about quality factor Q

i know the resonance frequency is a frequency that imaginary part of impedance is zero at that freaquency.

my question is:
consider a general resonance circuit( i mean, not just a simple parallel RLC);
does the impedance has a peak(max) at resonance freq?? and (if yes) why it must has a max at that freq? how you relate the "imaginary must be zoro" condition to "impedance is maximum" condition?

3 questions
thank you

In a series resonace circuit, the impedance is minimal at resonance. So as the general case, you have a local maximum or minimum of impedance.

Basically your adding susceptance (parallel resonance) respectively reactance (series resonance) amounts of opposite direction, they sum to zero in the resonance case, leaving the loss related real part of admittance respectively impedance.

In high speed digital circuit frankly speaking componnts having low Q factor has no place.

Fractional-N said:

i know the resonance frequency is a frequency that imaginary part of impedance is zero at that freaquency.
my question is:
consider a general resonance circuit( i mean, not just a simple parallel RLC);
does the impedance has a peak(max) at resonance freq?? and (if yes) why it must has a max at that freq? how you relate the "imaginary must be zoro" condition to "impedance is maximum" condition?

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You are asking for a "general resonance circuit" - not just "simple parallel RLC".
Well, the situation is not as easy as you probably think.
Sometimes its really surprising.
Example: Take C=100uF in series with 10 ohms and take L=100uH in series with 10 ohms. Then put both series connections in parallel. Now you have a LC parallel circuitry - both elements with some losses.
As a result - the impedance of the circuit exhibits a MINIMUM at some kHz. At this frequency the imaginary part and the phase shift is zero.

The example in fact shows that "general resonance circuit" is a dubious term, however I wouldn't regard a circuit Q of 0.05 as resonance, normally.

FvM said:

The example in fact shows that "general resonance circuit" is a dubious term, however I wouldn't regard a circuit Q of 0.05 as resonance, normally.

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Is there any lower Q limit for defining the state of resonance ?

Fractional-N,
The resonant frequency is the frequency at which the voltage and current are in phase. This is not necessarily the frequency at which the maximum impedance occurs. At the resonant frequency, the imaginary component of the impedance will be zero, but the magnitude of the impedance will not necessarily be maximum. A network consisting of an ideal inductor in parallel with an ideal capacitor has its peak impedance magnitude at its resonant frequency, but this condition is not true in most cases. Of course with a series resonant circuit, the only maxima are at frequencies of zero and infinity. In the circuit proposed by LvW, there is indeed a minimum that occurs at a frequency well below the resonant frequency and the frequency of maximum impedance.
Regards,
Kral

Kral said:

The resonant frequency is the frequency at which the voltage and current are in phase. This is not necessarily the frequency at which the maximum impedance occurs. At the resonant frequency, the imaginary component of the impedance will be zero, but the magnitude of the impedance will not necessarily be maximum.
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In the circuit proposed by LvW, there is indeed a minimum that occurs at a frequency well below the resonant frequency and the frequency of maximum impedance.
Regards,
Kral

Click to expand...

It is very easy to show that this minimum is not "well below the resonant frequency", instead it is identical to the resonant frequency as this is the only frequency with a real impedance.

Is there any lower Q limit for defining the state of resonance ?

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I think the term could be regarded ridiculous for a 0.05 Q. If you define resonance as cancellation of imaginary impedance component, it would be correct, but not meaningful in a technical sense. I prefer to reserve it for systems with less than aperiodical damping.

In general any circuit that has reactance can resonate at some frequencies. The resonance condition “sum of reactance is equal to zero” can occur in different part of electrical network and at different frequencies. When reactive part of impedance goes to minimum it does not mean that the total impedance goes to maximum. For parallel resonance (anti-resonance) impedance will be equal to the equivalent parallel resistance and will be maximal whereas for series resonance equivalent impedance will be equal to series resistance and will be minimal. There is variety of resonant circuits. The most simple of them are classified as resonant tanks of the 1st, 2nd and 3rd kind in electrical network theory. Even these simple circuits can have more than one resonance in the range of interest. Very often in RF and microwave analyses at least three resonances are considered and analyzed.
Regarding Q about 0.05 it is against the Q-factor definition. In this case we have power loss about 20 times higher than the total energy stored per one period. Definitely this is impossible.

My calculations show a minimum Z of approximately 7.5-j2.6 at a frequency of 57.3 KHz. This corresponds to a phase lag of approximately 19 degrees. I'll double check my calculations when I get a chance. In your reply, there is some undecipherable text “…is identical…”. Perhaps this is due to my browser.
Regards,
Kral

Added after 2 minutes:

This is in regards to FVM's post at 14:41

This is in regards to FVM's post at 14:41

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I'm not aware of.

Regarding Q about 0.05 it is against the Q-factor definition. In this case we have power loss about 20 times higher than the total energy stored per one period. Definitely this is impossible.

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I applied the Q definition usual in electronics Q = |Im(Z)|/|Re(Z)| to the proposed circuit (that has 1 ohm reactance and 20 ohm resistance):

Example: Take C=100uF in series with 10 ohms and take L=100uH in series with 10 ohms. Then put both series connections in parallel. Now you have a LC parallel circuitry - both elements with some losses.

Click to expand...

The problem is, that the circuit doesn't store energy for one period, cause it isn't oscillating at all. Thus I refused to regard it a resonant circuit. For circuits with usual Q values, both definitions have similar results.

Kral said:

My calculations show a minimum Z of approximately 7.5-j2.6 at a frequency of 57.3 KHz. This corresponds to a phase lag of approximately 19 degrees.

Click to expand...

Perhaps there is an error in your calculation ?
My results: Minimum of Z at Fo=1.593 kHz with Zmin=(L+R1*R2*C)/(R1+R2)*C=5.05 ohms and Zmax(w=0 and w=infinite)=10 ohms.

To FvM and RF-OM:
I agree that the classical definition of Q for the case under discussion is not meaningful. However, why should we call the state with IMG(Z)=0 not "resonance"?

Another remark: Don´t blindly trust any simulation program!!! I have simulated the circuit as described in my first reply with a current input of 1 A - and, therefore, the created voltage should be identical to the impedance. As a result, for ac analysis as well as for tran analysis a phase shift of 180 deg was displayed for the "resonant" frequency, which simply is not true. (This would be identical to a negative real resistance).