Isn't the the Q factor the ratio of resistance to inductance?

So a 100nH inductor with a resistance of 1mhm: has the same Q as a 1µH inductor with a resistance of 10mhm:.

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Coil resistance reduces the Q of a parallel resonant LC.
A capacitor with leakage resistance which is the same as a load resistance which also reduces the Q.

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Uncle $crooge

 

That's not correct. The Q of an inductor is the ratio of inductive reactance to its resistance at a particular frequency. The inductive reactance is equal to frequency x inductance x 2 x pi.
The resistance at high frequency is not the same as the DC resistance. It tends to be a lot higher due to skin effect and to material losses that increase with frequency.

A 100nH air-core coil made of reasonable sized wire might have a Q between 50 and 150 or thereabouts at 100MHz. The larger amount of wire needed to make a 1 uH inductor might increase the R as well and we often find that larger value inductors have worse Q than smaller ones. It is quite unusual to see Q values for a wire inductor higher than a couple of hundred and a value of 50 is pretty normal for a lot of air-core inductors at VHF frequencies, I think.

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RadioRon

 

Hi,
Another question. For LC tank circuit, usually I fix the L and use a trimmer cap to tune. Is it good to use larger L so that it won't be so sensitive when I tune it? For example 30 MHz:
A 12 pF trimmer with a 2.3 uH
A 33 pF trimmer with a 850 nH
which one is preffered? or both are the same?

EDIT: I have a 300 MHz crappy rf module that uses cmos oscillator as the modulating signal, doesn't the output of the cmos oscillator produce square wave? Can the square wave being modulated?

Thanks

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While it is true that both combinations will provide the same resonant frequency, there will be a difference. The Q of each combination will be different, partly because the reactance is different at resonance and partly because the resistance will be different in each of the two coils. The Q determines both the tank efficiency (which you want to be high) and the bandwidth (which you want to be low for an oscillator, but not so low for the output amplifier).

When using a 12pF trimmer, the highest capacitance will be 12pF and the lowest might be about 2 pF (guessing). In this case the tuning range would be from 30MHz to 74.2MHz. The other combination, using a 33 pF trimmer that has a minimum C of about, say, 4 pF, will tune from 30 MHz to 86.3 MHz. Similar result, but not the same. The lowest value that a variable cap can go to depends on the design of the capacitor and can vary widely.

To finally answer the question of which L value and which C value are the best, this is often determined by building the circuit and measuring performance and then altering the L and C values then remeasuing performance. This can be done over and over to find the best values. After many years of building similar circuits within one frequency range, engineers and amateurs have settled on a practical range of values vs frequency. You can see what they favor by studying examples of successful circuits in your frequency range.

Another way to start is by checking out what an inductor manufacturer recommends for, say, a 100MHz application. For example, Murata makes RF inductors. Their catalog has a selection tree that first asks you the question "above or below 100MHz". If you answer "above", then they recommend values only as high as 270nH. This implies that they don't think you should go above 270nH at 100MHz. That's a pretty good clue. Then, when I look at the characteristics for a 270nH SMT inductor (eg. LQW18A series), I can see that it has a minimum Q of 30 at 100MHz (which is not bad) and a self resonant frequency of 960 MHz, far enough away to not be a worry. So 270nH would work, but I would use a lower value, like 100nH, just based on my experience.

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RadioRon