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.
Tuesday, November 25, 2008
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.
Monday, October 27, 2008
Antennas: The Yagi, Bob, Week 23
Tonight we will cover another of the basic ham antennas, the Yagi. This is the most popular rotatable antenna as it is a good compromise between, cost, durability, manageability and performance.
Let me start by saying I fully expected to get a neat simple explanation of the theory of Yagis from the ARRL Antenna Book but it is not there. This seems to be one of those black magic designs that just work. Don't misunderstand, this can be modeled by the popular computer programs and you can see how it works but I didn't find any simple explanation of why it works. With that said, let's dive in anyway and at least describe it and what it does, along with some of the compromises in design.
It consists of a horizontal boom with two or more horizontal elements that are perpendicular to the boom. I believe most of you have seen several Yagis by now so I won't go too much into the appearance. The two necessary elements are the driven element, which is essentially a horizontal dipole like the kind we have covered previously, and the reflector. The reflector, as you might guess is placed "behind" the driven element, that is to say, the radiation of the antenna is primarily in the direction opposite the reflector. A Yagi has only one reflector. Any more elements after the driven element and the reflector are directors and are on the opposite side of the driven element from the reflector. So, going from back to front the elements are: reflector, driven element, director, director, etc.
Early designs of Yagis had all of the elements equally spaced at around 0.15 wavelengths between each one. Optimal designs now have the reflector, driven element and first director more closely spaced (about 0.1 wavelength or less) and the directors spaced farther apart. So, lets look at what we mean by an optimal design. First, what are the design trade-offs of a Yagi?
THE PERFECT YAGI
Even though we wouldn't all agree on what the perfect Yagi was we can agree on three things we would want:
REAL WORLD YAGIS
If we design for a maximum gain antenna what we get is an antenna that has a very narrow range of frequencies with a usable SWR. The ARRL Antenna Book has a nice set of graphs showing this which I will use to share some numbers. The example I've chosen is for a 10 Meter, 3 element Yagi. For those that have the book it is on page 11-5. The table below shows three Yagi designs: maximum gain antenna, the maximum gain per SWR antenna and the optimal antenna.
From this table you can see that you get a modest improvement in gain for the maximum gain design but at a cost of both SWR and the Front to Back gain ratio. The Gain per SWR gives you good SWR across the band and better gain than the optimized but at a cost of decreased Front to Back gain ratio. The optimized Yagi design sacrifices a bit of overall gain but gives you a good SWR across the band and a consistently good Front to Back ratio as well.
There are design considerations for adding more directors as well but I will leave that for another time. This is more specifically for VHF/UHF antennas and we may have a session just on that.
The ARRL Antenna Book rates two element Yagis well and indicates that the increased gain drops off as you start adding directors.
EZNEC Antenna Software by W7EL
Here is the promised link to get the EZNEC antenna modeling software. I have the free version now which limits you to 20 segments. Each wire should have several segments to allow for accurate modeling so 20 segments won't go very far on a multiple element antenna. I will probably end up buying the full version which is $89 for a web purchase and direct download or $99 to get the CD.
Let me start by saying I fully expected to get a neat simple explanation of the theory of Yagis from the ARRL Antenna Book but it is not there. This seems to be one of those black magic designs that just work. Don't misunderstand, this can be modeled by the popular computer programs and you can see how it works but I didn't find any simple explanation of why it works. With that said, let's dive in anyway and at least describe it and what it does, along with some of the compromises in design.
It consists of a horizontal boom with two or more horizontal elements that are perpendicular to the boom. I believe most of you have seen several Yagis by now so I won't go too much into the appearance. The two necessary elements are the driven element, which is essentially a horizontal dipole like the kind we have covered previously, and the reflector. The reflector, as you might guess is placed "behind" the driven element, that is to say, the radiation of the antenna is primarily in the direction opposite the reflector. A Yagi has only one reflector. Any more elements after the driven element and the reflector are directors and are on the opposite side of the driven element from the reflector. So, going from back to front the elements are: reflector, driven element, director, director, etc.
Early designs of Yagis had all of the elements equally spaced at around 0.15 wavelengths between each one. Optimal designs now have the reflector, driven element and first director more closely spaced (about 0.1 wavelength or less) and the directors spaced farther apart. So, lets look at what we mean by an optimal design. First, what are the design trade-offs of a Yagi?
THE PERFECT YAGI
Even though we wouldn't all agree on what the perfect Yagi was we can agree on three things we would want:
- 50 Ohm Impedance at the feedpoint; pure resistive (no reactance)
- Zero gain at the back and sides
- Maximum possible gain at the front
REAL WORLD YAGIS
If we design for a maximum gain antenna what we get is an antenna that has a very narrow range of frequencies with a usable SWR. The ARRL Antenna Book has a nice set of graphs showing this which I will use to share some numbers. The example I've chosen is for a 10 Meter, 3 element Yagi. For those that have the book it is on page 11-5. The table below shows three Yagi designs: maximum gain antenna, the maximum gain per SWR antenna and the optimal antenna.
| Value | Max Gain Design | Max Gain per SWR Design | Optimized Design |
|---|---|---|---|
| SWR at 28.4 MHz | 2 | 2 | 2 |
| SWR at 28.0 MHz | 7 | 2 | 2 |
| SWR at 28.8 MHz | 10 | 2 | 2.2 |
| Gain at 28.4 MHz | 8.4 | 7.6 | 7.2 |
| Gain at 28.0 MHz | 7.9 | 7.5 | 7.1 |
| Gain at 28.8 MHz | 8.2 | 7.8 | 7.4 |
| F/R at 28.4 MHz | 13 | 22 | 22 |
| F/R at 28.0 MHz | 20 | 15 | 20 |
| F/R at 28.8 MHz | 6 | 18 | 23 |
From this table you can see that you get a modest improvement in gain for the maximum gain design but at a cost of both SWR and the Front to Back gain ratio. The Gain per SWR gives you good SWR across the band and better gain than the optimized but at a cost of decreased Front to Back gain ratio. The optimized Yagi design sacrifices a bit of overall gain but gives you a good SWR across the band and a consistently good Front to Back ratio as well.
There are design considerations for adding more directors as well but I will leave that for another time. This is more specifically for VHF/UHF antennas and we may have a session just on that.
The ARRL Antenna Book rates two element Yagis well and indicates that the increased gain drops off as you start adding directors.
EZNEC Antenna Software by W7EL
Here is the promised link to get the EZNEC antenna modeling software. I have the free version now which limits you to 20 segments. Each wire should have several segments to allow for accurate modeling so 20 segments won't go very far on a multiple element antenna. I will probably end up buying the full version which is $89 for a web purchase and direct download or $99 to get the CD.
Wednesday, October 22, 2008
Potentiometers 101
October 22, 2008 Educational Radio Net, PSRG 22nd session, Lee Bond N7KC
The impedance series is now history. During the course of 13 weeks 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. My choice for the first study is the potentiometer or "pot" in the vernacular.
There is one wee problem with the word potentiometer which we must clear up before proceeding... there are two devices which share the same name but perform different duties in the electrical world. In early laboratories one could find a very elegant device, with many knobs, generally in a nicely crafted wooden box, and which was used to measure electrical potential differences with great accuracy. Today this function is performed by sophisticated digital voltmeters and one rarely sees the older instrument except in museums. The potentiometer that we will study is the familiar device commonly found on the front panels of our radios, which can be rotated to produce some desired action.
These devices are everywhere. Virtually all "level" controls such as audio volume, AGC, squelch, power supply voltage output, and many more are based on the lowly pot so a good grasp of the underlying operational details is a must for your bag of tricks. We all know what a pot looks like physically. It is a resistive device which has 3 contact points. Basically each end of the resistive "element" is attached to one of the points. The remaining contact point, generally known as the "wiper", connects to a sliding assembly which is controlled by some knob or motor, and which makes a mechanically movable contact which is adjustable from one end of the resistive element to the other.
The resistive element proper was carbon in the early days of this device but modern materials have largely replaced carbon. More common today is the very robust cermet element and the even more robust wire wound element. The carbon element tended to abrade as the wiper slid along its surface and they would become "scratchy" and very annoying. Cermet has much less tendency to abrade and also offers what is called infinite resolution. In contrast is the wire wound pot which may or may not offer infinite resolution depending on construction. If the resistance element is just a length of resistance wire formed in a circle then the resolution would be deemed infinite since the slider can find any point on the wire. If the wire resistance element is a helically wound structure which is then formed in a circle then the wiper can only contact discrete points along the main wire and the pot cannot be set infinitely fine.
The most common pot is structured with a linear taper meaning that doubling the angle of rotation will double the resistance from the wiper with respect to a designated end of the element. Additionally, there log taper pots where the resistance changes logarithmically with rotation angle. The log class includes the audio taper pot which produces a uniform change of loudness to your ear with uniform shaft rotation if used as a volume control. Variations here are log clockwise or counter clockwise.
There is a class of very high precision multiturn wire wound potentiometer devices called Helipots by Beckman. Bourns and others offer similar devices. These offer 5 turn, 10 turn, and 20 turn rotations so the total resistance can be controlled over as much as 7200 degrees of rotation. The linearity of these devices as deviations from a straight line are specified and they all offer extraordinary precision. Generally used with turns counting dials.
One last point concerning the use of wire wound pots is in order. In addition to the desired resistance mechanism there is an added component of inductance present. If the element is helically wound then the inductive component is much larger than that encountered with the simple wire element. Inductance/reactance effects limit the use of these sort of pots in AC circuits hence they are more commonly found in DC circuits.
Ok, let's build a circuit. We will need a power supply of some sort so how about using a 10 volt battery. 10 volts will be convenient for our discussion even though a 10 volt battery would be an oddity for sure. Then we need a pot to work with. Lets choose a simple 1000 ohm carbon unit rated at 2 watts and which is structured as a linear device. That's it for our circuit parts... just a battery and a pot. Lets connect the battery and pot in series in the following manner. Pot contacts are normally labeled 1, 2, and 3. Contact 1 is commonly the low potential reference so it will go to the battery negative terminal. Contact 2 is always the wiper and common convention states that the wiper, contact 2, moves toward the contact 3 end with clockwise rotation of the knob. So, to complete our circuit we connect contact 3 to the battery positive terminal.
Now we need a measuring device so let's choose a VOM as in Volt-Ohm-Milliamp meter. In fact we will need two of these meters so let's use the common Simpson 260 VOM. We want to measure the series current flowing in our circuit so disconnect the pot contact 3 from the battery positive and insert, in series, one of the VOM's with positive lead going to the battery positive and the negative (common) lead going to contact 3 on the pot. From Ohm's Law we expect the series current to be 10 volts divided by 1000 ohms and, sure enough, the series meter shows the current to be 0.01 amperes or 10 milliamperes. (Note: let me assert that we are using a "perfect" meter here... one that does not influence the circuit being measured. In real life no such device exists and all measuring instruments change the circuit to some degree. The effect is commonly described as "loading".)
From earlier discussions we know that 1 ampere is defined as 1 coulomb of charge per second past a given point so the 0.01 ampere represents 0.01 coulombs per second flowing in our circuit. Also from earlier discussions we know that you cannot impress any voltage on a resistor without the resistor becoming warmer than it's surrounding environment. The job of a resistor is to convert the energy of moving electrical charge to heat energy. Remember Joule's Law? The power calculation for our little circuit is voltage squared divided by resistance or 0.1 watt. From earlier discussions we know that 1 watt is one joule per second so we conclude that 100 milli-joules of electrical energy per second is being converted to heat in our pot resistive element and a sensitive thermometer would show some upscale movement.
Now, adjust the pot shaft fully clockwise, and let's add the second meter as a voltmeter and place the meter negative lead on the battery negative and the meter positive lead on contact 2 of the pot. Fully clockwise moves contact 2 to contact 3 and we see 10 volts on the meter as you would expect since both are in contact with the battery positive terminal. Now rotate the shaft to mid rotation, half way between rotational extremes, and notice that the meter indicates 5 volts or 1/2 of the previous initial reading. Moving the shaft again such that the wiper moves toward contact 1 shows that voltage goes toward zero whereas moving from midpoint toward contact 3 shows the voltage going toward maximum.
Now consider the shaft at mid position where we measured 5 volts on the meter. Since the pot is linear the mid position resistance should be 1/2 of the 1000 ohms or 500 ohms. At mid point we would expect 1/2 of the total power to be dissipated above the wiper position and 1/2 dissipated below. At mid point we measure 5 volts and we know that the resistance is 500 ohms. So, 5 squared divided by 500 from Joule's Law gives 0.05 watts which is 1/2 of the total 0.1 watts dissipation.
The idea of "voltage drop" follows directly from the lesser amount of energy dissipated as the wiper approaches the reference terminal or contact 1 on the pot. By extension, one could partition the resistor element into 10 equal sections and then argue that the total must be the sum of the parts so each part would then dissipate 0.01 watts. Each partition would then "drop" 1 volt over 100 ohms which computes to 0.01 watts.
My point here is to show that, yes, one can talk glibly about voltage drops around a resistive circuit, but the underlying principle is directly related to energy conversion to heat. Resistors always throw something away but the wiper on a pot allows you to choose at what level you want to save. Basically a pot is an attenuator. The output signal will never be larger than the input because of the energy conversion into heat phenomenon.
The pot is a simple voltage divider and the output voltage can be easily calculated. The fraction of the tapped off resistance divided by the total resistance times the input will yield the output voltage. For example, using our 1000 ohm pot, if the tapped resistance is 133 ohms and the input voltage were 8.5 volts then the output voltage is 133 ohms divided by 1000 ohms times 8.5 volts or 1.1305 volts. Conversely, if one knows the output voltage and the tap ratio then computing the input voltage is a piece of cake. In like fashion, if you know the input voltage and desired output voltage then calculating the tap point is one more piece of cake.
One last point... sometimes you will see a pot symbol wired with terminals 1 and 2 or 2 and 3 connected together. In this case the pot is wired as a rheostat and is nothing more than a variable resistor. It is not possible to voltage divide with a single rheostat. You must have at least two units to achieve voltage division.
In summary, all resistors dissipate energy and will be measurably warmer than their environment. Voltage drops are a direct consequence of energy dissipation in a resistive element. Kirchoff's voltage law which states that the algebraic sum of the voltages in a closed loop is zero is simply a restatement of conservation of energy where total energy converted to heat equals total input energy. Given that work and energy are identical it follows that work in equals work out hence the net work is zero.
This concludes the set up for the discussion of potentiometers or pots. Are there any questions or comments?
Something to ponder: Two atoms are leaving a bar when one says to the other "I left my electrons in the bar". The other says to the first "are you sure?" The first replies "I am positive".
This is N7KC for the Wednesday night Educational Radio Net.
The impedance series is now history. During the course of 13 weeks 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. My choice for the first study is the potentiometer or "pot" in the vernacular.
There is one wee problem with the word potentiometer which we must clear up before proceeding... there are two devices which share the same name but perform different duties in the electrical world. In early laboratories one could find a very elegant device, with many knobs, generally in a nicely crafted wooden box, and which was used to measure electrical potential differences with great accuracy. Today this function is performed by sophisticated digital voltmeters and one rarely sees the older instrument except in museums. The potentiometer that we will study is the familiar device commonly found on the front panels of our radios, which can be rotated to produce some desired action.
These devices are everywhere. Virtually all "level" controls such as audio volume, AGC, squelch, power supply voltage output, and many more are based on the lowly pot so a good grasp of the underlying operational details is a must for your bag of tricks. We all know what a pot looks like physically. It is a resistive device which has 3 contact points. Basically each end of the resistive "element" is attached to one of the points. The remaining contact point, generally known as the "wiper", connects to a sliding assembly which is controlled by some knob or motor, and which makes a mechanically movable contact which is adjustable from one end of the resistive element to the other.
The resistive element proper was carbon in the early days of this device but modern materials have largely replaced carbon. More common today is the very robust cermet element and the even more robust wire wound element. The carbon element tended to abrade as the wiper slid along its surface and they would become "scratchy" and very annoying. Cermet has much less tendency to abrade and also offers what is called infinite resolution. In contrast is the wire wound pot which may or may not offer infinite resolution depending on construction. If the resistance element is just a length of resistance wire formed in a circle then the resolution would be deemed infinite since the slider can find any point on the wire. If the wire resistance element is a helically wound structure which is then formed in a circle then the wiper can only contact discrete points along the main wire and the pot cannot be set infinitely fine.
The most common pot is structured with a linear taper meaning that doubling the angle of rotation will double the resistance from the wiper with respect to a designated end of the element. Additionally, there log taper pots where the resistance changes logarithmically with rotation angle. The log class includes the audio taper pot which produces a uniform change of loudness to your ear with uniform shaft rotation if used as a volume control. Variations here are log clockwise or counter clockwise.
There is a class of very high precision multiturn wire wound potentiometer devices called Helipots by Beckman. Bourns and others offer similar devices. These offer 5 turn, 10 turn, and 20 turn rotations so the total resistance can be controlled over as much as 7200 degrees of rotation. The linearity of these devices as deviations from a straight line are specified and they all offer extraordinary precision. Generally used with turns counting dials.
One last point concerning the use of wire wound pots is in order. In addition to the desired resistance mechanism there is an added component of inductance present. If the element is helically wound then the inductive component is much larger than that encountered with the simple wire element. Inductance/reactance effects limit the use of these sort of pots in AC circuits hence they are more commonly found in DC circuits.
Ok, let's build a circuit. We will need a power supply of some sort so how about using a 10 volt battery. 10 volts will be convenient for our discussion even though a 10 volt battery would be an oddity for sure. Then we need a pot to work with. Lets choose a simple 1000 ohm carbon unit rated at 2 watts and which is structured as a linear device. That's it for our circuit parts... just a battery and a pot. Lets connect the battery and pot in series in the following manner. Pot contacts are normally labeled 1, 2, and 3. Contact 1 is commonly the low potential reference so it will go to the battery negative terminal. Contact 2 is always the wiper and common convention states that the wiper, contact 2, moves toward the contact 3 end with clockwise rotation of the knob. So, to complete our circuit we connect contact 3 to the battery positive terminal.
Now we need a measuring device so let's choose a VOM as in Volt-Ohm-Milliamp meter. In fact we will need two of these meters so let's use the common Simpson 260 VOM. We want to measure the series current flowing in our circuit so disconnect the pot contact 3 from the battery positive and insert, in series, one of the VOM's with positive lead going to the battery positive and the negative (common) lead going to contact 3 on the pot. From Ohm's Law we expect the series current to be 10 volts divided by 1000 ohms and, sure enough, the series meter shows the current to be 0.01 amperes or 10 milliamperes. (Note: let me assert that we are using a "perfect" meter here... one that does not influence the circuit being measured. In real life no such device exists and all measuring instruments change the circuit to some degree. The effect is commonly described as "loading".)
From earlier discussions we know that 1 ampere is defined as 1 coulomb of charge per second past a given point so the 0.01 ampere represents 0.01 coulombs per second flowing in our circuit. Also from earlier discussions we know that you cannot impress any voltage on a resistor without the resistor becoming warmer than it's surrounding environment. The job of a resistor is to convert the energy of moving electrical charge to heat energy. Remember Joule's Law? The power calculation for our little circuit is voltage squared divided by resistance or 0.1 watt. From earlier discussions we know that 1 watt is one joule per second so we conclude that 100 milli-joules of electrical energy per second is being converted to heat in our pot resistive element and a sensitive thermometer would show some upscale movement.
Now, adjust the pot shaft fully clockwise, and let's add the second meter as a voltmeter and place the meter negative lead on the battery negative and the meter positive lead on contact 2 of the pot. Fully clockwise moves contact 2 to contact 3 and we see 10 volts on the meter as you would expect since both are in contact with the battery positive terminal. Now rotate the shaft to mid rotation, half way between rotational extremes, and notice that the meter indicates 5 volts or 1/2 of the previous initial reading. Moving the shaft again such that the wiper moves toward contact 1 shows that voltage goes toward zero whereas moving from midpoint toward contact 3 shows the voltage going toward maximum.
Now consider the shaft at mid position where we measured 5 volts on the meter. Since the pot is linear the mid position resistance should be 1/2 of the 1000 ohms or 500 ohms. At mid point we would expect 1/2 of the total power to be dissipated above the wiper position and 1/2 dissipated below. At mid point we measure 5 volts and we know that the resistance is 500 ohms. So, 5 squared divided by 500 from Joule's Law gives 0.05 watts which is 1/2 of the total 0.1 watts dissipation.
The idea of "voltage drop" follows directly from the lesser amount of energy dissipated as the wiper approaches the reference terminal or contact 1 on the pot. By extension, one could partition the resistor element into 10 equal sections and then argue that the total must be the sum of the parts so each part would then dissipate 0.01 watts. Each partition would then "drop" 1 volt over 100 ohms which computes to 0.01 watts.
My point here is to show that, yes, one can talk glibly about voltage drops around a resistive circuit, but the underlying principle is directly related to energy conversion to heat. Resistors always throw something away but the wiper on a pot allows you to choose at what level you want to save. Basically a pot is an attenuator. The output signal will never be larger than the input because of the energy conversion into heat phenomenon.
The pot is a simple voltage divider and the output voltage can be easily calculated. The fraction of the tapped off resistance divided by the total resistance times the input will yield the output voltage. For example, using our 1000 ohm pot, if the tapped resistance is 133 ohms and the input voltage were 8.5 volts then the output voltage is 133 ohms divided by 1000 ohms times 8.5 volts or 1.1305 volts. Conversely, if one knows the output voltage and the tap ratio then computing the input voltage is a piece of cake. In like fashion, if you know the input voltage and desired output voltage then calculating the tap point is one more piece of cake.
One last point... sometimes you will see a pot symbol wired with terminals 1 and 2 or 2 and 3 connected together. In this case the pot is wired as a rheostat and is nothing more than a variable resistor. It is not possible to voltage divide with a single rheostat. You must have at least two units to achieve voltage division.
In summary, all resistors dissipate energy and will be measurably warmer than their environment. Voltage drops are a direct consequence of energy dissipation in a resistive element. Kirchoff's voltage law which states that the algebraic sum of the voltages in a closed loop is zero is simply a restatement of conservation of energy where total energy converted to heat equals total input energy. Given that work and energy are identical it follows that work in equals work out hence the net work is zero.
This concludes the set up for the discussion of potentiometers or pots. Are there any questions or comments?
Something to ponder: Two atoms are leaving a bar when one says to the other "I left my electrons in the bar". The other says to the first "are you sure?" The first replies "I am positive".
This is N7KC for the Wednesday night Educational Radio Net.
Monday, October 13, 2008
General Test Grab Bag, Bob, Week 21
Tonight we will cover some of the procedural rules that appear in the General Class test.
First is a set of three questions dealing with an unusual situation in the ham bands. That is the situation where amateur radio is secondary to others that also use the band. In other words, the other service or services have priority over the amateur radio service in these bands. The bands are the 30 meter band and the 60 meter band.
The rule is a common sense one and allows the greatest flexibility to amateurs. Quoting from Part 97.303, "A station in a secondary service must not cause harmful interference to, and must accept interference from, stations in a primary service." In practice that means anytime there is interference between you and a primary service, where you are secondary, you must stop immediately, even if you are in the middle of operating and the primary service starts interfering with you. You are free to change to another frequency within the band where you aren't interfering and continue operating.
So on to the questions.
G1A14 (C) [97.303]
Which of the following applies when the FCC rules designate the amateur service as a
secondary user and another service as a primary user on a band?
A. Amateur stations must obtain permission from a primary service station before
operating on a frequency assigned to that station
B. Amateur stations are allowed to use the frequency band only during emergencies
C. Amateur stations are allowed to use the frequency band only if they do not cause
harmful interference to primary users
D. Amateur stations may only operate during specific hours of the day, while primary
users are permitted 24 hour use of the band
~~
G1A15 (D) [97.303]
What must you do if, when operating on either the 30 or 60 meter bands, a station in
the primary service interferes with your contact?
A. Notify the FCC's regional Engineer in Charge of the interference
B. Increase your transmitter's power to overcome the interference
C. Attempt to contact the station and request that it stop the interference
D. Stop transmitting at once and/or move to a clear frequency
~~
G1A16 (A) [97.303(s)]
Which of the following operating restrictions applies to amateur radio stations as a
secondary service in the 60 meter band?
A. They must not cause harmful interference to stations operating in other radio
services
B. They must transmit no more than 30 minutes during each hour to minimize harmful
interference to other radio services
C. They must use lower sideband, suppressed-carrier, only
D. They must not exceed 2.0 kHz of bandwidth
~~
Here is a question that is Emergency Communication related. Once again, the answer is both common sense and allowing the greatest flexibility to the amateur.
G1B04 (A) [97.113(b)]
Which of the following must be true before an amateur station may provide news
information to the media during a disaster?
A. The information must directly relate to the immediate safety of human life or
protection of property and there is no other means of communication available
B. The exchange of such information must be approved by a local emergency
preparedness official and transmitted on officially designated frequencies
C. The FCC must have declared a state of emergency
D. Both amateur stations must be RACES stations
~~
Music and Encryption...don't do it! (With a couple of very interesting exceptions!) The general idea about using codes and really about all communication in amateur radio is that you are not allowed to operate in a way that intentionally obscures the meaning of what you are communicating. If the codes you are using are generally known and so are understood generally then you are okay.
G1B05 (D) [97.113(a)(4),(e)]
When may music be transmitted by an amateur station?
A. At any time, as long as it produces no spurious emissions
B. When it is unintentionally transmitted from the background at the transmitter
C. When it is transmitted on frequencies above 1215 MHz
D. When it is an incidental part of a space shuttle or ISS retransmission
~~
So unless you happen to be in the Space Shuttle or the International Space Station, you don't get to transmit music.
G1B06 (B) [97.113(a)(4) and 97.207(f)]
When is an amateur station permitted to transmit secret codes?
A. During a declared communications emergency
B. To control a space station
C. Only when the information is of a routine, personal nature
D. Only with Special Temporary Authorization from the FCC
~~
Again, unless you happen to be controlling a space station (and how cool would that be!) you don't get to do it.
Here is another question about using codes.
G1B07 (B) [97.113(a)(4)]
What are the restrictions on the use of abbreviations or procedural signals in
the amateur service?
A. Only "Q" codes are permitted
B. They may be used if they do not obscure the meaning of a message
C. They are not permitted because they obscure the meaning of a message to FCC
monitoring stations
D. Only "10-codes" are permitted
~~
Finally here is a catch-all of prohibited activities.
G1B08 (D) [97.113(a)(4), 97.113(e)]
Which of the following is prohibited by the FCC Rules for amateur radio stations?
A. Transmission of music as the primary program material during a contact
B. The use of obscene or indecent words
C. Transmission of false or deceptive messages or signals
D. All of these answers are correct
~~
First is a set of three questions dealing with an unusual situation in the ham bands. That is the situation where amateur radio is secondary to others that also use the band. In other words, the other service or services have priority over the amateur radio service in these bands. The bands are the 30 meter band and the 60 meter band.
The rule is a common sense one and allows the greatest flexibility to amateurs. Quoting from Part 97.303, "A station in a secondary service must not cause harmful interference to, and must accept interference from, stations in a primary service." In practice that means anytime there is interference between you and a primary service, where you are secondary, you must stop immediately, even if you are in the middle of operating and the primary service starts interfering with you. You are free to change to another frequency within the band where you aren't interfering and continue operating.
So on to the questions.
G1A14 (C) [97.303]
Which of the following applies when the FCC rules designate the amateur service as a
secondary user and another service as a primary user on a band?
A. Amateur stations must obtain permission from a primary service station before
operating on a frequency assigned to that station
B. Amateur stations are allowed to use the frequency band only during emergencies
C. Amateur stations are allowed to use the frequency band only if they do not cause
harmful interference to primary users
D. Amateur stations may only operate during specific hours of the day, while primary
users are permitted 24 hour use of the band
~~
G1A15 (D) [97.303]
What must you do if, when operating on either the 30 or 60 meter bands, a station in
the primary service interferes with your contact?
A. Notify the FCC's regional Engineer in Charge of the interference
B. Increase your transmitter's power to overcome the interference
C. Attempt to contact the station and request that it stop the interference
D. Stop transmitting at once and/or move to a clear frequency
~~
G1A16 (A) [97.303(s)]
Which of the following operating restrictions applies to amateur radio stations as a
secondary service in the 60 meter band?
A. They must not cause harmful interference to stations operating in other radio
services
B. They must transmit no more than 30 minutes during each hour to minimize harmful
interference to other radio services
C. They must use lower sideband, suppressed-carrier, only
D. They must not exceed 2.0 kHz of bandwidth
~~
Here is a question that is Emergency Communication related. Once again, the answer is both common sense and allowing the greatest flexibility to the amateur.
G1B04 (A) [97.113(b)]
Which of the following must be true before an amateur station may provide news
information to the media during a disaster?
A. The information must directly relate to the immediate safety of human life or
protection of property and there is no other means of communication available
B. The exchange of such information must be approved by a local emergency
preparedness official and transmitted on officially designated frequencies
C. The FCC must have declared a state of emergency
D. Both amateur stations must be RACES stations
~~
Music and Encryption...don't do it! (With a couple of very interesting exceptions!) The general idea about using codes and really about all communication in amateur radio is that you are not allowed to operate in a way that intentionally obscures the meaning of what you are communicating. If the codes you are using are generally known and so are understood generally then you are okay.
G1B05 (D) [97.113(a)(4),(e)]
When may music be transmitted by an amateur station?
A. At any time, as long as it produces no spurious emissions
B. When it is unintentionally transmitted from the background at the transmitter
C. When it is transmitted on frequencies above 1215 MHz
D. When it is an incidental part of a space shuttle or ISS retransmission
~~
So unless you happen to be in the Space Shuttle or the International Space Station, you don't get to transmit music.
G1B06 (B) [97.113(a)(4) and 97.207(f)]
When is an amateur station permitted to transmit secret codes?
A. During a declared communications emergency
B. To control a space station
C. Only when the information is of a routine, personal nature
D. Only with Special Temporary Authorization from the FCC
~~
Again, unless you happen to be controlling a space station (and how cool would that be!) you don't get to do it.
Here is another question about using codes.
G1B07 (B) [97.113(a)(4)]
What are the restrictions on the use of abbreviations or procedural signals in
the amateur service?
A. Only "Q" codes are permitted
B. They may be used if they do not obscure the meaning of a message
C. They are not permitted because they obscure the meaning of a message to FCC
monitoring stations
D. Only "10-codes" are permitted
~~
Finally here is a catch-all of prohibited activities.
G1B08 (D) [97.113(a)(4), 97.113(e)]
Which of the following is prohibited by the FCC Rules for amateur radio stations?
A. Transmission of music as the primary program material during a contact
B. The use of obscene or indecent words
C. Transmission of false or deceptive messages or signals
D. All of these answers are correct
~~
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