February 2009 Archives

Single-Frequency Networks

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I'll expound on this later after I've thought about it more.

I just ran across Single frequency network on Wikipedia, and was struck by one paragraph:

"An SFN may also increase the coverage area and decrease the outage probability in comparison to an MFN, since the total received signal strength may increase to positions midway between the transmitters."

The FCC provides a "protected contour" of estimated signal level to a broadcaster according to the license of that broadcaster and other agreed upon terms and conditions. The broadcaster is responsible for engineering, construction, and maintenance of such facilities to permit distribution of an electromagnetic field over that contour without impacting the operations or protected contour of another broadcaster. The strength of the electromagnetic field determines received signal quality and essentially limits the possible audience of that broadcaster.

Within the above in mind, it may be possible that by switching to OFDM or "Digital TV," future television broadcasting opportunities may be presented through the use of translators.

At present, translators are used in television broadcasting, but are licensed to different television channels and are assigned callsigns which may bear no resemblance to the registered marks or brand of the owner, operator, or beneficiary of the translator. I say beneficiary as the translator may not be owned by the television or FM radio station, and may or may not be claimed by the broadcast station as an additional market presence.  In the FM radio band, the licensure of every available combination of frequency and power has turned most formerly small markets into what metropolitan radio markets resembled a decade ago: A wall of radio stations from band-edge to band-edge, with seemingly no space between stations. The translators further compound the problem by using another radio channel at a lower licensed power than the FCC would otherwise permit a broadcaster or would-be broadcaster to implement -- anywhere from one watt to four hundred watts. 

However, back to the idea of the single frequency network, it is possible to implement a signal frequency network or simulcast network using multiple transmitters in multiple locations to completely saturate the protected contour of that broadcast station. The chief difficulty in implementation is that each transmitter should have an extremely stable source of frequency synchronization, as interaction effects between the two radio waves will cause signal nulls and other phenomena which will reduce the coverage of the transmitters in spaces where both signals may be present.

This entry is at present incomplete.

Twist-Shift Keying or Primative PSK?

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Published, 2009-02-08 @ 21:08:58:

http://maxmcarter.com/twistmod/index.html or Twist-Shift Keying, documents an idea to modulate RF around the axis of the antenna ('boresight') instead of modulating the phase, amplitude, or frequency of the antenna.

I am at present formulating a response to this.

My current feelings are that this is a slow, imprecise version of phase shift keying, wherein the signal is phased at +90 or -90 degrees. This is a confusing idea to consider. According to documentation provided by the author, the transmitted signal is either left-hand circularly polarized, or right-hand circularly polarized. From the perspective of the discriminator, this should mean that the signal is approaching or receding, however one also has to think about the fact or concept that the antenna itself may force the signal to simply not appear at all.

I think that for the purposes of considering this signal or modulation method, it may be easier for the reader to work within the confines of linear polarization. Linear polarization is typically defined as either vertical or horizontal polarization, however one may also implement 45-degree and 135-degree polarization by implementing a dipole rotated to that particular alignment. Again, in simplifying mental math, vertical and horizontal polarization need only be considered because of the theoretical infinite loss caused by a linear polarization mismatch.

Moving further along the above idea, one may interpret that when a signal appears on the vertical plane, said signal is absent from the horizontal plane. This, in effect, makes the polarization modulation a crude form of a binary modulation, not unlike a form of Orthogonal frequency division multiplexing.  In the theoretical world, it is possible to determine four states from the two polarizations and the state of the transmitter for each polarization.  Realistically, this may approach the impossible as polarization may be affected by antenna location and/or nearby reflectors. In a long-distance implementation terrain, atmospheric, and ionospheric effects may render the signal completely unusable without some form of a transmitted reference or a guide signal or encoding. It is the opinion of this author that switching to circular polarization would not rid the signal of polarization modification.


The nice part of this supposed modulation method is that the receiver antenna orientation does not affect the capabilities of the receiver so long as the antenna area of sensitivity is pointed at the transmitter. The receiver is only required to differentiate between the two polarities of circular polarization.

Possible? Yes.
Implementable? Yes.
Practical? No.
A use for two Syntor X transcievers? Yes, better than holding down the dumpster. =)

Update: Now that I've had to opportunity to learn a bit more, I realize why this approach is novel but also useless. Previously, we have not modulated a signal based on polarity because polarity may be altered by the physical terrain the signal travels over and through. On HF, Faraday rotation may occur which causes a signal transmitted with a vertical polarization to be reflected in a different linear polarization, such as one at an arbitrary angle anywhere from zero to ninety degrees. For example, vertical polarization that has been shifted ninety degrees is horizontal polarization. Any shift from 90 to 180 degrees is indistinguishable from a shift of zero to ninety degrees without additional polarization information.  This shift may be resolved using interferometry and a second receiving antenna a fixed distance from the first.

The biggest practical reason I can see for not using Quadrature Polarity Modulation (QPM) is that it is often necessary to cross-polarize an antenna to minimize the effects of an interfering signal. Furthermore, using horizontal polarization for long-distance linking allows the reflections from the terrain to cancel each other out, resulting in less multipath interference at the receiving antenna.

I am certain the QPM was discovered at some point in the infancy of radio. I believe there are a number of factors which contributed to abandonment of this form of modulation.

2013-07-25: Edit and update

The fiber optic industry has, in fact, already done this:

http://blog.catonic.us/kirby/2011%20IEEE%20CTW_Peter%20J.%20Winzer_keynote%20slides.pdf

and did QPSK over it.

Another Use for Stella

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Another use for STELLA would be to improve the intermodulation characteristics of an amplifier. Any time you transmit two carriers into a satellite, it is possible to have the satellite's transponser -- or any linear amplifier -- generate a large number or mixing products. Using a system such as STELLA, an error signal may be generated. This error signal would contain all of the carriers that are desired to be notched out of the signal, out of phase with the signal by 180-degrees, so that when the two signals are combined (or in the digital domain, complex multiplied), the resulting signal will be devoid of the extraneous carriers. A technique not unlike this is used in modern TV (OFDM) transmitters to restore linearity to the signal as the amplifier moves through non-linear points in the performance curve of the amplifier.

Amateur Radio's Political Side

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Kris: so, are the hams there really just antisocial or what?
Tyler:
not really sure
Tyler:
they seem all nice over the air, but in person they are stand offish
Kris:
most radio folks are nerds or geeks, or just idiots
Kris:
or ZOMG ARES whackers
Tyler:
heh
Kris:
you know what I mean about ZOMG ARES whackers, right?
Tyler:
you have shown me photos
Kris:
some of them don't have the distinctive dress

There are some people who got into amateur radio for one crazy reason or another
. I got in because it was neat at the time, and I've met some neat people. By neat, I mean real engineers that I can bounce ideas off of and keep the crazy from infecting me or becoming part of another plan, only to have it unravel later due to a missed detail  Other people got in because of a want or need to spot weather or report weather to someone or something who cared.  Still others got into it because of a misguided desire to serve the public  It's the last category that causes the most trouble, and also provides the most visibility. Terms like "served agencies" further muddle the waters, and the attitudes of these people cause immense amounts of ill will between individuals and groups.

Consider, for example, a group that comes into or forms in a given area for the purpose of "emergency communication." The group has no repeater, no group resources to speak of, and only a marginal source of organization -- a monthly or weekly meeting that not every member attends. The group surveys the local airwaves and determines that there is a repeater that serves their needs. The group declares that they will meet on that repeater frequency for the purposes of furthering that function -- emergency communication -- and drills thereof. This strikes the owner of the repeater as presumptuous, because, like many other repeater owners, he has invested much time, energy and money in establishing that repeater, and the relationship with the repeater's site owner to make that repeater a possibility. This emergency communications group has not taken part in any of the above action until it involved keying a microphone on a radio that a group member himself owned.

Sadly, my example is actually generic; this situation has repeated itself numerous times throughout the country. When I initially wrote this document, another group was in mind. I can now say however, as a repeater trustee, that this situation has happened to myself. Some of the supposed emergency communications groups causing real harm and discomfort between the repeater owner and the site owner. These site owners are often not amateur radio operators, and don't understand the finer details of FCC Part 97, or what amateur radio is about. As a result, these persons, in a state of confusion, may take the easiest course of action in the face of controversy -- to order the repeater owner to come and get his equipment and vacate the premises effective immediately.  

There has been a movement in ham radio as if to find a purpose for spending all this money to either justify buying newer toys, or to justify taking tax money from federal agencies. Public safety has already proven to be a dangerous bedfellow; one need only look at the ReconRobotics case to realize why. I was rather amazed to see at one hamfest where even some of the most ardent of the "served agencies" crowd quickly about-faced and said "let them get their own frequencies."  With great freedom, comes great responsibilities. We asked for spectrum. In exchange for large swaths of space, we are responsible for self-policing and self-regulation, coordination of activities with other operators to avoid mutual interference, and generally interface with the FCC on a lesser basis than any of the other licensees in any of the other services that the FCC regulates.  We must be careful of who we choose to associate with, and avoid those who would harm our hobby. Few hams have the resources to stand as Free Men, and challenge bodies of government when missteps are taken or about to be taken. For this reason, we must continue to be as vocal as possible to keep our issues alive before the FCC, and to assure the FCC that we are doing everything in our power to both protect and use the spectrum afforded to us.

We must also strive to self-educate and redirect those hams who are getting too fanatical. It is certainly one thing to be nuts over contests, EME, or microwave. But to have this need to define one's purpose over or through an interaction with a group whose only interest in radio is that they carry one on their side for communication is just preposterous.

A Remote Control Station

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My extensive research has pretty well proven that there's no single source -- no product, software or hardware, that is manufactured and carried by one of the large ham radio stores that may be purchased through a purchase order.

This is a niche, and there is a void.

I+Q MoDem

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http://www.g6lvb.com/Articles/STELLA/index.htm
Documents one British ham's implementation of an RF equalizer network using a DSP and a pair of DAC/ADC stages at bandwidths of about 96KHz. What's interesting about this is several points. The implementation allows for spreading power evenly throughout a transponder, allowing the transponder to remain linear in the face of a signal that would otherwise swamp, dominate and further modulate the output. This could also be used to allow the transponder linearity to be matched to the current loading, keeping the transponder linear even in the face of extremely high channel loading. This sort of situation would be seen in the event of transponder oversell in the commercial world, or through the use of spread-spectrum and/or wide bandwidth signals such as QPSK, QAM, or OFDM.

What's further interesting about this system is that it allows for "audio bandwidth" processing of signals. Virtually every PC has a sound card that may capture a sixteen-bit signal at up to 44.1KHz, some as fast as 48KHz, and others at 96KHz with a depth of 24 bits. As far as audio performance is concerned, the bit levels are directly convertable to RF performance. Both are a means to describe the dynamic capabilities of the capture and reproduction aspects of the card. In the audio world, There is typically an upper limit of somewhere around +12 to +24dB, and the noise floor somewhere at -110dB to -130dB, with a reference of 0dB or +4dB for a professional sound card (96KHz, 24 bit). What these numbers translate into as voltage levels largely depends on how the manufacturer designed the card and what form of termination that manufacturer had in mind. A typical impedance would be 600 ohms, but some cards have a drive impedance of 100 ohms. 100 ohms is not a terrible match to 50 ohms, which is what may be expected to drive mixers and other RF gear at the baseband level. To assure there are no issues at the baseband level, I would recommend making an effort to match the impedance of each device or at least provide a buffer or attenuator to lessen the impact of an impedance mismatch.

The December 2008 issue of QST http://www.arrl.org/qst/?month=12&year=2008#toc contains an article entitled: "A Modular Reciever for Exploring The LF/VLF Bands [part 2]", which details and implementation of a Tayloe Detector. A Tayloe detector is an interesting piece of RF work in and of itself since it's not a detector (or rectifier) in the conventional sense, but a commutating detector. Now there's an term you don't hear bantered about often in RF or EE circles unless you're designing large civil projects like power generation or electric motor based facilities.  In essence, four switches, each one of which matches to the four phases (0, -90, -180, and -270) are switched to one of two outputs. This provides a means for detecting the sine and cosine components of the signal which are otherwise known as I and Q. The switches themselves function as the rectifier would, except with much narrower windows for conduction. This circuit would be almost impossible to implement conventionally without SCRs and a ninety-degree phase delay line. Here's a link on the Tayloe detector: http://rfdesign.com/mag/radio_lownoise_highperformance_zero/  The Tayloe detector is just another method for demodulating the RF once it's been downconverted to an IF frequency to pull out I and Q signals. From there, you step into the digital domain for further processing, or simply right back out to make a transponder.

If you capture the signals using a plain-old PC sound card, it's possible to capture a signal of 22KHz, because of the Nyqist limit. However, using a PC-sound card limits the dynamic range -- or how large a signal the signal processor can handle, or how soft a signal it can receive (reciever sensitivity).

Capturing I and Q from the baseband level allows any signal to be repeated, not just FM, AM, SSB, or D-Star for example.
 

TDM, The only way to go

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I have read to so much about various VoIP systems being pressed into radio use, but many of them ignore time as a requirement for audio. The chief reason why time is so important is that in a voted or simulcast system, you must have constant time figures across the link, or the noise comparators will be comparing dissimilar signals, resulting in unpredictable voting behavior. It may be simple enough to build a conventional FM repeater to pass a signal between two points, however the repeater has the notable disadvantage of "coloring" the audio passed through it. The audio that is recieved is subjected to the reciever's de-emphasis network as well as the transmitter's pre-emphasis (which is not a network, but a side-effect of phase- or frequency-modulation). This is documented and explained in depth here: http://www.repeater-builder.com/tech-info/flataudio.html However, due to this constant cycle of audio processing and deprocessing, the passed audio is "colored" after crossing each stage. This requires equalization of the path, to restore the audio back to something resembling a "flat" path, which does not express such characteristics. The simple way to avoid all of this complexity is to digitize the audio as soon as possible, and send it over the air as a digital signal. This is what Ma Bell started doing in the 1970s, and continues to do to this day.

Furthermore, if E&M signalling is used in the link, with E&M four-wire line cards, there is a seperate transmit, reciever and signalling pair presented to the end user. E&M signalling is bi-directional, so there is a local switch input, and a remote relay output. These two signals are very simple to connect to a reciever and transmitter, allowing carrier squelch detect to be sent and push-to-talk (PTT) signals to be sent!

There is Part 15 Microwave equipment manufactured which support a full-duplex T1 (1.544Mbit/s) or E1 (2.048Mbit/s) radio link. The equipment was manufactured by Western Multiplex, and put in use all over the country. One well known radio station located in Athens, AL used a T1 radio link to get a Huntsville-local phone number, while having a physical station location that is two LATAs away. Even if the station had subscribed to the "Area Calling" service from the telephone company to defray the cost of what would have otherwise been long-distance telephone calls to Huntsville, the stations's listeners would have had to dial a phone number that was not in the local Huntsville calling area to reach the station. Using the microwave TDM link prevented this, and subjected the station to telephony outages when the link failed during the projected downtime for the wireless link. The station management felt at that time (and still to this day) that the outages were an acceptable trade-off.

 
In the modern telecommunications arena, the sort of circuit is frequently implemented using wireless OC-3 hardware carrying DS1 trunks, as the ATM circuit may be seamlessly and automatically rerouted if a physical link goes down. One local public service provider has implemented such equipment in the fashion of a large ring around a tri-county area, and is using it to provide radio backhaul to a centralized switching location as well as supporting remote bases in that tri-county area. Since the system is full-duplex, the audio delays are static in length, and audio circuit response is flat. Predictably, the system is a smash hit. To date, the only complaints I've heard from the operators are that the combiner networks used to combine ten transmitters into a single antenna have too much loss. Unfortunately, big cavity resonators have quite a bit of loss outside of thier resonant frequency.

In amateur radio, the attempts to implement a similar solution have entirely too many cut corners, brought about largely by the availablity of affordable equipment, and a lack of solutions to fill a smaller need. For instance, in planning to accomplish a goal of a radio link between Birmingham, AL and Huntsville, AL, it is necessary to make at least one hop in the middle of the path, or two. Ma Bell chose to make five, but she was picking up other communities along the way. I have identified a site that would be perfect as a midpoint, however, I do not need twenty-four channels of voice, nor do I think that I could "resell" any of those channels to other amateur radio operators, or the owner of the tower on which the equipment would have to sit. Furthermore, the need to have two different frequencies complicates matters, as each T1 radio would need to have a solid dish, and hopefully nothing in near sight of the dish that would allow the signal to be bounced back into the other dish. The typical ham implementation uses 802.11b, 802.11g, or 802.11a for a wireless backhaul, each of which is half-duplex! This results in unpredictable delays, not to mention much wasted "air bandwidth" waiting for the reciever to lock once the transmitter is on the air. And since all transciever control is handled in the protocol and driver levels, it's virtually impossible for the end-user to tune the transmit-to-recieve times the way that a packet radio (AX.25) user may by altering PACLEN and TXDelay. 

A perfect solution for this problem would be a radio link that had an ISDN or double ISDN width over the air. This would permit call-status information to be sent, as well as two full-duplex audio paths. If one so desired, it would be possible to use the entire bandwidth to support a data transmission at 128 to 144 kbit/s. This would obviously require about 256KHz worth of radio bandwidth, not including guardbands for an MSK implementation. While QPSK and QAM may be used to lessen the radio spectrum requirements, delay is introduced as well as a requirement to use linear amplifiers. Using a linear amplifier increases cost, reduces sources of the amplifier (if pulled from other surplus or used equipment) and increases operational costs, as the amplifier efficency drops from eighty percent to thirty to fifty percent. GMSK is a possible modulation solution which may be implemented in such a fashion as to allow class-C amplifiers to be used.

GMSK achieves approximately 0.7 bits per Hz of occupied bandwidth, which for a 144kbit/s data channel (2B + 1D, ISDN standard) results in about 206KHz. Push that out to about 225KHz to allow a little guard banding, then realize you've got to have the same coming back in on another channel. Provided that the baseband doesn't experience a large group delays, and you can get filters wide enough, it should be possible to retrofit a two-way radio to handle the RF duties. From a signalling perspective, ISDN is clunky at best. There's no less than 500 different parameters, and you've got to order the standard from Bellcore or ITU in order to choose which ones to ignore and which ones to use. It would be a far better idea to pick two channels out of the twenty-four in a DS1 signal and send those over the link, rather than attempt to implement ISDN. Personally, I doubt that an implementer would suceed in finding E&M modules for an ISDN station adapter. It would be simple to use a DS1 channel bank or CSU/DSU with an E&M module or an Add/Drop CSU/DSU. The difficulty here is in implementing a solution cheaply and efficently, given the bar of providing a DS1 interface (and the 1.5Mbit/s signalling) or finding DS1 channel banks for cheap or free. 

D-Star Repeaters on the cheap

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Few amateur radio operators who are using D-Star have bothered to read the specifications of the protocol, or understand the mechanism which they are using. D-Star, over the air, is merely 4800 bps GMSK data. To sucessfully repeat D-Star, one does not need a complicated controller, or even a codec chip from DVSI! All you need is to change the callsigns on the fly in the protocol field, and copy the data from the "IN" modem to the "OUT" modem. You want a courtesy tone? Well, send a beep over the air on your HT, and record the data. When the data is played back over the air, you now have a courtesy tone!  And of course, you may use the same method to build a "dit" and "dah", as well as an unmodulated "tone" and make a MCW identifier.

Look in this space for some links to projects similar to this.

Update: Promised links:

http://www.qsl.net/kb9mwr/projects/voip/plan.html VoIP and Ham Radio
http://d-star.dyndns.org/rig.html.en D-Star modem, will interface to any packet rig.
http://d-star.dyndns.org/node_adapter.html.en D-Star modem capable of repeat.
http://www.moetronix.com/dstar/ Home-made D-Star transceiver implementation.
http://opendstar.org/ Under construction.

Update: The D-Star Hotspot now exists. This is a 10mW device which puts out a signal at two meter frequencies and receives on the same and converts to packet data for direct entry into the D-Star data backbone network.




Discone antennas

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All antennas are compromises. While the discone antenna promises on paper to be an extremely broadband antenna, manufacturer's claims of capability do not match the common man's understanding of assumed radiation patterns for this antenna. It is necessary study the antenna patterns carefully to understand conventional shortcomings and depending on desired range, to modify the antenna to achieve true broad bandwidth.

When using a discone antenna, few people are aware that the pattern of the antenna diverges from the accepted pattern of a dipole over the broad bandwidth of the antenna. It is possible, through the use of traps, to limit the operation of the antenna to one or more ranges of frequency, thus permitting the antenna to perform in a primary mode instead of a secondary mode.

The secondary nodes are marked by a pronounced null overhead, impacting the vertical pattern and reducing the effectiveness of the antenna as a 0-90 degree aperture. This is caused by the antenna's length approaching a full wavelength across the top of the antenna, a far from the idealized dipole nature of the disc, which is designed so as to be one-quarter wavelength in radius and one-half wavelength in diameter.

The tertiary nodes are marked by nulls in the elevation pattern along the horizontal axis.  These are caused by the antenna length exceeding 180-degrees in electrical wavelength, causing nulls in the pattern to be reflected off of the conical counterpoise. The reflections of the nulls in combination with the nulls cause the pattern to distort sufficiently so as to create nulls in the normally primary axis of radiation -- the horizontal axis.

Here is a computer model of a discone which is designed for 50 - 200MHz. I believe this antenna model ships with copies of MMANA-GAL.
discone1.PNG 
This is a simple discone, which does appear to have a gap between the disc and the cone. This gap, and the wire associated with it, will throw off some of the modeling by causing a slight directionality.

Modeled for 70 MHz, one can see the lop-sided pattern this antenna has. The red line is the vertical field generated around the vertical axis; the blue line is the horizontally polarized field. 
discone-70mhz-pattern.PNG
When the calculations are shifted up in frequency, one can see the pattern shifting around:

145MHz:
discone-145mhz-pattern.PNG
200 MHz:
discone-200mhz-pattern.PNG
400 MHz:
discone-400mhz-pattern.PNG
800 MHz:
discone-800mhz-pattern.PNG

Clearly, as the frequency increases, the pattern changes greatly. However, this antenna has a strange pattern to begin with, so here's a model I created that is smaller, and simpler:

discone-cut.PNG

The disc is one-half wavelength in diameter for approximately 145MHz. In effect, this antenna is somewhere between a discone and a biconical antenna. Since this antenna exists in only one axis, there is a deficiency in the other horizontal axis. Again, the vertical pattern is the red line (about the vertical axis), the horizontal pattern is the blue line.

Here's the pattern, resonant at 145MHz:
discone-cut-resonant-145.PNG
50MHz:
discone-cut-resonant-50.PNG
70MHz:
discone-cut-resonant-70.PNG
145MHz:
discone-cut-resonant-145.PNG
450MHz:
discone-cut-resonant-450.PNGBecause there is sufficient overlap between the horizontal and vertical patterns, here is the total resulting pattern:
discone-cut-resonant-450-total.PNG
900MHz:
discone-cut-resonant-900.PNGAgain, the total RF pattern:
discone-cut-resonant-900-total.PNGAs plainly shown in the models, the pattern starts twisting and changing as the frequency increases. This is because the antenna changes patterns from a half-wave dipole (90 degrees) to a five-eight-ths wavelength dipole, to a 180-degree or longer length antenna. Antennas longer than 180-degrees electrical length (total length: one wavelength and over) run into traveling wave theory, which causes the pattern the cancel unless sections are separated and phased together with respect to specific frequencies. Note however that I did not model a discone on both the X and Y axes. This further explains why the above patterns are odd looking. A true discone would have additional lobes matching those along the X-axis on the Y-axis. 

Putting traps on the diagonal wires as well as the top radials will allow the discone to remain in the resonant mode of radiation (half-wavelength) for a given frequency. However, the presence of traps in the antenna will increase losses at lower frequencies, as the lowest frequency has to traverse all traps to be radiated. Conversely, the higher frequencies will be trapped within the drive point and the trap of interest, where coax losses will determine the power radiated along with the radiation resistance.




Understanding antennas

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A log periodic and a helical antenna have so much in common, it in positively unfunny. For instance, if you take and look at a log periodic and a helical, you see they don't really seem to have much in common. If you build a pair of crossed log periodics, you'll start to see the resemblance: The crossed log periodics is merely missing the spiral wire of the helix. The lack of presence of this wire allows the crossed log periodics to be used in virtually any mode, provided proper phasing is performed.

Phasing these two antennas is the largest challenge in implementing a broadband, multifrequency solution. To cover more than one octave requires that the phasing network function across that octave. Most phasing networks are made or designed from Wilkenson dividers. A Wilkenson divider relies on quarter-wavelength sections of coax at an impedance which is typically above that of the input impedance. Because the divider is a resonant structure, it is a frequency dependent device. One makes a non-frequency sensitive divider using a hybrid combiner.

D-Star Multiplexing

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A D-Star radio signal is approximately 6.25 KHz wide, much narrower than the occupied bandwidth of a -/+4.5KHz FM signal (which is somewhere in the neighborhood of 9KHz). It should be possible to, within a 20KHz channel spacing, allocate two D-Star repeaters by offsetting either repeater from the center frequecy by 25 or 50KHz.

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