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Reply-To: "Kevin Aylward"
From: "Kevin Aylward"
References: <3DF99AEF.80FA3424@NAESPAM.yahoo.com> <%QhK9.email@example.com> <3DFA3DAA.E103628F@NAESPAM.yahoo.com>
Subject: Re: How to increase PLL order?
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Date: Fri, 13 Dec 2002 20:43:30 -0000
NNTP-Posting-Date: Fri, 13 Dec 2002 20:43:37 GMT
> 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."
>> 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
> 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.
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.
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