Impedance at resonance (parallel)

New info, how's this, Z(tank)~=(2*pi*F*L)^2/(RL + RC)

Thanks, MikeK

[snip] [snip]

You need a proper understanding so you can simply derive the information you need ;-)

Where did you get your schooling, Tulane ?:-) ...Jim Thompson

-- | James E.Thompson, CTO | mens | | Analog Innovations, Inc. | et | | Analog/Mixed-Signal ASIC's and Discrete Systems | manus | | Phoenix, Arizona 85048 Skype: Contacts Only | | | Voice:(480)460-2350 Fax: Available upon request | Brass Rat | | E-mail Icon at

| 1962 |

I can see November from my house :-)

...Jim Thompson sci.electronic.design

Remember Jim, I'm the shrimp monger, That's not going well either :-( I don't know what's worse the BP thing or the Obama economy. MikeK PS, I want an approximation, I don't have the math skills to go into phase angle of each component and then combine them.

If Obama hadn't mucked with the BP situation, there'd be no significant Gulf issue.

Obama _could_ learn a lot from Sebastian Piñera, but Obama has no clue about leadership... what I've come to expect from Harvard grads :-)

Learn rudimentary Heaviside (Laplace) notation: L => Ls, C => 1/(Cs), R => R.

Then just do the arithmetic of series/parallel circuits. Then s => jw and s^2 => -w^2

(w = lower-case omega)

Is there an alt-num-pad combination for lower-case omega ?:-) ...Jim Thompson

--
| James E.Thompson, CTO                            |    mens     |
| Analog Innovations, Inc.                         |     et      |
| Analog/Mixed-Signal ASIC's and Discrete Systems  |    manus    |
| Phoenix, Arizona  85048    Skype: Contacts Only  |             |
| Voice:(480)460-2350  Fax: Available upon request |  Brass Rat  |
| E-mail Icon at http://www.analog-innovations.com |    1962     |

               I can see November from my house :-)

Modeling your circuit as:

A resistor Rc in series with a capacitor C A resistor RL in series with an inductor L

Those two branches in parallel.

It's not too hard to derive the total impedance of the parallel combination of the two R/C and R/L branches using the standard Laplace variable s. Then deriving the magnitude of the impedance expression with the imaginary quantity i having been eliminated, things get a little messier.

Finally, deriving an expression for the resonance frequency depends on one's definition of resonance. Two common definitions are:

Definition 1: The frequency where the magnitude of the impedance is a maximum.

Definition 2: The frequency where the impedance has zero phase angle (the imaginary part of the impedance is zero).

These two frequencies can be different if the Q of the inductor/capacitor is low, or if Rc is not equal to RL.

I've posted a derivation over on alt.binaries.schematics.electronic

This topic began while discussing piezo elements for headphones driven by a crystal radio, that moved to how high is the impedance of the tank that ultimately drives the headphones. So, I don't know which resonant point would be called tuned for a crystal radio, it may not matter if the two points are so close that the are within the 3db bandwidth. I have made some assumptions about a circuit. 240uh with a Q=800 or 1.884 ohms,

105pf with a Q=400 or 3.768 ohms, resonant frequency near 1Mhz. From my knowledge, Laplace is a french restuarant. I have added a post at alt.binaries.schematics.electronic with additional formula, but I think they are messier than what you posted. Thanks, MikeK

Over on abse, you said you didn't understand the difference between the impedance formula and the magnitude formula.

It has to do with the arithmetic used to analyze circuits that contain capacitance and inductance as well as resistance. Complex arithmetic is used to do the analysis:

The impedance of the circuit is expressed as a complex number, and complex numbers can be in either rectangular form or in polar form.

In rectangular form, the number is expressed as a real part plus an imaginary part. The imaginary part involves j.

In polar form, the number is expressed as a magnitude and a phase angle.

For example, the complex number 4+j3 is in rectangular form, but can also be expressed in polar form as 5

As I recall the capacitive loading of the piezo elements is a major factor when trying to use them as headphones for a crystal radio.

But then it has been decades since I have done anything with crystal radios.

T24gT2N0IDE1LCAzOjUywqBwbSwgSmltIFRob21wc29uIDxUby1FbWFpbC1Vc2UtVGhlLUVudmVs b3BlLUkuLi5AT24tTXktCldlYi1TaXRlLmNvbT4gd3JvdGU6Cgo+ICh3ID0gbG93ZXItY2FzZSBv bWVnYSkKPgo+IElzIHRoZXJlIGFuIGFsdC1udW0tcGFkIGNvbWJpbmF0aW9uIGZvciBsb3dlci1j YXNlIG9tZWdhID86LSkKCldlbGwsIG9wdGlvbi16IGdldHMgbWUgYW4gdXBwZXJjYXNlIM6pLCBi dXQgdG8gZ2V0IHRoZSBsb3dlcmNhc2Ugd2l0aAp0aGlzIG1hY2hpbmUgaXQgdGFrZXMgYSBzaGlm dCB0byBHcmVlayBrZXlib2FyZCwgYW5kICd2JyB0dXJucyB0byAnz4knLgoKzqTOt861IM+Ez4HO v864zrLOu861IM65z4MsIM+EzrfOsc+EIM6zz4HOtc61zrogzrHOu8+AzrfOsc6yzrXPhCDOuc+D IM69zr/PhCDOvM+FIM64z4POuM6xzrsgz4jOt86/zrnPiM61LgoKSXQncyBhIGRpZmZpY3VsdHks IHRoYXQncyBmb3Igc3VyZS4gICBJJ20gb24gYSBNYWNpbnRvc2gsIGlmIHRoYXQKbWF0dGVycy4u Lg==

I found the original headphone discussion on the link below although you will need to search through them, subject may be, sound powered headphones or piezo headphones or Brandes. After supper I might be able to post the thread.

I started a thread on sci.physics.acoustics that has some info to. subject; Building better high sensitivity headphones. Thanks, MikeK

Sad :-( ...Jim Thompson

--
| James E.Thompson, CTO                            |    mens     |
| Analog Innovations, Inc.                         |     et      |
| Analog/Mixed-Signal ASIC's and Discrete Systems  |    manus    |
| Phoenix, Arizona  85048    Skype: Contacts Only  |             |
| Voice:(480)460-2350  Fax: Available upon request |  Brass Rat  |
| E-mail Icon at http://www.analog-innovations.com |    1962     |

               I can see November from my house :-)

It's all...Greek ;)

Doesn't work very well on Usenet, which is 7 or 8 bit ASCII.

Tim

--
Deep Friar: a very philosophical monk.
Website: http://webpages.charter.net/dawill/tmoranwms

There is something strange with the message. The charset is declared as UTF-8, which is OK, but then the whole message it is encoded with base64.

Try sending the message as plain text either with charset=UTF-8 or IEC

8859-7.

You said you blew up a lossy capacitor.

With a crystal radio, how?

--
"For a successful technology, reality must take precedence 
over public relations, for nature cannot be fooled."
                                       (Richard Feynman)

I didn't say that. If someone did say that, I missed the post.

Local 50,000 watt station ;-)

That's your root problem. For the design you're doing you have a choice between a great big sea of rules that constantly change with application and that you can never trust, or you can learn how to deal with phasor arithmetic and be able to do the circuit calculations yourself.

Even if you're just doing work at a technician's level you should learn how to do arithmetic with complex numbers, and how to represent AC impedances with phasors. Do that, and you won't have to ask these questions one-by-one -- you can just do the math.

In your case, you have a series-parallel circuit:

o-------------.-----------------. | | | | .-. .-. | | Rc | |Rl | | | | '-' '-' | | | | | | --- C| --- C C| L | C| | | | | o-------------o-----------------' (created by AACircuit v1.28.6 beta 04/19/05

To do the AC analysis, you first calculate the phasor impedances of the cap and coil: Zc = Rc + 1/(j*w*C), Zl = Rl + j*w*L (w = your radian frequency, i.e. 2*pi*(frequency in Hz)).

Then you convert them to admittances, and add:

Ytot = 1/Zc + 1/Zl

Then you convert that back to and impedance:

Ztot = 1/Ytot.

Note that I'm too damn lazy to do this for you -- but if you know your complex arithmetic (hint: j = sqrt(-1)) then it is straightforward, if rather tedious. Furthermore, with the right math package (Scilab, WxMaxima, Matlab, Maple, Mathcad, etc.), you can make the computer do the work for you. Hand this to a symbolic math package and you'll even get a 'universal' symbolic result.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Do you need to implement control loops in software?
"Applied Control Theory for Embedded Systems" was written for you.
See details at http://www.wescottdesign.com/actfes/actfes.html

Yes, I know. MikeK

Damn me -- I forgot to mention.

Get a copy of the ARRL handbook, and look up "complex impedance" in the index -- I'm looking in my 1988 edition and they do a competent job of explaining it; the latest should do so, too.

The nice thing about the ARRL handbook is that it's laid out for folks who want to _do_, and _do now_ -- you get all this stuff in far more depth if you get an EE degree, but relating it to real life is left as an exercise for the student. The Handbook is much better at starting from real life then saying "and here's how you find your numbers", although it does rely on hand-waving a bit more than your average college course.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Do you need to implement control loops in software?
"Applied Control Theory for Embedded Systems" was written for you.
See details at http://www.wescottdesign.com/actfes/actfes.html

1999, Listed more obtusely:

"Impedance, Calculating 6.31"

But still looks good... even several pages on "resonance". ...Jim Thompson

--
| James E.Thompson, CTO                            |    mens     |
| Analog Innovations, Inc.                         |     et      |
| Analog/Mixed-Signal ASIC's and Discrete Systems  |    manus    |
| Phoenix, Arizona  85048    Skype: Contacts Only  |             |
| Voice:(480)460-2350  Fax: Available upon request |  Brass Rat  |
| E-mail Icon at http://www.analog-innovations.com |    1962     |

               I can see November from my house :-)