-3Ω3 or 19.2 1/ Ω3 (or 19.2 S3) and doesn't result in A/V as depicted in the datasheet.

Thanks,

Bob

 

  • 0
    TI__Intellectual 1700 points

    Hi Robert,

    thank you for using our device!

    I get to the same conclusion, let me clarify that.

    Will get back to you latest by the end of this week.

    regards,

    Moritz

  • 0 in reply to Moritz.
    TI__Guru* 79475 points

    Hi Robert and Moritz,

    Thanks for posting.  The equations were derived by the original datasheet owner more than 10 years ago, and we are the group currently support this IC and we don't have the detailed info about the derivation, and we should be able to work it out soon.  For the time being, the first glance of the equation terms implies correctness of the equations.  The confusion seems caused by the coefficient 0.13.  It is not a unit-less parameter, but it should have a unit of Ohm-squared. Unfortunately the datasheet writer did not mention it.   

    Most probably the equations are correct.  We just need to re-derive it to confirm.  We will work on this and get back to you in next couple of days. 

    Thanks,

    Youhao Xi, Applications Engineering

  • 0 in reply to Youhao Xi
    TI__Guru* 79475 points

    Hi Robert,

    Just let you know that I am still working on the derivations.  Sorry for the delay.

    Thanks

    Youhao

  • 0 in reply to Youhao Xi
    Prodigy 60 points

    No problem, Youhao. I appreciate you doing that.

    Usually these equations are derived as a series of transfer functions and it helps document the part thoroughly.

    Also I know that LM5155 is often recommended as the go to boost converter .Nice part and I'd use that it a heartbeat except it comes only in a DFN package with EP (WSON). During manufacture, these packages can be more temperamental than an SOIC counterpart. They are also more difficult to deal with thicker copper layers also common for high current power supplies. I've seen companies move to an addon thin board for the controller. I'd like to avoid that complication too.

  • 0 in reply to Robert Alkire
    TI__Mastermind 46905 points

    Hi Robert,

    i re-assign the post to Youhao, he may miss the post.

  • 0 in reply to Jasper Li
    TI__Guru* 79475 points

    Hi Robert,

    Honestly speaking, my first derivation had something wrong in the process (I started with DCM) and I am re-working on it starting with CCM for simplicity.  Sorry for the delay. 

    Thanks,

    Youhao

  • 0 in reply to Youhao Xi
    TI__Guru* 79475 points

    I think I missed some assumptions which are not very obvious to me.  I am trying to find if anybody has the initial derivation. All these I assume the equation is valid, given it being released for more than 10 years without much dispute before you questioned.  Sorry for the delay but this must be clarified.    

  • 0 in reply to Youhao Xi
    Prodigy 60 points

    At this point, pursuing this further would simply satisfy curiosity. The equation probably does work fine, it just dropped the units for the constant 0.13.Its like a misspelled word, you can still understand what the writer meant it's just not the correct spelling. If people solve this by hand, they may never notice the units were dropped. You can use algebraic solvers to check to see if the equation has any omissions like this - I use mathcad. 15. . I'm going to call this resolved. If you wish, it would be interesting to know the derivation, as that will help us understand the chip better but I am satisfied with the first answer.

    Thank you,

    Bob