EMRFD Message Archive 3136

Message Date From Subject
3136 2009-06-03 11:23:59 Stephen Wandling Crystals, Ceramic Resonators and VXOs

Preface: I am not an engineer and my electronics training (US Navy) was
in the late 50s. My needs are more practical than theoretical. For me,
"design criteria" means simple, practical ways of achieving goals. I'm
looking for 'guides' more than theory. Thanks.

In my continuing need to understand things that I am building I have a a
few questions about VXOs. There are lots of circuits and examples for
VXOs out there, but typically, little or no detail on how that
particular circuit was chosen is provided. EMRFD (12.29) says
"Experimentation is almost always useful with VXO circuits."

In my searching I have gleaned some tidbits, but have not yet found what
I would call "design criteria" for a VXO. While it appears that having
too small a series inductance will limit the lowest frequency you can
tune, having too large an inductance creates 'instability'. What I am
looking for, in part, is how one determines what is a small/large
inductance? [Assume a 3560 Khz quarts crystal]

And maybe I need to start at an even more primary point: 'rubbering' a
crystal. What is happening when we adjust a variable capacitor in
series with a crystal, in a Colpitts oscillator?

The circuit that has triggered this email is a VXO circuit that
intrigued me. It had the typical crystal in series with a variable
capacitor, in series with an inductor. But, it also had a second,
apparently smaller, inductor in series that can be switched in or out.
The circuit did not have any values for these components and no text
explanation. While the switched inductor may have been intended to
lower the tuning range some, I saw it as a way to affect a transmit
offset frequency. If the small inductor was of a value that inserting
it changed the frequency by 600 Hz, then you have transmit offset. My
question was: how does one go about determining the values for such a
VXO, such that it give an optimum tuning range and the smaller inductor
gives a 600 Hz offset?

And finally, I have recently become acquainted with ceramic resonators.
I have experimented in various oscillators and find that a 3.58 Mhz
ceramic resonator can be made to cover most of the 80M CW band with just
a variable capacitor. So, the 'rubbering' that is done with a quartz
crystal appears to give a much expanded frequency range with the ceramic
resonator. Are the same factors in play with the ceramic inductor and
quartz crystal in a VXO? If not, at the practical level, what are the
main differences. Once again, I am looking for guides for design. One
source warns me that ceramic resonators are no more stable than an L/C
circuit, but I do not see evidence of this, and they seem to be popular.


3138 2009-06-03 16:06:36 Ed - K9EW Re: Crystals, Ceramic Resonators and VXOs
Hi Stephen,

> And maybe I need to start at an even more primary point: 'rubbering' a
> crystal. What is happening when we adjust a variable capacitor in
> series with a crystal, in a Colpitts oscillator?

In a Colpitts oscillator, the crystal (let's leave the variable
capacitor out for the moment) functions as a very high Q inductor that
is in parallel with two series capacitors. This forms a resonant
circuit, and the tap point between the series caps provides feedback
to make the circuit oscillate. [The equivalent circuit of a 5 MHz
crystal (see ARRL Handbook) is a parallel capacitance of about 3.8pF
across a series R(40 ohms), L(100mH), and C(.011pF). That can be
transformed into an equivalent resistor, inductor, and capacitor in
parallel with the parallel equivalent of the two series caps of the
Colpitts oscillator circuit. This forms your 3.560 MHz resonant

Now add the variable capacitor in series with the crystal, and it
changes the parallel equivalent capacitance that the crystal
(inductor) sees. This will change the resonant frequency of the
circuit. Since the crystal is providing a very large inductance, the
change in capacitance from the variable will only change the resonant
frequency of the circuit a small (few KHz) amount.

This same effect can be accomplished by inserting a series inductor,
except the frequency changes in the opposite direction.

The ceramic resonator operates in a similar manner, but the Q isn't as
high, so it can be warped over a larger frequency range, and the
frequency stabiltiy isn't as good as a crystal.

Hope this answers your question.

ed - k9ew
3141 2009-06-03 19:16:29 Nick Kennedy Re: Crystals, Ceramic Resonators and VXOs
Hello Stephen,

To get a bit of a handle on the VXO thing, I think you need a measurement or
at least an estimate of the series L and C (Lm and Cm) of the crystal. In a
Colpitts circuit, I make the assumption that the frequency of oscillation is
that of a series circuit of Lm and Cm and the Colpitts voltage divider
capacitors all in series, although you might neglect the latter for this
rough calculation.

How to estimate Lm & Cm if you don't measure them? I'm not sure. Looking
at some of my data, I see their reactance at about 1.1E6 ohms for crystals I
measured in the 7.6 to 8 MHz range. I didn't measure any 80 meter crystals,
but for some at 4.915 MHz, I see about 2.2E6 ohms. You could assume
something in that area and calculate the resulting Lm or Cm.

What I'm proposing is using the formula for resonance and the formula for
capacitors in series to calculate the added series C (the VXO capacitor)
needed to move the resonant frequency by the desired amount (realizing that
beyond a few kHz might exceed a practical limit). Or alternately, try a
value of series C and see what the resultant change in resonant frequency
is. On paper. Then see how close you get in your real live oscillator. So
your procedure or thought process for VXO series C to move up 1 kHz might
be: Here are the estimated (or measured) values of Lm and Cm to resonate at
3.58 MHz. Now, what new value of Cm would resonate with the same Lm to give
3.581 MHz? (Calculate it.) Finally what series C do I have to combine with
the orignal Cm to give the new Cm for that change. (Calculate it, that's
your VXO capacitance.)

To get some background on this, look at figure 7.69 of EMRFD, which shows
the schematic and formula for the famous G3UUR method of calculating the
parameters of a crystal. And by the way, it also illustrates exactly what
you're trying to understand.

I did a little presentation of crystal characterization at OzarkCon a year
or two ago, and you can see my slide show and notes here -


It includes some tinkering with the basic G3UUR formuals.

Regarding using an inductor to go the other way (or both ways), I'd figure
the reactance of your VXO trimmer at minimum capacitance, which is its
maximum reactance. Then choose an L of about half that reactance. When the
trimmer is at about half scale, the two should cancel. With more than
50% C, you should be below the natural series resonant frequency of the xtal
(net reactance inductive), and with less, you'll be above it (net reactance

Regarding the greater tuning range with a ceramic resonator, I think that's
because they have much lower Q than a quartz crystal has.

72--Nick, WA5BDU

[Non-text portions of this message have been removed]
3144 2009-06-03 20:57:02 Wes Hayward Re: Crystals, Ceramic Resonators and VXOs
Hi Stephen and gang,

This does have to do with the design details of your problem, for many other brought them up in posts that followed yours. I believe that Q has little to do with the problem. The greater difference is in the motional parameters related to the usual crystal model. The same model topology describes both, but with much different values.

I jumped into my junk box and found a ceramic resonator at 4.19 MHz and a quartz crystal at 4.00 MHz. These were close enough for comparisons. The ceramic part was a small orange blob from an order years ago from Digi-ouser. The quartz crystal was an ECS brand in a full sized HC49 can.

Measurements were done with a variation of the usual oscillator with a switched series capacitor. Parallel capacitance was measured with an AADE L/C meter. No Q measurements were done at this time, although earlier measurements indicated a Q of around 800 for the ceramic resonators and about 100,000 for the 4 MHz crystals.

The motional parameters for the quartz crystal were C0=3.4 pF, Cm=.0110 pF, and Lm=143.9 mH. These are very familiar and expected values.

The motional parameters for the ceramic resonator are C0=29.1 pF, Cm=4.92 pF, and Lm=312.3 uH, completely different from anything we would expect from the Quartz world.

The equations used with the oscillator measurements are derived in a note found on line at http://w7zoi.net/g3uuralator.pdf . The derivati
3145 2009-06-04 04:43:38 Harold Smith Re: Crystals, Ceramic Resonators and VXOs
Stephen and All,

Since Wes has already commented there is nothing I can add from a
theoretical standpoint. However, through the years I have built a lot of
VXOs, and I have come up with some rules of thumb for starting out.

I have found just what the Book says, that every VXO is an experiment,
probably because the crystals themselves are usually poorly characterized,
if at all. I have found that, for whatever reason, it helps the pullability
if the Colpitts capacitors -- the feedback divider pair from base to emitter
and emitter to ground -- are much larger than I would use for a fixed
frequency oscillator. For a fixed frequency oscillator I would typically
use 39 pF caps (because I have a lot of them, and they end up loading the
crystal near what most crystals are specified for) but in a VXO I'll start
with at least 100 pF there, and often as much as 330 pF.

And I have an assortment of fixed inductors, and I'll try them, one at a
time, until I get what I'm looking for. Ideally you want maximum pulling
range without the VXO taking off on its own and leaving the crystal behind.

Through all this experimenting you have to watch the frequency while you
vary the tuning cap through its range. The output frequency should tune
smoothly through the range. If it jumps, your crystal has lost control. If
it stops changing before the variable cap gets through its range, you might
as well go to a smaller inductor, because you've got all the change you can
get with the parts you're using.

I actually built up a small VXO test oscillator, with a 2-section variable
cap from a broadcast radio. I can use either or both sections - one is
about 100 pF max, the other about 300 pF - and I can easily change

The fixture also has two crystal sockets, to allow the Super VXO
configuration, with two crystals, of the same nominal frequency, in
parallel. The Super VXO can give much more than twice the pull than a VXO
with a single crystal. I have gotten about 40 kHz of very stable tuning
range from a Super VXO at 20.5 MHz, which, tripled, gave me more than 100
kHz of tuning range on six meters with an IF around 11 MHz.

And that's another thing. Pull range, all other things being equal, is
proportional to frequency. At 80 meters, you aren't likely to get much more
than 1 kHz total from a VXO no matter what you do. Even a Super VXO won't
tune more than two to four kHz, at best.

VXO experimentation can be fun and interesting. Keep good notes on your
work, and include crystal characteristics if you know them.

Good luck.

de KE6TI, Harold

3146 2009-06-04 04:57:17 joop_l Re: Crystals, Ceramic Resonators and VXOs
3147 2009-06-04 06:53:18 hal Re: Crystals, Ceramic Resonators and VXOs
Hi to all,

I am using since many years super VXO's for my reveiver and transmitter.
The oscillator is always the same : any small transistor like 3904, 100p between gate/ emitter and 100pf emitter/gnd in parallel to a 100Ohm.
The base connects via a100k to the collector and to +5V VCC !!!!! A higher voltage has NO advantages.

Of great importance is the tuning capacitor. Like in any good VFO it should be of a good quality with a low as possible starting capacitance.
The end capacitance should be between 70pf and 100pf.

The tuning range should not be greater than 50KHz in a frequency range from 12,5MHZ to 30Mhz.

As my VXO is switchable between 80m and 15m ( 9MHz IF) the bandstart should be always at the same position of the tuning capactor.
Therefore for each pair of crystals a variable inductor with a 22k resistorin in parallel is needed.

With the crystals I am using the values are as follows: 12,5µH/12,5MHz 7,5µH/16MHz 4,8µH/19MHz 3,9µH/ 23MHz 2,2µH/27MHz 2,0/30MHz.

The crystal frequency was chosen to be 68KHz above the lowest oscillating freqency. ( max capacitance )
I.e for 40m the XVO should work between 16,000 and 16,050KHz the crystal frequency was choosen to be 16,068KHz.

The high end of the frequency is being lost due to the bandswitching. The starting capacitance is increased!!!

Switching is done with small signal relays.

The inductor values maybe useful to start experimenting.

The benefit of the VXO is mainly the purity and the low phase noise of the signal. In addition it is reasonable stable like a good vfo.
When turning
3151 2009-06-05 20:49:35 Stephen Wandling Re: Crystals, Ceramic Resonators and VXOs
I want to thank Ed, Nick, Wes, Harold, Joop, Hal and Glen.

I certainly have received a lot of responses to my questions, and am in
the process of sorting through them all. I have been reminded that I
was on a similar path about a year ago when I wanted to model crystal
oscillators in Spice. But, this time I am being led further into the
territory. I am thankful to you all.

Amateur radio's collective knowledge and the willingness to share never
fails to amaze me.

3157 2009-06-06 21:01:30 Wes Hayward Re: Crystals, Ceramic Resonators and VXOs
Hi Gang,

Well, as promised, I did additional measurements on that same crystal and the ceramic resonator. The measurements were done with an N2PK type VNA. I'm hesitant to present the results, for they were so close to those obtained with a characterization oscillator that I'm afraid some of you will think my results were a "dry lab." Really, folks, this is what I saw.

The 4 MHz crystal came in with a motional L of 143.3 mH and C0 of 3.68 pF. The Q was pretty good at 165K. The values obtained with the AADE meter for C0 plus the characterization oscillator for Lm and C0 were C0=3.4 pF and Lm=143.9 mH. This is really a gratifying piece of data, for that suggests that the schemes we have been
using for crystal characterization are doing well.

The VNA determined ceramic resonator parameters were Lm=351.1 uH and C0=26.1 pF. The Q was poor at 543. The data for the same resonator determined with the characterization oscillator and the AADE L/C meter were Lm=312.3 uH and C0=29.1 pF. Again, not bad correlation.

Having characterized the ceramic resonator, it was time to build a VXO. The circuit that was built is at the top of an uploaded file titled "Ceramic Resonator VXO.gif" (June 6, 2009). The circuit started immediately and tuned over a considerable range. However, there was a hitch -- it stopped oscillating when the variable capacitor was at minimum. This was the low resonator Q coming into play. But oscillation commenced as soon as the variable C was advanced just a few degrees. The observed tuning range was from 4101.2 to 4272.2 kHz.

Next, we took the ceramic resonator model and combined it with the oscillator circuitry. The variable C had been measured with the every handy AADE L/C meter. The resonance calculations are shown on the file mentioned above. Again, we were able to predict frequencies with the measured resonator model parameters.

In checking things, I realized that the crystal test oscillator that I'm now using is not the G3UUR Colpitts circuit from EMRFD. Rather, it is that shown in the uploaded file "crystal characterization oscillator.gif". I switched to this oscillator in 2002, for some lower frequency crystals would not oscillate in the circuit from EMRFD. The circuit in the file oscillated on the crystal third overtone when the transformer was built with a FT-37-43 core. However, when the circuit was rebuilt with a higher permeability core, the behavior was with fundamental mode oscillation all the way to a 20 MHz crystal that was tried. Although this circuit will oscillate with 455 kHz ceramic resonators, operation is problematic, again with overtone oscillation. It works fine with ceramic resonators at 3 MHz and higher.

This was definitely an interesting set of experiments and calculations. While it is certainly fun to build these things and make them work from experiments "on the bench," it is equally gratifying, at least for me, to also be able to do more fundamental measurements and calculations to expand upon the bench results. There is still nothing like the final bench work. As one of our illustrious colleagues (K3NHI) is known to say, "Show me the measurements!"

73, Wes
3159 2009-06-07 15:02:09 Jim Kearman Re: Crystals, Ceramic Resonators and VXOs
3160 2009-06-07 15:31:14 Stephen Wandling Re: Crystals, Ceramic Resonators and VXOs

I have been sifting and digesting the other responses before I was going
to ask any further questions.

As I said, the circuit with this feature did not have any values for
either inductor or the variable capacitor, but it did show the switched
inductor as much smaller. Unfortunately, the rig I was going to use
this in is very minimalist and so there is not any heterodyning.

I had accepted the fact that the offset amount would shift across the
tuning range of the VXO. My hope was that it would be within a usable
range: 500 hz to 750 hz. I suspect that using Wes' data, I should be
able to come up with an inductance that would give a 600 hz shift when
the VXO is tuned about mid range and then measure the amount at the VXO

In thinking about it just now, I suspect that, using a DPDT switch, I
could switch in the inductor for the transmit offset and then switch in
a very small variable for RIT
3161 2009-06-07 21:04:32 Jim Kearman Re: Crystals, Ceramic Resonators and VXOs
3175 2009-06-10 22:27:44 rotfunkblau Re: Crystals, Ceramic Resonators and VXOs
Hi Wes,

thanks for your interesting measurements with ceramic oscillators.
Maybe you are aware of
Years ago the qrp transceiver "Sparrow" was sold in Germany with such an oscillator. But the osc was replaced by a DDS vfo, because of lacking long time (?) stability of the vfo. So maybe one should keep an eye
3188 2009-06-13 10:06:33 Wes Hayward Re: Crystals, Ceramic Resonators and VXOs
Hi Guenter and gang,

Now that you bring it up, I do remember seeing the la8ak posting. Many thanks! He has a load of really great info on his web site and we should all (myself included) go through it.

With that said, I still find it useful to do the measurements myself. If nothing else, it allows me to get another "calibration" point on my own measurements and to get them correlated with the work that others have done.

Next on the list would be to build up one of these ceramic resonator VXO circuits and do some temperature stability measurements in the Styrofoam oven. I'm also thinking that a 3 to 2.95 MHz VXO would do a nice job in place of the 17 MHz quartz VXO in the "S7C" from EMRFD Chapter 12. Hmmmm.......

Thanks again.

73, Wes

3189 2009-06-14 15:34:18 joop_l Re: Crystals, Ceramic Resonators and VXOs
3192 2009-06-15 13:40:00 Wes Hayward Re: Crystals, Ceramic Resonators and VXOs
Hi Joop and group,

Outstanding! Many thanks for doing similar measurements to those that I reported. I really appreciate it. Your parts had higher Qu than the ones I had here, but the parameters were otherwise similar, and much different than those of a quartz resonator.

I grabbed my oscillator and repeated the tuning until oscillati
3199 2009-06-17 15:41:35 joop_l Re: Crystals, Ceramic Resonators and VXOs