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PLL loop filter - phase margin problems

Hi,

I'm trying to design a 2nd order loop filter for a PLL but I'm running into difficulties following the analysis in National Semiconductors Application Note AN-1001.

In the App note, they find that the time constant T1 of the loop filter is:

T1=(sec(phi) - tan(phi))/w

However, when I do the derivation, I get:

T1=(sqrt(tan^2(phi) + 4) +/- tan(phi))/2w

This latter is very similar to what is given in PLL Performance, Simulation and Design by Dean Banerjee, although he's got a gamma symbol in there for some reason. I'm not too worried about the gamma as it doesn't make a significant different to the bode phase plot for small values of gamma.

However, there is a big difference in the phase plots between my derivation of T1 and the AN1001 derivation of T1 - does anyone have any idea why this is?

I've included a fuller description of the problem (my derivation of T1, the bode plots etc...) at the following location:

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If anyone has got any idea why these results differ, please let me know!

Thanks,

Steve

Reply to
steve
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I think you made a mistake at equation 10.

If phi = arctan(a) - arctan(b), tan(phi) is not a-b

Reply to
Andrew Holme

"Gamma" is the damping factor... 0.7 to 1 is a desirable range.

Why are you trying a second order filter? They're treacherous. Definitely NOT for the novice.

The safest way is to design first order, then add a roll-off well above the zero-crossing frequency to kill reference ripple.

...Jim Thompson

--
|  James E.Thompson, P.E.                           |    mens     |
|  Analog Innovations, Inc.                         |     et      |
|  Analog/Mixed-Signal ASIC\'s and Discrete Systems  |    manus    |
|  Phoenix, Arizona            Voice:(480)460-2350  |             |
|  E-mail Address at Website     Fax:(480)460-2142  |  Brass Rat  |
|       http://www.analog-innovations.com           |    1962     |
             
I love to cook with wine.      Sometimes I even put it in the food.
Reply to
Jim Thompson

Note that there are a couple of editions of the Banerjee book out there, and they have very different equations in many places. I'll leave further conclusions for others to draw.

Dean is (or at least was) pretty good about answering support questions posted to the wireless.national.com board for their WeBench product.

Unless you're just a glutton for mathematical punishment, or doing something truly offbeat, just use the free NatSemi or Analog Devices simulators. They work.

-- jm

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Reply to
John Miles

Did you try using National free online WEBENCH tools to see if your design matched to theirs?

Reply to
maxfoo

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