# Phase Locked Loop, Loop Filter

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#### lins13

##### Newbie level 4
Hi guys,
I am a student currently working on a project to design a phase locked loop and I have a problem with designing the loop filter, which is a passive lag like in most textbooks. Basicly I am designing and building a PLL for a pretty specific scenario where noise performance is the upmost concern. My question is this:

I have a chosen loop BW of my PLL, constrianed by where my XOSC (input reference) phase noise and VCO phase noise cross so to have the best phase noise at my PLL output. I also have the K values of my VCO and PD. Now what I am unsure of is wether this loop bandwidth frequency is equal to wn (dosent make sense to me from its definition) or whether it is the frequency I should make the 3db point of my loop filter. I can't find this anywhere and need to solve it to use the design equations from Roland E Best's PLL textbook

Would really appreciate if someone could clear this up for me

Thanks
Lindsay

#### Engineer4ever

##### Member level 3
Hi,

I have been working in the PLL sub-team in my graduation project. I was responsible for the design of PFD/CP/LF. I can truly understand how much these definitions are quite tricky, but this is what I came up with:

"Wc" is the cross-over frequency which is the same definition of the loop bandwidth, and the loop bandwidth is the bandwidth where the gain=1 (0 dB), it can be measured from the frequency response graph.

#### lins13

##### Newbie level 4
Thanks for the response

So just to be clear and confirm this:

wn is the same frequency as the loop bandwidth, i.e. the point were the loop gain is 1. The 3dB bandwidth of the filter chosen as the loop filter can then be calculated from wn through wn = sqrt (KoKd/t1+t2) if the filter is passive?

#### Engineer4ever

##### Member level 3
Here's what I did in my project: me reference frequency was 52 MHz, so wn=2*pi*f_ref*0.1, then I wrote a MatLab code to find the values of the loop filter components (I used a second order loop filter) then I got the transfer function formula and equated it to 1/sqrt(2) then I got the 3-dB bandwidth from that equation

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