Subject: Re: How to increase PLL order?
Date: Mon, 16 Dec 2002 08:42:51 +1300
Organization: Attica Communications
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Kevin Aylward wrote:
> tom wrote:
> > Kevin Aylward wrote:
> >> Chris Carlen wrote:
> >>> Kevin Aylward wrote:
> >>>> And this is exactly what I *explicitly* addressed above. You
> >>>> claimed that one usually used a lag-lead filter, and this, of
> >>>> *course*, rolls of the gain, i.e. limits the BW. To the contrary,
> >>>> I pointed out that in slow systems, it is quite possible to have a
> >>>> lead on its own that can stabilise the loop, with the advantage
> >>>> that it obviously keeps the BW up, i.e. no lag.
> >>>> Kevin Aylward
> >>> So would the correct terminology for what I have been calling a
> >>> "zero-pole" filter be a lead-lag?
> >> Yes and no. There is no "correct" terminology here, both can be used
> >> equally. I personally, always use describe things as poles and
> >> zeros. I think this is more usually in amplifier design. In control
> >> (mechanical) theory I think lead-lag is used more often.
> >>> When you say lead-lag does that imply that the zero occurs at a
> >>> lower f than the pole? Ie., would you call it a lead-lag just
> >>> because it contains a zero and a pole or would you change it to
> >>> lag-lead if the pole were at lower f than the zero?
> >> Frankly, I never really describe compensation in this lag/pole
> >> zero/lead way. I generally just describe in terms of the 20n.db/dec
> >> gain roll offs or increases.
> >> The usually scenery is that the lag/pole comes first in frequency.
> >> This reduces the gain right up to the x-ing point. The lead/zero is
> >> then inserted around the o-xing point to bring the phase back up.
> >> The *whole* point of the lag-lead is as I noted.
> >> "The only guaranteed way to make a small fortune, is to start with a
> >> large one, and lose some of it."
> >> Learn his well.
> >> If a gain stage in amplifier could be made to increases with
> >> frequency at the zero-xing point, you would not need a lag at all.
> >> You would simply add in the lead gain amp. All your trying to do is
> >> increases the phase away from a 180 degrees (in a neg feedback
> >> system) at the 0-xing point. This is obviously not likely, as the
> >> system is rolling off because the amp components are maxing out
> >> already. So to get around this you deliberately roll of the gain
> >> before the component limits kick in, this means everything rolls of
> >> sooner, you can then un-roll off the bit you rolled off prematurely.
> >> This results in the classic lag-lead.
> >> But if you are fortunate to be dealing with a slow system, e.g. 1khz
> >> type response, you can simple slap in a 100Mz op-amp and make a lead
> >> on its own without having (essentially) he lag at all. I have
> >> actually done this to stabilise a SMPS. Its rare to see this done
> >> becuse people get into a mindset.
> >>> Hmm, I just realized that a high pass is s/(s+wc), (I'm new at this
> >>> so I don't have it all ingrained yet), so that means what I think
> >>> you are calling a "lead" has an H(s) which contains both a pole and
> >>> a zero at DC, ie., a simple high-pass.
> >> Just about. Yes, in practise a lead is a single stage HP filter.
> >> Technically, a pure S term, e.g. a differentiator is a lead, but a
> >> practical one will always end up flattening off at HF.
> >>> What would you call my filter with H(s)=(s+wz)/(s+wp) ?
> >> That is a lag-lead, or a lead-lag, depending on what pole comes
> > (1+sT1)/(1+sT2) when T1>T2 this is a lead otherwise a lag.
> > For a lead-lag you need two of the above - one for the lead and one
> > for the lag.
> This interpretation of the phrase lag-lead is one that is used in
> control theory, not in general amplifier design, imo. The given transfer
> function has both a pole and a zero. It will therefore have regions
> where the gain and phases advances from what it was *and* regions where
> the gain and phases are retarding from what it was.
> For me, it don't make much sense to me to call a transfer function that
> is not a single simple pole or zero a lag or a lead. A lag (lead)
> implies a simple decrease (increase), it does not imply, by itself, a
> correction to that lag (lead) via another lead (lag). That is in control
> theory, a "lead" means adding both a pole and zero, where as in
> amplifier design the term "lead" would simple mean adding a zero.
> Although granted, in practice, at HF, a pole will kill this lead.
> > Often this is quoted inccorectly ie a lag-lead is shown to be the
> > above.
> It is not incorrect, it is because people use the same words to mean
> different things in their own speciality. The above describes a typical
> compensation for an amplifier that is indeed usually described as as
> pole-zero or lag-lead network. The fact that control people have a
> different interpretation is irrelevant.
> >A phase lag starts flat then has a -6dB/octave roll off then
> > flat again.
> But not in *amplifier* stability terminology. A lag (pole) has a
> magnitude response that falls of at 6db/dec, and rolls of forever. It
> has a phase response that falls from 0 degrees off then flattens out to
> 90 degrees. It confuses things no end to have a gain rollof (lag)
> actually mean a gain roll of, then a gain increase.
I agree with all that but I thought he was trying to stabilise a motor? not
and amplifier?(not the basic principles are different we only disagree on