Help with Laplace Transform for PLL VCO, Kvco?????

[Tim Wescott]

"Dr. Slick" <radio913@aol.com> wrote in message
news:1d15af91.0403200307.5bc25a5c@posting.google.com...

"Tim Wescott" <tim@wescottnospamdesign.com> wrote in message
news:<105mo25qvp66u23@corp.supernews.com>...

Question: how exactly does one actually MEASURE (not calculate)
the phase margin?


Slick

The most popular method is to put a summing junction somewhere in your
loop,
with one argument being the regular loop signal and the other being
under
your control. Inject a swept sine wave into the junction, and compare
the
amplitude and phase of the signal at the output of the junction and at
the
loop input. You can then calculate the open-loop amplitude and phase
directly.


Ok, but when you do this, the loop is never really opened, and the
site
that Kevin posted tells us that we shouldn't open the loop to measure
the open loop gain, as the DC points will be off.

So you measure the closed-loop response, and then calculate the
open-loop
gain from that right? And then find the 0 dB, or unity gain point,
and see what the distance from 180 degrees it is. This will be you
phase margin, eh?



There's things called "transfer function analysers", "dynamic system
analyzers" and "control system analysers" that will do this for you, but
you
have to part with many $.

Can you give us a model # or brand?


Slick

HP3562. By the real HP.

And no, you're never opening the loop, but you _are_ measuring both the
output and the input of the entire loop, and dividing the one by the other
to get the real open-loop transfer function. You can actually measure any
part of the loop if you want, so you can also get the plant transfer
function or the controller transfer function. Moreover, since you're doing
it with a swept sine you can do it to a nonlinear plant and get a sinusoidal
describing function out (this doesn't matter for a PLL, though).

 

[Kevin Aylward]

Dr. Slick wrote:

"Kevin Aylward" <kevindotaylwardEXTRACT@anasoft.co.uk> wrote in
message news:<ZhX6c.68$Kt4.22@newsfep3-gui.server.ntli.net>...

However, this is still a simulation method. I'm interested in
an actual
bench measurement of a phase margin.

Try and find a feedback node that is low impedance driving a high
impedance. If one knows what the circuit should be doing, one might
be able to get a reasonable approximation by using a floating, series
voltage source and calculating the ratio of its voltage to ground.
Sometimes a transformer is use to couple in the excitation signal.



The site mentions that:

"The problem when trying to simulate loop gain is that in
opening up the loop to make the proper measurements, the DC bias
point of the circuit will be altered. Since the circuit is
linearized around the DC bias point in AC analysis, this will throw
off the results of the entire simulation."

If you use SuperSpice this is not an issue. There is a special
resister that can be used that can be set automatically low for
operating point and transient and high for AC. See the example
LoopCutter.sss.

Secondly, if you know that the output impedance of a node is low, you
can simple use the series voltage source alone, and get quite
accurate results. Again, SuperSpice has this technique built right
into it. See that example, AutomaticLoopGain.sss.



Jesus, i didn't realize that you were advertising! heeheh!

Consider your self now so informed

Can Superspice analyze transient responses of PLL? Acquisition
times,
phase margin, and bandwidth, etc?

Well, you can do the normal spice runs. There are a few PLL examples.
Obviously, to do phase and frequency response, one would have to
actually construct an ac model of the PLL. The transient response, is of
course, what it is. You can manually calculate phase from the overshoot.

But it doesn't say if you cannot measure an ACTUAL CIRCUIT open
loop gain by opening the loop.

You can't in real life. Its way worse. In a simulation, sometimes you
have zero offsets such that the open loop still bias up correctly.


ok, so the phase margin can never really be measured on the
bench in
an actual circuit?

No. I was referring to the fact that you cant blindly open the loop. You
have to keep the loop connected at least for DC. You can bypass the AC
feedback with a capacitor.

It's just a theoretical calculation that might

help you achieve stability when designing the circuit?

Yes and no. You can measure it, if you take the time to do so, but in
general, I cant say that people bother much. The transient response
tells you pretty much all you need to now.

That's what it sounds like you are saying, which sounds
plausible.

But buy definition, the open loop gain is just all the blocks of
the PLL
in series, so there should be a way to measure its transfer function.

Yes, but is just not trivial in general.

Kevin Aylward
salesEXTRACT@anasoft.co.uk
http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.

"quotes with no meaning, are meaningless" - Kevin Aylward.

 

[Terry Given]

ok, so the phase margin can never really be measured on the
bench in
an actual circuit? It's just a theoretical calculation that might
help you achieve stability when designing the circuit?

That's what it sounds like you are saying, which sounds
plausible.

no, you CAN measure it, its just difficult - too difficult to DIY with just
a signal generator, due to the SNR (small-signal in, small signal out
sitting on what is usually a humongous DC level, often with bucketloads of
switching noise and the like....

look at the Venable 350

http://www.venable.biz/

or the model AP200 from

http://www.ridleyengineering.com/

these things are not just good for smps control loops, they are great for
EMI filters and suchlike, too. measure ALL of your transfer functions,
wall-to-wall carpeting and quadrophonic surround sound. But wait, theres
more, it slices, it dices....at least it should for the > US$10k price tag!

 

[Terry Given]

"Kevin Aylward" <kevindotaylwardEXTRACT@anasoft.co.uk> wrote in message
news:1pz6c.44$_r2.30@newsfep3-gui.server.ntli.net...
[snip]

It is the same situation in that one is considering the envelope of the
vco, not the vco frequency itself. Is the envelope stable or not, i.e.
constant.

one of the best sentences to turn up in this thread so far.

 

[Dr. Slick]

"Tim Wescott" <tim@wescottnospamdesign.com> wrote in message news:<105pn9hmq0ptpeb@corp.supernews.com>...

HP3562. By the real HP.

And no, you're never opening the loop, but you _are_ measuring both the
output and the input of the entire loop, and dividing the one by the other
to get the real open-loop transfer function. You can actually measure any
part of the loop if you want, so you can also get the plant transfer
function or the controller transfer function. Moreover, since you're doing
it with a swept sine you can do it to a nonlinear plant and get a sinusoidal
describing function out (this doesn't matter for a PLL, though).

I've seen the word "controller" used to describe the filter of the loop.

Is this what you mean?

And does the word "plant" refer to the open loop response, or just the
forward gain?


S.

 

[Dr. Slick]

"Kevin Aylward" <kevindotaylwardEXTRACT@anasoft.co.uk> wrote in message news:<ITc7c.35$cw6.9@newsfep3-gui.server.ntli.net>...

It's just a theoretical calculation that might
help you achieve stability when designing the circuit?

Yes and no. You can measure it, if you take the time to do so, but in
general, I cant say that people bother much. The transient response
tells you pretty much all you need to now.

Well, if the PLL never locks, then of course you are unstable.

And if you measure the period between the overshoot peaks, you get
the resonant frequency of the loop, and the damping factor.

It seems to me that perhaps people consider the phase margin in
the
initial design, but because it's too impractical to actually measure,
they
resort to "cut and try" electronics to find filter values that just
plain
work to allow them to the get the acquisition times, stability, and
phase noise that they want.

That's perfectly understandable to me: There are always limits to
text-book theory, and at some point, you have to use brute-force
engineering.




Slick

 

[Dr. Slick]

"Terry Given" <the_domes@xtra.co.nz> wrote in message news:<XUc7c.11795$rw6.222854@news.xtra.co.nz>...

no, you CAN measure it, its just difficult - too difficult to DIY with just
a signal generator, due to the SNR (small-signal in, small signal out
sitting on what is usually a humongous DC level, often with bucketloads of
switching noise and the like....

look at the Venable 350

http://www.venable.biz/

or the model AP200 from

http://www.ridleyengineering.com/

these things are not just good for smps control loops, they are great for
EMI filters and suchlike, too. measure ALL of your transfer functions,
wall-to-wall carpeting and quadrophonic surround sound. But wait, theres
more, it slices, it dices....at least it should for the > US$10k price tag!

How do these differ from your standard HP network analyzer?


S.

 

[Active8]

On 21 Mar 2004 10:36:24 -0800, Dr. Slick wrote:

"Tim Wescott" <tim@wescottnospamdesign.com> wrote in message news:<105pn9hmq0ptpeb@corp.supernews.com>...

HP3562. By the real HP.

And no, you're never opening the loop, but you _are_ measuring both the
output and the input of the entire loop, and dividing the one by the other
to get the real open-loop transfer function. You can actually measure any
part of the loop if you want, so you can also get the plant transfer
function or the controller transfer function. Moreover, since you're doing
it with a swept sine you can do it to a nonlinear plant and get a sinusoidal
describing function out (this doesn't matter for a PLL, though).


I've seen the word "controller" used to describe the filter of the loop.

Is this what you mean?

And does the word "plant" refer to the open loop response, or just the
forward gain?

Controller is the filter. Plant is the VCO. By properly modeling the

plant, you can determine the controller.

--
Best Regards,
Mike

 

[Tim Wescott]

"Dr. Slick" <radio913@aol.com> wrote in message
news:1d15af91.0403211036.3d1def21@posting.google.com...

"Tim Wescott" <tim@wescottnospamdesign.com> wrote in message
news:<105pn9hmq0ptpeb@corp.supernews.com>...

HP3562. By the real HP.

And no, you're never opening the loop, but you _are_ measuring both the
output and the input of the entire loop, and dividing the one by the
other
to get the real open-loop transfer function. You can actually measure
any
part of the loop if you want, so you can also get the plant transfer
function or the controller transfer function. Moreover, since you're
doing
it with a swept sine you can do it to a nonlinear plant and get a
sinusoidal
describing function out (this doesn't matter for a PLL, though).


I've seen the word "controller" used to describe the filter of the
loop.

Is this what you mean?

And does the word "plant" refer to the open loop response, or just
the
forward gain?


S.

Sorry about that -- your original question was a circuits one, and I dropped
into control systems terminology.

The "plant" is the thing you're controlling (the term originally came from
folks learning about controlling steam plants). In this case it's the VCO,
and probably the PD as well (although you can make the claim that the PD
isn't really the plant -- you get to define things the way you want to).
The "controller" is the part you build, so it's the loop filter, in your
case.

 

[Tim Wescott]

"Terry Given" <the_domes@xtra.co.nz> wrote in message
news:XUc7c.11795$rw6.222854@news.xtra.co.nz...

ok, so the phase margin can never really be measured on the
bench in
an actual circuit? It's just a theoretical calculation that might
help you achieve stability when designing the circuit?

That's what it sounds like you are saying, which sounds
plausible.

no, you CAN measure it, its just difficult - too difficult to DIY with
just
a signal generator, due to the SNR (small-signal in, small signal out
sitting on what is usually a humongous DC level, often with bucketloads of
switching noise and the like....

look at the Venable 350

http://www.venable.biz/

or the model AP200 from

http://www.ridleyengineering.com/

these things are not just good for smps control loops, they are great for
EMI filters and suchlike, too. measure ALL of your transfer functions,
wall-to-wall carpeting and quadrophonic surround sound. But wait, theres
more, it slices, it dices....at least it should for the > US$10k price
tag!

Oh good. I've been keeping my eyes open for this sort of thing since HP
isn't in current production.

National Instruments also has a VI for a dynamic system analyzer (transfer
function analyzer, call it what you will), but I don't have personal
experience with it.