# Inductor Sizing - .564615 uH for 97.7 MHz -- use in RCL tank ckt, 4.7 pF

#### au42

Joined Jan 24, 2017
8
I'm an junior electronics student working on a personal project.

I'm creating a number of "tank circuits," with a resonant frequency of 97.7 MHz. My capacitors will be of 4.7 microFarads and my inductors will be little over half of a microhenry, or .564615 uH.

Signal source is rated at 4100 ERP and I am trying to discern a couple of things:

1. How should I determine my inductor size -- I know how the equation and all that but I just need a light rundown of wth is really going on.

2. If I know the operating frequency of my signal source as well as the ERP, in addition to the other circuit values I have provided, how can I easily decide what type of voltage this will induce within two corresponding tank ckts within AT MOST 2 miles of the source.

I believe this entire post can be answered with mathematics and a little know-how beyond my current scope of realization. Perhaps a little basic electronics theory and some calculus. Which unfortunately I am without comprehension in regard to.

Thanks a lot and don't be afraid to ask questions back. I have a feeling I will be frequenting this forum often. I have been involved in the study of electrical science and electronics for a little over two years now and finally am nearing the pinnacle of my research.

Everything is gold.

Au42

#### Papabravo

Joined Feb 24, 2006
14,420
I'm guessing that you are unaware of the requirements of VHF circuits. Although you can purchase capacitors with the value you seek, they may not act very much like capacitors at 97.7 MHz. As for the inductor I would be surprised if you could construct a physically realizable one for that value with that level of precision. The resonant frequency of the pair is several orders of magnitude away from your frequency of interest.

Why don't you show us how you arrived at those values.

#### LesJones

Joined Jan 8, 2017
2,698
I assume you are using the term "ERP" to mean effective radiated power. You give numbers but not units so we have no idea how to start to answer your question. Also we need to work with power not ERP. Tell us what you think influences the relationship of these two values.

Les.

#### RayB

Joined Apr 3, 2011
9
If you have not played around with Falstad's online circuit simulator, you should give it a go ... easy to substitute values. Just remember at VHF/UHF frequencies simulators cannot take into account the issues around stray capacitance, etc.

#### au42

Joined Jan 24, 2017
8
Source is 4100 Watts
Signal is 97.7 MHz.

I am about 2 miles away.

Im trying to make a bandpass filter that peaks around 97.7. Which is so close to the middle of the FM band that this should be a relatively common inductor size.

I have been waiting a long time to start this project and clearly I have no idea where to start still. It's very simple. Just a dipole receiver hooked to hz to dc converter created using tank circuits.

I dont know how to figure out what kind of readings I should get before I actually prototype it. I'm overlooking some common formulas that would help me draft this system, I'm sure of it...just dont know what Im overlooking.

Ideally I want to make a 50V 250W power system with a charge bank but sizing these inductors has always kept me from moving forward. I know there are limitations to how much stable potential I can achieve just not sure how to discern that.

If someone could explain the err of my ways and set me on the straight and narrow it would be kindly appreciated.

#### au42

Joined Jan 24, 2017
8
I use EveryCircuit but have not simulated this circuit yet.

I have a lot of useful knowledge of electronics amd electrical but hardly any practical experience beyond school amd my work bench.

#### Alec_t

Joined Sep 17, 2013
11,649
Are you trying to harvest energy from the 4kW source?
At a distance of 2 miles the field strength won't be high enough to harvest much. Based on the calculations here, it will be about 0.1V/m.

#### au42

Joined Jan 24, 2017
8
I'm guessing that you are unaware of the requirements of VHF circuits. Although you can purchase capacitors with the value you seek, they may not act very much like capacitors at 97.7 MHz. As for the inductor I would be surprised if you could construct a physically realizable one for that value with that level of precision. The resonant frequency of the pair is several orders of magnitude away from your frequency of interest.

Why don't you show us how you arrived at those values.
I used a resonant frequencu calculator.

Basically I dont know how to manipulate the resonant frequency formula. I can only figure out frequency...not sure how to find missing inductance if I know capacitance and frequency or vice versa. That would be a big help if I knew how to use the equation in the same way Ohms law is used.

I generally use the pyramid scheme to help remember the relationships in simple equations like Q=CV or P=IV or V=IR etc...cant so that so simply with resonant frequency formula.

#### au42

Joined Jan 24, 2017
8
Are you trying to harvest energy from the 4kW source?
At a distance of 2 miles the field strength won't be high enough to harvest much. Based on the calculations here, it will be about 0.1V/m.
You're the guy I want to talk to.

Okay.

So what if I make my coils all bifilar and add a SSG style subckt...could that be useful.

#### Papabravo

Joined Feb 24, 2006
14,420
I used a resonant frequencu calculator.

Basically I dont know how to manipulate the resonant frequency formula. I can only figure out frequency...not sure how to find missing inductance if I know capacitance and frequency or vice versa. That would be a big help if I knew how to use the equation in the same way Ohms law is used.

I generally use the pyramid scheme to help remember the relationships in simple equations like Q=CV or P=IV or V=IR etc...cant so that so simply with resonant frequency formula.
It is just algebra

$$f\;=\;\frac{1}{2\pi\sqrt{LC}}$$
$$\sqrt{LC}\;=\;\frac{1}{2\pi f}$$
$${LC}\;=\;\left(\frac{1}{2\pi f}\right)^2$$
$${L}\;=\;\frac{1}{C}\left(\frac{1}{2\pi f}\right)^2$$
Also
$${C}\;=\;\frac{1}{L}\left(\frac{1}{2\pi f}\right)^2$$

For 4.7 μF and 97.7 MHz, I get L ≈ .56 picohenries

I told you in my first post post that this value would technically impossible to realize unless you could do a microstripline design on a PC board. To measure this value accurately you would need an instrument that costs as much as a medium size house in Northern Florida

What you want to do is just not feasible.

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#### Alec_t

Joined Sep 17, 2013
11,649
So what if I make my coils all bifilar and add a SSG style subckt...could that be useful.
I don't see how that would improve things. You can't magically increase the tiny amount of energy available. Is energy harvesting your goal?

#### BR-549

Joined Sep 22, 2013
4,938

#### au42

Joined Jan 24, 2017
8
Yes.

4100 Watts is not that much at all. There are further sources with much higher wattage. They broadcast at around 50-100kW and vary in position along the radial circumference of a unit circle 50 miles in diameter; 25 mile radius.

As far as I know the formula for resonant frequency or Fr is .159/sqrt(LC)

I've taken this to also mean:

1/2Pi(LC)

Or more simply:

1/Tau(LC)

I am trying to build a switchable, passive voltage collector that is optimized for several common frequency bands. FM/AM; CB; WiFi, blah blah....

It may have a rechargeable Li-Ion but that will be charged with voltage collection as well, perhaps a combination of solar, electrostatic, and RF. Of course the option to charge with an external Vs will be available. Plans to use PiZero for charge control and some level of embedded software, albeit it emulated. There should also be a needle gauge to help the user see if they are optimally tuned for the band they have selected, in the area they are receiving from. I have had most of the parts to build this stupid thing for a while now...just haven't mustered up the know-how to whip it out.

I am very handy with DC electronics and I love RF, magnetics and the like. Basically every area of electronics interests me except the Internet of Things. I mostly just care about transduction and energy harvesting in my personal endeavors though and I'm sort of at a loss since its not my main school of practice. More of a muse. Currently working on ETA-I CETa with specialty in RFID though...so I'm about to figure it out I guess.

Took an RFID class last year in college. Lot has happened since then...and as some of you might know. Industry RFID is not so much physics as it is supply chain management and service technicians.

#### au42

Joined Jan 24, 2017
8
It is just algebra

$$f\;=\;\frac{1}{2\pi\sqrt{LC}}$$
$$\sqrt{LC}\;=\;\frac{1}{2\pi f}$$
$${LC}\;=\;\left(\frac{1}{2\pi f}\right)^2$$
$${L}\;=\;\frac{1}{C}\left(\frac{1}{2\pi f}\right)^2$$
Also
$${C}\;=\;\frac{1}{L}\left(\frac{1}{2\pi f}\right)^2$$

For 4.7 μF and 97.7 MHz, I get L ≈ .56 picohenries

I told you in my first post post that this value would technically impossible to realize unless you could do a microstripline design on a PC board. To measure this value accurately you would need an instrument that costs as much as a medium size house in Northern Florida

What you want to do is just not feasible.

#### au42

Joined Jan 24, 2017
8
I have access to two Epilog laser engravers and a few other neat toys including 3d printers, CNC router, plasma cutter and potentially a couple others.

#### Alec_t

Joined Sep 17, 2013
11,649
And how would they be useful for energy harvesting ?
Do the maths and you will discover how little energy from man-made sources there is in the EM fields around you. If there were a lot your FM radio would be glowing red hot. Is it worth the effort to harvest enough to make a LED glow dimly?

#### Papabravo

Joined Feb 24, 2006
14,420
I use the TeX feature of the forum because it makes the algebra clearer. On the Laser engraver, good for you, but how does that help with algebra and an understanding of basic physics?

#### bertus

Joined Apr 5, 2008
20,771
Hello,

I think there is a contradiction between the tilte and your openings post.
The title says you are using a 4.7 pF capacitor, but i the openings post you are mentioning a 4.7 microF capacitor.
Wich are you actualy trying to use?
In your openings post you have calculated a 564 nH coil.
This should be not a great problem to make.
Have a look at the following page about aircoils: