Cette page était sur le site
de KA7OEI; mais le lien ayant disparu, j'ai reproduit ici
l'article que j'avais conservé. (F5AD)
Putting together an Interdigital Filter
What is a bandpass filter?
A Bandpass filter, as the name implies, is a filter that only passes a certain range of frequencies (a spectrum analyzer plot of the interdigital bandpass filter described below is shown to the left.) Bandpass filters are the elements that allow any receiver to have selectivity, eliminate image responses, and prevent overloads from off-frequency signals, to name a few examples. Bandpass filters take many physical forms including capacitors and coils, pieces of feedline, cavities, and waveguides. The interdigital filter is but one implementation of a bandpass filter. It is so-called because of the physical construction of filter itself. Referring to the image below, you can see that the elements are interleaved, and hence the name.
The Interdigital Filter consists of these interleaved rods
sandwiched between two parallel conducting plates (ground
planes), usually with conductive plates along the sides.
The "height" of the filter (the vertical dimension on
the image) is typically one-quarter wavelength while the elements
themselves are physically shorter (or else both ends of the rods
would touch the walls!) Because the dimensions of these
filters are one quarter of the physical wavelength at the
frequency at which they were designed, building such a filter
(using air as the dielectric) for frequencies much below the 70cm
amateur band would involve a physically large filter. It is
not uncommon to find an interdigital filter for frequencies as
high as 8-10 GHz.
Why go through the trouble of building such a filter? Why can't one simply use a pile of coils and capacitors? At the frequencies involved, the losses and small physical sizes of such components make them difficult to work with and can severely limit their power-handling capabilities. Why can't one simply use a cavity or two? Well, you can, but the precise application may dictate something other than a cavity filter.
The response of a single cavity is limited to that of just a single peak (in the area of the fundamental design frequency, that is.) Its shape can be stretched to a broad peak with gently sloping sides, a narrow spike with fairly steep sides, or anything in between by adjusting coupling and/or Q but you cannot get a broad, flat response with steep sides.
Why would you want a filter that was both wide and sharp? This sort of filter is invaluable for video, data, and other applications where this is precisely the sort of response that is desired. To get this type of response, one requires several filter sections. This could be done with several cavities, but it takes very careful attention to details like coupling and tuning in order to provide a desired response and the resulting filter network will likely be quite large, fragile, and very expensive.
One (of the several) way(s) to get a multi-pole filter that
can do what we want is with a properly designed interdigital
filter. We needed such a filter for the transmitter of the
WB7FID ATV repeater (a 70cm inband repeater) to attenuate the
lower sideband (which was regenerated somewhat by nonlinearities
in the amplifier chain) and to keep low-level intermod products
from the transmitter out of the receiver. The picture below
shows an example of a filter that we (Clint KA7OEI, Dale WB7FID,
and Marv KA7TPH, and Dave, N7UWQ) built several years ago.
It is constructed of 1/8" thick aluminum plate and it is
partly TIG welded and partly screwed together. (The
"top" cover and coaxial connectors are really the only
components that are held on by screws.)
Assembling a filter with the desired characteristics isn't trivial, though. The internal dimensions play a large part in determining the bandwidth, the steepness, the center frequency, and properties of the bandpass (i.e. ripple.) For design guidance, we have used a program that first appeared starting on page 12 in the January 1985 issue of Ham Radio magazine. This program was written in BASIC and it can downloaded . (Dale Heatherington, WA4DSY, has an online version of this same program - see the link at the bottom of this page.) In this form, it has been written to run under the old GWBASIC but it should run with minimal modification on more current BASIC implementations. (Note: To download this program, you might want to click on the link with the right mouse button and choose the "save link as" option. Note that although the listing of the program appears in the January 1985 issue of Ham Radio magazine, there is an errata that appears a few months later. The correction (which has been made to the listing provided) fixes a problem with the plots that the program generates and not with the datum that is produced.
How to run the program
Without having access to the article, the program may be somewhat cryptic, so I'll step through a sample design. Assuming that you've gotten the program to execute in your BASIC implementation, you might want to follow along. If you do use GWBASIC, I'd recommend starting it with the following command line:
gwbasic intdig.bas > outfile.txt
This will not only run the program, but it will cause the output of the screen to also be "piped" (output) to a text file (called "outfile.txt" in the example) so that you can review (and/or print) its output later using a text editor.
Let's design a filter for 426.25 MHz ATV.
Since the video goes from 425.0 to 431.0 MHz, our center frequency will be 428 MHz (0.428 GHz.) We want to pass 6 MHz of video with minimal distortion, so we should really design the filter to be 7 MHz wide (to allow for some fudge factor, as the overlap between theory and practice is sometimes smaller than we'd like...)
Another consideration has to do with how much ripple we wish to allow in our passband. If we specify 0db ripple, we have also specified a Butterworth filter response. If we do specify a certain amount of ripple, then the program will design a filter with a Chebychev response. Which type of response do we want? A Butterworth response has a nice, smooth passband (ideally) but the passband edges typically aren't as sharp as those of a Chebychev filter design with the same number of elements. A Chebychev has ripple, but it has the advantage of being sharper than a Butterworth filter of similar complexity.
We'll do a compromise: We'll specify 0.1db of ripple. This minor amount of ripple will have a negligible affect the video but, for the same number of filter elements, it results in much sharper skirts than you'd get if you'd specified no ripple at all.
We'll design for 7 elements. Why 7? I've run the program, and 7 is a nice number: It produces a fairly low-loss filter with excellent filter bandpass/bandstop properties, suitable for most transmit applications. For a receive filter, 5 elements would likely be adequate.
Of course, this filter will be designed to operate in a 50 ohm system.
Note that all dimension are in inches.
First, run the program. You'll be asked:
# OF ELEMENTS, P-P RIPPLE IN PASSBAND (DB)?
At this point, we'll enter:
for 7 poles and 0.1 db of ripple.
INPUT FILTER CENTER FREQ. (GHz), BW(MHZ)& LOAD IMPEDANCE ZO?
0.428, 7, 50
for 0.428 GHz (428 MHz), 7 MHz wide, and 50 ohms.
The next information it wants is:
INPUT GROUND PLANE SPACING, ROD DIAMETER
& DISTANCE TO CENTER OF FIRST AND LAST ROD?
If you look at the picture of the filter, you'll see the long, narrow dimension of the filter (with the tuning screws.) The "Ground Plane Spacing" is the inside dimension of the "thickness" of the filter. Again, from experience, a 2.5 inch space makes for comfortable filter dimensions. The filter elements are assumed to be round, and we'll use 1/2 inch diameter rods. The "distance to center of first and last rod" cryptically refers the spacing between the center of each end rod (the ones with the taps on them) and the adjacent inside end wall. 1.5 inches is a good distance for this. (Remember that that makes the rod 1.25 inches from the wall - we are measuring from the center of the rods.)
So, we enter:
2.5, 0.5, 1.5
for the "thickness," rod diameter, and rod-to-endwall spacing.
The next parameter we are asked for is:
NO. OF FREQU. REJECTION PTS AND STEP SIZE (mhz)?
This has to do with the ASCII plot that the program produces. You can ask for up to 40 points of data and specify the resolution of those steps. We'll specify 25 steps at 0.5 MHz spacing, so we'll enter:
At this point, the program will start spitting out data:
CENTER FREQ. .428 GHZ
CUTOFF FREQ. 0.4245 (ghz) AND 0.4315 GHZ
RIPPLE BW. 7.000029E-03 GHZ
3 DB BW. 7.476034-03 ghz
FRACTIONAL BW. 1.635521E-02
FILTER Q 57.24961
EST QU 3598.194
LOSS BASED ON THIS QU .809367 DB
DELAY AT BAND CENTER 249.5265 NANOSECONDS
press any key
At this point, you might want to write this information down (or at least start printing the screen if you didn't start GWBASIC with the output piped to a file.) Here is an explanation of the data:
My experience with the filter shown is that if it is tuned for maximum flatness, the group delay is pretty consistent throughout the passband.
Pressing a key will cause the program to generate an ASCII graph of the predicted filter response, the frequency of the data point, and the calculated insertion loss (rounded off to within 1db) of the filter.
Pressing a key again will give some more data:
QUARTER WAVELENGTH = 6.894159 INCHES
THE LENGTH OF THE INTERIOR ELEMENTS = 6.38665 INCHES
LENGTH OF END ELEMENTS = 6.407211 INCHES
GROUND-PLANE SPACE = 2.5 INCHES
END PLATES 1.5 INCHES FROM C/L OF END ROD
TAP EXTERNAL LINES UP .3113659 INCHES FROM SHORTED END
LINE IMPEDANCES: END ROD 108.2183, OTHER 110.9835, EXT. LINES 50 OHM
Pressing a key again (for the final time) will display the internal element spacings. The "END TO C" refers to the distance (in inches) of center of that particular element to the end wall, and the "C TO C" spacing just refers to the spacing between adjacent elements. The G(K) and Q/COUP are coupling coefficients for the given elements. Note that "Element 8" isn't an element at all, but is just the distance from one wall to another (the "width" or the horizontal dimension on the image above.)
A word of warning: The above lengths are those
predicted for exact tuning assuming that the predictions were
perfect. The reality is that you'll want to be able to tune
the elements slightly to allow for the (inevitable) departures
from the predicted parameters. So, you'll actually want to
make the elements a few percent shorter than the predicted
lengths and you should be prepared to shorten them even more!
Building a filter
Before you start building, design the filter that you believe you want. This may sound silly, but I strongly recommend that you try several variations of the filter (number of poles, ripple, ground-plane spacing, etc.) and carefully weigh the resulting properties for each predicted filter (i.e. insertion loss, physical size, etc.) One thing that you'll immediately notice is that the length of the filter increases dramatically with the increasing ground-plane spacing, but the insertion loss goes down.
What material to use? Silver-plated brass or copper would provide some of the best performance (i.e. lowest loss) but polished copper (without the silver) will work nearly as well (provided that it is protected from moisture...) Aluminum would be the second best choice, and brass would be the third.
How does one hold the filter together? Perhaps one of the most practical ways (although laborious and time-consuming) to assemble such a filter is with screws, with threads drilled and tapped. For this case, you will need at least one screw per element along the length of the filter (that's 4 screws per element if you count the top and bottom screws and the ones on the back. Along the sides, you'll need to put screws at intervals no larger than the spacing of the elements - and probably more than that, with at least two screws on the "thickness" part of the side walls.
In the case of copper, brass, (or other silver-plated metals) the filter can be (at least partially) soldered together. Of course, you would never want to solder the filter completely together as you would find it extremely difficult to disassemble should repairs (or modification) be necessary. For Aluminum, you would probably use screws to assemble the filter and using appropriate amounts of anti-oxidant on mating surfaces to assure continuity. Of course, it is possible to TIG weld the filter (as we did in the filter shown above) or even use aluminum-capable solder (which is expensive and usually contains cadmium - a toxic heavy metal.)
One of the somewhat unusual aspects of this particular filter
is that it uses tapped end-elements (tapped at the point at which
they exhibit the designed impedance) rather than the end-fed
resonators that are shown in the oft-quoted March, 1968 QST
article by Fisher. This makes for simpler
construction. The picture to the right shows the tap-point
for our aluminum filter. You can see the rear of the
chassis-mounted N connector and the conductor that goes through
the element at the tap point. In this case, it is a short
piece of #12 copper wire, held in place with a hex-head
(allen-type) setscrew. The connection is coated with
anti-oxidant to reduce the effects of electrical connections of
dissimilar metals. This filter was built in 1994 and we
have never had any problems with these connections.
The elements themselves are also aluminum, but they could have
been brass or copper. Since we had access to a TIG welder,
the elements themselves were first mounted with screws and then
tack-welded to the sidewall to assure mechanical strength and a
consistent electrical connection. If we had used
copper or brass, we would have just used a stainless-steel screw,
the connection would be coated with anti-oxidant, and the
wall-end of the element would have been counterbored in concave
so that the outside "rim" of the element would be
making solid contact and not the center of the element, which
could "wobble" about.
How does one tune the elements? Firstly, remember that
these elements are electrically shorter than 1/4
wavelength. Secondly, remember that the length of the
elements as predicted by the program are the idealized
lengths for the desired response. In other words, if
everything were perfect these would be the lengths of the
elements for the exact response desired. Since everything
is not perfect, you will have to make the elements
slightly shorter than the predicted lengths so that they can be
tuned for the desired response. The amount of this
shortening is on the order of a few percent and is rather
difficult to predict. Be prepared to trim the elements
slightly after the filter is assembled! In the case of
the filter shown, the elements had to be shortened by over 1/8 of
an inch. A rotary tool (such as a Dremel) and a file was
used for this task, as the element could not be removed
(remember: it was welded into place!) Normally, only
tuning screws are used and the proximity of the screw to the end
of the element adds just enough capacitance to tune the element
down into proper resonance. In the case of our filter, it
was originally designed to operate on the 439.25 MHz ATV
frequency but we needed to retune it to 426.25 MHz. While
the screws could tune the filter to frequency, the spacing
between the screw and the end of the element was very
small. This could reduce the mechanical stability of the
filter's tuning and the small spacing could permit arcing at
higher power levels. Small disks were soldered to the end
of the screws in order to increase their surface area and thus
the capacitance. On the outside of the filter, there are
jam nuts on the screws (both of which are brass, by the way) to
allow the filter tuning to be locked once the desired response is
The interior of the complete filter is shown to the left. Although they are difficult to see in the picture, you can just make out the tapped holes at each element and at several points along the sides. There are 20 screws (14 for the 7 elements, 3 along each side) that hold the top on the filter. It should be noted that during the initial tune-up of the filter, it was not possible to get any sort of representative filter response without putting the cover plate(s) on and the screws in. In other words: If you need to trim the elements to allow them to be tuned, you will have to put the cover(s) back on and the screws in every time you want to see if you have shortened the elements enough.
Tuning the filter
A bit of advice: Do not even waste your time trying to tune the filter unless you have some test equipment to tune the filter! Let me say that again. Unless you have some test equipment, you are going to pull your hair out trying to tune the filter! Even if you do have the equipment, it is likely that you will still lose some hair!
There are several equipment lineups that will allow tune-up:
WARNING, ATTENTION, ACHTUNG, AVIS, ALERT, NOTICE:
If you are using the sweep generator/detector or tracking/noise generator/spectrum analyzer method (or some combination) you must put resistive pads on the input and output of the filter, at the filter! Even though it may say 50 ohms on the test equipment, do not believe it! At the very least, the cables will transform the impedance to something other than 50 ohms resistive during the tuning process. Use at least 6 db pads (and preferrably, 10 db pads.) If you don't do this, you'll be chasing your tail. The two pictures above demostrate this very clearly: The picture on the left is shown using 10 db pads on both the input and the output while the picture on the right demonstrates the ripple that can result if you rely on the test equipment to source and terminate at 50 ohms (notice the almost 2db ripple on the one on the right!.) Unfortunately, it can be difficult to maintain a 50 ohm system (using ferrite isolators and watching VSWR helps) but it is important that you have a known starting point. YOU HAVE BEEN WARNED!
Assuming you have the equipment, you are now faced with trying
to tune the filter. It may not be easy to try
to tune a filter with numerous highly-interactive
adjustments. If you have a "knack" for such a
thing, sometimes you can get the "feel" of the filter
by tuning each screw, observing it's effect, and then tuning it
by the seat of your pants. Be forewarned: Not
everyone can do this, so don't kill yourself trying!
The "Dishal" Tuning method:
You must first determine if the elements are short enough (or long enough) so that there is adequate tuning range. While having a network analyzer is nice, Dale, WB7FID did some digging through old IRE and IEEE journals and reports that the easiest way to determine what your filter is going to do is with the Dishal method (named after the author of an article where this procedure was described.) This method requires a signal generator and a slotted line. The Dishal Method of tuning an interdigital filter is approximately thus:
By the way, since you are looking for standing waves, etc. you do not use attenuators for this procedure.
If you have a network analyzer, you can infer from the
above procedure what it is that you should be doing. If the
elements are of the proper length, you should be able to easily
tune through the null or peak (whatever it was that you tuned
for) without the screw being too close to element rod end or
being almost completely removed. In the case of the latter,
the element needs to be shortened. In the case of the
former, you cut the element too short and you either need to
lengthen it (preferred) or put a disk on the screw.
"But I don't have a slotted line.."
If you don't have access to a slotted line, you might want to ask around to find one. Alternatively, you can construct a "reasonable facsimile" (see the picture to the right.) This is essentially an open-air transmission line that is suspended above a ground plane. Ideally, it should be at least 1/2 wavelength long at the test frequency (to allow selection of a peak or a null) but you can make it shorter if you have an assortment of short pieces of coax that you can insert/delete: The idea is to place the peak (or null) somewhere along the slotted line. Strictly speaking, this is not really a slotted line, but but the whole point of this exercise is to get access to the center conductor so that you may sample some if its energy.
Place the line (consisting of some brass rod, stiff copper wire, etc.) about 1/8 inch above the ground plane (if you are a purist, you can go ahead and calculate the proper height for 50 ohms... Since we are utilizing the standing waves anyway, it isn't all that critical.) With the procedure above (with all elements shorted) you would place the probe very close (but not touching!) to the line and slide the probe (the diodes, etc.) along the ground plane until you find the peak/null.
You may need some reasonable amount of power for this in order to get enough energy to get a good detector reading: I used a handie-talkie on low power (1/2 watt) for this. Once you have found the peak/null, you can then tack-solder the ground of the probe to the plane. Once the ground is soldered down, you can usually move the probe back and forth slightly to fine-tune the peak/null. Using some circuit board material makes soldering much easier.
For the diodes, use 2835-type shottky mixer diodes, 1N34 types, or 1N914/1N4148 types (in order of most to least sensitive) and all but the 2835 types are available at Radio Shack. For the capacitor, a small 0.01 uf disk ceramic is adequate. Keep all leads (except for the probe lead - which could be the lead of one of the diodes) as short as practical.
Alternatively, you could etch (or cut) a 0.110 inch wide line into a length of G10 or FR4 0.062 inch thick double-sided glass epoxy (don't use any other kind!) circuit board. Leave about 0.1 inch gaps between the line and the surrounding ground plane. Wrap the edges of the board with copper foil and drill small holes in the ground planes alongside the strip and put small wires (soldered on both sides) to make sure the ground integrity is maintained. Like the suspended line, you would place the probe very close to (but not touching) the line.
This procedure also reveals something about what the "natural" response of the filter is supposed to be. If you built it exactly right, it will produce a response that somewhat resembles the original design parameters (you hope...) At this point the tuning should need to be only slightly changed to attain the desired response or, at the very least, you should have a good starting point for tuning. If you can't get the response that you desire, then there are at least four possibilities:
There are a few things we learned when building our filter (some of which fall under the heading "If we do this again, we'll do this differently!")
Remember, you still need to figure out how to hold the sides of the filter together (i.e. solder, welding, brazing, or with screws.)
Did you wonder what the specifications of the filter were when we finished it? Here they are as I recall them:
You'll no doubt notice that there is almost 1db more insertion loss at the chroma frequency than at the video carrier frequency. Again, I should mention that this is a filter that we would have built differently if we knew then what we know now!
When we did the final tuneup we were fortunate enough to have access to an HP Network Analyzer. After "diddling" the tuning for a while, we noticed that we could get the tuning absolutely flat if we wanted an insertion loss of about 1.8 db or so, or we could tune it to favor the video carrier frequency and cut our losses by about 0.5 db. We chose the latter since that is where most of the power is: We could always crank up the chroma a bit on the video processor (and we did) to make up the difference. I don't remember what the group delay parameters were precisely on the final tuneup, but they were more than acceptable for amateur use (the effects weren't visible in the video, anyway.)
When we recently retuned the filter for the 426.25 MHz video frequency (remember that this filter was designed for 439.25 MHz!) we got approximately the following results:
The range of the test equipment used prevented measurement of the filter's attenuation below 110 db.
The spectrum analyzer plots above (the one at the top of the article, plus the two showing the effects of not providing proper resistive termination of the filter) are of this filter, as tuned for the 426.25 MHz frequency (the filter center frequency is 428 MHz, 5 db/vert. div., 2 MHz/horiz. div.)
You'll have noticed two things here: The insertion loss was higher, and the filter was tuned for flatness and not for "minimum attenuation where it matters most." The increased insertion loss is likely the result of the taps being in the wrong positions for the frequency, and for the internal dimensions of the filter being a bit too small. Additionally, we had to put the disks on the tuning screws in order to load the resonators down to the proper frequency and that probably increases the losses slightly.
Dale, WB7FID, has been working on integrating the various components of the repeater. We have both been somewhat disappointed by the performance of the filter and have been determining ways to fix it, or mitigate its problems.
The apparent "lossiness" of this (or any) filter can be attributed to several things (this is not an exhaustive list):
We are fairly confident that the aluminum filter described above is primarily a victim of #2 above. The return loss (how much power was being reflected by the filter - essentially the same thing as VSWR but using db instead of the unitless number) indicated a return loss of 6-12 db (depending on frequency.) This fact immediately accounted for a pretty significant portion of the apparent "lossiness" of the filter.
What might cause the apparent mismatch? Here are some possibilities:
All of the above are interrelated to some degree. Because of the mechanical difficulty involved, we have chosen not to try to readjust the tap and have decided to concentrate on the second two.
Dale, who works at a local (to him) University (in a microwave/RF-type lab, as it turns out) has access to a network analyzer which allows him to do definitive "before" and "after" comparisons. The first item of business was to find the "natural" response of the filter using the dishal method (described above.) In very general terms, if the filter is too narrow, it is undercoupled. If it is too wide, it is overcoupled. In our case, Dale found that the filter was about 6 MHz wide - and our target was a bit over 7 MHz wide.
How does one increase coupling? One obvious solution is
to move the elements closer together. Equally obvious was
the fact that we weren't going to be able to do this with the
already-built (and welded) filter. Another way to increase
coupling is to increase the diameter of the rods
themselves. That wasn't much of an option, either, as the
elements themselves are aluminum (we didn't want to try welding
more metal onto them because we didn't know how much...)
The obvious solution (to us) was to put some very small hose
clamps on the elements: This will increase the apparent
diameter of the element, and (importantly) the amount of coupling
is variable by the virtue of the fact that the elements
may be moved about, and that a greater (or lesser) number of
clamps may be added as needed.
The picture shows two clamps in the center of one of the end (tapped) elements and its adjacent element. Dale did some extensive experimentation (with more and fewer clamps) and found that the above combination worked very well for this filter.
A note: Placing the clamps near the ground end of the elements will have less coupling effect from that element while placing it at the open (high impedance) end will possibly couple more energy, but it will also significantly change tuning (as the end of the element is effectively bigger) and, if high power is being used, the sharp edges of the clamp may allow corona or arcing to occur. We chose to put our "coupling clamps" in the middle of the elements.
The result? Look at the chart on the right! (and click on it to get a bigger view.) You'll notice that the insertion loss at the Chroma and Sound frequencies (which also pass through the filter) is higher, but since they represent only a small percentage of the total energy, the additional losses incurred may be compensated by increasing the chroma output of the video processor (if you have one) and the aural transmitter power (we use a completely separate audio transmitter as described ) The return loss isn't a whole lot better than it was, but we are either going to:
But that is to be left for a later time...
Actually, we are building a new filter. This one will also be made out of aluminum, but it will have silver-plated copper rods. It will be much larger (physically) and we are trying to get the insertion losses well under 1db. It will not be TIG welded together (as the heavier stock makes that more difficult) but rather it will be put together with lots of stainless-steel screws and anti-oxidant to maintain good connections and to prevent the screws from seizing in their threads. We have just acquired most of the material but, since we already have a useable filter (the old one) we'll go forward with the repeater project and get it on the air with the old filter first: We'll worry about replacing the filter once we're on the air.
From the WA4DSY site, there is an online calculator on the Design a custom Interdigital Bandpass Filter page.
Return to the Utah ATV Home Page or to the WB7FID Repeater Transmit Filter/Combiner subsystem page.
This is an evolving document so check back occasionally. If you have any questions or comments, please email them.
This page updated 20030513