Basic questions about digital phase locked loop

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tryyourbestok 19 years ago

Hey, everyone,

Hope you are doing great!

I just started learning about digital phase locked loop. I have a lot of things that I cannot figure out. It will be great if I can get some answers from here.

In the textbook,

The gain of the voltage controlled oscillator is

Kvco = 2 x Pi x (fmax - fmin) / (Vmax - Vmin)

The VCO output frequency, f clock, is related to the VCO input voltage by

W clock = 2 x Pi x fclock = Kvco x Vinvco + W0

Where W0 is a constant. However, the variable we are feeding back is not frequency but phase ( hence the name of the circuit). The phase of the VCO clock output is related to fclock by

The integration of Wclock = Kvco x Vinvco / jw

Here, I do not understand that why the integration of the Wclock is equal to Kvco x Vinvco / jw.

If I do Laplace transform on the integration of the Wclock, then I will get 1/ jw x Laplace transform of Kvco x Vinvco. And since these two are constant, the laplace transform will be Kvco x Vinvco / s. Hence the Laplace transform of the integration of Wclock will be Kvco x Vinvco / square of s. Here in the book, I do not think they are talking about taking a Laplace transform. And even they are taking Laplace transform, my answer will be Kvco x Vinvco / square of s. Not Kvco x Vinvco /s.

Do you have any idea here, please?

I can understand the equation about the natual frequency and damping factor. The book also just gives me the equations about pull in range, lock time, lock range. However, there is no deduction for these equations at all.

Specifically, the pull in range is

Pi/2 x square root of ( 2 x damping ratio x natual frequency x Kvco x Kpd - the square of natural frequency )

Here Kpd is the gain of phase detector.

The lock time is 2 x Pi / natual frequency.

The lock range is Pi / 2 x (1/ R x C ) , here R and C is the resistor and capacitor value of the low pass filter.

I have no idear how these equations are deducted.

Thanks for reading this post and any answers are greatly appreciated. Sarah

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Andrew Holme 19 years ago

See

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Don Lancaster 19 years ago

The key secret is that frequency (when definible) is the rate of change of phase.

Many thanks, Don Lancaster voice phone: (928)428-4073 Synergetics 3860 West First Street Box 809 Thatcher, AZ 85552 rss: http://www.tinaja.com/whtnu.xml email: don@tinaja.com Please visit my GURU\'s LAIR web site at http://www.tinaja.com

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Genome 19 years ago

Hello Sarah from the University of Cincinnati.....

I'm s*it myself but that seems normal.

You might need to ignore the mathematical analysis and wave your hands and brane about. I'm not certain about this but there is a good chance that the VCO only sort of behaves as an integrator within the loop when it is combined with the phase detector...... and the loop is stable.

I think you might find the 'botched' small signal maths takes a 'short cut' and stuffs the integration in the VCO term and gives you an answer that works...... for a small signal analysis.

Outside of that the overall 'loop', which has the filter in it, gives you stuff like the range (lock, pull in... large signal.... Squegging) things. It's a bit incestuous.

Start out by having a think about how the 'average' output of your phase detector varies according to the difference between your reference frequency and your VCO frequency without feedback. The phase detector is really some sort of mixer.

Long term, without the loop closed it's going to be all over the place. With the loop closed it might just get to the right answer.....

Yes, I have been bullshitting.

DNA

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Jim Thompson 19 years ago

DNA's comments written out in "maths"....

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If I hadn't gained a scholarship to MIT, the University of Cincinnati was one of my fall-back plans, particularly since it was only 150 miles away from home (Huntington, WV).

...Jim Thompson

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Tim Wescott 19 years ago

What textbook?

That looks right, although it's not very 'digital'.

Good so far.

It isn't. See below.

I have an idea that you needed to pay more attention in your signals class, and that you're confusing signals with systems. Vinvco is a signal which is being acted on by an integrator. You don't _know_ Vinvco's Laplace transform up front, you only know that a time-domain integrator acts to to multiply that Laplace transform by 1/s in the frequency domain.

"Phase Locked Loop Circuit Design" by Wolaver gives a very good discussion of the lock-in process, including approximate equations for a number of phase detectors (and yes, lock in is _heavily_ influenced by the phase detector).

By the way: where does the 'digital' come in? All I see is traditional PLL circuits stuff here.

Tim Wescott Wescott Design Services http://www.wescottdesign.com Posting from Google? See http://cfaj.freeshell.org/google/ "Applied Control Theory for Embedded Systems" came out in April. See details at http://www.wescottdesign.com/actfes/actfes.html

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Basic questions about digital phase locked loop

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