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# Order of the Loop Filter in PLL

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#### Engineer4ever

##### Member level 3
Hi again,

I was wondering how could I determine the PLL order. I know that stability and no. of poles are important parameters, but are there any other parameters that should be taken into consideration?

Hi again,

I was wondering how could I determine the PLL order. I know that stability and no. of poles are important parameters, but are there any other parameters that should be taken into consideration?

Here's a good / free PLL Book.

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Its been a while, but as I recall the order of the system is related to the exponent of S in the characteristic equation of the control loop. The VCO has a transfer function of Kv/S. The phase detector has a transfer function of Kp (comonly assumed independent of frequency). And the loop filter typically has an R-C pole. So that forms a 2nd order loop, since the characteristic equation looks like a S² + aS +b.

But such a pll is probably unstable unless you use a lead-lag loop filter, which adds a zero for stability. But I believe this is still a 2nd order loop.

https://leleivre.com/rf_pll_loop_filter_3rd.html
You will have a 3rd order loop.

The required order of the filter (and overall feedback loop) should depend on whether you need the output to be able to track different steady state references. For example, first order compensation will only create a frequency lock, with a phase offset between the PFD inputs. A second order compensation will lock both phase and frequency at the PFD inputs after a frequency step. But if you ramp the frequency then there will be a steady state phase offset. A third order compensation scheme is necessary to have zero phase error with a ramping reference frequency. And so on.

To track a frequency ramp with zero phase error I think you need 3 integrators...one in the vco and two in the loop filter. Not sure if that is the same as calling it a "3rd order loop".

"Order" refers to the number of significant poles in the loop (VCO always brings one at the origin). The number and location of poles is related with the transient behavior and stability.
"Type" refers to the number of integrators in the loop. It is related mainly with the steady-state errors.
Of course, type can not be greater than order.
Regards

Z

Thanks, it is coming back now. Type III = number of integrators is 3

"Order" refers to the number of significant poles in the loop (VCO always brings one at the origin). The number and location of poles is related with the transient behavior and stability.
"Type" refers to the number of integrators in the loop. It is related mainly with the steady-state errors.
In a general sense yes, order just refers to the number of significant/dominant poles, but in reading literature on PLLs, I've seen it equivocated with the number of poles at the origin (ie, number of integrators). I've also seen loop filters divided into "types" as you say, but that gets confusing as well since the PFD itself is identified with a type number.... seems that the terminology is overall pretty vague.

"Order" refers to the number of significant poles in the loop (VCO always brings one at the origin). The number and location of poles is related with the transient behavior and stability.
"Type" refers to the number of integrators in the loop. It is related mainly with the steady-state errors.
Of course, type can not be greater than order.
Regards
Z

Yes - I agree. The order is determined by the number of poles - that means: The order of the transfer functions denominator.
However, not all the poles are (and must be) created by integrators only.
Additional remark: Transfer function is derived for the linearized system only - that means: Phase domain in locked status.

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