Reply-To: "Kevin Aylward"
From: "Kevin Aylward"
References: <3DF99AEF.80FA3424@NAESPAM.yahoo.com> <%QhK9.email@example.com> <3DFA3DAA.E103628F@NAESPAM.yahoo.com> <3DFBF54D.778230B7@NAESPAM.yahoo.com>
Subject: Re: How to increase PLL order?
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Date: Sun, 15 Dec 2002 10:16:12 -0000
NNTP-Posting-Date: Sun, 15 Dec 2002 10:16:21 GMT
> Kevin Aylward wrote:
>> tom wrote:
>> 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.
> I am afraid you have similar ideas to the textbooks! The reason for a
> lag is to
> increase the gain at low frequencies ie an integrator over a limited
This discrepancy would appear to be due in part, to differing
terminologies in amplifier design and control theory, and differing
goals. Furthermore, there is a misunderstanding of what "low frequency"
means. It seems that your referring to DC to some lower bound, where as
reducing frequency in amplifier terms means the frequency response in
I agree, that you can use a gain roll off to increase the DC to low
frequency gain. However, this aspect is really secondary to the main
goal in *amplifier* design. The fundamental point is to stabilise the
amplifier. To do this one rolls of the gain before any of the millions
of other HF poles kick in. Rolling it of faster, than taking it back out
again at the zero x-ing point can achieve this goal. This is simply not
debatable. Its how it is.
>You always keep the bandwidth the same othrwise no
> comparison can be made.
Conceptually, that's not how its actually perceived. What one has is an
amplifier, set of with some required gain, and low and behold its
oscillating. This is the starting state of affairs. One than either
rolls of the gain to stabilise it, or trie to add a lead, e.g. a
capacitor across a feedback resister to increase the loop gain.
>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 step
> response time but this is rubbish. It only reduces the response time
> as they have in fact reduced the bandwidth - pretty obvious.
A gain roll off will reduce the response, however, your interpretation
of what a lag does is based on what one can do in a lagged *system*, not
the lag by itself.
>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.
This wording is poor. The lag does not increase the gain in a limited
region, it *allows* for increased gain at low frequencies if associated
design measures are taken in the system.
Consider a system with a basic single pole roll off, and some other
poles at HF. This roll off has to ensure that the unity gain point is
achieved prior to the HF poles. If you now add n times roll offs at some
frequency, after that frequency the gain will roll of much more rapidly.
This additional roll of is then knocked out around the o-xing point.
This means that you can increase the low frequency gain from what it was
and still have it intersect to 0 db point, prior to those other HF
>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.
Again, the issue her is one of definitions and starting assumptions. If
I have an oscillating system as a *given*, then add a zero (a pure lead)
it can stabilise the system and it don't reduce the BW one iota.
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