Quality factor of inductor

Why is R=QLw ? I suppose R=Lw/Q ?

Need to distinguish parallel and series R...

@FvM : Thanks for your advice.

https://en.wikipedia.org/wiki/Q_factor#RLC_circuits
https://en.wikibooks.org/wiki/Circuit_Theory/RLC_Circuits#Quality_Factor

How do we know that bandwidth = 2*damping factor ?

promach said:

How do we know that bandwidth = 2*damping factor ?

Click to expand...

It is

bandwidth = 2*damping_factor * F₀

Click to expand...

F₀ is the resonant or center frequency

s. your above citation:

promach said:

https://en.wikipedia.org/wiki/Q_factor#RLC_circuits

Click to expand...

ζ = damping_ratio = damping_factor

There are two different R here

Series R (Rs) and Parallel R (Rp)



For Series R:

Rs= LW/Q

For Parallel R:

Rp=QLW

How you calculate Q for two component network, write this down somewhere:


Q= Imaginary (Z) / Real (Z) -----> For series

Q= Imaginary (Y) / Real (Y) -----> For parallel


In the example you mentioned it is talking about parallel R which is Rp

promach said:

@FvM : Thanks for your advice.

https://en.wikipedia.org/wiki/Q_factor#RLC_circuits
https://en.wikibooks.org/wiki/Circuit_Theory/RLC_Circuits#Quality_Factor

How do we know that bandwidth = 2*damping factor ?

Click to expand...

Don't look at the resonator math, because this is an inductor only, and we want to get the inductor Q. This is done by evaluating the impedance and interpret it as series RL. In this calculation, existing parasitics will be cause a frequency dependent L and frequency dependent R. Q factor is calculated from that L(f) and R(f).



Practical RFIC example with Q(f), L(f) and R(f):

Q= Imaginary (Z) / Real (Z) -----> For series

Q= Imaginary (Y) / Real (Y) -----> For parallel

Click to expand...

@Ata_sa16 Could you shed more lights on these two statements above ?

I have found a simple explanation but "inductor stores energy half the time and releases the energy the other half."


Extracted from https://physics.stackexchange.com/a/109749

promach said:

@Ata_sa16 Could you shed more lights on these two statements above ?

I have found a simple explanation but "inductor stores energy half the time and releases the energy the other half."

Extracted from https://physics.stackexchange.com/a/109749

Click to expand...

you have completely misunderstood the Q here. S=P+j*Q here Q is not the same Q
This Q is reactive power not quality factor.

Do you know complex power ? this is totally different topic.

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As I mentioned in previous post. For now just forget about VCO and start reading about fundamental concepts like:

1) What is Quality factor? why it is important ? what is it relationship with Loss and Noise.
2) Quality Factor in two component networks (R-L and R-C series and parallel)
3) Quality factor in RLC resonant circuit (It is not the same Q as two component network)

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Maybe this helps you

https://www.electrical4u.com/quality-factor-of-inductor-and-capacitor/

Then the maximum energy stored in the inductor is written in terms of current

For parallel R-L you may use similar approach but this time rewrite terms in terms of voltage you will reach my formulae

Q= Imaginary (Z) / Real (Z) -----> For series

Q= Imaginary (Y) / Real (Y) -----> For parallel

It is not really important and necessary to know where are they coming from all you need to know is 2 formulae I have provided

Thanks. https://www.electrical4u.com/quality-factor-of-inductor-and-capacitor/ helps a lot in understanding about the derivation.

However, back to my first post in this thread. 1.26kΩ and 630Ω do not really match the calculation that I made. Any idea how does the author arrives at these two values.

I dont understand what are you talking about. It is explained there

Rp=QLW=630 and gmRp>1

Rp=QLW = (10*1nH*10GHz) != 630

Do you know w=2*pi*f ??? 8-O

you put w=10 GHz !! :shock:

You need to learn/review fundamental concepts before designing VCO.

1.2K is Rp of 2 inductors, here for calculations we need half of the circuit. As it is written fig.8.18

You need to read the book carefully.

promach said:

Rp=QLW = (10*1nH*10GHz) != 630

Click to expand...

You forget 2*PI..
2*PI*10*10^9*2*10^-9=1256.637