Saturday, 24 January 2015

Crystal Parameters --- Experiments with a Tracking Generator + Spectrum Analyzer


I love finding ways to measure parts and circuits with my tracking generator + spectrum analyzer (TG + SA).

I show early experiments with a jig developed to derive crystal motional parameters with a TG +SA plying the G3UUR method. Crystal parallel capacitance (C0) is measured separately with an LC meter. My hope is to accurately characterize fundamental crystals in the 20-50 MHz range to make crystal ladder filters for VHF projects.

Schematic of the series jig for characterizing xtals with the G3UUR method.

Above — Schematic of the series jig for characterizing xtals with the G3UUR method. Each 50 Ω port gets an impedance drop by a trifilar transformer and L-pad down to 1.811 Ω to help eliminate any xtal parallel capacitance effects during measurement. The L-pad attenuates the signal by ~ 10.1 dB to help establish the crystal input/output Z.

Cs, the series capacitor = a Vishay 1%, Q = 2500 MHz @ 1 MHz, size 0805 C0G capacitor measured at 30.8 pF before going into the circuit. The transformers = 8 trifilar windings on a FT37-43 ferrite toroid.

1 view of the early breadboard with a 40 MHz xtal in the holder

1 view of the early breadboard with a 40 MHz xtal in the holder

Above — 2 views of the early breadboard with a 40 MHz crystal in the holder. I shortened and better grounded the 9:1 Z transformers after taking these pictures. Built on double-side Cu board, several Cu via wires pass through to establish a solid ground plane. This helped boost the input + output return loss to get close as possible to the desired crystal 1.811 Ω source and load Z.

The switch  = a slide-on shorting switch often employed in computer motherboards.

Measures with a 40 MHz Crystal

A sweep of the crystal series resonant frequency.

Above — A sweep of the crystal series resonant frequency. I ran the RBW at 100 or 30 Hz but either worked fine — and of course, 100 Hz gives faster sweeps. The series resonant frequency = 40.002098 MHz.

A sweep with the switch shorting pin is added

Above — A sweep after adding the Cs switch shorting pin with a gloved hand and allowing time to stabilize before recording frequency and power. F = 39.990770 MHz. Power (referenced to 0 dBm) = -33.24 dBm.

A sweep with the shorting pin still on the switch --- but the crystal removed and replaced with a copper shorting wire stuck into the crystal holder.

Above — A sweep with the shorting pin still on the switch --- but the crystal removed and replaced with a copper shorting wire stuck into the crystal holder. Through power = -28.39 dBm.

Delta  P = the power difference in dB between the series resonant crystal measure and the power recorded with the crystal holder shorted by a Cu wire [both with the 30.8 pF capacitor shorted]. Delta P = 7.13 dB.

Crystal C0 = 2.73 pF as measured with an AADE meter.


 Professor Natasha shows Cm and Lm calculations.

Above — Cm is calculated with the standard formula. After --- calculate the capacitive reactance of Cm and insert this X into the formula to calculate Lm. A scientific calculator makes these equations easy to crunch. Typically we would express Cm as 1.99E-14 on a calculator.

At this point, we've calculated crystal Cm, Lm and have enough data to calculate the ESR at the series resonant frequency + the unloaded Q.

I asked Victor 4Z4ME for help with the calculations for ESR, since once you know the crystal series resistance, Qul may be calculated. Victor sent the below figure that shows how to derive the equation to crunch ESR. Note: 1.8 Ω was used instead of 1.811 for clarity.

In order to calculate ESR and unloaded Q, we first calculate the ratio of voltages V1/V2 from the base equation V1/V2 = 10^((P1-P2)/20 . Exquisite math yields Rx (ESR).

Equations to calculate the ESR and Qul.   Professor Natasha.

Above —Equations to calculate the ESR and Qul. The ESR formula that Victor showed earlier is further simplified to the right of the green arrow [ESR = 3.622 * (V1/V2 - 1) ]. We then use ESR to calculate the unloaded xtal Q as shown.

This 40 MHz job @ 43.4K = a low Q crystal, but it might work OK in a wide IF filter that follows a VHF receiver's first mixer. Most of the crystals >= 30 MHz fundamental I've tested have a Qu < 100K.

Building a collection of fundamental crystal >= 20 MHz proves difficult for me. Several eBay crystal offerings touted to operate on the crystal's fundamental frequency turned out to be overtone crystals. Crystal purchased from vendors like Mouser-Key have better obeyed the their datasheet specification, although, there too, I've found exceptions.

I fundamental frequency test these crystals in an oscillator that outputs to my 50 Ω terminated 'scope.

An oscillator I use to test fundamental crystals >= 20 MHz.
Above — An oscillator I use to test fundamental crystals >= 20 MHz. Although, the BJT listed is a MPSH10, a 2N3904 works OK.

The 40 MHz crystal shown in the earlier Cm, Lm, ESR, and Qul calculations vibrating in my crystal test oscillator.

Above — The 40 MHz crystal used for the earlier Cm, Lm, ESR, and Qul calculations vibrating in my crystal test oscillator.

A 30 MHz fundamental crystal in the test oscillator.

Above — A 30 MHz fundamental crystal in the test oscillator.

1 of the many 50 MHz "fundamental" crystals that turned out to be an overtone job.

Above — 1 of the many 50 MHz "fundamental" crystals that turned out to be an overtone job.


I measured a 12.0 MHz crystal with the classic G3UUR crystal oscillator method and compared it to the series jig result. The classic xtal oscillator gave an Lm = of 0.0052 H, while the TG + SA series jig gave an Lm of 0.0041 H.

I'm not sure which 1 is correct? Likely the proof of the pudding lies in the transfer functions of the crystal filters I build informed by this new crystal parameter tool.

While it's no panacea, I enjoyed these experiments and learned a lot. For example, I now have 3 methods to measure crystal Q and feel I've advanced a little in my TG + SA skill set
My sincere thanks to Wes, W7ZOI for getting me started on this project and also for a few breadboard parts — plus — big thanks to Victor, 4Z4ME for his equations and support.


Monday, 12 January 2015

A Crowdfunded Si5351 Breakout Board From Jason NT7S

Cool event from our friend Jason NT7S ...
Dave AA7EE wrote about this well ---- so I'll just link his post:

I got 1 ordered.
Love the whole warm thought of hams helping hams!


Thursday, 1 January 2015

21.4 MHz VCO frequency modulated with 1 KHz

Testing -- first personal video upload to YouTube. (Content from 2013)

Sunday, 28 December 2014

Food and Science

Bad coffee

I like science and measurement  -- a theme that underpins this blog. Let's take a major source of pleasure for all of us (food!) and think about it in the scientific context.

Remember when fat was vilified? Now it's wheat. What's next, water?  -- oops, sorry, that's been done; most people I work with drink bottled water. At home, I guzzle from the tap, but drink bottled water in foreign lands based on analysis from biologists and recommendations from public and population health professionals.

Less than ~1% have gluten allergy. Now, scores say they are gluten sensitive and a myriad of so-called experts and opinions run amuck. We've got 3 friends with biopsy-proven celiac disease and I know how to cook to keep them happy and healthy.

I think most of my other gluten sensitive friends and colleagues are caught up in the latest food fad. But they all retort -- it says so on the web and TV; so it must be true! Why can't people just avoid the foods they don't tolerate and get on with life -- I see no need to buy the related magazines/cookbooks, watch quacks on TV, tell everyone they've discovered a life changing truth and turn it into a theology. Back to science:

Time for a primer on the best available food evidence set to parody of a nice pop song:

Video link :

I changed the blog background format for better reading and to eliminate the dark feel.
Happy New Year from the cats and us!

Thursday, 25 December 2014


Best to you in 2015!

I got 2 new books this holiday season. I read them lying down — for low back and hip pain kept me off a chair for several weeks until I regained the needed core muscle strength plus re-established hip flexion and extension. I now appreciate that quality of life and back health lie directly related. Perhaps you might relate? I better go stretch; back in a moment...

Small Signal Audio Design: 2nd edition by Douglas Self.

Above — Small Signal Audio Design: 2nd edition by Douglas Self. With its content boosted by about 50%, Self took his great first edition into the stratosphere with this follow-on. I wish someone with his writing skills (epic clarity, practical insight and warmth) would write about RF topics. This book could serve as your the AF design bible for a long time.

Handbook of Microwave Component Measures by Joel Dunsmore.

Above — Handbook of Microwave Component Measures by Joel Dunsmore. Dr. Joel (a staffer who comments on the Agilent (now Keysite) Network Analyzer forums) wrote this book as a follow-on to his original and it's not a book for people who dislike math, theory and equations. I love this book for opening my eyes into the ways modern engineers measure Scattering parameters, consider the DUT, + calibration and also how an exciting "VNA design evolution" is exploding big-time.

My dad told me "if you hang out with and/or read stuff  by smart people you just might get smarter; so choose friends and authors wisely".  This book serves as a case in point. Although, I don't understand every chapter, equation or concept, I've got a new appreciation for and direction to go in home lab measurement know-how.

In short, modern microwave measures get done on VNAs, not 'scopes nor spectrum analyzers. New VNAs, although very expensive, may feature multiple signal sources and receivers with advanced calibration techniques to deliver amazing accuracy.

Each month, I hope to read that someone has released a fast but relatively cheap 3 GHz network analyzer with a dynamic range of  >= 120 dB (with at least 10 Hz minimum resolution) across its bandwidth. I'm not alone (see this thread for example), I've read many opinions and only 1 thing is certain, I want small gear and not bloated boat anchors from the past. At this point, getting a VNA for my desired minimum 3 GHz bench BW is not affordable.

No question homebrew or commercial hobbyist VNAs are a real option for some — just not me. The aforementioned book, an EE friend, and my experiences show a big source of bench error in network analysis is mismatch between the source and the DUT. All manner of mismatch may occur because of DUT reflections, crosstalk, receiver to source leakage etc.. It can take serious VNA design, added hardware and bench effort to isolate the source and receiver plus establish the proper 50 Ω test environment — even down at VHF - UHF.

Further, the calibration sets may cost ++ ; especially as you go into microwave. Consider this link by Kirkby Microwave Ltd. Modern commercial network analyzers allow you to input your particular calibration test set (or perhaps calibration connector parameters) to boost accuracy. Up-to-date, 2-port, professional grade network measurement costs $1500-2500 per GHz it seems.

All things considered, as amateur radiophiles, we live in exciting times and I'm sure you have your own thoughts and opinions on VNAs for 2015 and on.

Photography with cats proves difficult.

Photography with cats proves difficult.

Photography with cats proves difficult.

Above — Photography with cats in the house proves difficult. It never fails — depress the shutter and 1 cat or the other comes from nowhere and jumps in front of my intended subject. So here they are (hamming it up) with the lights set up for a dark colored book  — fairly strong + directional lighting at 5500 degrees Kelvin color temperature. I love experimenting with lighting and strive for different looks: some good, some harsh.

Blogger further processes photos so they look about 1/2 stop brighter than actual and this bothers me.

I run a calibrated monitor so the color and brightness of my local commercial lab color prints look like just my onscreen jpegs.


I get much less email with the blog. Some people are still quite upset I shut down the old website, even though I had no alternative. The traffic trouble continues and at least for me, vindicates my decision. That's fine — I respect your opinion to a point. 1 guy called me a f***head for stopping the site in October and then later in December bluntly asked for substantial design help. Sorry, I'm a f***head and can't help you.


An emailer shared respectful concern about my use of #43 material for broadband transformers at VHF ( ~100 MHz ). He strongly felt that #61 material was better suited at VHF.

So glad I made these experiments, here's an excerpt of my email reply:

10 turns on a FT37-43 ferrite toroid were placed in-series between 2 SMA connectors.

Above —10 turns on a FT37-43 ferrite toroid were placed in-series between 2 SMA connectors, padded at input and output and then swept from 0 to 500 MHz in a TG-SA.

10 turns on a FT37-61 ferrite toroid

Above —10 turns on a FT37-61 ferrite toroid swept as above. You see little clinical difference and if anything, the 43 mix ferrite looks a tad better down lower. Somewhere above ~20 MHz, the ferrite "disappears" and the results of both mixes look similar. Both are lossy and work about the same. More windings on the #61 toroid does not boost the attenuation and actually may drop the SRF due to extra interwinding capacitance. I normally use a small 43 mix binocular or FT23-43 bifilar wound ferrite at lower VHF in my feedback amps.

Again, all the very best in 2015!

Tuesday, 9 December 2014

Mixer IIP3 Notes


As a measuring experimenter with a homebrew POV, I like to add new test equipment and procedures to my lab each year. With digitally processed spectrum analyzers getting more able and relatively cheaper over time, I think a spectrum analyzer (with a built in tracking generator) might prove one of the best toys to consider buying. As ever, a homebrew SA remains a valid option for more advanced builders.

A bench experiment challenges us at many levels: we'll often combine equations + calculations, intuitive analysis and quality measures to advance our understanding of what's going on inside these little silicon parts. Best of all, we gain the experience, confidence and know-how that may allow us to interpret phenomena outside our comfort zone.

Over time — applying curiosity and effort, we acquire and get to enjoy a small arsenal of analytic methods at both AC and DC: For example, measuring drain current, or transistor beta — or perhaps learning small signal analysis using hybrid parameters, or making return loss measures, inferring resonator Q, or measuring magnitude and phase (vector analysis). 3 other measures rank highly important to me: 2 tone intercept techniques to assess IMD, noise figure and phase noise. The latter 2 may take awhile, but I'm sure I'll get there.

IIP3 in Mixers

Pretty much everything about IMD measures we need to know lays in the pages of EMRFD Chapters 2 and 7. Further; many have written web sites or tutorials to help us. 1 great example is Rob, KD6OZH's Mixer IMD Page

As a new builder, I initially felt surprised that we needed to learn about both non-linear and linear behavior in AC circuits. Now I know better. Non-linear conditions like saturation, compression, crossover, intermodulation, plus other species of non-linear phenoms such as IMD in higher level (passive) LC circuits can lead to distortion and/or noise that may be quantified or inferred to aid design and understanding.

Much of this flies over my head. I measured the IIP3 of an ADE-1 mixer to learn the ropes.

I won't go into IIP3 definition and theory — it's been done by those much smarter than I.
In the mixer IIP3 context, this MCL file really helped me.

Let's explore the needed parts and set up for mixer IIP3 measures:

 Test Equipment
  1. 3 low noise signal generators
  2. A combiner such as a 6 dB hybrid (your HF-VHF return loss bridge)
  3. Attenuators
  4. Cables and 50 Ω connectors
  5. A 50 Ω detector -- I'll use a spectrum analyzer
  6. A device to test: ADE-1 mixer or....
Please know, I'm showing these experiments to foster discovery and discussion — and to document some early experiences. I don't go into a comprehensive diatribe or even show the best way to go : just 1 method to get it done. Our test equipment varies widely and you'll have to determine what works best for you in your lab.

I'm going to insert 2 tones into the RF port of an ADE-1 mixer: 9.00 MHz and 9.050 MHz. I tried a 20KHz, 50 KHz and 100 KHz tone spacing and when the mixer was assessed wideband (without a xtal filter after it), I found the exact tone spacing made little difference to the IIP3 within reason.

Above: My bench setup. The first order of business in IIP3 measurement is to assess the input intercept of your basic measurement apparatus. You should not see distortion on your spectrum analyzer screen — if so, eliminating this distortion is job #1. I learned that if you drive the SA too hard, you just might measure the IIP3 of your SA! 

To clarify. Your injected tones can create IMD products on your SA screen and we need eliminate these so we only measure the intercept of the device under test. Correspondence with an EE who measured intercepts with a very excellent Agilent SA that sells for many 10's of thousand dollars yielded insight. He found input intercept products may show up when driving that SA input with signals hotter than -20 dBm. This could also happen with a much cheaper SA. Judicious use of input attenuators will solve these woes and I'll show some experiments that demonstrate this.

The 9.050 MHz signal generator = a very low phase noise device [ tested by an engineer at -140 dBc @ a 20 KHz offset ]. The 9 MHz signal came from a homebrew LC signal generator ( EMRFD Figure 7.27) assumed to also exhibit low phase noise.  The 6 dB hybrid combiner is Figure 7.41 from EMRFD.

I tested my basic setup with a variety of powers from the signal generators. For example: -10 dBm, 0 dBm or 10 dBm. With the various signal generator powers, I got the most consistent measures with a 6 dB pad connected to each SG output. 

This in theory assures that 1 signal generator would be 18 dB down in output of the opposing signal generator and prevent them "talking to" or modulating each other during measures with higher signal generator power. I've since standardized these 6 dB pads in my personal intercept procedure. I typically run the 2 generators at 0 or - 10 dBm and insert at least 20-25 dB of  attenuation on the spectrum analyzer input.  Setups may vary and your experiments will guide you.
    Above — My 2 injected tones and "grass".

Above — My 2 injected tones and "grass". Love this. I saved this spectrogram to file with 20 dB SA attenuation switched in plus an external SMA 5 dB pad threaded on the SA input. Compare this to the transfer function below. I’m trying to keep the 2 tones around -20 dBm.

pectrogram with 25 dB SA attenuation switched in and no external 5 dB pad.

Above —  Spectrogram with 25 dB SA attenuation switched in and no external 5 dB pad. Look 3rd order products emerged from the noise @ 50 KHz out.  Same input attenuation as above: but why the difference?

Above — ADE-1 mixer and 70 MHz LO added.  The available power at the mixer RF port = -12.21 dBm and was used for all IIP3 measures shown. My 70 MHz LO signal came for a 3rd overtone Butler oscillator with serious buffering, a low-pass filter and a 6 dB pad to help ensure measurement fidelity.

Above — The mixer IIP3 measure. Wes shares the calculation as Equation 7.2 in EMRFD: IIP3 (in dBm) = Input power (dBm) + IMDR (dB) / 2 . My IMD ratio from above =  62.09 dB so IIP3 = -12.21 dBm + (62.1 dB/2) = 18.8 dBm. Now let's try with that external 5 dB pad connected and 20 dB of SA attenuation switched in:

Above — 5 dB external padded and SA internal attenuator set to 20 dB.

 IIP3 = -12.21 dBm + (60 dB/2) = 17.8 dBm.

Above — IIP3 = -12.21 dBm + (60 dB/2) = 17.8 dBm. The 1 dB power difference between this and the previous measure is about the power resolution of many spectrum analyzers.

 External 5 dB pad removed and SA attenuation switched to 30 dB.

Above — External 5 dB pad removed and SA attenuation switched to 30 dB.  IIP3 = -12.21 dBm + (58.95 dB/2) = 17.3 dBm.  Switching the internal attenuator to only 10 dB caused all manner of noise and products to emerge and IIP3 results were inconsistent when testing various devices.

I'll stop here since more than anything these experiments show you'll need to experiment to find a consistent technique for your measures. The real beauty of IIP3 or its cousin OIP measurement comes from the math. We can input intercepts into equations or programs to determine the performance of a system  — i.e. you measure individual stages and then design a complete receiver or a transmitter and enjoy the fruit.

At the very least, intercepts serve as figures of merit that allow us to compare, or to meet or beat our design goals. In the case of beloved amplifiers, we can measure stuff like gain, return loss, OIP3, gain compression and really get a handle on what we're stuffing onto a circuit board.

Thanks to my mentors and to Jason, NT7S for his measure comparisons and thoughts on mixer IIP3 measurement. 


During these experiments, I also advanced my wide band FM receiver design and made a few new bench modules. Here's a dash of pictures:

1 version of my ADE-1 mixer under test.

Above — 1 version of my ADE-1 mixer under test. This build features a diplexer on the IF port. On my first version I ran inductors wound on FT37-10 toroids for the diplexer, but the resonator Qu was only 85.7 so I substituted air wound coils. The diplexer boosted IIP3 by about 2 dB.

I bolted the SMA connectors onto the mixer circuit board. The green breakout board is well soldered to the copper ground plane at 6 points.

I built a bench module low-pass filter for 50 MHz using an ARRL handbook and Ladbuild and GPLA from the EMRFD CD

Above — I built a bench module low-pass filter for 50 MHz using an ARRL handbook + Ladbuild and GPLA from the EMRFD CD. The cursor is ~set at the 3 dB frequency

A TG + SA sweep of the filter breadboard

Above — A TG + SA sweep of the filter breadboard showed that the "2nd harmonic": 100 MHz lies ~ 61 dB down. OK, it's a keeper.
The boxed up and mislabeled LP filter.

Above — The boxed up and mislabeled LP filter. The 3 dB or half-power frequency is actually 51 MHz — still the ladpac software simulated pretty close considering 5% capacitors, inadvertent coil mounting changes and stray reactance. I soldered the parts right onto a solid copper ground plane.

A 88 --108 MHz double-tuned filter with green coupling wire.

Above — An 88 --108 MHz double-tuned filter with green coupling wire. I later changed the coupling, but in all cases double humped the response and then lightened the coupling while watching the 3 dB or half-power bandwidth, insertion loss and S11-S22. With the TG and SA plus a return loss bridge, you can sweep the input/output return loss and gain valuable insight.

I simply love frequency domain measures — and I'm a 'scope guy!


Monday, 24 November 2014

Crystal Qu and Other Doggerel

A reader saw a photo of my old W7ZOI crystal characterization oscillator (with the suggested switch from Dr. Gordon-Smith, G3UUR) in the site archive. I had removed its crystal holders to yet another such oscillator and just soldered in a crystal as a PROP for the photo. This photo "suggested" it was OK to solder in the various crystals under test. 

The reader found serious temperature drift during crystal frequency measures and then emailed me with deserved concern. Yikes.  My bad — I apologize.  Securing a crystal under test in its holder must never involve heat. Wes, W7ZOI even puts a crystal into its holder while wearing gloves to minimize body temperature effects.

I prefer to characterize crystal motional L and C with the G3UUR formula and measure C0 with a LC meter. For Qu, I'm adopting Wes' series trap method shared in EMRFD Chapter 7. I'll blog my humbling Qu experiments after this introductory bit.

Oscillator photos

 Oscillator photos

Above — 3 photos of an actual oscillator I've used to characterize crystal motional parameters. In the third photo I replaced the gimpy toggle with a slider switch. Studying the effects of switch types might require experiments, however, I've learned that switch lubricants may affect measures. Regardless, the C of the toggle switch plus the 33 pF fixed series capacitor get accommodated in the calculations.

The ultimate switch might include the latching microwave relays like those found in the K2 VCO, or perhaps small pin bridging connectors like those found on motherboards? Building on a single-sided Cu board seems prudent to avoid unwanted Q side effects.

My alligator clip crystal holders might not rank as rave stuff, but they've worked well for me from 2 - 12 MHz.  I'm not a builder known for handsome breadboard techniques — I'm more a framing carpenter: but hope to grow in my understanding of component-level engineering over time.

A new circuit with the the holders for the xtal + capacitor & shorting bar built above a copper ground plane is under development. This fixture uses a tracking generator plus spectrum analyzer to get the values needed to calculate Lm with the G3UUR formula. Further, an IL measure and 3 dB measurement will provide ESR and Qu. "One and done" it will be!
I need to characterize some xtals for the 30-40 MHz crystal ladder IF filters in my future NBFM receiver experiments. I'll share all these experiments in the future.

My current oscillator schematic

Above — My current oscillator schematic. The original version by Wes shown in EMRFD works great and I recommend it . The 2 Colpitts caps should be >=10 times the series 33 pF, so my 390 pF caps work OK. I added a green "power on" LED with a 1K current limiter resistor in my build.

Most of my lower current DC power supplies connect to my breadboards via RCA jacks. This helps prevent DC supply alligator probe shorts during experiments involving many components. Whatever works.

Measuring the capacitance of the open switch plus the 33 pF fixed value cap wired in-situ

Above — Measuring the capacitance of the open switch plus the 33 pF fixed value cap wired in-situ. This will give you the total circuit capacitance of the open switch, the 33 pF fixed value capacitor, and any stray capacitance from your crystal holder, wires, etc. The switch itself plus stray wiring  will be a few pF so the total should be 36 to 40 pF or so.

My open switch total circuit capacitance

Above — My open switch total circuit capacitance.

 Qu Method

Whenever I write about crystal characterization, I spark passionate emails. I've read it all — "gotta use a VNA" , "there's a better way to measure crystal holder capacitance", " a VXO signal generator", "you should use this program, or that fixture". All are good comments and appreciated. 

I think we're lucky to have so many crystal ladder filter experts in our midst.

Certainly, professionals measure crystal parameters with network analyzers, however, we amateurs could debate this forever. Gear and measurement techniques change over time. Digital boxes keep getting cheaper to make, write code for, or buy: even the new Ham down the street bought a VNA to match his antenna. I had to show him how to use it though.

The proof of the pudding lies in in your filter breadboards. Sticking measures/values such as Lm into a program should result in a build that matches the simulated transfer response. If you make and then confirm a good filter; all is well!

Sometimes standard value capacitors, or matching errors from stray L and C, or the lack of shielding may produce extra ripple, or reduce the stop-band response and/or boost insertion loss. Then, too, we sometimes have to make a narrow filter with low Q crystals and suffer high insertion loss because we can't find better xtals at the time. 

Instrument accuracy, measurement quality and arithmetic errors also factor. My gear gets calibrated regularly and it costs me dearly. I know a "expert" builder with old, crusty gear who never pays for professional calibration and then goes off on a new builder because he rounded too much during calculations.

Do your best — forget the folklore — relax, and enjoy your test bench. A desire to know, grow and learn brings its own rewards. I've mentioned this before: ours is often a difficult, frustrating hobby.

Whatever method you characterize your crystals with — it should match your budget, skill and needs.

Measuring Qu

Qu or Unloaded Quality Factor in RF tuned circuits and filters can help with simulations and breadboards alike. I'll show an early attempt to measure crystal Qu. We enjoy a few methods for Q and Qu — enough, at least, to make it a fun challenge.

To preface, I recently bought my first non-home brew signal generator. It's old, but accurate, low noise, and freshly calibrated for I'm on a mission to run a 3 GHz bandwidth lab. A signal generator plus tracking generator/spectrum analyzer will serve as the main signal power measurement instruments as I move well above HF.

In part, wishing to improve my measurement techniques with this gear informed my choice of  Qu measurement technique.

I examined a 4.0 MHz crystal from a batch of 10 "high quality, well matched crystals" purchased in 1996 from a reputable vendor from Germany. To my delight, I found 6 within ~10 Hz frequency and built a N=6,  500 Hertz wide CW filter with 0.1 dB ripple and an IL ~1 dB.

Here's the crystal motional L and C measures plus C0 of a remaining, unused crystal:

my motional L and C measures plus C0:

Above — The series trap set-up.  You need a flat amplitude versus frequency signal generator with 1 Hz tuning resolution, plus a detector that can measure power/amplitude and frequency in a narrow notch. I used a spectrum analyzer with a narrow span + RBW to best pick off the trap or notch frequency. 

The crystal was soldered in a fixture and allowed to cool for 6 hours. I recorded the power measure with the crystal in place, then substituted a through connector to learn the crystal's attenuation at its series resonant frequency,

I've learned that Z0 is the critical piece. I got better data by threading a SMA 10 - 15 dB attenuator pad on either side of the crystal to boost measurement fidelity. 

Above — I measured the attenuation of the notch as 9.46 dB and took equation 7.4 from EMRFD with Lm substituted for Lu. These are fabulous crystals and a Qu of ~275K explains why the IL was so low in my aforementioned narrow CW filter. I've got some glass encased crystals with a Qu of 720K in my parts collection. Now those are sweet.

Above — As a lark, I tried to measure Qu with a direct 3 dB method. Lots of attenuation made the measure difficult and I'm not sure I've truly got Qu. Transformers would work better, but I abandoned this little adventure since I'm happy with the series trap method. I'll also apply the trap technique to infer resonator Q at VHF for filter measures.

Big thanks to all those greats who pioneered crystal measurement and to Wes, W7ZOI for his support.

If you're building the Minima, I recommend viewing this page/site on the xtal filter and more by Steve, VK2SJA. He's got a link to a great crystal ladder filter summary by Nick Kennedy, WA5BDU and also applies the latest version of Dishal by Horst Steder, DJ6EV that embeds the work of Jack Hardcastle, G3JIR and he. Horst, DJ6EV link


Here's a quick Qu measurement of a resonator using the series trap method with a tracking generator and spectrum analyzer. Please see EMRFD Figure 7.66. A 96 nH heavy gauge Cu wire coil was soldered in series with a small air variable capacitor. I measured the resonator's attenuation at SRF after normalizing/zeroing the sweep system. I forgot to photograph the coil and cap in my fixture.

Above — The attenuation at the series resonant frequency.

Above — The attenuation at the resonator's series resonant frequency.

Above — The Qu of this resonator at 112.3 MHz. I then measured and calculated Qu using the 3 dB method shown on November 11, 2014 and got 280 -- pretty close.

Above — A solid copper ground plane and connector holder eliminates any possible unwanted "capacitor" effects of FR4 board. The series resonator was soldered to the center of the copper wire at 1 end and ground at the other.