RadioBanter - Tank circuits: achieving maximum Q

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In article , Paul Burridge
writes:

On Sun, 21 Mar 2004 16:02:18 GMT, "W3JDR" wrote:

Airy,
What you said would be relevant only if you were trying to determine circuit
losses due to "unloaded" Q of the components. I believe Paul is trying to
determine the 'loaded" Q in order to obtain best selectivity (narrowest
bandwidth). Is this true Paul?

Some clarification is necessary!
The application is the tank in a frequency multiplier.
I am seeking to select for the 5th harmonic. Therefore, the tank needs
to have as little loss as possible given the fact that the 5th will be
way down dB-wise on the fundamental. I can't afford to attenuate it
too much as it's already weak to begin with. Ergo, I need the lowest
loss components and the best selectivity for the desired 5th harmonic.
Thanks,

Design of that is a two-step process. First, you need to establish
the impedance (or admittance) of both source and load. For a
parallel-resonant circuit selectivity device, they are both in parallel
with the unloaded Q of the resonant circuit. For a series-resonant
selectivity device, they are in series with it.

With vacuum tube and FET circuits, staying in the linear I/O bias
region, the first step is easy. Just parallel drain or plate resistance
and a gate or grid circuit resistance for a parallel-resonant circuit.
With bipolar transistors, the base resistance is quite low compared
to tube (valve) and gate inputs, must be impedance-magnitude
adjusted such as with tapping down on an inductor. There are
several other ways to do impedance-magnitude adjustment; that
coil tap is a very common one.

Once into a non-linear operation region the overall impedances
become dynamic rather than static and depend on drive level and
the amount of time an input spends in non-linear region versus the
linear region. Using digital logic devices means that the non-linear
regions are above saturation and below cutoff but the saturation
does not behave the same as with valve grid current run positive
on part of the cycle. That is NOT easy to calculate and quite
complex for those who take the time to do that.

For home workshop design efforts in getting to the task in the
most expeditious way, simply Cut And Try. Reg Edwards
pointed that out semi-directly. :-)

The second step is to select and inductor with, for your needs
in being selective to that elusive 5th harmonic, of the highest Q_u
(unloaded or "not in-circuit" quality factor) that will fit in the space
(physical space) you've alloted. That selection is a compromise
in size - cylindrical or "solenoid" cores mean (as Reg said) the
bigger the better. I'll also add "the bigger the wire diameter, the
higher the Q" for the same coil former size. For iron powder
toroid forms, the powder mix is important as well as the size as
well as the wire size.

Just from memory of a few years ago, a Micrometals T37-6 core
(the "37" meaning 0.37 or 3/8ths inch, powder mix 6) will yield a
Q_u of 80 minimum at 18 MHz using the largest wire that will fit
through the center hole. Q_u at 17 MHz will be very close to that.

Unloaded Q is a result of many factors and all of those can be
modified by things such as the dielectric material of a solenoidal
former and the presence of adjacent shielding and even dielectric
material. For the easiest application and less time worrying nit-
picky details, pick an iron powder core toroidal form...such can
be smaller than cylindrical formers allow and are much more
forgiving of adjacent/nearby objects. But only if space is at a
premium. Small toroidal forms can be difficult to wind for some
and multi-turn inductors need lots of wire which can build up in
the center hole, precluding use of larger magnet wire diameters.

Part of the second step is to combine what you know (or guess)
in the first step with a selection of inductance and capacitance
for resonance. As others have said, inductive Q_u is the
determining factor at HF and capacitive Q_u will be at least 10
times higher, probably in the neighborhood of 500 to 1000 for
ceramic or mica capacitors. Do a quick model of the resonant
circuit "resistance" (actually the magnitude of impedance) at
parallel resonance - parallel the (inductive Q_u times inductive
reactance) and the (capacitive Q_u times the same reactance
since capacitive reactance is equal to inductive reactance at
resonance). Parallel that with the source and load impedance
magnitude combined magnitude and you have the total magnitude
at resonance. This can be very quick to do with a scientific
pocket calculator.

To verify the selectivity, run the whole thing again at adjacent
harmonics to get the total magnitude of impedance there. Those
off-resonance L-C circuit magnitudes can use just the reactance
as an approximate step and be very close to those using the
unloaded L-C Qs. The ratio of magnitudes on-resonance versus
off-resonance will give you a picture of the selectivity possible.

If that "doesn't seem to be good," THEN pick a different L:C
ratio and do it again...but use what you know about the inductive
Q_u at that different inductance. Compare the new on-resonance
impedance magnitude to the adjacent off-resonance magnitudes.
Is that magnitude ratio worse than before? If so use an opposite
L:C ratio. If better, try the same-direction different L:C ratio and
compare that. If better, repeat. If worse, hold on the previous
L-C combination...you are zeroing-in on what is useful.

SELECTIVITY is the thing desired in your application and the
relatively-simple calculation of magnitudes and resulting ratios
will point in the right direction for something to try in hardware.
Selectivity is needed because the lower harmonics have more
energy than the 5th.

If stumped for a starting L and C value, try the literature on
previous multiplier designs as a starting point...then dance
through this two-step procedure.

In practical hardware, many others besides myself have been
led astray by simplistic "L:C ratio Q determination rules" that
can be just the reverse. Lots of those old maxims were
generated way back in time of large "coils and condensers"
one needed both hands to pick up...

Len Anderson
retired (from regular hours) electronic engineer person

In article , Paul Burridge
writes:

On 22 Mar 2004 01:46:20 GMT, (Avery Fineman)
wrote:

[snip]

Phew! Thanks, Len. There's rather more to these ''simple inductors"
than meets the eye, it seems. :(

Yes, but it probably took longer to write the procedure out than
to actually do it. :-)

As a _starting_ procedure, work with magnitudes of impedance,
or the square-root of the sums of the squares of resistance and
reactance. That's easy enough on a conventional "four-function"
pocket calculator that has the added square-root function.

For a single resonant circuit you should be interested in the ratio
of magnitude at desired frequency to the magnitudes at the
undesired frequency. The bigger the ratio, the better selectivity.

If you want to investigate toroidal coils (for their smaller size), you
can find Q curves at - http://www.amidoncorp.com. Those look
exactly like the Q curves in my Micrometals Q Curve subsection
of their (surface mail only) catalog. Under one of the links at the
top right you will get a rather long html page with over a dozen
curves on it representing over a half dozen typical inductors per
graph over a wide frequency range. Save that page if you can,
it is good for reference later.

www.micrometals.com seems to be down on Monday, probably
for website revision; haven't heard any rumors that Micrometals
went out of business. Micrometals has foreign (to the USA)
distributors and sales reps so I was hoping to show some of
those in or near the UK.

For cylindrical coil shapes, Reg Edwards program is about as
good as it gets to save wear and tear on pencil and paper.

Len Anderson
retired (from regular hours) electronic engineer person.

Of course, maybe you don't need such a high Q, Paul. Qu of 30 is
quite reasonable for small SMT RF inductors, at least the type I use.
In the following list, "series" means in series from the gate output
to the next gate input, in order, and "shunt" means shunt to ground at
that point. Anyway, try this (build it or SPICE it or RFSim99
it...add resistors to any simulation to account for the Qu. I'd
suggest 3 ohms series and 12k ohms shunt for each 1.8uH.)

47pF series
1.8uH series
470pF shunt
45pF series
1.8uH shunt
3.3pF series
40pF shunt
1.8uH shunt
DC blocking cap series
high-value DC bias resistors, and the gate input (I assumed to be
about 4k net resistance to ground at the gate input, including the
bias resistors).

It should give you enough voltage gain at 18MHz to drive the second
gate at the fifth harmonic, and should attenuate the third at least
50dB if you build it properly, even with low-ish Qu inductors. This
is rather a "hack" circuit, but works. The premise is that it's
easier to get three inductors all the same value than muck about
tuning the inductors. Make the 47pF, 45pF and 40pF caps variable and
you can peak up the response at your desired frequency. Your
simulation should show a reasonably flat bandpass characteristic,
centered at about 18MHz.

Paul Burridge wrote in message . ..
Hi guys,

ISTR that one can improve Q in resonant tanks by having a low L-C
ratio. Or was it high L-C ratio. I can't remember but need to know.
Can any kind soul help me out? Thanks.

p.