## LC circuit - how to choose L and C?

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Hi all,

I know the formula F = 1 / (2 pi sqrt (LC))... that's not what I'm asking. "Theoretically" any L and C can plug into the equation and work numerically, but how to choose PRACTICAL values for L and C?

If I have a desired frequency (such as 100 MHz.), how do I choose a practical value for L and C?

All I can come up with in my mind is to choose an arbitrary reactive impedance and solve for L and C to have the same impedance. Say, 100 "ohms" for L and for C, but there must be a "correct" way to do it, right?

Info will be appreciated!

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Last Edited: Mon. Apr 26, 2021 - 12:42 AM

What is this L C circuit to be used for?

jim

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Is this a signal or a 3 amp circuit?

Inductors & capacitors have current limitations

Inductors are often uH or sometimes mH for larger ones (for high current amps they can get very large if mH)

Take a look at some on Digikey to see their size.

Caps, such as ceramic are good at almost any freq.  Electrolytics, are pretty crappy, especially when getting into higher MHz

At the very least you need to say the freq & current range needed.   If 100MHz, then try 10 nH & 253 pF (use 220pF)   ---both very reasonable values.   When you get down to a few pF , stray effects will rapidly increase, such as holding your hand close by, or  board capacitance--so avoid being less than 22 pf or so (more is better)...or maybe 22nH & 115 pF (use 100 pF).  Your scope probe is loaded with some pf, so it will affect (throw off, detune) a lower board value a lot more than a higher board value.

When in the dark remember-the future looks brighter than ever.   I look forward to being able to predict the future!

Last Edited: Mon. Apr 26, 2021 - 02:36 AM

Krupski wrote:

"Theoretically" any L and C can plug into the equation and work numerically, but how to choose PRACTICAL values for L and C?

The problem is that no inductor or capacitor behaves anything like the theory says. A real-world inductor also has capacitance and resistance. A real world capacitor also has some resistance and, depending on its type, it's capacitance will vary with the applied voltage. Two real-world inductors placed near each other will make a (poor) transformer.

So you need to start by choosing the 'type' of inductor or capacitor first, look at the range of values you can get for the chosen type, and then see what values fit your spec.

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avrcandies wrote:

Is this a signal or a 3 amp circuit?

Inductors & capacitors have current limitations

Inductors are often uH or sometimes mH for larger ones (for high current amps they can get very large if mH)

Take a look at some on Digikey to see their size.

Caps, such as ceramic are good at almost any freq.  Electrolytics, are pretty crappy, especially when getting into higher MHz

At the very least you need to say the freq & current range needed.   If 100MHz, then try 10 nH & 253 pF (use 220pF)   ---both very reasonable values.   When you get down to a few pF , stray effects will rapidly increase, such as holding your hand close by, or  board capacitance--so avoid being less than 22 pf or so (more is better)...or maybe 22nH & 115 pF (use 100 pF).  Your scope probe is loaded with some pf, so it will affect (throw off, detune) a lower board value a lot more than a higher board value.

It's not a power circuit. It's an oscillator which will be followed by a power (50 mW or so) stage. The point of my question is that for a given frequency, I could plug a 1 pF cap and 1H coil into the formula and get a result, but of course that combo is rediculous. Same with 1 uF and 1 uH.

That is, for a given frequency a coil and capacitor value range from "way too small" to "just right" to "way too large" and I want to know how to find the "Goldilocks" value. Make sense?

(edit to add): Where did you get the values "10 nH and 253 pF" that you posted? Why not, say, a larger value cap and smaller coil? Or, vice-versa? Those values "sound" reasonable, but how did you come up with THOSE values?

Gentlemen may prefer Blondes, but Real Men prefer Redheads!

Last Edited: Mon. Apr 26, 2021 - 08:41 AM

jgmdesign wrote:

What is this L C circuit to be used for?

jim

See previous post.

Gentlemen may prefer Blondes, but Real Men prefer Redheads!

Krupski wrote:
It's an oscillator

So what oscillator circuit (topology) are you using?

What frequency?

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Those values "sound" reasonable, but how did you come up with THOSE values?

I'm not sure what you mean--you answered the question already

Those values "sound" reasonable

If they didn't sound reasonable, I'd come up with some ones that did!!

Are you not using a list of standard  L  & C values?   Do you have a decent calculator?

When in the dark remember-the future looks brighter than ever.   I look forward to being able to predict the future!

Krupski wrote:
It's an oscillator which will be followed by a power (50 mW or so) stage.

Getting to know what "feels right" takes some time and experience, so start by looking at what other engineers have used is similar circuits operating in the range of frequencies you want to build your circuit using.

One possible source for this is reference books such as "The Art of Electronics", the "ARRL Handbook", to name a couple.  Learning to read schematics of known working circuits will be a handy skill.

A good engineering library will be useful, I know that is old school, but it works.

Good luck!

Jim

FF = PI > S.E.T

ki0bk wrote:

Getting to know what "feels right" takes some time and experience, so start by looking at what other engineers have used is similar circuits operating in the range of frequencies you want to build your circuit using.

So you're saying that there is no set way to determine "good" values for L and C?

Gentlemen may prefer Blondes, but Real Men prefer Redheads!

avrcandies wrote:

Those values "sound" reasonable, but how did you come up with THOSE values?

I'm not sure what you mean--you answered the question already

Those values "sound" reasonable

If they didn't sound reasonable, I'd come up with some ones that did!!

Are you not using a list of standard  L  & C values?   Do you have a decent calculator?

"Standard list of values"?

As far as a "decent calculator", it doesn't take much to take the square root of LC, multiply by 2 PI, then reciprocal it.

I think:

1. There is no way to determine OPTIMAL L and C values for a resonant circuit -- or --
2. I am not explaining what I am looking for clearly enough.

Gentlemen may prefer Blondes, but Real Men prefer Redheads!

Krupski wrote:

1. There is no way to determine OPTIMAL L and C values for a resonant circuit -- or --

You are going about it wrong. The application will determine the type of L or C: their construction. Each type will only cover a certain range of values so this constrains the values you can choose.

For example, this is an inductor for use with audio...

...and this is one for RF...

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Krupski wrote:
So you're saying that there is no set way to determine "good" values for L and C?

No, I said look what others have used, that will guide you to proper values for your circuit! i.e. spend some time in the library looking at real circuits and the values they used.

Books, magazines, published circuits, patent filings, radio kits, etc....

Over time you will know what makes sense.

To become a "good" engineer will require much work, there are no short cuts!

Good luck with your studies.

Jim

FF = PI > S.E.T

Last Edited: Mon. Apr 26, 2021 - 01:38 PM

Krupski wrote:
I am not explaining what I am looking for clearly enough.

That one.

You still haven't said what type of oscillator circuit (ie, what topology) you're using, or what frequency. That will have an influence on what values are "suitable".

Is it a fixed or variable frequency?

There's also the question of Q ...

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Last Edited: Mon. Apr 26, 2021 - 02:11 PM

ki0bk wrote:

Krupski wrote:
So you're saying that there is no set way to determine "good" values for L and C?

No, I said look what others have used, that will guide you to proper values for your circuit! i.e. spend some time in the library looking at real circuits and the values they used.

Books, magazines, published circuits, patent filings, radio kits, etc....

Over time you will know what makes sense.

To become a "good" engineer will require much work, there are no short cuts!

Good luck with your studies.

Jim

LOL! I've been an EE for over 40 years. But, I guess I still have more to learn!

Gentlemen may prefer Blondes, but Real Men prefer Redheads!

Krupski wrote:
LOL! I've been an EE for over 40 years. But, I guess I still have more to learn!

ME too!

FF = PI > S.E.T

awneil wrote:

Krupski wrote:
I am not explaining what I am looking for clearly enough.

That one.

You still haven't said what type of oscillator circuit (ie, what topology) you're using, or what frequency. That will have an influence on what values are "suitable".

Is it a fixed or variable frequency?

There's also the question of Q ...

I don't think the type of oscillator is relevant. 1/2π√LC does not ask what type of oscillator is used. Indeed, the circuit can be series resonant, parallel resonant, a tuned input stage, a tuned output stage, an oscillator tank, etc... and they all use the same formula.

Gentlemen may prefer Blondes, but Real Men prefer Redheads!

Krupski wrote:
1/2π√LC does not ask what type of oscillator is used.

Of course it doesn't - it assumes ideal components!

you wrote:
I know the formula F = 1 / (2 pi sqrt (LC))... that's not what I'm asking. "Theoretically" any L and C can plug into the equation and work numerically, but how to choose PRACTICAL values for L and C?

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ki0bk wrote:
"The Art of Electronics"

The Art of Electronics 3rd Edition | by Horowitz and Hill

[page 20, top of left column]

APPENDIX E: LC Butterworth Filters 1109

E.1 Lowpass filter 1109

E.2 Highpass filter 1109

E.3 Filter examples 1109

"Dare to be naïve." - Buckminster Fuller

ki0bk wrote:
, the "ARRL Handbook"

https://www.arrl.org/shop/ARRL-H...

FF = PI > S.E.T

There really is very little to go on for oscillator tank circuits. It depends strongly on the oscillator and also on the frequency.

My general ballpark mental estimator uses the reactance of the individual elements (the C and the L). I shoot for a few thousand ohms (impedance magnitude) below a few MHz and taper that to a few hundred ohms up to 100MHz or so. I have never read that this is right, it just "feels" right to me.

Now, there are OTHER factors that may be more significant than impedance. For example, is this going to  be tunable? If so, then you have to look at what variable components are available, their value range, and the required tuning range. Another factor is the likely circuit stray impedances. Yet another is the signal amplitude at the tank; the reactance will set the circulating current in the tank at resonance and that goes up with signal amplitude.

Jim

Until Black Lives Matter, we do not have "All Lives Matter"!

There is no way to determine OPTIMAL L and C

Too many ways to define:

lowest cost?

smallest size?

highest stability?

get parts the quickest?

temperature rating?

matched impedance?

best tasting?

...that's why they pay you the big bucks!!

When in the dark remember-the future looks brighter than ever.   I look forward to being able to predict the future!

Krupski wrote:

As far as a "decent calculator", it doesn't take much to take the square root of LC, multiply by 2 PI, then reciprocal it.

I think:

1. There is no way to determine OPTIMAL L and C values for a resonant circuit -- or --
2. I am not explaining what I am looking for clearly enough.

If you consider only C and L, you are correct, there are many possible solutions.

However, if you want a resonant circuit you also need to worry about Q and that means the R matters.

Once you add R, or physics adds it for you :), the 'practical' range of values reduces. Simple web search can help limit the possible, to practical.

Krupski wrote:

If I have a desired frequency (such as 100 MHz.), how do I choose a practical value for L and C?

All I can come up with in my mind is to choose an arbitrary reactive impedance and solve for L and C to have the same impedance. Say, 100 "ohms" for L and for C, but there must be a "correct" way to do it, right?

Physics can again come to your aid, and Spice is a very useful tool for checking the range of possible values.

If you pick 100MHz, you can range-limit Capacitance fairly quickly, Stray C on PCBs and wiring etc are in the low pF region, so you want that to be insignificant. That means C above 10pF

You also want HiQ C, and higher precision C, with good temperature stability. Such precise, NPO caps quickly thin-out over about 1nF

Now you have a range that excludes femto-farads and micro-farads, even tho the formula itself allows 'any-value'.

Next, try searching inductor on Digikey - here we look at what you can buy, to start to constrain the practical values.

All inductors have a Self Resonant frequency, which DK lists.

For example 100MHz resonance, you want a SRF well above 100MHz, and you want a Q not too poor, so let's pick >= 22

DK then shows up to Q=285 is possible, nothing greater than that lists.

If we ask for Q >=40 and tolerance of 1% 2% 3% the choices drop to  3.6nH to 1uH

If you decide Q is very important and constrain to values above 100, you have just 6 Q choices and just 18 parts. They range from 5.45nH to 28nH

Notice here, the choice of what you can buy Practical L is much more constrained

If we select the 28nH & 100MHz, a Web calculator gives 0.000090465 µF  so 90pF yields Resonant Frequency (f) = 100.258190321 MHz

So we now look for 90pF and find the nearest preferred values at 82pF and 91pF,  so you might choose 82pF and target 8pF of stray layout capacitance, or parallel 2 caps.

If we constrain C to be High Q and low ESR/ESL, and ask for 1% tolerance, the in-stock choices drop to 19, in sizes of 0402~0805+.  Prices vary from 9c/1k to \$4.67/1k

Now you have L and C, you can enter the parasitic R/C/L parts into Spice and check the second order effects to select which of those C's is 'good enough'

Maybe that \$4.67/1k cap has some feature you really must pay that much for :)    ( I see it is tagged Porcelain Superchip® ATC 100B 500V)

One suggestion is:  Go shopping.  Find out what's for sale, and at what cost (they didn't teach me that in school.  They should have).

If your design calls for a 1MF capacitor (yes, one megaFarad) you will soon find out that it's the size of an Army duffel bag and costs more than your car.  A megaHenry inductor might be the size and cost of a nice house.  Contrariwise, a 10megaOhm resistor costs exactly the same as a 10ohm one.

As pointed out before, a lot of other stuff intrudes into the design phase.  Too much current, and your inductor will saturate and not filter anymore.  Too much voltage, and your capacitor will explode and not filter anymore (as well as a puff of smoke and a bad smell).  &c.  There's more to circuit design than putting numbers into a formula!   S.

Last Edited: Tue. Apr 27, 2021 - 01:09 AM

Who-me has excellent and important points. They are what "design" is all about.

In aeons past, there was huge emphasis on "Hi-C" vs "Low-C" oscillator tank circuits. That was all about stability and component size but typically for frequencies below 10MHz or so. That was when 30MHz was really high frequency spelled "30Mc" and caps had values of 100uuf (100 micro-micro farads = 100pf). That is no longer the issue. Now, it is Q and temperature coefficient and what you can purchase with a reasonable number of coins of the realm.

Jim

Until Black Lives Matter, we do not have "All Lives Matter"!

avrcandies wrote:
Too many ways to define:

lowest cost?

smallest size?

highest stability?

get parts the quickest?

temperature rating?

matched impedance?

best tasting?

Absolutely!

Coincidentally, this just appeared on my Twiter:

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+1 on Who Me's answer!

One more real world factor to consider, (unfortunately):

The parts that are listed as available today, (DigiKey, Mouser, etc.), may not be available in a few weeks!

(That can be a big disappointment / hassle.  You found what you rthink you are going to use, and continue the design, and when it comes time to order parts from your Bill of Materials it is no longer available!)

Another factor is that if you will be using an RF chip as part of the design, (Osc, Mixer, Amp, etc.), the data sheet itself may have a table listing some example (or preferred) values, and even part numbers, for which the circuit has been tested and validated.

There are an incredible number of RF chips available these days from Analog Devices and others.

If you are building your circuit from scratch then that won't help.

JC

Edit: Typo

Last Edited: Wed. Apr 28, 2021 - 05:39 PM

DocJC wrote:
... and when it comes time to order parts from your Bill of Materials it is no longer available!)
Can periodically run the BOM though distributors' tools to identify parts that have gone long lead-time or out-of-stock.

Or, a parts list that's parts with a known low risk (risk = probability of failure * consequence of failure, failure in this case is long lead-time)

Or, order multiple trays or reels such that production will continue for "a while"; a relative few lead times exceed one year.

DocJC wrote:
If you are building your circuit from scratch then that won't help.
"Try" to design with what's next to your bench (easier said than done); periodically inventory your bench's stock.

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"Dare to be naïve." - Buckminster Fuller

Maybe we should step  back a moment and summarize some of the points made:

1. There is likely no "optimum". More likely is a range of "reasonable".

2. The reasonable values do depend on the operating frequency.

3. Values do depend on whether it is fixed or tuned frequency. And, if tuned, what range is needed. This, in turn, strongly depends on the tuning component(s) and what is available.

4. There are a host of secondary factors that range from component availability and cost to a bunch of other things including size, operating voltage levels, temperature stability, phase noise, and such.

5. If there is a "start up" requirement (time required to reach stable operation), that can effect the value choice.

The point of this list is that there really are too many factors at play when it comes to choosing "optimum" values. As a result, most designers rely pretty heavily on experience (well, these values worked for those conditions last time, and that condition is only slightly different, so ... ). Lacking experience, it is very common to fall back on application notes, schematics of things that are similar to what you need, magazine articles and blog postings, spice simulations (using realistic component models including stray impedances), and such.

Less obvious is that RF is still something that has an "art" factor to it. Experimentation is a Good Thing. It is an area where you can learn useful things through careful observation. And, you can actually have fun with it!

Jim

Until Black Lives Matter, we do not have "All Lives Matter"!

ka7ehk wrote:
And, you can actually have fun with it!

++

FF = PI > S.E.T

That doesn't even include getting your own core (toroidal or other shape) & winding your own!!   That was done a lot more in the past (pre-surface mount), nowadays there is a seaload of choices.

So winding your own is more relegated to transformers, mutil tap cools, etc.....even those are becoming plentiful.

The government will soon be banning resistors from all circuits and any PCB assemblies containing more than 5 IC's.  The green movement is afoot.  No more components that continually sap our energy & turn it into wasteful heat.

Licensing to purchase resistors will allow those who need them to still be able to.  100W resistors will be completely out of the question.

When in the dark remember-the future looks brighter than ever.   I look forward to being able to predict the future!

I Am Scroungre Of Borg.  We have room-temperature superconductors.  Resistance Is Futile.  S.

/ Slightly off topic...

That doesn't even include getting your own core (toroidal or other shape) & winding your own!!

Who in their right mind would be crazy enough to do that?

JC

Who in their right mind would be crazy enough to do that?

Someone still lies to experiment!  That's where knowledge comes from.  Otherwise there'd be no flux capacitor

When in the dark remember-the future looks brighter than ever.   I look forward to being able to predict the future!

avrcandies wrote:

Who in their right mind would be crazy enough to do that?

Someone still lies to experiment!  That's where knowledge comes from.  Otherwise there'd be no flux capacitor

Really, Honey, I was winding a coil!  I wasn't anywhere near seeing what the capacity of that blonde from the electric company's oscillation frequency was!

S.