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**posted on**

- Phil Newman

February 19, 2007, 1:50 pm

Hi there,

In a filter I've designed, I have a series LC with additional

reactance, X, which gives a transmission zero in the filter.

How can I absorb the reactance into either the L or the C or both?

In a simple series LC, the reactance of the product at resonant

frequency is 0, so

jX (reactance) = jwL - j/wC = 0

from which you get

w^2 = 1/LC

however, with the additional reactance (which is frequency invariant -

i.e constant)

jX = X + jwL - j/wC = 0

the value of X, w, L and C are known.

I'm not entirely sure where i'm supposed to go with this though!

the value of reactance/susceptance in the series arm is -0.865

the value of inductance is 5.406H (this is normalised to one radian)

the value of capacitance is 0.18F (again normalised)

resonance is measured at 0.7130/1.404 (normalised, it's a band-pass

filter)

If you can help me make sense of this apparently easier algebra in

which i'm missing something, that would be great!

Phil

Re: absorbing reactance into series LC

On a sunny day (19 Feb 2007 05:50:53 -0800) it happened "Phil Newman"

If your X is frequency invariant then it is a resistor.

If you have L C R in series (where R can be the resistance of the L),

then in resonance you will see R (real).

R also sets the Q factor of your series circuit, so its bandwidth.

http://en.wikipedia.org/wiki/RLC_circuit

Re: absorbing reactance into series LC

On Mon, 19 Feb 2007 19:44:32 GMT, Jan Panteltje

---

At resonance there'll be an infinitely deep notch, so it'll short

the output of the generator and you'll get the bandstop function

At resonance there'll be an infinitely deep notch, so it'll short

the output of the generator and you'll get the bandstop function

We've slightly trimmed the long signature. Click to see the full one.

Re: absorbing reactance into series LC

This is another bandpass: (View in Courier)

+--------+--------+

| | |

| +--+--+ |

| | | |

[GEN] [L] [C] [R]

| | | |

| +--+--+ |

| | |

+--------+--------+

This is another bandstop:

+--[L]--+

| |

+---+ +---+

| | | |

| +--[C]--+ |

[GEN] [R]

| |

+---------------+

Cheers!

Rich

Re: absorbing reactance into series LC

To drop the res freq you increase the inductance and/or capacitance.

Increasing resistance increases the bandwidth not the resonant

(center) frequency. Reactance is XL=2

***pi***F

***L, XC=1/(2***pi

***F***C), so

changing the reactance requires change L, C, or F.

Re: absorbing reactance into series LC

L),

just a

Yes. But ... It's not the size of that resistor that's the problem, it's

knowing where to put it!.

As example, for a parallel tuned circuit we always go ...

Fres=1/2

***pi***root (L/C). Fine, no problem!.

It's not correct. The true formula is ...

Fres=1/2

***pi***root(1/L*C-R^2/L^2). [a ballache to use so we don't]

But ... look how that coil resistance "R" has slimed itself in and

ingratiated itself with the resonant frequency. (only rears it's head at

very very low Q values ). That "R" can become big enough to noticeably

poison the reactive effect of the inductor and drop the Fres.

Idle thought could suggest maybe it's not unreasonable that a series tuned

circuit, which is a kind of inversion of a parallel one, might for a similar

reason also suffer an "R" caused resonant frequency shift. I.e same lousy Q

and lower Fres.

In this case (as you note), the "R" can have no Fres effect if in series

with the inductor, so maybe it needs to go in ... with the ... :)

(Dragged out I know but I'm constantly surprised at the number of ways a few

RCL components can be put together yet offer distinct features)

john

--

Re: absorbing reactance into series LC

Thanks, how can I do this? my network theory isn't great.

basically, I've been using the equation Lw^2 + Xw + 1/C to find the

resonant frequency, and then using w^2 = 1/LC to calculate the new

values of L or C.

This works in terms of shifting the resonant frequency, but in terms

of the whole circuit really doesn't work very well.

How can I do these norton transforms?

Phil

Re: absorbing reactance into series LC

If I have a series LC (in a one-ohm circuit, everything normalised)

then S21 is resonates at w = 1 radian, and had magnitude of 0dB at w =

1. S11 has magnitude of -infinite dB (or -80dB as ADS doesn't

interpolate that far!)

If i put in my frequency invariant susceptance/reactance which isn't a

resistor, it is just constant reactance, then this shifts the resonant

freqency from w = 1 to w = 1.15 (eg)

S21 still resonates at a level of 0dB and S11 and -infinite dB.

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