Tuesday, 9 December 2014

Mixer IIP3 Notes

Greets###

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 in consistent 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. 

More

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!

Best!



Monday, 24 November 2014

Crystal Qu and Other Doggerel



Hello!
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", "...run 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

Update:

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.

Best!

Tuesday, 11 November 2014

Measuring Resonator Q at VHF

Greetings!

I've long enjoyed broadcast FM DX chasing. This post covers the first chapter in my pursuit to design and make a homebrew broadcast (wideband) FM DX receiver.

Traditional FM DX superheterodyne receiver ran single conversion with a 10.7 MHz IF and usually a dual-gate MOSFET mixer behind 1-2 dual gate MOSFET preamplifers embedded in 2-4 doubled-tuned bandpass filters.  To cover 88-108 MHz with decent skirts + bandwidth, the band-pass filters were tuned with ganged, air-variable capacitors that simultaneously tuned the VFO.

Fast forward to this day in time. Following low-pass filters and T/R switch circuitry, some modern narrow band FM transceivers run varactor tuned band-pass filters, 1 or 2 dual gate MOSFET amplifier(s) and a MOSFET mixer in the receiver chain.

I explored varactor tuned band-pass filters for wideband FM and learned a few things along the way.


Above — My first FM band-pass filter that tuned all 20 MHz of the FM band without a double humped filter response. In order to get the BB639's capacitance down to its lowest value (~ 3 pF to tune 108 MHz), you need 28 volts applied reverse DC. I keep a homebrew bench DC-DC converter for just that purpose. The filter's 3 dB bandwidth ran from about 2.2 MHz at 88 MHz to 3.3 MHz wide at 108 MHz

In order to boost the filter low-pass response, I tapped the inductors for the input and output ports. Light loading improved the filter response, but reduced the input/output return loss. Tuning a filter over a 20 MHz span proved a lesson in compromise.

60 nH isn't a lot of L and my coils were 6 turns of bare copper 22 gauge wire wound on a small bolt and then stretched to allow room for tapping and to set the correct measured inductance. I further tweaked them in-situ. Later, I placed this filter after various preamplifiers including a dual-gate MOSFET and a common gate JFET amp.


Above — A snippet of 1 of my amplifier + band-pass filter circuits. I got a better filter response with a 96 nH inductor, although this should technically worsen it.

1 major problem arose with my filters: a horrible insertion loss of 8-9 dB!!  I expected about half that. Later I wrote some great friends for advice and after reading their wisdom, I came up with 2 sane theories: the insertion loss was due to lowered Q and input + output port mismatch.

Resonator Q Measurement

I then realized that I'd never measured resonator Q at VHF. If you own a Q meter such as the
HP4342a stop reading now, get a coffee and go to another blog-site.

As amateur experimenters, to derive resonator Q we may employ 2 techniques: calculate Q after measures with a parallel tuned L C tank, or calculate Q after measuring with the L and C set in a series tuned trap circuit.

I've not enjoyed much success with the latter, so will present the method where our parallel L and C are loosely coupled to a 50 Ω source and load. Please refer to EMRFD page 7.36 for more details.

Supplies:
  • Signal generator with level output amplitude,  50 Ω output Z and enough output power to allow measurement with your particular detector.
  • 50 Ω detector: spectrum analyzer,  50 Ω terminated 'scope, or measurement receiver etc.
  • 50 Ω patch cables.
  • A homebrew jig with RF connectors, coupling capacitors and ground plane.
  • Frequency counter.
  • Through connector.

Setup:


Above — The basic paralleled tuned resonator measurement set up including gimmick probes as the input and output coupling capacitors.



Above — My test jig with the inductor and air variable capacitor soldered in place. I copied this jig from Bob, K3NHI and received advice from Wes, W7ZOI. Bob made a circuit at his QTH, measured the resonator Q and sent me a photo and some measures by email. I re-created his circuit to compare results. The coil = ~ 300 nH or 10 turns on a 1/4 inch bolt. The capacitor to resonate it @ ~100 MHz on my bench = 7.27 pF.

 Method to Set Jig Insertion Loss at VHF

In order to measure a resonators unloaded Q, or Qu, the insertion loss of the jig must minimally be 30 dB. To clarify, join the input and output cables together with a barrel or through connector and measure power. Unsplice and then connect the cables to the jig and measure power once again — power should drop by at least 30 dB at the test frequency.

To create the >= 30 dB insertion loss we lightly couple the jigs input and output with low value capacitors. At HF, we may insert small series capacitors, but this is nearly impossible at VHF unless you own some special microwave parts. Instead of series capacitors, we couple with gimmick wires.  Experiment to find the correct wire distance from the resonator to create the needed insertion loss.

Here are my 2 jig measurements with a DSO plus the IL calculation:





Above — My insertion loss fulfills the require >= 30 dB needed for proper resonator coupling
I calculated the IL in dB with JavaScript Tool G. It's difficult to measure under 50 mV with a 'scope for some; your power meter or spectrum analyzer might work better.

To get the needed IL or measure for Qu calculations, set your signal generator to the desired frequency and then tweak the resonator variable capacitor to give the highest possible AC voltage/power. Then re-tweak your signal generator to ensure you've peaked the signal. You might have to re- tweak the variable cap again and so forth.

Optionally, If your resonator capacitor is fixed, adjust your signal generator frequency to peak the signal.

After properly setting the IL and peaking for the strongest signal, the final measures go quickly:

  1. Record the frequency where you measured maximum power: that's FO, or center frequency.

  2. While watching your detector, lower the signal generator frequency until FO power drops by 3 dB [easier to do with an SA or power meter]. Record that frequency.

  3. Bring the signal generator back up to FO and then increase frequency until the power drops by 3 dB. Record that value.
  4. Calculate Qu as Frequency/Bandwidth.
I'll show my measures performed with a homebrew signal generator with less than ideal tuning resolution; however, you'll get the idea.



Above — FO or center frequency = -25.84 dBm, therefore my 3 dB down target = 28.84 dBm when I change my signal generator below and above FO.



Above 2 images — The 3 dB measures below and above FO (getting as close as possible with a homebrew VCO).  My VHF VCO sports a >= 30 dB output return loss from 98 - 149 MHz.
Calculate B or the 3 dB bandwidth by subtracting the lower frequency from the higher.


My calculated resonator Qu = 289. Bob, K3NHI measured then calculated 300 on his. Pretty close.

Bob's homebrew jig and resonator.

Above — Bob's homebrew jig and resonator. Bob measures everything: including his breadboard length! 

Varactor Measurement

I removed the air-variable trimmer cap and inserted a small piece of copper clad break-out board to hold a tiny BB639 varactor (size SOD-323). I voltage tuned it to resonance and then repeated the whole resonator Q measurement routine. Q = 174: a drop of 115 which would boost my original FM band-pass filter insertion loss by at least 1.5 dB compared to an air variable capacitor.


Measuring resonator Q with a varactor.

Above — Measuring resonator Q with a varactor.

Through experiments with the the aforementioned parallel + series resonator measurement techniques, I learned that carved squares and traces in boards may also lower Q. Even a Manhattan or carved pad nearby may couple to the resonator and drop its Q during measurement. My worse case measure produced a drop in Q of 20 from nearby islands carved in the copper board. Clearly we need board traces, but they can affect resonator Q and thus add to filter insertion loss.

Further, good VHF filter designs stick each resonator in an RF tight compartment. Whatever filter I eventually keep, I'll mind my Qs.


Footnotes

Thanks to Bob, Bob, Wes, Ken, John and others who kept me on track  — I know just enough to act foolishly on the bench.

I made 1 varactor tuned band-pass filter on single-sided copper board and compared it to the double-sided board versions. The single-sided board suffered poor stopband shape and didn't tune as well.

double clad board


Above — A board set up for a dual-gate MOSFET surface mount circuit where the FET source runs a shunt resistor and capacitor to ground, plus has DC voltage on both G1 and G2. Some via holes connect the top and bottom ground plane.

double clad board


Above — I placed 22 gauge copper wire in the via holes and soldered them top and bottom.
Grounded parts are placed near a via wire. Sometimes, I'll add more via wires near grounded parts.

100 MHz amp

Above — A single frequency amplifier carefully matched to see how much gain the BF998 could deliver. 21.2 dB rocks my world.

Some of my (mostly) 50 Ω homebrew bench modules for test and measurement

Above — Some of my (mostly) 50 Ω homebrew bench modules for test and measurement.



return loss bridge

Above — My favorite design project of 2014: a return loss bridge with directivity >= 30 dB from 5 MHz to 1.5 GHz.   You may read more about it in the old site pops.net archive: Topics 2012 - 2014 : Caitlyn 310 — UHF Beginnings : 3. Return Loss Bridge Experiments : Bridge #4