PLL loop filter - phase margin problems

[steve]

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:

http://www.teamlinux.org.uk/steve/pll_3rd_order_filter.pdf

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

Thanks,

Steve

 

[Andrew Holme]

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:

http://www.teamlinux.org.uk/steve/pll_3rd_order_filter.pdf

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

Thanks,

Steve

I think you made a mistake at equation 10.

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

 

[Jim Thompson]

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:

http://www.teamlinux.org.uk/steve/pll_3rd_order_filter.pdf

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

Thanks,

Steve

"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

 

[John Miles]

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.

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

 

[maxfoo]

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.

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