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Subject: Re: How to increase PLL order?
Date: Sun, 15 Dec 2002 16:21:49 +1300
Organization: Attica Communications
References: <3DF99AEF.80FA3424@NAESPAM.yahoo.com> <%QhK9.firstname.lastname@example.org> <3DFA3DAA.E103628F@NAESPAM.yahoo.com>
NNTP-Posting-Date: Sun, 15 Dec 2002 03:21:16 +0000 (UTC)
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Kevin Aylward wrote:
> tom wrote:
> > Kevin Aylward wrote:
> >> tom wrote:
> >>> "Christopher R. Carlen" wrote:
> >>>> Kevin Aylward wrote:
> >>>>> A frequency/phase detector is a digital logic detector, of which
> >>>>> there are various implementations. In contrast to multipliers and
> >>>>> ex-or type that lock on at 90 deg for the center frequency only,
> >>>>> frequency/phase types always lock exactly in phase (ideally) no
> >>>>> mater what the centre frequency is.
> >>>> I think that depends on what the transfer function of the VCO is.
> >>>> Of course, we are used to Kvco/s, but for motors things go haywire.
> >>>> I am using the Z-state detector from a 4046, and it doesn't produce
> >>>> zero phase error with a motor, though it most certainly does with a
> >>>> normal VCO.
> >>>> The reasons are in the control theory, at which I am not yet good
> >>>> enough to explain why this happens. But I have observed it
> >>>> nonetheless. A crude attempt at my explaining it would go
> >>>> something like:
> >>>> The motor/VCO transfer function is wierd, so that the loop filter
> >>>> transfer function is not that of a simple low pass filter with a
> >>>> finite high frequency gain. Instead it is a "zero-pole" as I have
> >>>> OPed. This filter doesn't integrate. Phase error is thus some
> >>>> non-zero constant.
> >>> I have just seen this post and apologise for not reading all the
> >>> other posts but many of them. You seem to be adding a phase-lead at
> >>> unity gain which is quite common in closed-loop systems. What you
> >>> need to do is add a lag at low frequencies so you have a lag-lead
> >>> filter - like this
> >> Actually, this is one of those rare occasions that you might not
> >> really need to add a lag. In most cases one is usually stuck with:
> >> "The only guaranteed way to make a small fortune, is to start with a
> >> large one, and lose some of it."
> >> e.g.
> >> http://www.anasoft.co.uk/EE/feedbackstability/feedbackstability.html
> >> In most cases (e.g. amplifiers), you don't have any high frequency
> >> gain left to bring the system into a 20db/dec roll off at the unity
> >> gain point. So what you do is deliberately roll off the gain and
> >> then take it back out again. i.e. a lag-lead. However, in a motor
> >> control system the response is usually so slow that you can simple
> >> add an op-amp with sufficient BW to give a simple lead around the
> >> zero x-ing point, without having to throw away gain at low
> >> frequencies.
> > Not sure what you mean by throwing away gain at low frequencies.
> > Usually with a lag you increase the overall gain of the loop
> Nahh... your definition of lag is non standard. A lag is an extra
> 20db/dec roll off from the existing roll off. It is a pole, which
> reduces the gain of the loop.
> > maintain the same unity gain crossover frequencies.
> But that's not the point of a lag. Its point is to reduce the gain
> before the unity gain frequency, so you can increase it back up again at
> the unity frequency, as I explained in my paper. It needs to do this
> before other poles kick in.
> >In text books
> > they make great play of reducing gain at low freuencies with a lag
> Because its a useful thing to do if you want to stabilise the loop.
> > but it is not comparing oranges with
> > oranges - for comparison you have to maintain the same bandwidth
> > each time you do a modification of the compensator (where possible).
> That's simple not the point of the lag. Sure, it would be nice if you
> *could* keep the same BW, but the main idea of compensation is to
> stabilise the loop, which usually means restricting the BW as a given
> > It is always possible to squeeze a lag or integrator (P+i) into a loop
> > but at the expense of phase margin of course.
> Not at all. The *deliberate* gain roll off of a lag is what *allows*
> you, in general, to un roll off the gain near the zero x-ing point. e.g.
> just slap a capacitor across a node with a small resistor in series with
> it, it will roll off the gain until the resistor kicks in. The resistor
> kicking in will *correct* the phase margin. That's its point. Its to
> obtain the phase margin that you require.
> >That is where bandwidth
> > is important
> > - you must know the limiting factor on bandwidth.
> 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
> SuperSpice, a very affordable Mixed-Mode
> Windows Simulator with Schematic Capture,
> Waveform Display, FFT's and Filter Design.
I am afraid you have similar ideas to the textbooks! The reason for a lag is
increase the gain at low frequencies ie an integrator over a limited
range. You always keep the bandwidth the same othrwise no
comparison can be made.That is how I have always done it - I respect your
point of view.For instance in text books they say that a lag reduces the
response time but this is rubbish. It only reduces the response time as
they have in fact reduced the bandwidth - pretty obvious. So for a lag
with a span of 1:10 (20dB attenuation) you need to increase the overall
loop gain by 20dB and all is well.A lag increases gain in a limited range
of frequencies at low frequencies and this increases disturbance rejection,
gives better tracking etc. The converse is thrue of course when you put a
phase lead into a system - you need to lower the gain to maintain
the same bandwidth. The bandwidth is dictated by the resonance normally
where motors are concerned - oh and that is another thing missed in all the
books - they never say what limits bandwidth - you could have infinite
bandwidth for all they care!
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