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TPS62170 Loop Gain Transfer Function

Arne Krueger
Prodigy 170 points
Other Parts Discussed in Thread: TPS62170, TPS62130, TINA-TI

Hi,

I am investigating TPS62170 buck regulator stability related to various input filters and for this purpose I would like to derive a rough approximation of the converter loop gain.

I've read SLVA463 (Optimizing the TPS62130/40/50/60/70 Output Filter) and I'm struggling to interpret the Loop Gain plots in Figure 3. The Gain looks pretty much like a second order system with it's corner frequency close to 1/(2*pisqrt(LC))  which is the corner frequency of the output filter. This makes sense to me since according to the book Fundamentals of Power Electronics by Erickson (p. 327) the loop gain is defined as:

T = H(s)*G_c(s)*G_vg(s) / V_M = X(s)*G_vg(s)

where H(s) and V_M are supposed to be constants and G_vg(s) is the open-loop transfer function v_o / v_i derived from a small-signal model of the converter. From the small signal model of the converter G_vg(s) can be approximated as the second order filter formed by the L-C output filter which leaves the term X(s) = H(s)*G_c(s) / V_M unknown.

However since G_vg(s) is a L-C low-pass the loop gain plot suggests some nearly constant gain amplitude for X(s).

Now, what I don't understand is the phase plot which roughly is a shift from 112° to -112° (or +90° to -90° for a even more optimistic approximation). G_vg(s) alone would clearly give a phase shift from 0° to -180° which leaves me puzzled what kind of transfer function for X(s) gives +90° to 0° phase at constant gain.

Thanks for any tips,

Arne

  • 0
    TI__Guru**** 150900 points

    DCS-Control is a hysteretic topology that responds with some voltage mode attributes.  This app note explains how to measure the loop gain: http://www.ti.com/lit/an/slva465a/slva465a.pdf  A transfer function is proprietary.

    Please remember to begin your post titles with the part number.

  • 0 in reply to Chris Glaser
    Prodigy 170 points

    I'm afraid we don't have the required equipment nor time to do a proper measurement. That's exactly the reason why I want to derive a rough approximation of the loop gain from the published sources. 

    Chris Glaser said:
    Please remember to begin your post titles with the part number.

    Didn't I?

  • 0 in reply to Arne Krueger
    TI__Guru**** 150900 points

    Measured data is always better than rough calculations or approximations.  If you can't measure the stability through a loop measurement or transient response, then I recommend you stay very near to the datasheet recommended output filters to remain stable.  If you can evaluate the loop, the SLVA463 is a good starting point for stable ranges.

    I edited the title so that the first word is the part number, TPS62170.

  • 0 in reply to Chris Glaser
    Prodigy 170 points

    Chris Glaser said:
    Measured data is always better than rough calculations or approximations.

    You are of course right. However I have to manage with the tools I'm given. Perhaps I will be able to organize proper equipment but definitively not any time soon. Still, I would like to make my guess as educated as possible before the first PCBs are build.

    Chris Glaser said:
    I recommend you stay very near to the datasheet recommended output filters to remain stable

    I'm not too much concerned about the output filter. Instead I wonder how the Input filter may affect stability.

    I've tried to simulate the loop gain in Tina-TI according to the method briefly explained here:  However the result simply does not seem right. The magnitude is way too small. This makes me wonder whether the method is at all applicable to the Transient Model provided by TI. Also, while the transient analysis using the TPS62170 transient model takes arount 5 minutes to calculate, the AC analysis is ready in seconds, which makes me question if the proper operating point is used. I've attached the Tina-TI model I am using.

    Toying around with the SwitcherPro tool I noticed that at least for some parts (unfortunately not the TPS62170) the approximate loop gain over a rather wide frequency range is output. Could you check if similar data is available for the TPS62170? The plots in SLVA463 only show a single decade. I don't ask for an analytical expression or tabular data, but only a plot of the loop gain over a wider frequency range to verify my approximation.

    Chris Glaser said:
    I edited the title so that the first word is the part number, TPS62170.

    Sorry, no offence intended.

    Thanks for your efforts.
    Arne

    TPS62170-loop-gain.tsc
  • 0 in reply to Arne Krueger
    TI__Guru**** 150900 points

    Yes, TINA is the right program to use for this.  There is a models forum for the TINA models.

    There is a loop gain plot in the UG: http://www.ti.com/lit/ug/slvu483/slvu483.pdf 

  • 0 in reply to Chris Glaser
    Prodigy 170 points

    Thanks for the hint. The plot in SLVU483 unfortunately shows a single decade on the frequency scale, too.

    Thanks for the hint, though. I will repost in the models forum.