[EE] What's up with this one wierd trick?

[David Van Horn]

I've been having a debate on resonance.

Assume a frequency of 1 MHz, and L value of 200uH, just because.
ZL = 1256 ohms, so we end up with a C of 127pF (close enough)

Now I'm told that to find the "best" values, I should take these values and calculate Sqrt (LC) and use that value for the inductor and capacitor.

When I pull the Sqrt of (L*C) the result is in time. 159nS in this case.
I start to feel like we're doing something sketchy here, but I plug in 159uH and 159pF and I get another resonant pair at 1MHz with ZL or Zc = 1k.

Running a couple of different examples, it seems I always end up with 1k Impedances.

Is this wierd trick legit?

The question I was trying to get to, is how to find the "optimum" LC pair for a resonant tank circuit used as an antenna.
Ignoring parasitics for a moment, in broadcast radios one sees 365pF variable caps a lot of the time. That would work out to 278uH at 500kHz
Sqrt LC here gives me 318.5nS, so I then sub 318 in as L and C numerics, and I get another resonant pair at 1k ohm.

[David Van Horn]

Here's my Smath file showing what happens.

Start off with 126.6uH and 200pF for resonance at 1MHz.
Then take the Sqrt of LC, which gives 0.1591uS.
Plug 159.1 in as the L and C values, in microhenries and picofarads.
And you get a nice resonant pair at 1k ohm.

But why does it work, given that it seems dimensionally bogus?
Why is 1k impedance "magic".. Is it even "magic"
Is this whole approach bogus?


--
http://www.piclist.com/techref/piclist PIC/SX FAQ & list archive View/change your membership options at http://mailman.mit.edu/mailman/listinfo/piclist

[Mike]

R=SQRT(10^-6/10^-12) = 1000

The result is simply down to the ratio of the capacitor (pF) and
inductor (uH) values, and since all your solutions end up with L=C*10^6
you always end up with the end same impedance.

Post by David Van Horn
Here's my Smath file showing what happens.
Start off with 126.6uH and 200pF for resonance at 1MHz.
Then take the Sqrt of LC, which gives 0.1591uS.
Plug 159.1 in as the L and C values, in microhenries and picofarads.
And you get a nice resonant pair at 1k ohm.
But why does it work, given that it seems dimensionally bogus?
Why is 1k impedance "magic".. Is it even "magic"
Is this whole approach bogus?
--
http://www.piclist.com/techref/piclist PIC/SX FAQ & list archive View/change your membership options at http://mailman.mit.edu/mailman/listinfo/piclist

[Dave Tweed]

Post by David Van Horn
Now I'm told that to find the "best" values, I should take these values and
calculate Sqrt (LC) and use that value for the inductor and capacitor.
When I pull the Sqrt of (L*C) the result is in time. 159nS in this case.
I start to feel like we're doing something sketchy here, but I plug in 159uH
and 159pF and I get another resonant pair at 1MHz with ZL or Zc = 1k.
Running a couple of different examples, it seems I always end up with 1k Impedances.
Is this wierd trick legit?

No.

The "wierd trick" is simply based on the fact that you chose an L value that
is 1,000,000 times larger than the C value. The square root of that ratio is
1000.

If you had instead *followed instructions* and used 159 nH and 159 nF, you
would have gotten impedances of 1 ohm for both.

And if you keep going, 159 pH and 159 uF gives you 0.001 ohms.

There is no "best" set of values, except as determined by other constraints
such as manufacturability.

-- Dave Tweed

[David Van Horn]

Yeah, I sort of figured when Smath told me sqrt(LC)= time.

For general tank circuits I agree, but tank circuits used as antennas may act differently, especially inside the evanescent field area.


-----Original Message-----
From: piclist-***@mit.edu <piclist-***@mit.edu> On Behalf Of Dave Tweed
Sent: Monday, October 22, 2018 2:16 PM
To: ***@mit.edu
Subject: Re: [EE] What's up with this one wierd trick?

Post by David Van Horn
Now I'm told that to find the "best" values, I should take these
values and calculate Sqrt (LC) and use that value for the inductor and capacitor.
When I pull the Sqrt of (L*C) the result is in time. 159nS in this case.
I start to feel like we're doing something sketchy here, but I plug in
159uH and 159pF and I get another resonant pair at 1MHz with ZL or Zc = 1k.
Running a couple of different examples, it seems I always end up with 1k Impedances.
Is this wierd trick legit?

No.

The "wierd trick" is simply based on the fact that you chose an L value that is 1,000,000 times larger than the C value. The square root of that ratio is 1000.

If you had instead *followed instructions* and used 159 nH and 159 nF, you would have gotten impedances of 1 ohm for both.

And if you keep going, 159 pH and 159 uF gives you 0.001 ohms.

There is no "best" set of values, except as determined by other constraints such as manufacturability.

-- Dave Tweed
--
http://www.piclist.com/techref/piclist PIC/SX FAQ & list archive View/change your membership options at http://mailman.mit.edu/mailman/listinfo/piclist

[s***@interlog.com]

Post by Dave Tweed

Post by David Van Horn
Now I'm told that to find the "best" values, I should take these values and
calculate Sqrt (LC) and use that value for the inductor and capacitor.
When I pull the Sqrt of (L*C) the result is in time. 159nS in this case.
I start to feel like we're doing something sketchy here, but I plug in 159uH
and 159pF and I get another resonant pair at 1MHz with ZL or Zc = 1k.
Running a couple of different examples, it seems I always end up with 1k Impedances.
Is this wierd trick legit?

No.
The "wierd trick" is simply based on the fact that you chose an L value that
is 1,000,000 times larger than the C value. The square root of that ratio is
1000.
If you had instead *followed instructions* and used 159 nH and 159 nF, you
would have gotten impedances of 1 ohm for both.
And if you keep going, 159 pH and 159 uF gives you 0.001 ohms.
There is no "best" set of values, except as determined by other constraints
such as manufacturability.
-- Dave Tweed

One such constraint is the parasitics in the parts.

The Q will be affected by the non-ideal nature of the components, usually the
inductor is dominant there.

For a series RLC circuit Q = (1/R)*sqrt(L/C).


The higher the series resistance of the inductor the lower the Q. And there is
the self-resonant frequency of the inductor.

I'm not clear where that rule of thumb comes from- it does seem "reasonable"
in real world situations but it may not be optimum in any mathematical sense.
Or maybe I'm missing something there.

--sp

[Brooke Clarke]

Hi David:

Here's some info on choosing the optimum L & C for a loop antenna.
https://prc68.com/I/Loop.shtml

As the Q gets higher the bandwidth gets narrower leading to better s/n ratios.  BUT . . . .
very high Q circuits become sensitive to things like temperature and so may tune themselves to a frequency that excludes
the desired signal.
Another consideration is the input impedance of the circuit you are connecting to.
--
Have Fun,

Brooke Clarke
https://www.PRC68.com
https://www.end2partygovernment.com/2012Issues.html
axioms:
1. The extent to which you can fix or improve something will be limited by how well you understand how it works.
2. Everybody, with no exceptions, holds false beliefs.

-------- Original Message --------

RE: [EE] What's up with this one wierd trick?