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PLL closed-loop bandwidth proof?

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jlee

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Hi all,

I am reading Shu's PLL book, but now I get stuck in one step... I don't understand how the authors derived the closed-loop bandwidth. Attached the page I am reading.

It is discussing the third order PLL (second-order passive loop filter), and I understand up the open-loop gain equation (3.18). However, I don't see how the authors conclude eq. (3.19) from eq.(3.18). Especially, I am bothered by how there are cos() and sin() functions appearing suddenly....

PLL experts... please help me understand the proofs.

Thank you very much.
 

hello,
sorry i dont know how this can be proved , but i wanted to ask if u have a soft copy of this book , if so can u upload it?
thnx
a.safwat
 

I remember i worked it out somewhere....will try to find it and scan it for you...i hope you can wait a bit..

Regards

Added after 26 minutes:

safwatonline said:
hello,
sorry i dont know how this can be proved , but i wanted to ask if u have a soft copy of this book , if so can u upload it?
thnx
a.safwat

The book you requested is available at



Regards
 

Hi jlee,

I am attaching the solution with this post...the sine and cosine terms are just to make the expression beautiful...actually there are two trigonometric identities which are used to translate an expression from wz, wp2 and wc to an expression in cos and sine...

Also, the formula derived is not an explicit formula for wc....as both Right hand side and Left hand side consists of wc terms...

Let me know if you have any confusion...

Regards
 
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