L vs C tradeoff in a tank circuit

Discussion in 'Wireless & RF Design' started by WBahn, Jun 25, 2012.

  1. WBahn

    Thread Starter Moderator

    Mar 31, 2012
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    As some know, I am interested in getting into RF over the next few months and years and I'm still only at the stage of dabling on the side while I wrap up some other projects. So I'm playing with the math on paper and not actually playing with anything in hardware (I know myself too well and I can't afford the hours that it would suck out of me right now).

    I really want to understand the stuff and so am working from the basics and not taking anything for granted.

    My question here has to do with designing and LC tank circuit, say for an oscillator or an antenna or a filter. Leaving aside parasitics for the moment, since it is the product of L and C that count, what are the practical considerations that lead to choosing the specific values for each (i.e., how much L vs how much C)? The only thing I can think of is to choose as small an L as you can so as to minimize the parasitic resistance in an attempt to increase the Q. What other factors, either theoretical or hand-on practical, go into making the tradeoff decision?
     
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  2. K7GUH

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    The availability of parts, either store bought or homebrew manufactured, and the contents of your junk box. If you have an 88 mh toroid coil (common in mil surplus two generations ago) it is no big deal to find a capacitor in the range for an audio oscillator at about 3 KHz.
     
  3. t_n_k

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    Yes I recollect in the old days one might make a simple radio set using a scavenged air vane multi-plate tuning capacitor. The capacitance range might be typically 10-415pF. So this then had significant influence on the inductor value required to [say] tune across the AM band.

    I guess 'Q' factor is an important consideration - also at higher frequencies skin effect and parasitic capcitance begin to play an increasingly significant role. I think I recollect once seeing [as a trainee tech] a silver plated air wound RF tank inductor on an FM transmitter rig.

    One probably wouldn't use an inductor with a self resonant frequency lower than the required operating RF frequency.

    For higher power applications [such as RF induction heaters] one might consider using water cooled copper tubing for the resonant inductance component.

    I'm not really up to date on modern industry practice on this matter. At microwave frequencies even interconnecting conductors become a problem to be dealt with - looking rather more like transmission lines.
     
  4. WBahn

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    For my initial forays into this world, I want to play in the AM and then FM broadcast bands. Once I gain a level of comfort and some proficiency with a lot of things there, then I would like to move up to the ISM bands progressively. I would like to eventually have some ability to tinker with at least the 2.4GHz band.

    So for now I am thinking in terms of oscillators and filters in the 500kHz to 3MHz ranges.

    So is it safe to say that, aside from the parasitics and the issues they bring to the table, that it truly, even in the practical world, doesn't matter how the LC is split? It just strikes me as hard to imagine that I would expect very similar performance from a 88mH inductor with a 0.3pF capacitor as from a 88nH inductor and a 300nF capacitor.

    Wait a minute. I wouldn't expect the same performance, would I? Since the Q is proportional to L or to 1/C, I would want the largest L and the smallest C I can manage (keeping in mind that large L brings larger R), right?

    So, what are common inductor sizes when working in the 1MHz region?
     
    Last edited: Jun 26, 2012
  5. #12

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    You are in fantasy land as far as I'm concerned but I would say one of your examples went a little too far. You mentioned .3pf
    I wish the lower limit on a chosen capacitor was, "large enough that parasitic capacitance becomes insignificant". However, I don't think that is possible. It seems that people that play with RF, regularly deal with parasitics being significant. How about, "The capacitor should be at least 10 times the capacitance of the parasitics"? It would be nice if you could always achieve that.
     
  6. WBahn

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    Why the hell do you think I'm asking the damn question!

    I specifically mentioned more than once that I realize that parasitics are critical and that the intent was to set those aside for the moment to get at an understanding of the tradeoffs involving just the nominal values. If I don't have those down, what hope is there of dealing properly with the issues presented by the parasitics?

    The values given were meant to cover an extreme range. At the time I posed that I was under the impression that (again, let me say this clearly, in an ideal case in which parasitics do not exist) that it appeared that it didn't matter how that LC product was obtained, that the circuit performance would be the same. Just as I finished writing it, it dawned on me that the Q equation was not in terms of LC and, a little closer look showed that it is in terms of L/C which means that your choice of component values is dictated (again, let me say this clearly, in an ideal case in which parasitics do not exist) by the desired center frequency and the desired Q. In the case of a circuit in which you want the highest Q you can get, you would want to maximize L and minimize C. But I realize, as stated several times, that parasitics play a limiting and sometimes even dominant part, which is why I asked what inductor sizes were commonly used in the specific frequency range I am interested in to start with. It would also be nice to hear what factors are driving those choices: parasitics associated with the inductor, parasitics associated with the capacitor, size, cost, weight, etc., etc.
     
  7. #12

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    Unfortunately, it is all magic to me. That's what I meant when I said you were in fantasyland. I will try to be more careful when exchanging hypotheticals in the future.
     
  8. WBahn

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    My apologies.

    This is one of those examples of something written in text that is so easy to read two completely different ways. I thought you were saying that I, specifically, was in fantasy land because I was talking about ideal components and ignoring parasitics. Now, knowing what you meant, I can easily see how those exact same words can be interpretted the way you meant them. It's not even so much a matter of a tone of voice or emphasizing certain words, but just the matter of the length of a pause between two words. Perhaps a comma after 'concerned' would have had be pause long enough to read it the way you intended, but I far from sure.

    You would think I would have learned by now (which, by and large, I think I have) to read messages that I am taking objection to a few different ways to see if there isn't a more sedate way of reading it.
     
  9. KL7AJ

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    I've spent decades designing R.F. circuits and twiddling tank circuits. Where the tradeoff in L/C ratio comes into play (or confusion) is the difference between loaded and unloaded Q. IF you redraw the circuit using two resistors, one INTERNAL to the circulating current, and one in parallel with the tank circuit, the difference becomes very clear. You want the INTERNAL resistance as low as possible...this never does you any good. The EXTERNAL (parallel) resistance determines your loaded Q, and this is your desired resistance. Think of the INTERNAL resistance and the EXTERNAL resistance as forming a voltage divider, and the confusion all goes away. :)

    Eric
     
  10. WBahn

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    No, the confusion was that I had developed a mental block where I was thinking that, on paper, it was always the product LC that mattered. But as soon as I looked closely enough to see that Q is not dependent on LC but, rather, L/C, then that removed the confusion. You have two variables, L and C, and two goals, center frequency and Q. So you don't have any broad choices. Now, in practice, it may not be a matter of the Q you want so much as the Q you can get, but the tradeoff is clear.

    As for internal versus loaded Q, I definitely see and agree that the loaded Q is the one that counts since, after all, I am interested in the circuit working properly when it is under load. But that begs the question -- does unloaded Q have any significance (other than if it is something that can characterize the circuit in such a way that the loaded Q can be readily determined by knowing the unloaded Q and the load)?
     
  11. KL7AJ

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    Yes the unloaded Q has everything to do with circuit efficiency!

    Eric
     
  12. WBahn

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    Okay. I guess I can qualitatively see how that might be. I'm certainly not anywhere near the point of seeing it intuitively, and probably won't be for some time. But thanks for pointing it out so that I can be on the lookout.
     
  13. KL7AJ

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    This is actually quite easy to model in SPICE. For a typical R.F. tank circuit in the H.F. range a single ohm of internal resistance can DRASTICALLY reduce the efficiency.

    Just calculate the circulating current in a Pi network of a simple 1KW amateur linear amplifier, with a typical Q of 25! (Use a source impedance of 2 Kilohms and a load impedance of 50, for a first approximation)

    You'll be shocked and amazed at what this circuit has to accomplish!

    Eric
     
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