Home |
Search |
Today's Posts |
#1
|
|||
|
|||
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 |
#2
|
|||
|
|||
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! =----- |
#3
|
|||
|
|||
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! =----- |
#4
|
|||
|
|||
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 |
#5
|
|||
|
|||
"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. |
#6
|
|||
|
|||
"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. |
#7
|
|||
|
|||
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 |
#8
|
|||
|
|||
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 |
#9
|
|||
|
|||
|
#10
|
|||
|
|||
"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 Ã…kerberg-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. |