Carl G. Lodstrom, SM6MOM
Measurements on Ceramic Resonators
VHF Communications 3/1998
BACKGROUND:
Recently I designed some filters based upon ceramic resonators. After
modelling the filters in =SuperStar= Pro, I came up with frequencies for the
resonators, as well as the capacitances they should be coupled with.
Expecting no problems I went ahead and ordered samples from a few leading
manufacturers of ceramic resonators here in the US. They arrived and one
supplier even had a list of the frequencies they had measured up on the
samples. I now know that a spread of ±5 MHz is pretty good in my range of
1600 to 1700 MHz. The resonators are 6 x 6 mm size, about 7 mm long and made
of a (r=38 material. This gives a (/4 shorted coaxial resonator with Zo =
9.4 Ohms and an unloaded Q of about 600.
I assembled my filter and it did not look good. It was way off in frequency
for one thing!
Something was very wrong. I proceeded to measure the resonant frequencies of
the resonators with a Vector Network Analyser. The problem immediately
arose: how do one measure these resonators? A call to each supplier
revealed that they too used Vector Network Analysers and measured the
frequency by sticking a little wire, the centre pin of the connector in a
test fixture, into the hole in the middle of the resonator. From the
non-metallized end of the resonator. They then pushed the resonator up on
the pin until the capacitive coupling got large enough for the response to
cut through the middle of the Smith Chart. Then they moved the marker to
this point and read off the frequency.
I built a little fixture and repeated the feat. Now I observed that the
frequencies from the two suppliers did not agree with each other or with my
measurements!
The PROBLEM:
I modelled the fixture with resonator in =SuperStar= Pro and found the
capacitance had to be in the vicinity of 0.15 pF for to give this much
coupling, also enough for to pull the resonator down by at least 15 MHz! The
thickness and length of the wire also mattered. For a thinner wire; more
length is needed, but more inductance is introduced as well. And the other
way around. The method is not very 'scientific'.
Then the resonators should be fitted with little tabs soldered into the
holes. The capacitance of this I found lowered the frequency by 6 MHz and
required another kind of test fixture with a little fork instead of a wire.
The resonator tab is now slid in between the prongs of the fork. More
possibilities for errors!
Several tours of samples and trials followed, the 'theoretical' frequencies
from =SS= were tweaked by +15 MHz, more samples were ordered and time was
fleeting fast. It became more and more obvious that another method for to
measure the resonators was needed. Not only did it take a long time to wait
for samples, although one can grind down (up in frequency) the resonators on
a sandpaper, but in the meantime one may loose the market for the filters.
Obviously it is too much load on the resonator with 0.15 pF. The equivalent
circuit for a 1650 MHz resonator is 8.04 pF and 1.16 nH with 7.2 kOhm in
parallel.
Transtech, a subsidiary of Alpha Industries (e-mail: transtech@alphaind.com)
has a nice Design Guide program on a disk (and probably on their web site as
well) that calculates these resonators as well as "puck" resonators,
cavities and tuning screws.
SOLUTION:
It dawned on me that some kind of transformer was needed. The VNA needs to
see a low impedance, and the resonator needs to see a high one. A lambda/4
transmission line, or even such an "antenna" might do it! I fired up =SS=
again and put in a slab line kind of transmission line. It is a round wire
above ground. I found that the method ought to work just fine with a 43 mm
wire for my ~1650 MHz resonators. I built one fixture and it worked just
like predicted! The pull is now only about 0.5 MHz. The resonator can have a
tab or not, it does not matter, the coupling wire is so far from the open
end that it does not matter. Neither do the resonator need to be positioned
with any accuracy. When you get a reading on the VNA, that's it! A sweeper
with a directional coupler for S11 will do just as well as the Smith Chart
on a VNA, saving about $65,000... It even easier. Now you are in business!
I realised that the solution I came up with may be of general interest, so I
decided to write this article. I am probably not the only one who have had
these problems!
A 1 dB dip in S11 should be more than sufficient for detection, the wire
length and coupling capacitances for this are listed below for some
frequencies and a 0.1 mm diameter wire: (Notice, the coupling capacitance is
in fF! 10E-15.)
(Table omitted)
The diameter of the wire is not important, but it got to be small! I used a
0.1 mm wire, although =SS= claims that a 0.05 mm wire would give
considerably more sensitivity => even less coupling needed. But 0.1 mm is
good enough though since the values above gave less than 1 MHz pull.
The length is by no means critical either. The little loop the resonator
creates on the Smith Chart goes in from the periphery, and the diameter of
it follows the resistance circles, so it is largest at 180°, but large
enough to be seen (in a S11 plot as well) over ±120°. The values above gives
the exact length for the listed frequencies.
In reality the wire radiates and has skin effect losses as well, so the loop
does not have its base at the periphery of the Smith Chart (S11 is not 0 dB
outside resonance), but it can be read without problems anyway.
In the model above a 100° line corresponds to the connector body for
rotation of the Smith Chart plot to the one observed on the VNA. There is
the wire probe and a "fake" resistor. The resistor helps to simulate the
radiation losses. The =SS= program will not run without an output anyway, so
I connected the resistor to this 50 Ohm output. You can see a 6 fF capacitor
coupling to the resonator.
Actual measured values, to which the model was "tweaked". The S11 plot to
the right has a vertical range from -70 to +30 dB. About 11 - 12 dB return
loss is observed due to radiation and skin effect losses.
SUMMARY:
A method for measuring the self resonant frequencies of (ceramic) resonators
has been described.
It is sensitive, simple and accurate, as well as at least magnitude of order
faster than the prevalent method. It even lends itself to automated sorting.
It is most likely applicable to other kinds of resonators as well, i.e.
helices in helix filters. A (/4 transmission line, with an open end, can
easily be assembled for just about any frequency with a lab cable instead of
a wire, for instance. If one can safely detect a 0.1 dB dip, a 50 Ohm cable
(of about 2/3 the length of the wire) should work also with 10 - 15 fF
coupling to a resonator like the ones I use. Pull is then about -1 MHz.
Although a (/4 coaxial cable does not have the high Zo of a thin wire, it
still transforms a high impedance of the open end (and it's diminutive
loading) to a low impedance at the other end.
With a longer cable, much lower frequency resonators can be measured. A
quartz crystal is another animal. It may still get pulled too much!