Equivalent mechanical system for a simple filter
dave.harper
more well-versed in circuit analysis could give me a little help in
figuring out a filter I'm interested in. I believe it is a
Butterworth filter.
I'm a mechanical engineer, and it'd be easier to set up the
differential equation if I could visualize it mechanically. What
would the equivalent mechanical system be for the following filter?
www.wenzel.com/graphics/pinet.gif
I think that it's a dashpot and spring in parallel with a mass, but I
can't figure out where to place the left-most capacitor.
The end result is that I want to model the transient response for
different voltage inputs (square, saw, etc).
Thanks in advance for any help!
Dave
dave.harper
John Larkin
An LC filter is, ideally, lossless, so a mechanical model wouldn't
include dashpots, which are dissipative.
One mechanical model is spring-mass-spring-mass... corresponding to
L...C...L...C...
----
| |
in-----/////----| |----////-----etc---out
| |
----
which is a lowpass.
Collins makes mechanical filters sort of like this...
http://www.rockwellcollins.com/content/images/img_1789.gif
http://www.delphelectronics.co.uk/filter390a/
I think the discs may be machined out of a solid rod, which makes this
a bandpass filter.
I've also seen a string of anchored rods, sort of like a row of
flagpoles connected by coupling wires, which would also be a bandpass.
John
dave.harper
<jjlar...@highNOTlandTHIStechnologyPART.com> wrote:
> On Mon, 5 Jan 2009 21:19:15 -0800 (PST), "dave.harper"
>
>
>
> <dave.har...@gmail.com> wrote:
> >I'm a little rusty on my circuit analysis, so I was hoping someone
> >more well-versed in circuit analysis could give me a little help in
> >figuring out a filter I'm interested in. I believe it is a
> >Butterworth filter.
>
> >I'm a mechanical engineer, and it'd be easier to set up the
> >differential equation if I could visualize it mechanically. What
> >would the equivalent mechanical system be for the following filter?
>
> >www.wenzel.com/graphics/pinet.gif
>
> >I think that it's a dashpot and spring in parallel with a mass, but I
> >can't figure out where to place the left-most capacitor.
>
> >The end result is that I want to model the transient response for
> >different voltage inputs (square, saw, etc).
>
> >Thanks in advance for any help!
> >Dave
>
> An LC filter is, ideally, lossless, so a mechanical model wouldn't
> include dashpots, which are dissipative.
>
> One mechanical model is spring-mass-spring-mass... corresponding to
> L...C...L...C...
>
> ----
> | |
> in-----/////----| |----////-----etc---out
> | |
> ----
Thanks for the response! I included the dashpot because it was in the
original schematic, and I think it's to limit the current going into
the circuit. I don't know if it'd be accurate for me to call this a
"filter", since it was suggested as a way to convert square to semi-
decent sine waves.
So (excluding the resistor), are you suggesting that it's a spring-
mass-spring system?
Thanks again!
Dave
John Larkin
An electrical passive Butterworth is a string of Ls and Cs. It is
usually designed to be terminated on one or both ends by a resistive
source and/or a resistive load, which would have mechanical
equivalents, perhaps source and load, perhaps dashpots if the
mechanical impedances weren't right.
If your excitation frequency is constant, you could use a bandpass
filter, coupled resonators like the Collins things or coupled
rods/flagpoles. If not, you'd need a lowpass, like the spring-mass
example.
John
dave.harper
It looks like I was wrong in calling it a Butterworth filter. After
some more searching, it looks like it's a pi section filter / pi
filter. Back to the original question, what would the mechanical
equivalent of a pi filter be?
Thanks again,
Dave
John Larkin
"Pi" expresses the topology of the filter. "Butterworth" expresses the
transfer function. A pi filter could be a Butterworth, a Bessel, a
Chebychev, or some other transfer function, depending on the values of
the elements.
A pi filter would be pretty much the spring-mass thing I sketched. The
basic pi might be mass-spring-mass, or spring-mass-spring. It could
have more L-C (spring-mass) sections; the more sections, the
higher-order the transfer function and potentially the sharper the
frequency cutoff.
The simplest lowpass is an R-C filter, sloppy first-order transfer
function, which would correspond to
dashpot
______
|
in -----| ======-------/mass/-----------out
|______
Mechanical filters are cool, since many sections can be machined out
of a hunk of stuff, and Qs are usually higher than electronic parts
can achieve, especially at low frequencies.
John
Joel Koltner
news:kc67m45ust1so27vb...@4ax.com...
> Mechanical filters are cool, since many sections can be machined out
> of a hunk of stuff, and Qs are usually higher than electronic parts
> can achieve, especially at low frequencies.
How do you transfer an electrical signal to a mechanical filter and then back
again at the other end? Voice coils? I seem to recall those Rockwell
mechanical filters have rather large insertion losses -- >10dB -- which I
always figured was primarily due to the electrical<-->mechanical transfers
rather than losses inherently within the mechanical parts themselves.
dave.harper
<jjlar...@highNOTlandTHIStechnologyPART.com> wrote:
> On Tue, 6 Jan 2009 09:28:17 -0800 (PST), "dave.harper"
>
>
>
Wouldn't an R-C filter be a dashpot and a spring? I thought caps were
modeled as springs (i.e. they store energy and their voltage is
dependent on charge), and inductors were modeled as masses (i.e. they
resist a change in current, like a mass resists acceleration).
Thanks,
Dave
Rich Grise
> On Jan 6, 10:33 am, John Larkin
>>
>> >differential equation if I could visualize it mechanically. What
>> >would the equivalent mechanical system be for the following filter?
>> >www.wenzel.com/graphics/pinet.gif
>> >I think that it's a dashpot and spring in parallel with a mass, but I
>> >can't figure out where to place the left-most capacitor.
>> >The end result is that I want to model the transient response for
>> >different voltage inputs (square, saw, etc).
>>
>> include dashpots, which are dissipative.
>
> mass-spring system?
>
and stuff, but I visualize it differently from what it sounds like
you guys are talking about.
I use the "water pipe" model. I see a resistance (which is, duh,
resistance ;-)), a spring-loaded membrane (a cap; the membrane is parallel
to the plates - actually, it's the gap)[1], a flywheel coupled to a
positive- displacement pump/turbine (the inductor)[1], and another cap
(see above ;-)).
From what I was told "dashpot" means, it sounds like what you'd put in
parallel with the cap to represent its losses. With the inductor
(flywheel-turbine/pump assy) you'e probably achieve the same thing with
a Prony brake or some such.
And, of course, the load is whatever the water moves.
Notes:
1. A capacitor opposes a change in voltage; an inductor opposes a change
in current.
Hope This Helps!
Rich
Jasen Betts
> "John Larkin" <jjla...@highNOTlandTHIStechnologyPART.com> wrote in message
> news:kc67m45ust1so27vb...@4ax.com...
>> Mechanical filters are cool, since many sections can be machined out
>> of a hunk of stuff, and Qs are usually higher than electronic parts
>> can achieve, especially at low frequencies.
>
> How do you transfer an electrical signal to a mechanical filter and then back
> again at the other end?
one way is to build it from piezoelectric material
resonators, crystals, and SAW filters are mechanical filters.
> Voice coils?
at lower frequencies, yes.
J.A. Legris
Sorry, but your water pipe model is probably going to muddify rather
that illuminate. Idealized dash-pots, springs and masses are *exact*
mathematical analogs of their lumped electrical cousins - no fudging,
hedging or hand waving is required.
However, it might be a good idea for Dave to bite the bullet and study
electric circuits, for the sake of notational convenience if anything.
There are lots of sources on the web. For example:
http://www.national.com/an/AN/AN-779.pdf
http://en.wikipedia.org/wiki/Laplace_transform
You can experiment with circuits using a simulator such as LTspice,
which is free:
http://www.linear.com/designtools/software/#Spice
--
Joe
Jasen Betts
the water model works well down to DC,
the springs and masses model doesn't seem to.
here's a boost converter implemented in the water model :)
http://en.wikipedia.org/wiki/Hydraulic_ram
bye
J.A. Legris
Idealized springs, masses and dash pots work just as well as their
lumped electrical analogs at DC (and all other frequencies), because
the underlying differential equations are identical. Of course, they
are all idealizations so their behaviours diverge from those of real
devices, but that's another issue.
q (charge) <==> x (position)
q' (current) <==> x' (velocity)
q'' (rate of change of current) <==> x'' (acceleration)
V (voltage) <==> F (force)
R (resistance) <==> b (viscosity)
1/C (inverse of capacitance) <==> k (spring constant)
L (inductance) <==> m (mass)
V = Lq'' + Rq' + q/C resonance at SQRT(1/LC)
F = mx'' + bx' + kx resonance at SQRT(k/m)
--
Joe
christofire
"J.A. Legris" <jale...@sympatico.ca> wrote in message
news:e18a9eed-82d9-4429...@m2g2000vbp.googlegroups.com...
On Jan 8, 2:18 am, Jasen Betts <ja...@xnet.co.nz> wrote:
> On 2009-01-07, J.A. Legris <jaleg...@sympatico.ca> wrote:
>
Idealized springs, masses and dash pots work just as well as their
lumped electrical analogs at DC (and all other frequencies), because
the underlying differential equations are identical. Of course, they
are all idealizations so their behaviours diverge from those of real
devices, but that's another issue.
q (charge) <==> x (position)
q' (current) <==> x' (velocity)
q'' (rate of change of current) <==> x'' (acceleration)
V (voltage) <==> F (force)
R (resistance) <==> b (viscosity)
1/C (inverse of capacitance) <==> k (spring constant)
L (inductance) <==> m (mass)
V = Lq'' + Rq' + q/C resonance at SQRT(1/LC)
F = mx'' + bx' + kx resonance at SQRT(k/m)
Joe
Sure, but what's the mechanical analogue of a series inductor - which
doesn't have one end earthed/grounded? Isn't that the sort of thing that
demands transformation from series to shunt, which complicates the problem
beyond the normal electrical solution?
Chris
J.A. Legris
> "J.A. Legris" <jaleg...@sympatico.ca> wrote in message
Mathematically, it's just another term of a loop equation in x''.
Physically it might take up a lot of room!
I'm no advocate of mechanical analogues - I've already suggested that
the O.P. should learn the electrical ones.
--
Joe
sideli...@gmail.com
> You can experiment with circuits using a simulator such asLTspice,
> which is free:http://www.linear.com/designtools/software/#Spice
>
May I suggest another tool instead of LTSpice. I'm using NL5 (http://
nl5.sidelinesoft.com) for simulating quite complex heat transfer
processes (same heat-to-electricity analogy). Two reasons: 1) NL5
deals with ideal componants, is very fast, zero learning curve. 2) I'm
an author (sorry for self-adverising :)
Thank you,
Alexei
dave.harper
> "J.A. Legris" <jaleg...@sympatico.ca> wrote in message
>
> doesn't have one end earthed/grounded?
>
You mean with one end open? Then i (current) has to always equal
zero, which is a constant. Therefore, di/dt also equals zero. So the
mechanical equivalent would be a massless mass... correct?
Dave
christofire
"dave.harper" <dave....@gmail.com> wrote in message
news:36b095b9-1d68-4db7...@v39g2000pro.googlegroups.com...
Dave
The given 'pi' circuit has each terminal of the inductor connected to a
capacitor, whose other terminal is earthed, and to either the output or
input port. There would be some current flowing through the inductor in
this case when the circuit was excited.
Chris
JosephKK
IIRC, the mappings work like this: Resistance <-> Dashpot,
Capacitance <-> Springs, Inductance <-> Mass; but i do not quite
remember how the connections map. That said, the circuit shown is
intended for fixed frequency PWM use; and the inductor and the two
capacitors form a tank circuit tuned to the PWM carrier frequency. Try
looking up m-derived filters.
Perhaps:
__R___ C L C
----_____|---////---|||||---////------+
|
load
|
============================================= reference bar
Notice that the C is not connected to reference, thus my comment about
not remembering how connections map.
JosephKK
Just curious, but what are the model equivalences?
Jim Thompson
wrote:
>On Fri, 9 Jan 2009 10:51:29 -0800 (PST), sideli...@gmail.com wrote:
>
>>>
>>> You can experiment with circuits using a simulator such asLTspice,
>>> which is free:http://www.linear.com/designtools/software/#Spice
>>>
>>
>>May I suggest another tool instead of LTSpice. I'm using NL5 (http://nl5.sidelinesoft.com) for simulating quite complex heat transfer
>>processes (same heat-to-electricity analogy). Two reasons: 1) NL5
>>deals with ideal componants, is very fast, zero learning curve. 2) I'm
>>an author (sorry for self-adverising :)
>>
>>Thank you,
>>Alexei
>
>Just curious, but what are the model equivalences?
>
It's probably a behavioral-model-based system simulator. I regularly
write my own behavioral models to substitute for complex
slow-simulating device-level stuff.
I do that in PSpice. LTspice is similar enough that I would guess you
can do it there as well.
NL5 is a "Cirucit" simulator, which probably makes it faster ;-)
Question for NL5 author: Are your models text-based?
...Jim Thompson
--
| James E.Thompson, P.E. | mens |
| Analog Innovations, Inc. | et |
| Analog/Mixed-Signal ASIC's and Discrete Systems | manus |
| Phoenix, Arizona 85048 Skype: Contacts Only | |
| Voice:(480)460-2350 Fax: Available upon request | Brass Rat |
| E-mail Icon at http://www.analog-innovations.com | 1962 |
I love to cook with wine Sometimes I even put it in the food
christofire
"JosephKK" <quiett...@yahoo.com> wrote in message
news:8olkm4h5jjed5mffn...@4ax.com...
The unanswered question is really how to simulate the series inductor, in a
pi CLC circuit, as its mechanical counterpart.
Chris
JosephKK
Part of the point that i was trying to make is that the springs should
go to reference (like the caps), not series. Doing so leaves no
reasonable connection for mass (mass is not a two terminal kind of
thing, unlike an inductor).
Alexei Smirnov
> On Fri, 9 Jan 2009 10:51:29 -0800 (PST), sidelines...@gmail.com wrote:
>
> >May I suggest another tool instead of LTSpice. I'm using NL5 (http://
> >nl5.sidelinesoft.com) for simulating quite complex heat transfer
> >processes (same heat-to-electricity analogy).
>
Electricity-to-heat analogy?
Capacitor = heat capacity
Resistor = thermal resistance (1 / "thermal conductance")
Current = heat flow
Voltage = temperature
Thanks,
Alexei.
Alexei Smirnov
Web-Site.com> wrote:
>
> NL5 is a "Cirucit" simulator, which probably makes it faster ;-)
It is still fast even as "Circuit"... already fixed :)
>
> Question for NL5 author: Are your models text-based?
>
It's normal graphical schematic entry. Usiing common ad terms:
"interactive, easy to use, highly intuitive, .." etc.
Thakns,
Alexei.
krw
@r10g2000prf.googlegroups.com>, sideli...@gmail.com says...>
Inductor = ??????
;-)
Alexei Smirnov
>
> > Capacitor = heat capacity
> > Resistor = thermal resistance (1 / "thermal conductance")
> > Current = heat flow
> > Voltage = temperature
>
> Inductor = ??????
> ;-)
You've already answered: ;-)
No inductors, no diodes, no transformers... Heat is so simple! Not
talking about convection though...
JosephKK
Then it is too simple to do the modeling that is needed.
JosephKK
And what models to inductance?
Rich Grise
> On Tue, 13 Jan 2009 10:00:26 -0800 (PST), Alexei Smirnov
>>> Just curious, but what are the model equivalences?
>>
>>Electricity-to-heat analogy?
>>
>>Capacitor = heat capacity
>>Resistor = thermal resistance (1 / "thermal conductance") Current = heat
>>flow
>>Voltage = temperature
>
> And what models to inductance?
"Thermal mass"?
Hope This Helps!
Rich