# What is the phase margin for a PLL of critically damped?

Started by July 22, 2018
```Hello, all:

I read an online PLL tutorial, which says "the design of critically damped
loops, a PM of about 70 degrees, does not lead to the fastest settling time
for third order CP PLLs."
It is known that a critically damped second order loop has zeta=1, i.e. two
real roots of the same value. But I can't get its phase margin 70 degrees.

What do you think about phase margin remark?

Thanks,
```
```On 2018-07-22 08:02, fl wrote:
> Hello, all:
>
> I read an online PLL tutorial, which says "the design of critically damped
> loops, a PM of about 70 degrees, does not lead to the fastest settling time
> for third order CP PLLs."
> It is known that a critically damped second order loop has zeta=1, i.e. two
> real roots of the same value. But I can't get its phase margin 70 degrees.
>
> What do you think about phase margin remark?

As you correctly stated, a 2nd order system is critically damped when
zeta=1 (or Q=1/2) and gives the phase margin of 75 degree.

I do not know (and don't know the reference) but this might be the
reason why they say "of ABOUT 70 deg". A third pole parasitic may damp
the system even further such that they argue that it's a couple of deg
less than 75 ... "around 70".

jm2c
Peter

```
```On Tuesday, August 14, 2018 at 5:33:51 PM UTC+12, Peter Mairhofer wrote:
> On 2018-07-22 08:02, fl wrote:
> > Hello, all:
> >
> > I read an online PLL tutorial, which says "the design of critically damped
> > loops, a PM of about 70 degrees, does not lead to the fastest settling time
> > for third order CP PLLs."
> > It is known that a critically damped second order loop has zeta=1, i.e. two
> > real roots of the same value. But I can't get its phase margin 70 degrees.
> >
> > What do you think about phase margin remark?
>
> As you correctly stated, a 2nd order system is critically damped when
> zeta=1 (or Q=1/2) and gives the phase margin of 75 degree.
>
> I do not know (and don't know the reference) but this might be the
> reason why they say "of ABOUT 70 deg". A third pole parasitic may damp
> the system even further such that they argue that it's a couple of deg
> less than 75 ... "around 70".
>
> jm2c
> P

That's a highly damped system all right. Usually 60 degrees is more than enough for most systems. It all depends on your application. With high phase margin you often have to trade off bandwidth and hence rise-time.
```
```Peter Mairhofer <63832452@gmx.net> writes:

> On 2018-07-22 08:02, fl wrote:
>> Hello, all:
>>
>> I read an online PLL tutorial, which says "the design of critically damped
>> loops, a PM of about 70 degrees, does not lead to the fastest settling time
>> for third order CP PLLs."
>> It is known that a critically damped second order loop has zeta=1, i.e. two
>> real roots of the same value. But I can't get its phase margin 70 degrees.
>>
>> What do you think about phase margin remark?
>
> As you correctly stated, a 2nd order system is critically damped when
> zeta=1 (or Q=1/2) and gives the phase margin of 75 degree.
>
> I do not know (and don't know the reference) but this might be the
> reason why they say "of ABOUT 70 deg". A third pole parasitic may damp
> the system even further such that they argue that it's a couple of deg
> less than 75 ... "around 70".

Wouldn't further damping increase the phase margin?
--
Randy Yates, DSP/Embedded Firmware Developer
Digital Signal Labs
http://www.digitalsignallabs.com
```
```On Sunday, August 26, 2018 at 2:28:01 PM UTC+12, Randy Yates wrote:
> Peter Mairhofer <63832452@gmx.net> writes:
>=20
> > On 2018-07-22 08:02, fl wrote:
> >> Hello, all:
> >>=20
> >> I read an online PLL tutorial, which says "the design of critically da=
mped=20
> >> loops, a PM of about 70 degrees, does not lead to the fastest settling=
time=20
> >> for third order CP PLLs."=20
> >> It is known that a critically damped second order loop has zeta=3D1, i=
.e. two
> >> real roots of the same value. But I can't get its phase margin 70 degr=
ees.
> >>=20
> >> What do you think about phase margin remark?
> >
> > As you correctly stated, a 2nd order system is critically damped when
> > zeta=3D1 (or Q=3D1/2) and gives the phase margin of 75 degree.
> >
> > I do not know (and don't know the reference) but this might be the
> > reason why they say "of ABOUT 70 deg". A third pole parasitic may damp
> > the system even further such that they argue that it's a couple of deg
> > less than 75 ... "around 70".
>=20
> Wouldn't further damping increase the phase margin?
> --=20
> Randy Yates, DSP/Embedded Firmware Developer
> Digital Signal Labs
> http://www.digitalsignallabs.com

well it's all trade off. You can't have unlimited bandwidth so first we nee=
d to know what is the upper limit on bandwidth. Usually it is the 2fc carri=
er feedthrough term. Make it too high and you get too much of it coming thr=
ough and this leads to other problems
```