PLL phase error in steady state

[d_sl4y3r]

How to determine the phase error of a PLL in steady state knowing only:

- open loop dc gain (kv)
- vco gain (kd)
- the phase detector is a 4 quadrant multiplier

 

[MrAl]

Hello,

Isnt the steady state error very very small, or did you mean the error with change in frequency?

 

[d_sl4y3r]

I would say that the goal is to find the phase error when the PLL is very close to the VCO center frequency.
This is confusing to me, as I expected that it would be necessary to know the transfer functions* in order to perform the phase error calculation.

*(of the open loop and/or feedback?)

 

[MrAl]

Hello again,

Yes, wouldnt that be the same as any other type of feedback system steady state error? It's usually very small with enough gain in the circuit. Should be the same as an integrator type system, which makes the error very small.

 

[crutschow]

You need to include the characteristics of the phase detector. A four-quadrant multiplier used as a phase detector has an output that goes from maximum positive when the two signals are in-phase, to maximum negative when the two signals are 180 degrees out-of-phase. For 0V phase error, then the two signals would be 90 degrees out of phase.

Thus, with high loop gain, the steady-state phase error would be near 90 degrees.

An exclusive-or gate used as a digital-phase detector gives a similar type output.

 

[d_sl4y3r]

Hi everyone,

This is what is given to me:
- open loop dc gain: G(s)H(s)=10^6 s^-1
- vco gain: 700 kHz/V
- phase detector is a 4 quadrant multiplier

Possible multiple choice answers: {-2pi, -3/2pi, -pi, -1/2pi, 0, 1/2pi, pi, 3/2pi, 2pi, None}

I didn't write it before because I was looking for a generic way to solve this for any situation where I have the gains.

 

[crutschow]

So for a 90 degree phase shift, which multiple choice is the right answer?

 

[d_sl4y3r]

That's what I would like to know, what is the rigth one, and how to get there..

 

[crutschow]

That's what I would like to know, what is the rigth one, and how to get there..

If you don't know what 90 degrees is in radians then you need to go back to some math fundamentals.

 

[MrAl]

Hi,


When we talk about error, we usually dont refer to some level as being part of the error itself. For example, if this were a feedback loop that regulated voltage at say 10v output but actually put out 10.010v we would not refer to the error as 10v or 10.010v, but it would be 0.010v.
That means i would have said zero (0) because that would be the error whether or not it was 90 degrees or not, because if we expect 90 degrees and we get 90 degrees then that means there is zero error.
Interestingly, it's not, strictly speaking, zero either really, but depends on the gain in the circuit, but it could be very very close to zero even with some reasonable gain not considered to be exceptionally high.
I could be wrong there though, as they could in fact consider 90 degrees to be the error as Carl suggests. These kinds of questions sometimes depend on what the 'instructor' is looking for as part of the course material.

 

[d_sl4y3r]

Hello again everyone,

I think you misunderstand my question.
My point is, you are interprating the problem and deducing an answer without taking in consideration the gains given as parameters for this problem.
If I'm correct, what you are considering here is the 4 quadrant multiplier, but what about the effect of the gains?
You are free to do so of course, but in an exam where I can only check a box, I need to be certain my interpretation is correct.

So what I mean to know is if there is a way of getting to one of the proposed answers by means of (simple?) calculations, based on all the 3 parameters that were given?..
Obviously some parameters might be there only to misguide someone like me, with limited knowledge in this subject.

 

[crutschow]

Since the multi-choice answers you presented are all multiples of 90 degrees, I believe the givers of the test are assuming that the gain is high enough to not affect the phase error. Thus they are apparently only concerned about the phase error (which is not really an error) of the phase detector.

 

[d_sl4y3r]

Thank you both for helping me in this question, I understand it better now.

So in this case could I say that two answers are correct: pi/2 and -pi/2?

The phase error would be positive or negative, depending on the signal from the VCO being to low or too high in phase/frequency.
Is this last thought correct?