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JRE
JRE
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How can one Value Describevalue describe the Impedanceimpedance of a Groupgroup of Reactive Componentsreactive components at all Frequenciesfrequencies?

enter image description here

The author of the textbook containing this circuit states that the filter input and output impedance is given by:

Z = (L/C)^1/2

He then shows that by setting the source and load impedance to this value (316 ohms), we can "flatten" the frequency response of this filter.

Before impedance matching  after impedance matching

But thisThis leaves me with three questions:

  1. Why does impedance matching flatten the response?
  2. Where does this input / output impedance equation come from?
  3. Why doesn't the equation account for frequency, since the reactance of capacitors and inductors varies with frequency?

Thanks for your time.

Also, before it is pointed out, I know this is the second post about a really simple circuit. But, theseThese three questions are new and I have not been able to answer them on my own, despite a lot of time invested.

How can one Value Describe the Impedance of a Group of Reactive Components at all Frequencies?

enter image description here

The author of the textbook containing this circuit states that the filter input and output impedance is given by:

Z = (L/C)^1/2

He then shows that by setting the source and load impedance to this value (316 ohms), we can "flatten" the frequency response of this filter.

Before impedance matchingafter impedance matching

But this leaves me with three questions:

  1. Why does impedance matching flatten the response?
  2. Where does this input / output impedance equation come from?
  3. Why doesn't the equation account for frequency, since the reactance of capacitors and inductors varies with frequency?

Thanks for your time.

Also, before it is pointed out, I know this is the second post about a really simple circuit. But, these three questions are new and I have not been able to answer them on my own, despite a lot of time invested.

How can one value describe the impedance of a group of reactive components at all frequencies?

enter image description here

The author of the textbook containing this circuit states that the filter input and output impedance is given by:

Z = (L/C)^1/2

He then shows that by setting the source and load impedance to this value (316 ohms), we can "flatten" the frequency response of this filter.

Before impedance matching  after impedance matching

This leaves me with three questions:

  1. Why does impedance matching flatten the response?
  2. Where does this input / output impedance equation come from?
  3. Why doesn't the equation account for frequency, since the reactance of capacitors and inductors varies with frequency?

Also, before it is pointed out, I know this is the second post about a really simple circuit. These three questions are new and I have not been able to answer them on my own, despite a lot of time invested.

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solenoids are cool
solenoids are cool
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How can one Value Describe the Impedance of a Group of Reactive Components at all Frequencies?

enter image description here

The author of the textbook containing this circuit states that the filter input and output impedance is given by:

Z = (L/C)^1/2

He then shows that by setting the source and load impedance to this value (316 ohms), we can "flatten" the frequency response of this filter.

Before impedance matchingafter impedance matching

But this leaves me with three questions:

  1. Why does impedance matching flatten the response?
  2. Where does this input / output impedance equation come from?
  3. Why doesn't the equation account for frequency, since the reactance of capacitors and inductors varies with frequency?

Thanks for your time.

Also, before it is pointed out, I know this is the second post about a really simple circuit. But, these three questions are new and I have not been able to answer them on my own, despite a lot of time invested.