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February 20th 04, 10:37 PM

In article ,
(Diego Stutzer) writes:

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.

"Everyone" doesn't know that. You have the basic formula for
ADMITTANCE, not impedance. Let's clarify some terms first. The
admittance of a simple parallel R-C is more commonly written:

Y = (1 / R) + j (omega x C)

Whe Omega = 2 x pi x frequency in Hz, the whole quantity
often referred to as "radian frequency"

The "j" is used in electronics in place of the lower-case "i"
for the imaginary part of a complex quantity. Electronics
folks do that to avoid confusion with AC current normally
written as "i".

To find the impedance, take the COMPLEX INVERSE of admittance
to get impedance from the identity:

Z = 1 / Y = [ a / d ] - j [ b / d ] whe

a = real part b = imaginary part

d = denominator = a^2 + b^2 [sum of the squares]

For the final equation the impedance of the parallel R-C is:

a = (1 / R) b = (1 / (omega x C)) and

d = [R^2 + (omega x C)^2] / [omega^2 x R^2 x C^2]

or, in final form:

Z = [ (omega^2 x C^2 x R) / ( R^2 + (omega^2 x C^2)) ]

- j [ (omega x C x R^2) / (R^2 + (omega^2 x C^2)) ]

Like it or not, the above is what tens of thousands of electronikers work
with every day worldwide. Obviously one can do some approximations
for real-world applications where the errors are allowed to be kind of
gross, but that depends on the (unspecified) application.

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?

At very near DC, the impedance is governed by R since the reactance
of C is going to be so high that it becomes one with the dielectric
material all around.

The "rate of decrease" of impedance is governed by the value of C.
Graphed, it begins at pure R and then decreases at a slope
governed only by C..

Is there some kind of procedure like the one for syntesizeing LC-Filters
(Butterworth, Chebychev,..)?

First of all, the procedure should be to get the terms correct. From
there on, it is some grunt work with a scientific calculator.

Suggestion: For those who use an HP 32S II programmable with
long-term power-off storage of program and constants, I keep 2 x Pi
in constant storage in register T for handiness in getting radian
frequency values. A recall and multiply by frequency yields "omega"
which can be stored in register W. Easy to punch through the
numbers that way.

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.

Simply increasing C most definitely sets the higher frequency impedance.
There's nothing else in there in a two-component circuit that is frequency
sensitive...except for the Q or quality factor of the capacitor and lead
lengths of components. If one needs to get very fussy, there's always
a SPICE analysis where everything can be modeled, lead lengths, stray
capacity, everything.

Yes, modern network theory can make all kinds of impedance-varying
circuits with many parts and there are many, many textbooks on the
subject, all costing much money. In order to use all that material, one
has to know the difference between impedance and admittance and how
to convert from one to the other.

Len Anderson
retired (from regular hours) electronic engineer person

February 20th 04, 10:37 PM

In article ,
(Diego Stutzer) writes:

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.

"Everyone" doesn't know that. You have the basic formula for
ADMITTANCE, not impedance. Let's clarify some terms first. The
admittance of a simple parallel R-C is more commonly written:

Y = (1 / R) + j (omega x C)

Whe Omega = 2 x pi x frequency in Hz, the whole quantity
often referred to as "radian frequency"

The "j" is used in electronics in place of the lower-case "i"
for the imaginary part of a complex quantity. Electronics
folks do that to avoid confusion with AC current normally
written as "i".

To find the impedance, take the COMPLEX INVERSE of admittance
to get impedance from the identity:

Z = 1 / Y = [ a / d ] - j [ b / d ] whe

a = real part b = imaginary part

d = denominator = a^2 + b^2 [sum of the squares]

For the final equation the impedance of the parallel R-C is:

a = (1 / R) b = (1 / (omega x C)) and

d = [R^2 + (omega x C)^2] / [omega^2 x R^2 x C^2]

or, in final form:

Z = [ (omega^2 x C^2 x R) / ( R^2 + (omega^2 x C^2)) ]

- j [ (omega x C x R^2) / (R^2 + (omega^2 x C^2)) ]

Like it or not, the above is what tens of thousands of electronikers work
with every day worldwide. Obviously one can do some approximations
for real-world applications where the errors are allowed to be kind of
gross, but that depends on the (unspecified) application.

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?

At very near DC, the impedance is governed by R since the reactance
of C is going to be so high that it becomes one with the dielectric
material all around.

The "rate of decrease" of impedance is governed by the value of C.
Graphed, it begins at pure R and then decreases at a slope
governed only by C..

Is there some kind of procedure like the one for syntesizeing LC-Filters
(Butterworth, Chebychev,..)?

First of all, the procedure should be to get the terms correct. From
there on, it is some grunt work with a scientific calculator.

Suggestion: For those who use an HP 32S II programmable with
long-term power-off storage of program and constants, I keep 2 x Pi
in constant storage in register T for handiness in getting radian
frequency values. A recall and multiply by frequency yields "omega"
which can be stored in register W. Easy to punch through the
numbers that way.

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.

Simply increasing C most definitely sets the higher frequency impedance.
There's nothing else in there in a two-component circuit that is frequency
sensitive...except for the Q or quality factor of the capacitor and lead
lengths of components. If one needs to get very fussy, there's always
a SPICE analysis where everything can be modeled, lead lengths, stray
capacity, everything.

Yes, modern network theory can make all kinds of impedance-varying
circuits with many parts and there are many, many textbooks on the
subject, all costing much money. In order to use all that material, one
has to know the difference between impedance and admittance and how
to convert from one to the other.

Len Anderson
retired (from regular hours) electronic engineer person

February 20th 04, 10:53 PM

In article ,
(Diego Stutzer) writes:

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.

"Everyone" doesn't know that. You have the basic formula for
ADMITTANCE, not impedance. Let's clarify some terms first. The
admittance of a simple parallel R-C is more commonly written:

Y = (1 / R) + j (omega x C)

Whe Omega = 2 x pi x frequency in Hz, the whole quantity
often referred to as "radian frequency"

The "j" is used in electronics in place of the lower-case "i"
for the imaginary part of a complex quantity. Electronics
folks do that to avoid confusion with AC current normally
written as "i".

To find the impedance, take the COMPLEX INVERSE of admittance
to get impedance from the identity:

Z = 1 / Y = [ a / d ] - j [ b / d ] whe

a = real part b = imaginary part

d = denominator = a^2 + b^2 [sum of the squares]

For the final equation the impedance of the parallel R-C is:

a = (1 / R) b = (1 / (omega x C)) and

d = [R^2 + (omega x C)^2] / [omega^2 x R^2 x C^2]

or, in final form:

Z = [ (omega^2 x C^2 x R) / ( R^2 + (omega^2 x C^2)) ]

- j [ (omega x C x R^2) / (R^2 + (omega^2 x C^2)) ]

Like it or not, the above is what tens of thousands of electronikers work
with every day worldwide. Obviously one can do some approximations
for real-world applications where the errors are allowed to be kind of
gross, but that depends on the (unspecified) application.

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?

At very near DC, the impedance is governed by R since the reactance
of C is going to be so high that it becomes one with the dielectric
material all around.

The "rate of decrease" of impedance is governed by the value of C.
Graphed, it begins at pure R and then decreases at a slope
governed only by C..

Is there some kind of procedure like the one for syntesizeing LC-Filters
(Butterworth, Chebychev,..)?

First of all, the procedure should be to get the terms correct. From
there on, it is some grunt work with a scientific calculator.

Suggestion: For those who use an HP 32S II programmable with
long-term power-off storage of program and constants, I keep 2 x Pi
in constant storage in register T for handiness in getting radian
frequency values. A recall and multiply by frequency yields "omega"
which can be stored in register W. Easy to punch through the
numbers that way.

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.

Simply increasing C most definitely sets the higher frequency impedance.
There's nothing else in there in a two-component circuit that is frequency
sensitive...except for the Q or quality factor of the capacitor and lead
lengths of components. If one needs to get very fussy, there's always
a SPICE analysis where everything can be modeled, lead lengths, stray
capacity, everything.

Yes, modern network theory can make all kinds of impedance-varying
circuits with many parts and there are many, many textbooks on the
subject, all costing much money. In order to use all that material, one
has to know the difference between impedance and admittance and how
to convert from one to the other.

Len Anderson
retired (from regular hours) electronic engineer person

February 20th 04, 10:53 PM

In article ,
(Diego Stutzer) writes:

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.

"Everyone" doesn't know that. You have the basic formula for
ADMITTANCE, not impedance. Let's clarify some terms first. The
admittance of a simple parallel R-C is more commonly written:

Y = (1 / R) + j (omega x C)

Whe Omega = 2 x pi x frequency in Hz, the whole quantity
often referred to as "radian frequency"

The "j" is used in electronics in place of the lower-case "i"
for the imaginary part of a complex quantity. Electronics
folks do that to avoid confusion with AC current normally
written as "i".

To find the impedance, take the COMPLEX INVERSE of admittance
to get impedance from the identity:

Z = 1 / Y = [ a / d ] - j [ b / d ] whe

a = real part b = imaginary part

d = denominator = a^2 + b^2 [sum of the squares]

For the final equation the impedance of the parallel R-C is:

a = (1 / R) b = (1 / (omega x C)) and

d = [R^2 + (omega x C)^2] / [omega^2 x R^2 x C^2]

or, in final form:

Z = [ (omega^2 x C^2 x R) / ( R^2 + (omega^2 x C^2)) ]

- j [ (omega x C x R^2) / (R^2 + (omega^2 x C^2)) ]

Like it or not, the above is what tens of thousands of electronikers work
with every day worldwide. Obviously one can do some approximations
for real-world applications where the errors are allowed to be kind of
gross, but that depends on the (unspecified) application.

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?

At very near DC, the impedance is governed by R since the reactance
of C is going to be so high that it becomes one with the dielectric
material all around.

The "rate of decrease" of impedance is governed by the value of C.
Graphed, it begins at pure R and then decreases at a slope
governed only by C..

Is there some kind of procedure like the one for syntesizeing LC-Filters
(Butterworth, Chebychev,..)?

First of all, the procedure should be to get the terms correct. From
there on, it is some grunt work with a scientific calculator.

Suggestion: For those who use an HP 32S II programmable with
long-term power-off storage of program and constants, I keep 2 x Pi
in constant storage in register T for handiness in getting radian
frequency values. A recall and multiply by frequency yields "omega"
which can be stored in register W. Easy to punch through the
numbers that way.

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.

Simply increasing C most definitely sets the higher frequency impedance.
There's nothing else in there in a two-component circuit that is frequency
sensitive...except for the Q or quality factor of the capacitor and lead
lengths of components. If one needs to get very fussy, there's always
a SPICE analysis where everything can be modeled, lead lengths, stray
capacity, everything.

Yes, modern network theory can make all kinds of impedance-varying
circuits with many parts and there are many, many textbooks on the
subject, all costing much money. In order to use all that material, one
has to know the difference between impedance and admittance and how
to convert from one to the other.

Len Anderson
retired (from regular hours) electronic engineer person

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