# PLL terms: Natural frequency(Wn) and Loop bandwidth(Wc)

1. ## PLL terms?

hi

Can you pls explain the meaning and physical significance of the following terms which we usually use with PLL.

1. Natural frequency ( Wn)
2. Loop bandwidth. (Wc)

yours
SavithRu

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2. ## PLL terms?

Every electronic device tends to oscilate to a specific frequency called Natural frequency. Even a mechanic device tends to oscillate to a frequency called natural frequency.

The other term is very specific, is the bandwith of the device in the feedback loop.

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3. ## Re: PLL terms?

the nature frequency exists in a closed loop system;but the wc exists in an open loop system.
you can calculate wn in root locus by the closed loop root .
and you also can get wc by phase margin. that is my thought.

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4. ## Re: PLL terms?

Thanks a lot for giveing me the insight on these rems..

I need to know few more terms...

kindly tell me what exactly are these wrt pll.

kindly tell me what are these Δf and α in the following eqn of ts.

4.3. Settling time
Settling time is another important performance metric that is directly related to the
loop transfer function. Settling time determines how fast the frequency synthesizer
can change the frequency of its output signal.
An analytical solution for the settling time can be obtained from the step response
of the closed-loop transfer function, see Eq. (10). Settling time is a function
of the natural frequency (ωn = √KDKo) and the damping factor (ζ = ωn/(2ωz)).
It can be shown that

ts=

( 1/ ζωn) * ln { Δf/ (α fo sqrt(1 − ζ2) } ......................if ζ < 1 (under damped )

ts=

(1 / ζωn) * { ln (Δf / αfo ) } ................if ζ = 1 (critical)

ts =
(1 / (ζ −sqrt (ζ2 − 1)) ωn ) * ln { Δf(sqrt (ζ2 − 1 + ζ)) / (2αfo sqrt (ζ2 − 1)) } ......... if ζ > 1 (over)

(17)
where fo is the frequency from which the synthesizer starts the transition, Δf is the
amount of frequency jump, and α is the settling accuracy. As the loop bandwidth
ωc increases, the settling time gets shorter if the damping ratio is fixed. The effect
of the damping ratio on settling time is shown in Fig. 11. It is a plot of Eq. (17)
with ωc fixed but not ωn, which is more realistic in the sense of design procedure.
In this condition, the settling time is fastest when the loop is critically damped, and
further underdamping does not improve the settling time. Note that the analytic
solution in Eq. (17) is only an approximated result for the second-order closed-loop

pls tell me that what are these terms wrt pll .

1. α = settling accuracy..

2. Δf = amount of frequency jump.

SavithRU

5. ## PLL terms?

settling time is the time need when introducing a frequency step (delta f) , we say the the loop is setteled "locked" when the frequency is less than a certain settling accuracy.
i.e. when freq. synthesizer change its frequency by
delta f=50MHz and if the setling accuracy is 10kHz >> we say the loop is locked when the frequency is less than ff+10k And
the frequency is more than ff-10k.

; ff is the final freuency value = fo+ delta f >> fo=initial freq.
delta f =freq. step

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