I'm having a bit of a difficult time with analyzing this circut:
http://www.dvanhorn.org/TankCkt.gif

This is an oscillator tank, where C2 and L2 are parallel resonant.
The operating frequency is around 280kHz, with C2 at 3300pF and L2 at 98uH.
The interesting part is where I add L1 at about 40mH and Cg at 0-1pF with
Ctrim at some small but significant value. (ideally, series resonant at
about 290 kHz, but you have to take parasitics into account)

What I'm trying to do, is to determine the oscillating frequency as Cg
changes, and also to evaluate different values of L1 as the series resonance
of L1/Ctrim+Cg moves around the tank resonance. Obviously if the two
resonances collide, it's not nice.

I'm having a hard time finding how to express the change in Cg as a shift in
the resonant point of the oscillator tank.

The formulas that I have for impedance show only the magnitude of the
impedance, and probably aren't applicable to this situation. Where can I
find a better approach for analysis?

Once I have this down, I have to consider the parasitics and series
resistance, especially in L1 which are pretty significant, but I have a
handle on how to apply that.


--
A: Because it messes up the order in which people normally read text.
Q: Why is top-posting such a bad thing?
A: Top-posting.
Q: What is the most annoying thing on usenet?

"Dave VanHorn" wrote in message
...

I'm having a bit of a difficult time with analyzing this circut:
http://www.dvanhorn.org/TankCkt.gif

This is an oscillator tank, where C2 and L2 are parallel resonant.
The operating frequency is around 280kHz, with C2 at 3300pF and L2 at
98uH.
The interesting part is where I add L1 at about 40mH and Cg at 0-1pF with
Ctrim at some small but significant value. (ideally, series resonant at
about 290 kHz, but you have to take parasitics into account)

What I'm trying to do, is to determine the oscillating frequency as Cg
changes, and also to evaluate different values of L1 as the series
resonance
of L1/Ctrim+Cg moves around the tank resonance. Obviously if the two
resonances collide, it's not nice.

I'm having a hard time finding how to express the change in Cg as a shift
in
the resonant point of the oscillator tank.

The formulas that I have for impedance show only the magnitude of the
impedance, and probably aren't applicable to this situation. Where can I
find a better approach for analysis?

Once I have this down, I have to consider the parasitics and series
resistance, especially in L1 which are pretty significant, but I have a
handle on how to apply that.


It might help if you told what you are ultimately trying to do.
Is this just a thought experiment designed to help you learn something?
Is it a circuit you have/see and are trying to understand it?
That antenna is an unknowns, as well, which I guess you are ignoring...?
From what I see/read, you are trying to do something which is very
awkward...that is, multiple coupled resonances.

Looks like you want to see what kind of "pulling" effect the Delta Cg is
going to have on your oscillator. Why inductive coupling?
The conditions which determine the frequency of oscillation are not confined
to the resonant frequency of your tank, but include phase and gain of the
active device as well.

I modeled a 1 MHz Colpitts in PSpice and it oscillated nicely. Adding other
stuff to muck about with it could be done...

--
Steve N, K,9;d, c. i My email has no u's.

On Thu, 12 Aug 2004 19:34:28 -0500, "Dave VanHorn"
wrote:

I have yet to see a formula for the capacitance of a
rod in space.

Hi Dave,

That is not particularly hard if you have mathematical software like
Mathcad. You simply do it "by parts." That is reduce the cylinder to
a sheet 1mm tall and figure its surface area (pi · D · mm²). This
will be a constant value. Iterate that value over succeedingly remote
distances from an infinite conducting plane. Add up all the
iterations. (This is simply the integral of the capacitance formula
for dz where z varies from an initial separation to a value equal to
the height - 1mm.) For capacitors, capacitance is always described by
the smallest plate so this is an accurate first pass approximation.

For instance (forgive the mix of units) a 1" thick rod, 9.4M tall,
standing 10mm off of ground presents a 0Hz capacitance of 5pF. You
could move it closer to ground (1mm) and raise this to 7pF, or you
could lop off 8 meters and lower it to 3pF (not much variation).

However (and this is one of those points so ill-treated in this group)
you cannot treat this capacitance as an equivalent capacitor for RF.
The real component is much too big and this violates the first
principles of Kirchhoff's requirements that physical dimensions must
be extremely short with comparison to wavelength. The last time this
one got wrapped around the axle was over the issue of lumped
impedances.

The antenna may present any complex value of reactance to its
terminals, including capacitances that belie this simple first pass
analysis above. This, I doubt, is something that SPICE is
sophisticated enough to deal with, as it also expects all lumped
components and circuits to exist within very small dimensions relative
to the wavelengths being supported.

Time to break out that XXth century museum piece, the Smith Chart.

73's
Richard Clark, KB7QHC

On Thu, 12 Aug 2004 21:13:33 -0500, "Dave VanHorn"
wrote:

Well, it's certainly not going to work with the flat plate close spacing
model.

Later, I want to look at the effects that happen if the cylinder isn't
circular, when the hand is very close, as opposed to say 10's of diameters
away. I do think that carving it into pieces might get to a pretty good
approximation ala FEA.

Hi Dave,

Shape will probably have very little to do with it. If anything, the
computation by parts reveals that the last 90% of the rod is more or
less superfluous to the total value (at least for my example).

Time to break out that XXth century museum piece, the Smith Chart.

Hmm.. I just picked up a smith chart implementation in mathcad.

Post me that file, would you?

73's
Richard Clark, KB7QHC

Hmm.. I just picked up a smith chart implementation in mathcad.

Post me that file, would you?

http://www.circuitsage.com/matching.html

Look down just a bit.

Shape will probably have very little to do with it. If anything, the
computation by parts reveals that the last 90% of the rod is more or
less superfluous to the total value (at least for my example).

Trying actual hardware, the last 1/8 inch is very significant, shifting the
oscillator several hundred Hz.