December 17, 2008 Educational Radio Net, PSRG 30th session, Lee Bond N7KC
The subject of tonight’s discussion material is amplitude modulation and the fundamentals thereof. This is the first of a three part series dealing with the process of transmitting voice band frequencies via radio. My next session will focus on single sideband processes and the third session will focus on frequency modulation.
If one looks at the bandwidth required to transmit various signals it is immediately apparent that three designations will suffice to describe the bandwidth required to do the job. The first segment is very narrow bandwidth and this includes CW and several of the popular digital modes. The second definable segment would be moderate bandwidth and this includes voice transmissions, facsimile, and slow scan television. The third segment is the very wide bandwidth signals such as fast scan television.
For this session we are interested in moderate bandwidth voice transmissions and, in particular, the amplitude modulation approach to transmitting voice using radio techniques. As a practical matter we are interested in somehow shifting voice range frequencies to a range more suitable to fit our antennas since the antenna is really where the ‘rubber hits the road’. We will assume that our antennas are cut to fit whatever amateur band we choose to use.
Lets define voice range frequencies for radio purposes as those starting at 20 hertz and extending to 2500 hertz. The, so called, high fidelity range extends to 20,000 hertz but most of the important voice energy required for communications is contained in the region under 3000 hertz. The ratio of the high voice frequency to the low frequency is about 125:1. In principle one can transmit audio frequencies in the same manner as ‘radio’ frequencies but the antenna dimensions would be enormous. For example, assuming standard propagation velocity, a half wavelength at 20 hertz is about 4600 miles and a half wavelength at 2500 hertz is about 37 miles. If you were to cut the antenna for midrange then it would be seriously de-tuned at either end frequency. So what to do?
Mathematics to the rescue. Everyone has heard the rule that two frequencies, if mixed, will produce sum and difference frequency spectra and this spectra will include the original two frequencies as well. This ‘mixing’ behavior is predicted using trig product identities and the mathematics is valid for audio frequencies right up through radio frequencies. Let’s play with some numbers to get a feel for how this mixing business works.
First however, we want to appreciate a couple of terms often used to describe the behavior of circuits. Linear and non linear. A linear circuit processes signals in a straight line fashion. For example, if you double the signal feeding a linear amplifier circuit then the output signal will precisely double. There is no perfectly linear active electrical circuit but it is possible to come very close to perfectly linear. A perfectly linear amplifier will process multiple signals without any interaction between signals. One simple measure of linearity is harmonic distortion. If you drive an amplifier with a single perfect sine wave signal then you would expect a perfectly linear amplifier circuit to present only a single output frequency. If a spectrum analyzer shows any energy at multiples of the driving frequency then these added frequencies are a result of harmonic distortion caused by the amplifier and harmonic distortion is an artifact of non linear performance.
On the other hand, there are circuits which have been deliberately designed to be non linear. If a non linear circuit is used as a ‘mixer’ then you can assume that at least two frequencies are being processed by this circuit. Mixing, in actuality, is really multiplication or the product of at least two frequencies as defined by the product identities in trigonometry.
Now, with that aside, let’s get back to playing with our numbers. Assume that we are feeding two audio frequencies into a non linear ‘mixer’. One frequency is 1000 hertz and the other is just twice the first or 2000 hertz. The sum output is 3000 hertz and the difference is 1000 hertz which is the same as one of the driving frequencies.
Now let’s mix another pair, this time 1000 hertz and 3000 hertz. This time the sum is 4000 hertz and the difference is 2000 hertz. A look at the spectra would show four frequencies namely 1 Khz, 2 Khz, 3 Khz, and 4 Khz.
In like manner let’s mix 1000 hertz and 100,000 hertz. The sum is 101,000 hertz and the difference is 99,000 hertz. The spectra shows our original ‘mixing’ frequencies, 1 Khz and 100 Khz, and the product frequencies of 101 Khz and 99 Khz. The maximum difference between upper sideband frequency and lower sideband frequency is just 5000 hertz so the percentage of bandwidth compared to carrier is just 5%.
Finally, let’s mix 1000 hertz and 10,000,000 hertz or 10 Mhz. This time the sum frequency is 10001000 hertz and the difference is 9999000 hertz. The spectra shows our mixing frequencies of 1 Khz and 10 Mhz plus the product frequencies of 10.001 Mhz and 9.999 Mhz. The audio range frequency, 1000 hertz, could be any frequency between 20 hertz and 2500 hertz and would produce mixing products with the ‘carrier’ frequency (10 Mhz) that extend from 9.9975 Mhz to 9.99998 Mhz and from 10.00002 Mhz to 10.0025 Mhz. The, so called, carrier frequency has energy below it called the lower sideband energy and energy above it called the upper sideband energy. The maximum difference between upper sideband frequency and lower sideband frequency is just 5000 hertz so the percentage of bandwidth compared to carrier is just 0.05%. This indicates that both the carrier frequency and sideband frequencies will ‘fit’ our antennas nicely in the band we choose to transmit within. Voice modulating frequencies in the range of 20 to 2500 hertz are so far removed from the carrier energy that they are filtered out of the final product.
Voice modulation is the process of imprinting intelligent baseband information upon a signal suitable for radio transmission. In the case of amplitude modulation the baseband voice information causes the instantaneous carrier amplitude to change and this change can be detected at great distance to reconstruct the original baseband voice information.
Nothing is free and so it is with amplitude modulation. To 100% modulate a 1000 watt carrier using AM it is necessary to provide 500 watts of audio power. The 500 watts ends up being split between the upper sideband and the lower sideband and, spectrally, the carrier amplitude remains constant. Amplitude modulation is inefficient from the power standpoint since the full carrier power is transmitted but this power contributes nothing to the impressed intelligence. Amplitude modulation is also inefficient from the bandwidth standpoint since identical upper and lower sideband information is transmitted requiring a bandwidth twice as large as the modulating signal.
Recovering the impressed information from an AM signal can be as simple as detecting the, so called, envelope of the signal. This amounts to rectifying the signal and filtering out the carrier. What remains is just the analog of the original modulating signal. This is the precise method used by simple ‘crystal’ sets which are still popular with experimenters. One particularly nasty artifact of operating AM is the heterodyning of adjacent carriers. Radio operators put up with this howling until improved techniques made AM obsolete.
In summary, amplitude modulation or AM is a very simple but inefficient means of impressing information on a ‘carrier’ signal. The AM process is very straight forward and easy to understand but lacks the elegance of improved methods of communication.
This concludes the set up for the discussion of AM. Are there any questions or comments?
This is N7KC for the Educational Radio Net
Tuesday, December 16, 2008
Wednesday, December 10, 2008
EmComm, Brian Daly, WB7OML, week 29
Amateur Radio Emergency Communications, or “Emcomm”
Brian Daly, WB7OML
Let’s start out by defining - what is a communication emergency? According to the definition in the ARRL Level 1 course, a communication emergency exists when a critical communication failure puts the public at risk.
What are some circumstances that can overload or damage critical day-to-day communication systems?
What are some potential Communications Emergencies in Seattle?
Can a communication emergency occur in “normal” circumstances? Yes, definitely, some examples being:
So what makes a good emcomm volunteer? Amateur emcomm volunteers come from a variety of backgrounds with a range of skills and experience. Emcomm volunteers share one common characteristic – the desire to help others without personal gain, the ability to work as a member of a team, and to take direction from others. An emergency situation will bring a lot of stress and pressure, thus an emcomm volunteer needs the ability to think and act quickly.
Where do you fit in? We amateurs bring equipment, skills, and frequencies necessary to create emergency communications networks under poor conditions. We have licenses; we have pre-authorization for national and inter-national communication. Many of the skills we bring to emcomm are the same things we do on a day-to-day basis; other skills are specific to emcomm and needs to be learned through courses like the ARRL ARECC Level 1 and through drills and exercises.
Radio equipment, frequencies and basic radio skills are not enough. Without specific emergency communication skills, you can easily become part of the problem.
It is also important to know your limits of responsibility as an emergency communicator. What an emcomm volunteer is not - we need to know where to draw the line, what our limitations are. We are not “first responders”, generally we do not have authority – we don’t make decisions for our served agencies, nor do we place demands on them. But we can make some decisions – the decision on whether to participate or not, and decisions affecting your own life and safety. In general we are not in charge – we are there to fulfill the needs of the served agency.
You cannot “do it all”. If the served agency runs short of specialized help, it is not your job to fill it especially if you are not trained for the job. But you can fill in an urgent need or perform jobs where communication is an integral part, if you are qualified.
And remember, leave your ego at the door!
There are differences between “day-to-day” communication and “emergency communication”. First and foremost, in day-to-day communications there is no real pressure to “get the message through”. No one’s life depends on it. You do things at your leisure. Emcomm can involve both amateurs and non-amateurs, it happens in real-time, there is a lot going on simultaneously perhaps on several nets, there may be little or no warning, you may have to set up and be operational anywhere in a short period of time, and there is no schedule. Public service events may come close to emcomm, as they can be “planned disasters” – about the only know piece is the schedule!
Your job as an emcomm volunteers is simple – communicating is job #1. Notice it is “communicating” and not “amateur radio” – there is a significant difference. Our job is to get the message through regardless of how that happens. We as amateurs have many tools available for this job, and amateur radio is just one of those tools. FAX machine, Internet email, cell phones, landline phones, amateur radio, CB radio, FRS radio, served agency radio – all of these are at our disposal and should be considered. We bring communicating skills to the table, not just amateur radio. There are stories of amateurs that pass long supply lists over the radio, tying up repeaters or frequencies, while sitting next to an operational FAX machine. It is not our job to “show off” our radios – it is our job to “communicate”. Just think about the best and fastest way to send it. Of course, when all else fails we do have the amateur radio.
So what happens during a communication emergency? Some scenarios will not require immediate action, for example during a “watch” or “warning” for a severe storm. This is the period to make sure you go-kit is together, and you are ready to go if called. Other scenarios will happen fast and will require immediate need – for example, an earthquake. Once the need for emcomm is identified, the served agency will put out the call for amateurs to help. Most emcomm groups have defined procedures for activation, such as defining a “rapid response team”. Nets will be established to handle resources and logistics, such as the processing and directing of incoming volunteers. Once these operations begin, things can happen quickly – message traffic grows, confusion exists. Do we have relief operators? Do we have food and water? Where will the volunteers sleep? Do we have batteries, fuel, other logistical needs? Communication assignments need to be made – shelters, gathering damage reports, handling supply requests and other logistical needs of the served agency. Nets will be established, rearranged and disassembled as the needs arise. Volunteers need to remain flexible. Finally, the demands of the emcomm communication effort will decrease, nets can be closed, and volunteers released.
But the emcomm event does not end when the last net is shut down. This starts the after action report period, which will help to improve the response next time around.
There are many additional skills to learn to help you become a successful emcomm volunteer – knowing who your served agency is, their organization, basic communication skills, message handling, net operating, and of course, personal safety, survival and health considerations. We will cover more of these topics on this net in the coming months. Also, the ARRL Amateur Radio Emergency Communication Course Level 1 is another opportunity to learn these skills.
Brian Daly, WB7OML
Let’s start out by defining - what is a communication emergency? According to the definition in the ARRL Level 1 course, a communication emergency exists when a critical communication failure puts the public at risk.
What are some circumstances that can overload or damage critical day-to-day communication systems?
- Storm knocks down telephone lines or radio towers
- A massive increase in the use of a communication system that causes it to be come overloaded
- Failure of a key component in a system
- Earthquake
- Volcano
What are some potential Communications Emergencies in Seattle?
Can a communication emergency occur in “normal” circumstances? Yes, definitely, some examples being:
- Underground cables being dug up
- Fires in telephone equipment buildings
- Car crash knocks down a key telephone pole
- 9-1-1 systems can fail
- Hospital systems can fail
So what makes a good emcomm volunteer? Amateur emcomm volunteers come from a variety of backgrounds with a range of skills and experience. Emcomm volunteers share one common characteristic – the desire to help others without personal gain, the ability to work as a member of a team, and to take direction from others. An emergency situation will bring a lot of stress and pressure, thus an emcomm volunteer needs the ability to think and act quickly.
Where do you fit in? We amateurs bring equipment, skills, and frequencies necessary to create emergency communications networks under poor conditions. We have licenses; we have pre-authorization for national and inter-national communication. Many of the skills we bring to emcomm are the same things we do on a day-to-day basis; other skills are specific to emcomm and needs to be learned through courses like the ARRL ARECC Level 1 and through drills and exercises.
Radio equipment, frequencies and basic radio skills are not enough. Without specific emergency communication skills, you can easily become part of the problem.
It is also important to know your limits of responsibility as an emergency communicator. What an emcomm volunteer is not - we need to know where to draw the line, what our limitations are. We are not “first responders”, generally we do not have authority – we don’t make decisions for our served agencies, nor do we place demands on them. But we can make some decisions – the decision on whether to participate or not, and decisions affecting your own life and safety. In general we are not in charge – we are there to fulfill the needs of the served agency.
You cannot “do it all”. If the served agency runs short of specialized help, it is not your job to fill it especially if you are not trained for the job. But you can fill in an urgent need or perform jobs where communication is an integral part, if you are qualified.
And remember, leave your ego at the door!
There are differences between “day-to-day” communication and “emergency communication”. First and foremost, in day-to-day communications there is no real pressure to “get the message through”. No one’s life depends on it. You do things at your leisure. Emcomm can involve both amateurs and non-amateurs, it happens in real-time, there is a lot going on simultaneously perhaps on several nets, there may be little or no warning, you may have to set up and be operational anywhere in a short period of time, and there is no schedule. Public service events may come close to emcomm, as they can be “planned disasters” – about the only know piece is the schedule!
Your job as an emcomm volunteers is simple – communicating is job #1. Notice it is “communicating” and not “amateur radio” – there is a significant difference. Our job is to get the message through regardless of how that happens. We as amateurs have many tools available for this job, and amateur radio is just one of those tools. FAX machine, Internet email, cell phones, landline phones, amateur radio, CB radio, FRS radio, served agency radio – all of these are at our disposal and should be considered. We bring communicating skills to the table, not just amateur radio. There are stories of amateurs that pass long supply lists over the radio, tying up repeaters or frequencies, while sitting next to an operational FAX machine. It is not our job to “show off” our radios – it is our job to “communicate”. Just think about the best and fastest way to send it. Of course, when all else fails we do have the amateur radio.
So what happens during a communication emergency? Some scenarios will not require immediate action, for example during a “watch” or “warning” for a severe storm. This is the period to make sure you go-kit is together, and you are ready to go if called. Other scenarios will happen fast and will require immediate need – for example, an earthquake. Once the need for emcomm is identified, the served agency will put out the call for amateurs to help. Most emcomm groups have defined procedures for activation, such as defining a “rapid response team”. Nets will be established to handle resources and logistics, such as the processing and directing of incoming volunteers. Once these operations begin, things can happen quickly – message traffic grows, confusion exists. Do we have relief operators? Do we have food and water? Where will the volunteers sleep? Do we have batteries, fuel, other logistical needs? Communication assignments need to be made – shelters, gathering damage reports, handling supply requests and other logistical needs of the served agency. Nets will be established, rearranged and disassembled as the needs arise. Volunteers need to remain flexible. Finally, the demands of the emcomm communication effort will decrease, nets can be closed, and volunteers released.
But the emcomm event does not end when the last net is shut down. This starts the after action report period, which will help to improve the response next time around.
There are many additional skills to learn to help you become a successful emcomm volunteer – knowing who your served agency is, their organization, basic communication skills, message handling, net operating, and of course, personal safety, survival and health considerations. We will cover more of these topics on this net in the coming months. Also, the ARRL Amateur Radio Emergency Communication Course Level 1 is another opportunity to learn these skills.
Wednesday, December 3, 2008
BALUNS, Jim K7WA, No. 28
BALUNS
December 3, 2008 – Educational Radio Net
Jim Hadlock K7WA
What does a balun do?
What happens if you don't use one?
Bal-Un is a term formed from the words balanced and unbalanced. It refers to a device used to couple an Unbalanced transmission line to a Balanced load. In the real world, we use a balun to couple a coaxial transmission to a balanced antenna, such as a dipole.
Coaxial transmission lines are commonly used to connect our transceivers to antennas. Coax comes in several sizes and types for different applications. It consists of an inner conductor with an insulated covering (dielectric), which is then covered with a braided wire sheathing (shield). The sheathing is covered with a flexible outer jacket. Coax is weatherproof and may be buried underground, run inside a metal mast or taped to a tower without harmful effects. At the transceiver, the center conductor is connected to the transmitter output (or receiver input), and the shield is connected to the chassis. This arrangements works well with an unbalanced load, such as a vertical monopole antenna fed against a ground plane or radials. However, when coax is used to feed a balanced load, such as a dipole antenna, some provision should be made for converting from the unbalanced transmission line to the balanced load. Otherwise, RF currents will flow on the outer conductor of the coax, compromising the effectiveness of the antenna.
To understand this problem, think of a coaxial transmission line as a wire centered inside a metal pipe. When we connect the coaxial transmission line to our transmitter, the RF current flows on the center wire and on the inside surface of the pipe. This is due to what's called the "skin effect". The "skin effect" describes how RF currents flow in a thin layer on the surface of a conductor, proportional in depth to the wavelength of the signal. If we connect the other end of the coaxial transmission to a balanced antenna, such as a dipole, RF current from the center wire flows to one side of the antenna. The current from the inside surface of the pipe however, is connected to two conductors: the other side of the antenna and the outside surface of the pipe. Current flowing on the outside of the pipe is subtracted from the current that should be flowing on the antenna creating voltage and current nodes on the outside surface of the pipe back down to the transmitter where it is grounded. To go back to our coax fed dipole example, RF current on the outside surface of the coaxial transmission line shield will distort the radiation pattern of the antenna and detract from its effectiveness. It may also contribute to television interference.
A properly connected balun will reduce or eliminate the RF current flow on the outside surface of the coaxial transmission line shield. While the most common use of a balun is at the feedpoint of a balanced antenna, they are also used at the output of an antenna tuner to feed a balanced transmission line (Twin Lead) and even part way down a feedline to convert from balanced transmission line to coaxial transmission line (as in the G5RV antenna).
There are several types of baluns available to radio amateurs and described in the literature. Let's begin with the Current Balun (also called the Choke Balun). Current Baluns have become popular for application in the high frequency range (1.8 mHz to 30 mHz) because they are simple, cheap, and effective. In its simplest form, a Current Balun consists of a number of turns of coaxial cable wound into a close coil at the feedpoint of the antenna. The size of the coil is determined by the operating frequency. For example, the installation directions for the Cushcraft A3S tri-band yagi specify eight turns of RG8/U coaxial cable with a six inch diameter. This coil is a high impedance RF choke at the operating frequency of the antenna and prevents RF current from flowing on the outside of the coaxial transmission line shield. Another approach to the Current Balun was introduced by Walter Maxwell, W2DU. This involves slipping a stack of high-permeability ferrite beads over the coaxial transmission line at the feedpoint of the antenna. The stack of ferrite beads creates a high impedance effectively suppressing any RF current from flowing down the outside surface of the transmission line. Current Baluns and ferrite bead kits are available from many sources.
Another approach is the Voltage Balun as described by Jerry Sevick, W2FMI, and others. This design uses inductors to produce equal, opposite phase voltages into the two resistances, or halves of the antenna. An additional feature of the Voltage Balun is that, by using a combination of inductors as a broad-band RF transformer, it can accommodate impedance conversion in addition to balancing the RF voltages. Typical impedance conversion is 4:1, although Sevick describes transmission line transformers with many other ratios in his classic book: Understanding, Building, and Using Baluns and Ununs.
A third balun technique, most often used at VHF and UHF, is the Coaxial Balun made from a half wavelength loop of coaxial transmission line and presenting a high impedance to any RF current that might otherwise flow on the outer shield of the coaxial transmission line. The half wavelength Coaxial Balun gives a 4:1 impedance step-up.
While I have described how a balun improves the effectiveness of a coax fed balanced antenna, it also has other uses. Consider a vertical antenna with elevated radials. The outer surface of the coaxial transmission line shield will "look" to the antenna like another radial. A Current Balun at the feedpoint of the vertical will prevent RF current from flowing on the feedline. According to author John Devoldere, ON4UN, in Low- Band DXing: "Is it harmful to put a current balun on all the coaxial antenna feed lines for all your antennas? Not at all. If the feed point is symmetric, there will be no current flowing and the beads will do no harm. As a matter of fact they may help reduce unwanted coupling from antennas into feed lines of other nearby antennas."
Baluns are an effective means of preventing unwanted RF current on the outer shield of coaxial feedlines from distorting antenna patterns, as well as reducing TVI (radiation coupling into nearby television sets, house wiring, etc.) and RF in the shack.
References:
ARRL Technical Information Service: An Analysis of the Balun, by Bruce A. Eggers
WA9NEW: www.arrl.org/tis/info/pdf/9409061.pdf
Some Aspects of the Balun Problem, by Walter Maxwell W2DU:
www.w2du.com/r2ch21.pdf
Baluns: What They Do and How They Do It, by Roy W. Lewallen W7EL:
www.eznec.com/Amateur/Articles/Baluns.pdf
Understanding, Building, and Using Baluns and Ununs, by Jerry Sevick W2FMI, CQ
Communications, Inc.
Low-Band DXing (4th Edition), by John Devoldere ON4UN, The ARRL, Inc.
The ARRL Antenna Book (21st Edition), The ARRL, Inc.
The ARRL Handbook, The ARRL, Inc.
Palomer Engineers (1:1 Current Balun Kit): www.palomer-engineers.com
The Radio Works (Baluns, Coax, Antenna Parts, etc.): www.radioworks.com
December 3, 2008 – Educational Radio Net
Jim Hadlock K7WA
What does a balun do?
What happens if you don't use one?
Bal-Un is a term formed from the words balanced and unbalanced. It refers to a device used to couple an Unbalanced transmission line to a Balanced load. In the real world, we use a balun to couple a coaxial transmission to a balanced antenna, such as a dipole.
Coaxial transmission lines are commonly used to connect our transceivers to antennas. Coax comes in several sizes and types for different applications. It consists of an inner conductor with an insulated covering (dielectric), which is then covered with a braided wire sheathing (shield). The sheathing is covered with a flexible outer jacket. Coax is weatherproof and may be buried underground, run inside a metal mast or taped to a tower without harmful effects. At the transceiver, the center conductor is connected to the transmitter output (or receiver input), and the shield is connected to the chassis. This arrangements works well with an unbalanced load, such as a vertical monopole antenna fed against a ground plane or radials. However, when coax is used to feed a balanced load, such as a dipole antenna, some provision should be made for converting from the unbalanced transmission line to the balanced load. Otherwise, RF currents will flow on the outer conductor of the coax, compromising the effectiveness of the antenna.
To understand this problem, think of a coaxial transmission line as a wire centered inside a metal pipe. When we connect the coaxial transmission line to our transmitter, the RF current flows on the center wire and on the inside surface of the pipe. This is due to what's called the "skin effect". The "skin effect" describes how RF currents flow in a thin layer on the surface of a conductor, proportional in depth to the wavelength of the signal. If we connect the other end of the coaxial transmission to a balanced antenna, such as a dipole, RF current from the center wire flows to one side of the antenna. The current from the inside surface of the pipe however, is connected to two conductors: the other side of the antenna and the outside surface of the pipe. Current flowing on the outside of the pipe is subtracted from the current that should be flowing on the antenna creating voltage and current nodes on the outside surface of the pipe back down to the transmitter where it is grounded. To go back to our coax fed dipole example, RF current on the outside surface of the coaxial transmission line shield will distort the radiation pattern of the antenna and detract from its effectiveness. It may also contribute to television interference.
A properly connected balun will reduce or eliminate the RF current flow on the outside surface of the coaxial transmission line shield. While the most common use of a balun is at the feedpoint of a balanced antenna, they are also used at the output of an antenna tuner to feed a balanced transmission line (Twin Lead) and even part way down a feedline to convert from balanced transmission line to coaxial transmission line (as in the G5RV antenna).
There are several types of baluns available to radio amateurs and described in the literature. Let's begin with the Current Balun (also called the Choke Balun). Current Baluns have become popular for application in the high frequency range (1.8 mHz to 30 mHz) because they are simple, cheap, and effective. In its simplest form, a Current Balun consists of a number of turns of coaxial cable wound into a close coil at the feedpoint of the antenna. The size of the coil is determined by the operating frequency. For example, the installation directions for the Cushcraft A3S tri-band yagi specify eight turns of RG8/U coaxial cable with a six inch diameter. This coil is a high impedance RF choke at the operating frequency of the antenna and prevents RF current from flowing on the outside of the coaxial transmission line shield. Another approach to the Current Balun was introduced by Walter Maxwell, W2DU. This involves slipping a stack of high-permeability ferrite beads over the coaxial transmission line at the feedpoint of the antenna. The stack of ferrite beads creates a high impedance effectively suppressing any RF current from flowing down the outside surface of the transmission line. Current Baluns and ferrite bead kits are available from many sources.
Another approach is the Voltage Balun as described by Jerry Sevick, W2FMI, and others. This design uses inductors to produce equal, opposite phase voltages into the two resistances, or halves of the antenna. An additional feature of the Voltage Balun is that, by using a combination of inductors as a broad-band RF transformer, it can accommodate impedance conversion in addition to balancing the RF voltages. Typical impedance conversion is 4:1, although Sevick describes transmission line transformers with many other ratios in his classic book: Understanding, Building, and Using Baluns and Ununs.
A third balun technique, most often used at VHF and UHF, is the Coaxial Balun made from a half wavelength loop of coaxial transmission line and presenting a high impedance to any RF current that might otherwise flow on the outer shield of the coaxial transmission line. The half wavelength Coaxial Balun gives a 4:1 impedance step-up.
While I have described how a balun improves the effectiveness of a coax fed balanced antenna, it also has other uses. Consider a vertical antenna with elevated radials. The outer surface of the coaxial transmission line shield will "look" to the antenna like another radial. A Current Balun at the feedpoint of the vertical will prevent RF current from flowing on the feedline. According to author John Devoldere, ON4UN, in Low- Band DXing: "Is it harmful to put a current balun on all the coaxial antenna feed lines for all your antennas? Not at all. If the feed point is symmetric, there will be no current flowing and the beads will do no harm. As a matter of fact they may help reduce unwanted coupling from antennas into feed lines of other nearby antennas."
Baluns are an effective means of preventing unwanted RF current on the outer shield of coaxial feedlines from distorting antenna patterns, as well as reducing TVI (radiation coupling into nearby television sets, house wiring, etc.) and RF in the shack.
References:
ARRL Technical Information Service: An Analysis of the Balun, by Bruce A. Eggers
WA9NEW: www.arrl.org/tis/info/pdf/9409061.pdf
Some Aspects of the Balun Problem, by Walter Maxwell W2DU:
www.w2du.com/r2ch21.pdf
Baluns: What They Do and How They Do It, by Roy W. Lewallen W7EL:
www.eznec.com/Amateur/Articles/Baluns.pdf
Understanding, Building, and Using Baluns and Ununs, by Jerry Sevick W2FMI, CQ
Communications, Inc.
Low-Band DXing (4th Edition), by John Devoldere ON4UN, The ARRL, Inc.
The ARRL Antenna Book (21st Edition), The ARRL, Inc.
The ARRL Handbook, The ARRL, Inc.
Palomer Engineers (1:1 Current Balun Kit): www.palomer-engineers.com
The Radio Works (Baluns, Coax, Antenna Parts, etc.): www.radioworks.com
Tuesday, November 25, 2008
Open Mic Night, Bob and Lee, Session 27
Because it is the Wednesday before Thanksgiving we will be doing an informal session this week. There is no prepared topic. Come with your questions, tips, stories, etc.
If you would prefer, you can add your question in the comments section and we will address it.
If you would prefer, you can add your question in the comments section and we will address it.
Wednesday, November 19, 2008
Electrical Resonance
November 19, 2008 Educational Radio Net, PSRG 26th session, Lee Bond N7KC
The impedance series is now history. During the course of that 13 week series we looked at several of the most fundamental ideas in the physics of electrical phenomenon and, hopefully, gained some practical knowledge of how these ideas link together to form a basis for our understanding of all things electrical. Let's exercise some of this earlier impedance series material and see how it can be applied to solve practical problems which are routinely encountered on the bench. The first study examined the potentiometer or "pot" and its behavior when used as a voltage divider. The second study examined how energy is moved from a source to a load and also considered the effect of a transmission line in this process. This third study will look at the phenomenon of resonance in both the mechanical and electrical worlds and extend the idea to antennas.
Lets consider mechanical systems first to get an intuitive feel for resonance.
We have all experienced autos which produce nasty sounds at certain speeds or engines where certain parts tend to vibrate depending on engine rpm. Suppose that we have an engine with some sort of attached bracket and the engine is at idle. If we very slowly advance the engine throttle to increase rpm’s there may be a engine rotational speed where the bracket starts to vibrate very strongly. If we continue to advance the throttle, the bracket vibration diminishes and disappears altogether. The mechanical configuration of the bracket has a "natural" frequency which is the frequency of vibration which develops when excited by the engines complicated sounds.
Another demonstration example is a wine goblet shattering when excited by acoustic energy which matches the natural frequency of the goblet. Finally, lets consider the pendulum in a clock. If the clock is unwound and the pendulum is activated we know that it will oscillate back and forth with diminishing amplitude until it stops. The pendulum has a natural frequency primarily determined by its length. If the clock is wound, however, there is a bit of clock mechanism which "taps" the pendulum very slightly at the correct moment to keep the pendulum swinging at constant amplitude, at the natural frequency, and for as long as the energy to produce the tap is present.
All of these examples show that very small forcing energies at the natural frequency of a mechanical system may cause dramatic vibration amplitudes due to resonance. Resonance frequency is where the forcing frequency matches the natural frequency of a system.
The situation in the electrical world is much the same as in the mechanical. Small signals (forcing energy) can appear dramatically larger due to electrical circuit resonance. Such circuits are always structured with resistance, inductance, and capacitive elements. The resistance element stands alone in being immune to the effects of forcing frequencies since the resistance converts energy directly to heat and stores nothing. In contrast to the resistance element, inductance and capacitive elements do not dissipate energy rather they store energy in the form of electric or magnetic fields during one portion of the cycle and return it to the circuit during the next.
Inductance associated with a forcing frequency creates a reactance product which increases with frequency whereas capacitance associated with a forcing frequency creates a reactance product which decreases with frequency. Therefore, given an assembly of resistance, inductive reactance, and capacitive reactance, there is a possibility that at some specific frequency the reactive components value will be equal and opposite hence cancel since they carry opposite sign. Electrical resonance generally indicates that net reactance is zero at a particular frequency. At this resonant frequency the circuit impedance is purely resistive.
One good example of electrical resonance is given by the tuning circuit in a typical radio receiver. The broadcast band, for instance, contains various amounts of energy from 550 Khz to 1500 Khz. The radio needs to respond to a specific station located in this continuum of signals. Using a parallel resonant circuit which is tunable allows one to slide across the band in search of the desired signal. Very slight amounts of received energy from the antenna will excite the resonant circuit and produce signal levels much higher than the excitation level. It is important to note that incoming signal energy is not increased by resonance rather signal amplitude is increased which is then amplified by a suitable active circuit.
Trapping circuits can be constructed from resistive, capacitive, and inductive elements as well. To facilitate this function the elements should be wired in series. At the resonant frequency the net reactance will be zero leaving only resistance as the circuit element. At frequencies off resonance the circuit impedance will always be larger than at resonance due to the combination of series resistance and predominate reactance.
Another example of impedance changing with frequency is the antenna. Lets consider a simple dipole cut to the center of any band. If you were to connect an antenna analyzer to the dipole and sweep from the lower to the upper band edge you would see the antennas feed point impedance, or combination of resistance and reactance, dip at the cut frequency and show only a resistive component. This is the radiation resistance of the antenna at resonance. Resonance frequency is that frequency where net reactance is zero.
Given that the antenna inductance and capacitance values are fixed, at frequencies above the resonance point the antenna is too long, inductive reactance increases, and the antenna impedance increases. Conversely, at frequencies below the resonance point the antenna is too short, capacitive reactance increases and the antenna impedance increases. Since maximum power transfer occurs when transmission line characteristic impedance matches the radiation resistance of the antenna, the trick is to adjust antenna elements such that, at the desired operating frequency, the net reactance is zero and maximum radio frequency current flows in the antenna elements. Since the dipole has a feed point impedance of about 72 ohms at resonance, driving it directly with 50 ohm coaxial line and a 1:1 balun would yield a VSWR of 72/50 or 1.44:1 minimum. Various matching schemes are available to adjust the feed point impedance to match the transmission line.
In certain circumstances electrical resonance can be a nuisance. For example, consider the guy wires associated with a tower installation. Wires similar in length to the radiating elements can seriously detract from a desired radiation pattern. A careful look may reveal that many compressive egg shell insulators may be used to break up the total length of the guys such that any single guy length cannot produce harmonically related radiation in concert with the actual antenna.
In summary, resonance can be a help or hindrance. Electrical resonance is a fundamental concept of electrical theory and, in practical terms, makes our radio endeavors possible.
This concludes the set up for the discussion of resonance. Are there any questions or comments?
This is N7KC for the Educational Radio Net
The impedance series is now history. During the course of that 13 week series we looked at several of the most fundamental ideas in the physics of electrical phenomenon and, hopefully, gained some practical knowledge of how these ideas link together to form a basis for our understanding of all things electrical. Let's exercise some of this earlier impedance series material and see how it can be applied to solve practical problems which are routinely encountered on the bench. The first study examined the potentiometer or "pot" and its behavior when used as a voltage divider. The second study examined how energy is moved from a source to a load and also considered the effect of a transmission line in this process. This third study will look at the phenomenon of resonance in both the mechanical and electrical worlds and extend the idea to antennas.
Lets consider mechanical systems first to get an intuitive feel for resonance.
We have all experienced autos which produce nasty sounds at certain speeds or engines where certain parts tend to vibrate depending on engine rpm. Suppose that we have an engine with some sort of attached bracket and the engine is at idle. If we very slowly advance the engine throttle to increase rpm’s there may be a engine rotational speed where the bracket starts to vibrate very strongly. If we continue to advance the throttle, the bracket vibration diminishes and disappears altogether. The mechanical configuration of the bracket has a "natural" frequency which is the frequency of vibration which develops when excited by the engines complicated sounds.
Another demonstration example is a wine goblet shattering when excited by acoustic energy which matches the natural frequency of the goblet. Finally, lets consider the pendulum in a clock. If the clock is unwound and the pendulum is activated we know that it will oscillate back and forth with diminishing amplitude until it stops. The pendulum has a natural frequency primarily determined by its length. If the clock is wound, however, there is a bit of clock mechanism which "taps" the pendulum very slightly at the correct moment to keep the pendulum swinging at constant amplitude, at the natural frequency, and for as long as the energy to produce the tap is present.
All of these examples show that very small forcing energies at the natural frequency of a mechanical system may cause dramatic vibration amplitudes due to resonance. Resonance frequency is where the forcing frequency matches the natural frequency of a system.
The situation in the electrical world is much the same as in the mechanical. Small signals (forcing energy) can appear dramatically larger due to electrical circuit resonance. Such circuits are always structured with resistance, inductance, and capacitive elements. The resistance element stands alone in being immune to the effects of forcing frequencies since the resistance converts energy directly to heat and stores nothing. In contrast to the resistance element, inductance and capacitive elements do not dissipate energy rather they store energy in the form of electric or magnetic fields during one portion of the cycle and return it to the circuit during the next.
Inductance associated with a forcing frequency creates a reactance product which increases with frequency whereas capacitance associated with a forcing frequency creates a reactance product which decreases with frequency. Therefore, given an assembly of resistance, inductive reactance, and capacitive reactance, there is a possibility that at some specific frequency the reactive components value will be equal and opposite hence cancel since they carry opposite sign. Electrical resonance generally indicates that net reactance is zero at a particular frequency. At this resonant frequency the circuit impedance is purely resistive.
One good example of electrical resonance is given by the tuning circuit in a typical radio receiver. The broadcast band, for instance, contains various amounts of energy from 550 Khz to 1500 Khz. The radio needs to respond to a specific station located in this continuum of signals. Using a parallel resonant circuit which is tunable allows one to slide across the band in search of the desired signal. Very slight amounts of received energy from the antenna will excite the resonant circuit and produce signal levels much higher than the excitation level. It is important to note that incoming signal energy is not increased by resonance rather signal amplitude is increased which is then amplified by a suitable active circuit.
Trapping circuits can be constructed from resistive, capacitive, and inductive elements as well. To facilitate this function the elements should be wired in series. At the resonant frequency the net reactance will be zero leaving only resistance as the circuit element. At frequencies off resonance the circuit impedance will always be larger than at resonance due to the combination of series resistance and predominate reactance.
Another example of impedance changing with frequency is the antenna. Lets consider a simple dipole cut to the center of any band. If you were to connect an antenna analyzer to the dipole and sweep from the lower to the upper band edge you would see the antennas feed point impedance, or combination of resistance and reactance, dip at the cut frequency and show only a resistive component. This is the radiation resistance of the antenna at resonance. Resonance frequency is that frequency where net reactance is zero.
Given that the antenna inductance and capacitance values are fixed, at frequencies above the resonance point the antenna is too long, inductive reactance increases, and the antenna impedance increases. Conversely, at frequencies below the resonance point the antenna is too short, capacitive reactance increases and the antenna impedance increases. Since maximum power transfer occurs when transmission line characteristic impedance matches the radiation resistance of the antenna, the trick is to adjust antenna elements such that, at the desired operating frequency, the net reactance is zero and maximum radio frequency current flows in the antenna elements. Since the dipole has a feed point impedance of about 72 ohms at resonance, driving it directly with 50 ohm coaxial line and a 1:1 balun would yield a VSWR of 72/50 or 1.44:1 minimum. Various matching schemes are available to adjust the feed point impedance to match the transmission line.
In certain circumstances electrical resonance can be a nuisance. For example, consider the guy wires associated with a tower installation. Wires similar in length to the radiating elements can seriously detract from a desired radiation pattern. A careful look may reveal that many compressive egg shell insulators may be used to break up the total length of the guys such that any single guy length cannot produce harmonically related radiation in concert with the actual antenna.
In summary, resonance can be a help or hindrance. Electrical resonance is a fundamental concept of electrical theory and, in practical terms, makes our radio endeavors possible.
This concludes the set up for the discussion of resonance. Are there any questions or comments?
This is N7KC for the Educational Radio Net
Tuesday, November 11, 2008
Log Periodic Dipole Antennas, Bob, Session 25
Tonight we will talk about another class of antennas, log periodic antennas. There are different forms of log periodic antennas but we will talk about the most common one, the Log Periodic Dipole Array (LPDA).
This antenna looks and acts similar to the Yagi but unlike the Yagi it covers a wide range of frequencies. This is the LPDA's defining characteristic. A typical design will cover a range of frequencies where the highest frequency is double the lowest. For example you could have one antenna that covered 14 MHz to 30 MHz with very good gain, front to back, and SWR figures over the entire range. You are not limited to the 2:1 frequency coverage. In fact you are only limited by the ability to physically construct the antenna and use it.
GENERAL DESCRIPTION
The log periodic antenna looks somewhat like a Yagi but, unlike the Yagi, the length of the parallel elements vary so that the tips form a straight line that gets progressively smaller. If you imagine lines running along the tips of both ends of the elements from the largest element to the smallest and extend the lines beyond the end of the antenna until they meet, they would form an angle with the boom as the bisector. The elements are connected in a criss-cross pattern so that, if you are looking down from the top of the antenna, the smallest element on the left side would be connected to the next larger element on the right side, and vice versa. This crisscrossing continues through all of the elements. The antenna is fed at the small end with a balanced signal.
BASIC THEORY
I found a greatly simplified explanation of how this antenna works at radio-electronics.com. The link is at the bottom of the blog post. Let's say we are feeding our antenna with a signal about in the middle of the range. Because of the crisscross arrangement most of the adjacent elements cancel each other. But at the two elements in the middle of the array, which are closest to resonant length, you also have the width between them such that the wave will be 180 degrees out of phase when it reaches the other element. That combined with the crisscross feed causes the two elements to reinforce each other.
One other point, the smaller elements which don't contribute to the radiation, act like the shorter director elements of a Yagi, while the longer elements act like reflectors. This creates a radiation pattern much like a Yagi.
As you tune up and down the usable frequency range, you find that at the higher frequencies the radiation primarily comes from the smaller elements and at the lower frequencies, the larger elements are the ones that radiate.
Of course it's never quite this simple. Depending on design you may have many of the elements contributing to the radiation.
DESIGN CONSIDERATIONS
Because the imaginary line along the tips is straight, and the extended lines on each side form an angle, there are some relationships that have to hold. Hopefully it is obvious to all that if you go twice as far away from where the lines meet (the vertex) then the length of the line going across (the element length) will be twice as much. This leads to the formula that the ratio of the length of successive elements has to equal the ratio of the distance from the vertex. This ratio is given the Greek letter tau. This ratio defines the relative distance between elements. In our example of doubling the distance, tau would equal 0.5. To make an effective LPDA you want to have a tau that is as close to 1.0 as is feasible. You can see that tau of 1 would result in parallel lines which wouldn't work. To cover the range you want of double the initial frequency you need a change of length that is actually more than double. If tau is very close to 1 then you will need many elements and a very long boom to achieve that. These are the trade-offs to building a LPDA.
BEYOND THE BASICS
There are ways to add true parasitic elements to the LPDA to improve performance. This is beyond the scope of this discussion and can be found in the Antenna Book.
As usual, I want to point you to the ARRL Antenna Book for an excellent in-depth discussion of building real world LPDA's. Also, as a bonus, you get a LPDA Design program for the PC when you buy the Antenna Book.
Log Perodic Antennas on radio-electronics.com
This antenna looks and acts similar to the Yagi but unlike the Yagi it covers a wide range of frequencies. This is the LPDA's defining characteristic. A typical design will cover a range of frequencies where the highest frequency is double the lowest. For example you could have one antenna that covered 14 MHz to 30 MHz with very good gain, front to back, and SWR figures over the entire range. You are not limited to the 2:1 frequency coverage. In fact you are only limited by the ability to physically construct the antenna and use it.
GENERAL DESCRIPTION
The log periodic antenna looks somewhat like a Yagi but, unlike the Yagi, the length of the parallel elements vary so that the tips form a straight line that gets progressively smaller. If you imagine lines running along the tips of both ends of the elements from the largest element to the smallest and extend the lines beyond the end of the antenna until they meet, they would form an angle with the boom as the bisector. The elements are connected in a criss-cross pattern so that, if you are looking down from the top of the antenna, the smallest element on the left side would be connected to the next larger element on the right side, and vice versa. This crisscrossing continues through all of the elements. The antenna is fed at the small end with a balanced signal.
BASIC THEORY
I found a greatly simplified explanation of how this antenna works at radio-electronics.com. The link is at the bottom of the blog post. Let's say we are feeding our antenna with a signal about in the middle of the range. Because of the crisscross arrangement most of the adjacent elements cancel each other. But at the two elements in the middle of the array, which are closest to resonant length, you also have the width between them such that the wave will be 180 degrees out of phase when it reaches the other element. That combined with the crisscross feed causes the two elements to reinforce each other.
One other point, the smaller elements which don't contribute to the radiation, act like the shorter director elements of a Yagi, while the longer elements act like reflectors. This creates a radiation pattern much like a Yagi.
As you tune up and down the usable frequency range, you find that at the higher frequencies the radiation primarily comes from the smaller elements and at the lower frequencies, the larger elements are the ones that radiate.
Of course it's never quite this simple. Depending on design you may have many of the elements contributing to the radiation.
DESIGN CONSIDERATIONS
Because the imaginary line along the tips is straight, and the extended lines on each side form an angle, there are some relationships that have to hold. Hopefully it is obvious to all that if you go twice as far away from where the lines meet (the vertex) then the length of the line going across (the element length) will be twice as much. This leads to the formula that the ratio of the length of successive elements has to equal the ratio of the distance from the vertex. This ratio is given the Greek letter tau. This ratio defines the relative distance between elements. In our example of doubling the distance, tau would equal 0.5. To make an effective LPDA you want to have a tau that is as close to 1.0 as is feasible. You can see that tau of 1 would result in parallel lines which wouldn't work. To cover the range you want of double the initial frequency you need a change of length that is actually more than double. If tau is very close to 1 then you will need many elements and a very long boom to achieve that. These are the trade-offs to building a LPDA.
BEYOND THE BASICS
There are ways to add true parasitic elements to the LPDA to improve performance. This is beyond the scope of this discussion and can be found in the Antenna Book.
As usual, I want to point you to the ARRL Antenna Book for an excellent in-depth discussion of building real world LPDA's. Also, as a bonus, you get a LPDA Design program for the PC when you buy the Antenna Book.
Log Perodic Antennas on radio-electronics.com
Wednesday, November 5, 2008
Impedance matching 101
November 5, 2008 Educational Radio Net, PSRG 24th session, Lee Bond N7KC
The impedance series is now history. During the course of that 13 week series we looked at several of the most fundamental ideas in the physics of electrical phenomenon and, hopefully, gained some practical knowledge of how these ideas link together to form a basis for our understanding of all things electrical. Let's exercise some of this earlier impedance series material and see how it can be applied to solve practical problems which are routinely encountered on the bench. The first study examined the potentiometer or "pot" and its behavior when used as a voltage divider. This second study will firstly examine how energy is moved from a source to a load and secondly, consider the effect of a transmission line in this process.
First, we need to understand a very elementary concept in describing mathematical plots. Imagine that we are walking along a straight path which starts to curve uphill. We notice that the walking is getting tougher as the path curves upward. We might make the observation that this is a steep upward slope. As we continue our walk along the path, it levels out and immediately starts to slope downward and we must hold back to avoid running. We might make the observation that this is a steep downward slope. Looking back on our route we see that the high point on the walk was at the highest point on the hill and, further, that the slope was actually zero at that point. So it is with graphical plots. A maximum point (or minimum for that matter) on a graph always occurs at exactly zero slope. If you are skilled with your math then it is an easy matter to set the slope to zero and determine the conditions which will then cause the maximum or minimum on the plot.
It seems to be common knowledge that one must match the antenna impedance to the transmission line to transfer maximum energy per unit time (power) across the connection. What is not so widely known is that we can use a resistive voltage divider to demonstrate the idea directly and with ease.
Let’s set up a demonstration circuit to test the idea. We will set a powerful oscillator to a frequency to 10 Mhz and adjust the output voltage to 100 volts rms. Consider this to be a "perfect" voltage source with zero internal impedance. This means that our oscillator will stubbornly maintain the 100 vrms at its output without regard to load. Now, let’s convert this oscillator to a real world device by adding 50 ohms to the output. This is the equivalent to your radio transmitter which has a 50 ohm output.
Next, we have a large carbon resistor and we can change the resistance value from zero ohms to 200 ohms by merely turning a calibrated knob. Since we suspect that heating of the resistor might be an interesting thing to watch let’s attach a thermometer to the resistor to see how its temperature changes during the demonstration.
Finally, attach the carbon load resistor to the 50 ohm output of our demonstration oscillator to complete the circuit. Let’s also attach an RF voltmeter to the load resistor so that we can log some numbers during the demo process. (see spreadsheet data and plot at end of this article)
So, we are ready to start the test and take some data. To make our point and to keep this short we will just do 3 measurements so set the load resistor to 30 ohms and we notice that the voltage across the load resistor is 37.5 volts. We know from Joule’s Law that power is just voltage squared divided by the resistance so the power (energy per time) dissipated in the load is 46.88 watts or 46.88 joules per second. Checking the thermometer we see that it has moved upscale from room temperature to level 1.
Next, set the load resistor to 50 ohms and we notice that the voltage across the load resistor is 50 volts. Applying Joule’s Law once again we see the dissipated power to be 50 watts or 50 joules per second. The thermometer is now reading higher than level 1 from the first measurement.
Finally, set the load resistor to 80 ohms and we notice that the voltage across the load resistor is 61.5 volts. Applying Joule’s Law once again we see the dissipated power to be 47.34 watts or 47.34 joules per second. The thermometer is now reading very close to level 1 from the first measurement.
Taking a look at our data we see that the load resistor temperature was highest at 50 ohms and dropped off either side of 50. If we were to take multiple data points and plot them on graph paper, such that the vertical axis, the ordinate, represented power and the horizontal axis, the abscissa, represented values of load resistance then we would show a "hill" much like the hiking hill we traversed earlier. The maximum value would occur at zero slope (top of the hill), when the "source" resistance of the oscillator equaled the load resistance. By extension, resistance can be replaced with impedance and you will obtain exactly the same results.
We have taken the graphical approach here but mathematically this is a very clean problem. One simply writes the equation for power dissipated in the load in terms of the simple voltage division associated with the source and load impedance. Compute the slope, set it to zero, and notice that both source and load impedance must be equal to achieve zero slope.
Fine you say but what happens when I separate the source impedance and load impedance with a transmission line? Now things start to become very interesting. If, instead of RF energy, we had used DC then the transmission line could be a simple wire to complete the circuit. I deliberately used RF in the demonstration example to make a point about transmission lines. Although transmission lines are tagged with an impedance value they are not resistors. If you were to connect an ohmmeter across an open 50 ohm transmission line the meter would indicate an open circuit. If you connected the same meter across a 50 ohm resistor then the meter would read exactly 50 ohms. The solitary mission of a resistor is to convert electrical energy to heat. The mission of a transmission line is to transfer energy from point A to point B with minimum loss of energy. For example, the 50 ohm transmitter provides the energy, the 50 ohm transmission line directs the energy with intended minimum loss, and the 50 ohm load consumes the energy. So, what is going on here when the line is in play?
To answer this question we need to understand that transmission lines, coaxial cables for example, have distributed inductance and capacitance throughout. The, so called, characteristic impedance of a transmission line is defined by the square root of the ratio of the distributed inductance over the distributed capacitance of a tiny cross section of the line and is resistive. Our 50 ohm line simply scales the line current such that the ratio of line voltage to line current is 50 and no energy is lost in the process. However, there are two primary energy losses in a transmission line which we need to address. Skin effect currents flowing in the copper conductors and dielectric absorption losses in the insulating material between conductors produces heat loss. Both losses vary as a function of frequency.
There are three cases which we need to consider for the transmission line between the source and load in the demonstration example.
First, consider the infinitely long 50 ohm transmission line. Energy entering and moving down the line is constantly reduced by the skin effect losses and dielectric losses and, eventually, this energy is reduced to zero. Input energy is totally dispersed nearest the input end of the infinite length line. Our demo system behaves as if the line were a 50 ohm resistor and maximum energy is transferred from the source. No useful work has been done.
Secondly, consider a very much shorter 50 ohm line which is terminated with a 50 ohm resistor. This line is so short that skin effect losses, and others, are small so that almost the entire input energy is converted to heat in the load resistor. The 50 ohm termination matches the line so there is no impedance discontinuity and there is no reflected energy. The line and load are matched and maximum power is transferred by the line to the load. Maximum useful work has been done.
Thirdly, using the same short line as above we arrange for the load to be something other than a 50 ohm resistor. Perhaps a 60 ohm resistor is now the load. When the incident energy first encounters the 50 ohm line the characteristic impedance of the line scales the current appropriately for the 50 ohms. Then, at some later time, the traveling energy encounters the 60 ohm termination. Obviously there is now an impedance mismatch and some small fraction of the incident energy is reflected back toward the generating end. Given these circumstances, with the reflected energy in play, it is clear that maximum energy transfer can never be achieved. Less than maximum useful work has been done.
In summary, one can show either graphically or mathematically that maximum energy is transferred when the source impedance equals, or matches, the load impedance. Transmission lines do not dissipate energy as do resistors. The entire system must be matched to realize maximum energy transfer. Transmission line to load mismatches cause energy reflections which always reduce system throughput and degrade performance.
This concludes the set up for the discussion of impedance matching. Are there any questions or comments?
This image is a scan of spreadsheet data and associated plot for the demonstration circuit described above.
Double click the image to see a larger version.
This is N7KC for the Wednesday night Educational Radio Net.
The impedance series is now history. During the course of that 13 week series we looked at several of the most fundamental ideas in the physics of electrical phenomenon and, hopefully, gained some practical knowledge of how these ideas link together to form a basis for our understanding of all things electrical. Let's exercise some of this earlier impedance series material and see how it can be applied to solve practical problems which are routinely encountered on the bench. The first study examined the potentiometer or "pot" and its behavior when used as a voltage divider. This second study will firstly examine how energy is moved from a source to a load and secondly, consider the effect of a transmission line in this process.
First, we need to understand a very elementary concept in describing mathematical plots. Imagine that we are walking along a straight path which starts to curve uphill. We notice that the walking is getting tougher as the path curves upward. We might make the observation that this is a steep upward slope. As we continue our walk along the path, it levels out and immediately starts to slope downward and we must hold back to avoid running. We might make the observation that this is a steep downward slope. Looking back on our route we see that the high point on the walk was at the highest point on the hill and, further, that the slope was actually zero at that point. So it is with graphical plots. A maximum point (or minimum for that matter) on a graph always occurs at exactly zero slope. If you are skilled with your math then it is an easy matter to set the slope to zero and determine the conditions which will then cause the maximum or minimum on the plot.
It seems to be common knowledge that one must match the antenna impedance to the transmission line to transfer maximum energy per unit time (power) across the connection. What is not so widely known is that we can use a resistive voltage divider to demonstrate the idea directly and with ease.
Let’s set up a demonstration circuit to test the idea. We will set a powerful oscillator to a frequency to 10 Mhz and adjust the output voltage to 100 volts rms. Consider this to be a "perfect" voltage source with zero internal impedance. This means that our oscillator will stubbornly maintain the 100 vrms at its output without regard to load. Now, let’s convert this oscillator to a real world device by adding 50 ohms to the output. This is the equivalent to your radio transmitter which has a 50 ohm output.
Next, we have a large carbon resistor and we can change the resistance value from zero ohms to 200 ohms by merely turning a calibrated knob. Since we suspect that heating of the resistor might be an interesting thing to watch let’s attach a thermometer to the resistor to see how its temperature changes during the demonstration.
Finally, attach the carbon load resistor to the 50 ohm output of our demonstration oscillator to complete the circuit. Let’s also attach an RF voltmeter to the load resistor so that we can log some numbers during the demo process. (see spreadsheet data and plot at end of this article)
So, we are ready to start the test and take some data. To make our point and to keep this short we will just do 3 measurements so set the load resistor to 30 ohms and we notice that the voltage across the load resistor is 37.5 volts. We know from Joule’s Law that power is just voltage squared divided by the resistance so the power (energy per time) dissipated in the load is 46.88 watts or 46.88 joules per second. Checking the thermometer we see that it has moved upscale from room temperature to level 1.
Next, set the load resistor to 50 ohms and we notice that the voltage across the load resistor is 50 volts. Applying Joule’s Law once again we see the dissipated power to be 50 watts or 50 joules per second. The thermometer is now reading higher than level 1 from the first measurement.
Finally, set the load resistor to 80 ohms and we notice that the voltage across the load resistor is 61.5 volts. Applying Joule’s Law once again we see the dissipated power to be 47.34 watts or 47.34 joules per second. The thermometer is now reading very close to level 1 from the first measurement.
Taking a look at our data we see that the load resistor temperature was highest at 50 ohms and dropped off either side of 50. If we were to take multiple data points and plot them on graph paper, such that the vertical axis, the ordinate, represented power and the horizontal axis, the abscissa, represented values of load resistance then we would show a "hill" much like the hiking hill we traversed earlier. The maximum value would occur at zero slope (top of the hill), when the "source" resistance of the oscillator equaled the load resistance. By extension, resistance can be replaced with impedance and you will obtain exactly the same results.
We have taken the graphical approach here but mathematically this is a very clean problem. One simply writes the equation for power dissipated in the load in terms of the simple voltage division associated with the source and load impedance. Compute the slope, set it to zero, and notice that both source and load impedance must be equal to achieve zero slope.
Fine you say but what happens when I separate the source impedance and load impedance with a transmission line? Now things start to become very interesting. If, instead of RF energy, we had used DC then the transmission line could be a simple wire to complete the circuit. I deliberately used RF in the demonstration example to make a point about transmission lines. Although transmission lines are tagged with an impedance value they are not resistors. If you were to connect an ohmmeter across an open 50 ohm transmission line the meter would indicate an open circuit. If you connected the same meter across a 50 ohm resistor then the meter would read exactly 50 ohms. The solitary mission of a resistor is to convert electrical energy to heat. The mission of a transmission line is to transfer energy from point A to point B with minimum loss of energy. For example, the 50 ohm transmitter provides the energy, the 50 ohm transmission line directs the energy with intended minimum loss, and the 50 ohm load consumes the energy. So, what is going on here when the line is in play?
To answer this question we need to understand that transmission lines, coaxial cables for example, have distributed inductance and capacitance throughout. The, so called, characteristic impedance of a transmission line is defined by the square root of the ratio of the distributed inductance over the distributed capacitance of a tiny cross section of the line and is resistive. Our 50 ohm line simply scales the line current such that the ratio of line voltage to line current is 50 and no energy is lost in the process. However, there are two primary energy losses in a transmission line which we need to address. Skin effect currents flowing in the copper conductors and dielectric absorption losses in the insulating material between conductors produces heat loss. Both losses vary as a function of frequency.
There are three cases which we need to consider for the transmission line between the source and load in the demonstration example.
First, consider the infinitely long 50 ohm transmission line. Energy entering and moving down the line is constantly reduced by the skin effect losses and dielectric losses and, eventually, this energy is reduced to zero. Input energy is totally dispersed nearest the input end of the infinite length line. Our demo system behaves as if the line were a 50 ohm resistor and maximum energy is transferred from the source. No useful work has been done.
Secondly, consider a very much shorter 50 ohm line which is terminated with a 50 ohm resistor. This line is so short that skin effect losses, and others, are small so that almost the entire input energy is converted to heat in the load resistor. The 50 ohm termination matches the line so there is no impedance discontinuity and there is no reflected energy. The line and load are matched and maximum power is transferred by the line to the load. Maximum useful work has been done.
Thirdly, using the same short line as above we arrange for the load to be something other than a 50 ohm resistor. Perhaps a 60 ohm resistor is now the load. When the incident energy first encounters the 50 ohm line the characteristic impedance of the line scales the current appropriately for the 50 ohms. Then, at some later time, the traveling energy encounters the 60 ohm termination. Obviously there is now an impedance mismatch and some small fraction of the incident energy is reflected back toward the generating end. Given these circumstances, with the reflected energy in play, it is clear that maximum energy transfer can never be achieved. Less than maximum useful work has been done.
In summary, one can show either graphically or mathematically that maximum energy is transferred when the source impedance equals, or matches, the load impedance. Transmission lines do not dissipate energy as do resistors. The entire system must be matched to realize maximum energy transfer. Transmission line to load mismatches cause energy reflections which always reduce system throughput and degrade performance.
This concludes the set up for the discussion of impedance matching. Are there any questions or comments?
This image is a scan of spreadsheet data and associated plot for the demonstration circuit described above.Double click the image to see a larger version.
This is N7KC for the Wednesday night Educational Radio Net.
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