What kind of thing, within linear systems theory, is a
frequency dependant resistor? If I construct the IFFT of a
frequency domain function is purely real I get what looks
like a linear phase filter rotated so that the peak is at
the front which seems like nonsense to me.
This question came up on a list where it is claimed that
physical devices can have the properties of a frequency
dependant resistor and I just can't see how to map that into
our LTI world.
Confused,
Bob
--
"Things should be described as simply as possible, but no
simpler."
A. Einstein
Frequency Dependant Resistor
Started by ●May 23, 2005
Reply by ●May 23, 20052005-05-23
Bob Cain wrote:> > What kind of thing, within linear systems theory, is a frequency > dependant resistor? If I construct the IFFT of a frequency domain > function is purely real I get what looks like a linear phase filter > rotated so that the peak is at the front which seems like nonsense to me.I can not respond to that paragraph> > This question came up on a list where it is claimed that physical > devices can have the properties of a frequency dependant resistor and I > just can't see how to map that into our LTI world.I can't map it, but I might build suitable approximation. first take an idealized temperature dependent resistor (R1) then enclose it in a resistive heater apply current to heater proportional to input frequency applied to temp dependent resistor current thru R1 now dependent on applied frequency [ and yes I see many many many implementation problems ;] BUT, any flaws logically ?> > > Confused, > > Bob
Reply by ●May 23, 20052005-05-23
Bob Cain wrote:> > What kind of thing, within linear systems theory, is a frequency > dependant resistor? If I construct the IFFT of a frequency domain > function is purely real I get what looks like a linear phase filter > rotated so that the peak is at the front which seems like nonsense to me. > > This question came up on a list where it is claimed that physical > devices can have the properties of a frequency dependant resistor and I > just can't see how to map that into our LTI world. > > > Confused, > > BobYou might be able to approximate one over a limited range with a circuit similar to to a gyrator. Those clever guys who can make negative capacitors -- so useful with scope probes -- can probably do anything. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●May 23, 20052005-05-23
"Richard Owlett" <rowlett@atlascomm.net> ha scritto nel messaggio news:1194j6fmo55bu3c@corp.supernews.com...> Bob Cain wrote: > >> >> What kind of thing, within linear systems theory, is a frequency >> dependant resistor? If I construct the IFFT of a frequency domain >> function is purely real I get what looks like a linear phase filter >> rotated so that the peak is at the front which seems like nonsense to me. > > I can not respond to that paragraph > > >> >> This question came up on a list where it is claimed that physical devices >> can have the properties of a frequency dependant resistor and I just >> can't see how to map that into our LTI world. > > > I can't map it, but I might build suitable approximation. > > first take an idealized temperature dependent resistor (R1) > then enclose it in a resistive heater > apply current to heater proportional to input frequency applied to > temp dependent resistor > current thru R1 now dependent on applied frequency > [ and yes I see many many many implementation problems ;] > > BUT, any flaws logically ? > > >a current sensor... sense an input current and return as output a voltage. tranfer function is a resistor. apply classical system theory methods to such device and you have your answer. it's not so naive... if you want to control a current you need a sensor for sensing it. a sensor that transduce such current to a voltage may be useful. such device is a resistor (better called a shunt) now... a shunt doesn't have the same response all the frequencies of its input (the sensed current) when the spectrum of the input current become wide... from Hz to MHz... like for example in PWM inverters... shunts do not exibit a theoretically flat response... if you need a very accurate model of your resistor you must take into account parasitc effects due to capacitance between the two "pins" of your shunt... you must also take into account of the skin effect that is responsible of the amount of impedence of your shunt because as the frequency increase, the current will tend to flow on the surface of you shunt. increasing the impedence of your shunt as the frequency increase mean increasing the gain of your transducer.... in other words ...you have a frequency dependent shunt. hope this could help bye
Reply by ●May 23, 20052005-05-23
Bob Cain wrote:> > What kind of thing, within linear systems theory, is a frequency > dependant resistor? If I construct the IFFT of a frequency domain > function is purely real I get what looks like a linear phase filter > rotated so that the peak is at the front which seems like nonsense to me. > > This question came up on a list where it is claimed that physical > devices can have the properties of a frequency dependant resistor and I > just can't see how to map that into our LTI world.My interest is not in actually making such a thing but how to analyze it's response. For starters, what would the voltage to current transfer function be? Bob -- "Things should be described as simply as possible, but no simpler." A. Einstein
Reply by ●May 23, 20052005-05-23
"Bob Cain" <arcane@arcanemethods.com> wrote in message news:d6tor301vs1@enews4.newsguy.com...> > > Bob Cain wrote: > > > > What kind of thing, within linear systems theory, is a frequency > > dependant resistor? If I construct the IFFT of a frequency domain > > function is purely real I get what looks like a linear phase filter > > rotated so that the peak is at the front which seems like nonsense to me. > > > > This question came up on a list where it is claimed that physical > > devices can have the properties of a frequency dependant resistor and I > > just can't see how to map that into our LTI world. > > My interest is not in actually making such a thing but how > to analyze it's response. For starters, what would the > voltage to current transfer function be?Doesn't a voltage to current transfer function imply DC (or a very slow change in voltage)? What is the voltage to current transfer function of a capacitor or inductor?
Reply by ●May 23, 20052005-05-23
Jack Ace wrote:> "Richard Owlett" <rowlett@atlascomm.net> ha scritto nel messaggio > news:1194j6fmo55bu3c@corp.supernews.com... > >>Bob Cain wrote: >> >> >>>What kind of thing, within linear systems theory, is a frequency >>>dependant resistor? If I construct the IFFT of a frequency domain >>>function is purely real I get what looks like a linear phase filter >>>rotated so that the peak is at the front which seems like nonsense to me. >> >>I can not respond to that paragraph >> >> >> >>>This question came up on a list where it is claimed that physical devices >>>can have the properties of a frequency dependant resistor and I just >>>can't see how to map that into our LTI world. >> >> >>I can't map it, but I might build suitable approximation. >> >>first take an idealized temperature dependent resistor (R1) >>then enclose it in a resistive heater >>apply current to heater proportional to input frequency applied to >> temp dependent resistor >>current thru R1 now dependent on applied frequency >> [ and yes I see many many many implementation problems ;] >> >>BUT, any flaws logically ? >> >> >> > > > a current sensor... sense an input current and return as output a voltage. > > tranfer function is a resistor. apply classical system theory methods to > such device and you have your answer. > > it's not so naive... if you want to control a current you need a sensor for > sensing it. > a sensor that transduce such current to a voltage may be useful. such device > is a resistor (better called a shunt) > > now... a shunt doesn't have the same response all the frequencies of its > input (the sensed current) > > when the spectrum of the input current become wide... from Hz to MHz... like > for example in PWM inverters... shunts do not exibit a theoretically flat > response... > if you need a very accurate model of your resistor you must take into > account parasitc effects due to capacitance between the two "pins" of your > shunt... you must also take into account of the skin effect that is > responsible of the amount of impedence of your shunt because as the > frequency increase, the current will tend to flow on the surface of you > shunt. > > increasing the impedence of your shunt as the frequency increase mean > increasing the gain of your transducer.... in other words ...you have a > frequency dependent shunt. > > hope this could help > byeThe shunt's high-frequency response varies because it isn't really a resister, To a first-order approximation, it is modeled by a resistor in series with an inductor, the pair being in parallel with a capacitor. That it is not a frequency-dependent resistor is made evident by the phase shift it imposes when the response to current changes from the low-frequency value. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●May 23, 20052005-05-23
Jon Harris wrote:> "Bob Cain" <arcane@arcanemethods.com> wrote in message > news:d6tor301vs1@enews4.newsguy.com... > >> >>Bob Cain wrote: >> >>>What kind of thing, within linear systems theory, is a frequency >>>dependant resistor? If I construct the IFFT of a frequency domain >>>function is purely real I get what looks like a linear phase filter >>>rotated so that the peak is at the front which seems like nonsense to me. >>> >>>This question came up on a list where it is claimed that physical >>>devices can have the properties of a frequency dependant resistor and I >>>just can't see how to map that into our LTI world. >> >>My interest is not in actually making such a thing but how >>to analyze it's response. For starters, what would the >>voltage to current transfer function be? > > > Doesn't a voltage to current transfer function imply DC (or a very slow change > in voltage)? What is the voltage to current transfer function of a capacitor or > inductor?For any device, V = IZ. For a capacitor, Z=1/jwC; for an inductor, Z=wL, and for a normal resistor, Z=R. It's easy enough to define a frequency-dependent resistor as, say, Z=wR. The trick is building or simulating one. (A voltage-to-current transfer function is a conductance. Strictly, I should have written I=VY etc., where Y=1/Z.) Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●May 23, 20052005-05-23
Jerry Avins wrote:> Jon Harris wrote: > >> "Bob Cain" <arcane@arcanemethods.com> wrote in message >> news:d6tor301vs1@enews4.newsguy.com... >> >>> >>> Bob Cain wrote: >>> >>>> What kind of thing, within linear systems theory, is a frequency >>>> dependant resistor? If I construct the IFFT of a frequency domain >>>> function is purely real I get what looks like a linear phase filter >>>> rotated so that the peak is at the front which seems like nonsense >>>> to me. >>>> >>>> This question came up on a list where it is claimed that physical >>>> devices can have the properties of a frequency dependant resistor and I >>>> just can't see how to map that into our LTI world. >>> >>> >>> My interest is not in actually making such a thing but how >>> to analyze it's response. For starters, what would the >>> voltage to current transfer function be? >> >> >> >> Doesn't a voltage to current transfer function imply DC (or a very >> slow change >> in voltage)? What is the voltage to current transfer function of a >> capacitor or >> inductor? > > > For any device, V = IZ. For a capacitor, Z=1/jwC; for an inductor, Z=wL, > and for a normal resistor, Z=R. It's easy enough to define a > frequency-dependent resistor as, say, Z=wR.Hmmm, how is that different than Z=wL? See the problem here? What would it's response be, for example, to a rectangular pulse given that you know R(w)? Is a transfer function with an R(w) linear, i.e. however the transfer function is formulated are its eigenfunctions sinusoids? What would the FFT be of the transfer function? It would seem that the complex frequency domain definition would be entirely real with a magnitude that is a function of frequency yet when you IFFT that you get time sequence that looks like a linear phase FIR except that its peak is rotated to t=0. That can't be right for a number of reasons, not the least being that it becomes time dispersive which resistors aren't by definition. Bob -- "Things should be described as simply as possible, but no simpler." A. Einstein
Reply by ●May 23, 20052005-05-23
Bob Cain wrote:> > > Jerry Avins wrote:...>> For any device, V = IZ. For a capacitor, Z=1/jwC; for an inductor, >> Z=wL, and for a normal resistor, Z=R. It's easy enough to define a >> frequency-dependent resistor as, say, Z=wR. > > > Hmmm, how is that different than Z=wL? See the problem here?If Z=wL, L is a frequency-dependent resistor in disguise. In our familiar world, Z=jwL.> What would it's response be, for example, to a rectangular pulse given > that you know R(w)?To see the response, find the Fourier series of the pulse, divide the amplitude of each component by its relative frequency while leaving the phase intact, then sum the new series. An inductor would shift all the phases 90 degrees, delaying lower frequencies more than higher ones.> Is a transfer function with an R(w) linear, i.e. however the transfer > function is formulated are its eigenfunctions sinusoids?Yes.> What would the FFT be of the transfer function? It would seem that the > complex frequency domain definition would be entirely real with a > magnitude that is a function of frequency yet when you IFFT that you get > time sequence that looks like a linear phase FIR except that its peak is > rotated to t=0. That can't be right for a number of reasons, not the > least being that it becomes time dispersive which resistors aren't by > definition.So put the FFT in perspective, see my previous remark about the pulse shape. Dispersion is the result of characteristics that change with frequency. Normal resistors aren't dispersive, but they aren't frequency dependent either. Do you have reason to believe that frequency-dependent resistors can't be dispersive? Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
