Reply-To: "Kevin Aylward"
From: "Kevin Aylward"
References: <3DF99AEF.80FA3424@NAESPAM.yahoo.com> <%QhK9.firstname.lastname@example.org> <3DFA3DAA.E103628F@NAESPAM.yahoo.com> <3DFBF5FC.C3112E2@NAESPAM.yahoo.com>
Subject: Re: How to increase PLL order?
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Date: Sun, 15 Dec 2002 10:16:02 -0000
NNTP-Posting-Date: Sun, 15 Dec 2002 10:16:11 GMT
> 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
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.
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