Designing Frequency-Dependent Impedances?
 

Hi,
Every one knows, that e.g. a simple RC-parallel circuit has a
frequency-dependent impedance-characteristic (Absolute Value) - the
impedance (Abs) raises as the Frequency approaches zero. As a formula: Zin
= 1/(1/R + i w C) , where i ist the imaginary number and w the frequency.

Now the hard part. How does one create an Impedance, which decreases
"slower", for frequencies close to zero but then decreases "faster" for
higher frequencies, than the simple parallel RC-Circuit?
Is there some kind of procedure like the one for syntesizeing LC-Filters
(Butterworth, Chebychev,..)?

Simply increasing C does not really help, because this equals a factoring of
the frequency.
Increasing R does not help as well, as it seems.


I hope one of you cracks can help me out.
So far, thanks for reading.
Diego Stutzer

Diego Stutzer wrote:
Now the hard part. How does one create an Impedance, which decreases
"slower", for frequencies close to zero but then decreases "faster" for
higher frequencies, than the simple parallel RC-Circuit?
Is there some kind of procedure like the one for syntesizeing LC-Filters
(Butterworth, Chebychev,..)?

For emulation modeling, there exist programmable resistors,
capacitors, and inductors. Is that what you have in mind?
--
73, Cecil http://www.qsl.net/w5dxp



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or perhaps...
http://rfdesign.com/ar/radio_interac...oupled_filter/


"Cecil Moore" wrote in message
...
Diego Stutzer wrote:
Now the hard part. How does one create an Impedance, which decreases
"slower", for frequencies close to zero but then decreases "faster" for
higher frequencies, than the simple parallel RC-Circuit?
Is there some kind of procedure like the one for syntesizeing LC-Filters
(Butterworth, Chebychev,..)?

For emulation modeling, there exist programmable resistors,
capacitors, and inductors. Is that what you have in mind?
--
73, Cecil http://www.qsl.net/w5dxp



-----= Posted via Newsfeeds.Com, Uncensored Usenet News =-----
http://www.newsfeeds.com - The #1 Newsgroup Service in the World!
-----== Over 100,000 Newsgroups - 19 Different Servers! =-----

Diego Stutzer wrote in message
m...
Hi,
Every one knows, that e.g. a simple RC-parallel circuit has a
frequency-dependent impedance-characteristic (Absolute Value) - the
impedance (Abs) raises as the Frequency approaches zero. As a formula:
Zin
= 1/(1/R + i w C) , where i ist the imaginary number and w the frequency.

Now the hard part. How does one create an Impedance, which decreases
"slower", for frequencies close to zero but then decreases "faster" for
higher frequencies, than the simple parallel RC-Circuit?
Is there some kind of procedure like the one for syntesizeing LC-Filters
(Butterworth, Chebychev,..)?

Simply increasing C does not really help, because this equals a factoring
of
the frequency.
Increasing R does not help as well, as it seems.


I hope one of you cracks can help me out.
So far, thanks for reading.
Diego Stutzer

You need to graph out the required frequency-impedance slope then
approximate the required roll off rates using a segmented breakpoint scheme
consisting of a number of CR series sections in parallel. Essentially it's a
straight line approximation to the required Z-F curve. The CR's adding
zeroes as the frequency goes up.

Estimating the individual time constants can be irksome as each has effect
outside it's area of interest. Use a 'least-squares approximation' to obtain
a best curve fit for the number of sections involved.

It's an interesting subject but I've come across nothing out there that's of
use.

regards
john

"John Jardine" wrote in message
...

Diego Stutzer wrote in message
m...
Hi,
Every one knows, that e.g. a simple RC-parallel circuit has a
frequency-dependent impedance-characteristic (Absolute Value) - the
impedance (Abs) raises as the Frequency approaches zero. As a formula:
Zin
= 1/(1/R + i w C) , where i ist the imaginary number and w the
frequency.

Now the hard part. How does one create an Impedance, which decreases
"slower", for frequencies close to zero but then decreases "faster" for
higher frequencies, than the simple parallel RC-Circuit?
Is there some kind of procedure like the one for syntesizeing LC-Filters
(Butterworth, Chebychev,..)?

Simply increasing C does not really help, because this equals a
factoring
of
the frequency.
Increasing R does not help as well, as it seems.


I hope one of you cracks can help me out.
So far, thanks for reading.
Diego Stutzer

You need to graph out the required frequency-impedance slope then
approximate the required roll off rates using a segmented breakpoint
scheme
consisting of a number of CR series sections in parallel. Essentially it's
a
straight line approximation to the required Z-F curve. The CR's adding
zeroes as the frequency goes up.

Estimating the individual time constants can be irksome as each has
effect
outside it's area of interest. Use a 'least-squares approximation' to
obtain
a best curve fit for the number of sections involved.

It's an interesting subject but I've come across nothing out there that's
of
use.

regards
john



In other words YES. You use combinations of resistors and capacitors or
inductors. Understanding the concept of "poles" and "Zeroes" is one way
which allows the synthesis of such circuits. Another is the concept of
"corner Frequency".

--
Steve N, K,9;d, c. i My email has no u's.

"Cecil Moore" wrote in message
...
Diego Stutzer wrote:
Now the hard part. How does one create an Impedance, which decreases
"slower", for frequencies close to zero but then decreases "faster" for
higher frequencies, than the simple parallel RC-Circuit?
Is there some kind of procedure like the one for syntesizeing LC-Filters
(Butterworth, Chebychev,..)?

For emulation modeling, there exist programmable resistors,
capacitors, and inductors. Is that what you have in mind?
--
73, Cecil http://www.qsl.net/w5dxp


I think he is looking for slopes of less that 6 dB per octave.

--
Steve N, K,9;d, c. i My email has no u's.

John Jardine wrote:
Diego Stutzer wrote in message
m...
Hi,
Every one knows, that e.g. a simple RC-parallel circuit has a
frequency-dependent impedance-characteristic (Absolute Value) - the
impedance (Abs) raises as the Frequency approaches zero. As a
formula: Zin = 1/(1/R + i w C) , where i ist the imaginary number
and w the frequency.

Now the hard part. How does one create an Impedance, which decreases
"slower", for frequencies close to zero but then decreases "faster"
for higher frequencies, than the simple parallel RC-Circuit?
Is there some kind of procedure like the one for syntesizeing
LC-Filters (Butterworth, Chebychev,..)?


You need to graph out the required frequency-impedance slope then
approximate the required roll off rates using a segmented breakpoint
scheme consisting of a number of CR series sections in parallel.
Essentially it's a straight line approximation to the required Z-F
curve. The CR's adding zeroes as the frequency goes up.

Estimating the individual time constants can be irksome as each has
effect outside it's area of interest. Use a 'least-squares
approximation' to obtain a best curve fit for the number of sections
involved.

It's an interesting subject but I've come across nothing out there
that's of use.

___
o-|___|--+--------+--------+---o
10k | | |
| | |
--- --- ---
--- --- ---
|100n |10n | 3n3
.-. .-. |
| | | | |
| |15k | |10k |
'-' '-' |
| | |
o--------+--------+--------+---o
created by Andy´s ASCII-Circuit v1.24.140803 Beta www.tech-chat.de
use fixed font to view

This does exactly what you want, in the beginning the slope is less than
3dB/oct. and at 10kHz it goes to 6dB/oct.
This is how to produce a pink noise that rolls off faster at the end of
range, or to make some weighted filters (dBA) etc.

ciao Ban

Ban wrote in message
...
John Jardine wrote:
Diego Stutzer wrote in message
m...
Hi,
-clip-

___
o-|___|--+--------+--------+---o
10k | | |
| | |
--- --- ---
--- --- ---
|100n |10n | 3n3
.-. .-. |
| | | | |
| |15k | |10k |
'-' '-' |
| | |
o--------+--------+--------+---o
created by Andy´s ASCII-Circuit v1.24.140803 Beta www.tech-chat.de
use fixed font to view

This does exactly what you want, in the beginning the slope is less than
3dB/oct. and at 10kHz it goes to 6dB/oct.
This is how to produce a pink noise that rolls off faster at the end of
range, or to make some weighted filters (dBA) etc.

ciao Ban


[Slightly OT].These 'spread CR' things are *weird*. How else can 1Hz to 1MHz
be set with just one pot!.

,-------------------+--------------.
| | |
.-. .-. |
2k7| | | | |
| | | | |
'-' '-'220 |
| | |
| ¦ V+ |
| | |\| |
,---+---+--++---+---+--------- | ------|-\ |
| | | | | | Min.-. | ---'-o
.-. .-. .-. .-. .-. .-. | |-----|+/ Square wave out
| | | | | | | | | | | | | | |/|
| | | | | | | | | | | | Max'-'Pot V-
'-' '-' '-' '-' '-' '-' | 10k
| | | | | | |
--- --- --- --- --- --- Comparitor
--- --- --- --- --- --- |
A| B| C| D| E| F| .-.
'---+---+---+---+---' | |680
| | |
0V '-'
A=10K:10u |
B=4k7:1u 0V
C=2k2:100n
D=1k2:100n
E=680:1n
F=330:100p

created by Andy´s ASCII-Circuit v1.24.140803 Beta www.tech-chat.de

regards
john

On 19 Feb 2004 02:30:00 -0800, (Diego Stutzer)
wrote:
Is there some kind of procedure like the one for syntesizeing LC-Filters
(Butterworth, Chebychev,..)?

Hi Diego,

This can be done in a number of ways employing active components (I've
just seen the drift of the thread take on this complexity).

The Bi-Quad filter comes to mind and has been around implemented with
Op-Amps for quite a while.

Another is the cascaded, bucket-brigade chip from reticon (haven't
played with this for 20 years tho').

You could also build an MCU interfacing ADC and DAC chips or simply
step up to DSP chips for filters that are impossible to implement in
any combination of passive L-C-R combinations.

However, the Bi-Quad offers simultaneous Low Pass, Band Pass, Band
Reject, and High Pass outputs from one circuit configuration. For
playing around with, that flexibility is hard to beat.

73's
Richard Clark, KB7QHC

"Diego Stutzer" in m...

Now the hard part. How does one create an Impedance, which decreases
"slower", for frequencies close to zero but then decreases "faster" for
higher frequencies, than the simple parallel RC-Circuit?
Is there some kind of procedure like the one for syntesizeing LC-Filters
(Butterworth, Chebychev,..)?

What you are asking about is a form of what's traditionally called the
network synthesis problem (creating a network of components to realize a
prescribed signal response) and specifically the synthesis of a one-port, or
impedance.

At one time (when phone companies ruled the earth and computers had
conquered few signals and DSP was reserved for BIG things like the US
Perimeter Acquisition Radar at Concrete, North Dakota -- affectionately the
"PAR"), this was a popular subject in engineering schools at the
advanced-undergrad or graduate level. It is still extremely important
sometimes, especially with the sophisticated signal processing used today on
continuous-time signals in consumer products. A host of
applied-mathematical techniques (Foster and Cauer synthesis, Brune's
impedance-synthesis lemma, etc.) apply even to one-ports. Some of them are
highly counterintuitive. Not, in other words, a subject perfectly matched
to the contraints of brief advice on newsgroups. (Note also that
Butterworth and Chebyshev approximants are mathematical methods to approach
one group of curves out of things that naturally give you a different type
of characteristic -- "Butterworth and Chebyshev" have nothing to do with
specific circuit topologies or components). If you want to pursue it
further I could suggest investigating "network synthesis." Temes and
LaPatra had a reasonable modern (1970s) book about it. Karl Willy Wagner
started it all in 1915 by inventing filters.

Richard Clark suggested also investigating the small op-amp "biquad"
networks for designable frequency response (actually you can turn them into
one-ports, the so-called shunt-filter class, but again a bit of a subject
for a brief response). Note that technically a "bi-quad" is any network
giving a biquadratic transfer function (2nd-order numerator and denominator)
though in RC-active filters it's often applied to the closely related
Åkerberg-Mossberg and Tow-Thomas configurations. For practical info see van
Valkenberg's excellent general introductory book on filters from the 1980s.

For an accessible modern example of these small op-amp-based "biquad"
networks, look up the LTC1562 from Linear Technology, a commercial chip with
four trimmed "biquad" networks, programmable by outboard components for
applications from a few kHz to a few hundred kHz.