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Kart_Mann

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Chennai, India

Binary PD transfer function non linearity
Jul 08^th, 2005, 5:37am

Hi,

A binary phase detector is a highly non linear element. Normally in PLLs we can use the continuous time approximation to write down the transfer function for small phase errors. However for systems using a binary PD I am unable to justify the asssumption of linearity, even for small phase errors. Yet, the transfer function derived from this assumption of linearity is used for phase noise estimation in a number of tutorials that i have referred ^{( 1,2)}.

How is this valid?

Is this only because of the linearity of the BBPDs for small phase due to flip flop metastability etc. as described in by Ken and Behzad Razavi in their paper⁽³⁾ or am I missing the plot somewhere.

1. R.C. Walker :: Clock and Data Recovery for serial digital communication
2. Dean Banerjee:: PLL performance simulation and design
3. Kenneth Kundert, Behzad Razavi :: Analysis and Modelling of Bang Bang CDR circuits.

Thanking in advance,
Regards,
Kartik

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Kartik

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Paul

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Switzerland

Re: Binary PD transfer function non linearity
Reply #1 - Jul 8^th, 2005, 1:43pm

Kartik,

Ken can probably give more information with respect to their exact hypothesis, but as an infinite gain is not realizable in a physical circuit (e.g. due to metastability), you can always consider the phase detector as long as you sufficiently limit the input phase error. I believe this is valid as long as you consider a locked loop with limited input jitter. With a lot of input jitter, I would expect the phase error to become large and the above hypothesis to become invalid.

I am surprised to see Walker's paper in your list. I am not sure whether I misinterpreted his paper, but I had the impression he was not making the hypothesis of linearity... IMHO, that's what makes his BB approach very different from other analysis techniques. Would be interested to discuss this in more detail.

Paul

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Ken Kundert

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Silicon Valley

Re: Binary PD transfer function non linearity
Reply #2 - Jul 8^th, 2005, 2:59pm

Kartik,
Metastability provides some linearity, but I believe most of the linearity is provided by the jitter, particularly the deterministic jitter. And here what I mean by linearity is average linearity. In otherwords, on any particular cycle the PD acts abruptly nonlinear, but on average acts relatively linear or at least smooth.

-Ken

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