The 2023-2027 General License question pool asks you to compute power usage from a voltage and a load in a DC circuit: G5B03: How many watts of electrical power are used if 400 VDC is supplied to an 800 ohm load? A. 0.5 watts B. 200 watts C. 400 watts D. 3200 watts Let’s define a couple of terms within this question first, and then we’ll see how to solve it by deriving the proper mathematical relationship from our two old Technician Class friends, Ohm’s Law and Power Law. Electrical power is the rate at which electrical energy is transferred in a circuit. It is a rate of doing work, measured in units of watts. As power increases, more work can be done in a given unit of time. In this question some work is being accomplished at an 800-ohm load. What’s a load in electrical terms? An electrical load is the resistance (or impedance for AC) imposed by the components in a circuit. A load may be the resistance presented by a device that converts electrical energy into another form of energy. For instance, an antenna converts electrical energy into electromagnetic radiation (and some heat), and the antenna imposes a load on the transmitter circuit, impeding the flow of AC. A radio receiver’s speaker in an audio circuit imposes a load when converting electrical energy into mechanical sound waves. A common fan imposes a load and converts electrical energy into mechanical energy, creating a breeze along with the resistance or impedance presented to the circuit. In this question there is an unspecified load to which 400 volts of direct current is being supplied. We need to calculate power in watts based upon the voltage (EMF or ‘E’) and the load resistance (R) in ohms. Remember from your Technician Class studies Ohm’s Law and Power Law. You may remember them arranged in a graphic like these below in which you cover the quantity that you seek to compute, and the remaining quantity graphical relationship tells you what to calculate: Ohm’s Law: E = I x R Also, I = E ÷ R and R = E ÷ I Power Law: P = E x I Also, I = P ÷ E and E = P ÷ I By the Power Law we get an initial relationship for calculating power: P = E x I. From our question we know that E = 400 volts. However, we are not provided any information on the current (I). Rather, we have been provided the resistance of the load, 800 ohms. Aha! Check out the Ohm’s Law relationship, I = E ÷ R. We can substitute E ÷ R for I in the Power Law relationship! So, it goes like this: P = E x I, and I = E ÷ R, so P = E x (E ÷ R), otherwise denoted P = E² ÷ R, also written P = E²/R Let’s plug in the values for E and for R and see what we calculate: P = (400v)² / 800 ohms P = 160,000 / 800 P = 200 watts Notice also from Ohm’s Law that E = I x R. If we make the substitution for E within the Power Law we obtain: P = E x I, and E = I x R, so P = I x R x I, otherwise denoted P = I² x R Given a known current (I) and load resistance (R), you can also compute the power transferred in a circuit, even without knowing the voltage (E). Keep the two bold type formulas above in your hip pocket for exam time calculation of power, or run through the derivation from Ohm’s Law and Power Law a few times so that you can do it again when needed. The answer to General Class question G5B03, “How many watts of electrical power are used if 400 VDC is supplied to an 800-ohm load?” is “B. 200 watts.” -- Stu WØSTU

One question we often hear from new hams (and maybe some not-so-new hams) is “why can’t I get into the repeater?” They get their hands on a new radio, set it up to use one of the local repeaters and it’s not working. Now what? There can be a whole bunch of reasons why you can’t get into a repeater so it is difficult to come up with a quick fix for all situations. However, in this article we’ll talk about some basic troubleshooting steps to help diagnose the problem. For this article, I am assuming that your first rig is a handheld vhf/uhf transceiver but the general approach will work with mobile or base transceivers, too. FOT Many times the problem is due to not having the transceiver programmed correctly. The key things we have to pay attention to are: Frequency, Offset and Tone (FOT). To access a repeater you need to have its Frequency entered into your radio, have its transmit Offset set correctly and have the right CTCSS Tone turned on. You might not need to check all of these things in that exact order but it is a good way to approach the problem. Using the programming software (and suitable cable) for your radio can be a big help. Frequency –First you need to program in the frequency of the repeater you want to access. The actual key strokes or knob turns will depend on the particular model of radio so consult your operating manual. The frequency you enter is the repeater transmit frequency which will be your receive frequency. Repeaters are always referred to by their transmit frequency, which can be found in an online or printed repeater directory. Offset – Next, we need to make sure the proper transmit offset is programmed into the radio. This is the difference in frequency between the repeater transmit frequency and its receive frequency. Your transceiver will automatically shift your frequency when you transmit, if you have the right offset programmed. In most parts of the US, the standard offset is 600 kHz on the 2m band and 5 MHz on the 70cm band, and can be either in the positive (+) or negative (-) direction. Your repeater directory will list the offset and direction. Most radios will default to the standard offset but you may have to select + or – offset. Usually a + or – symbol will appear in the display to indicate the offset selected. As an example, my repeater is on 447.725 MHz with a – 5 MHz offset. So you would enter 447.725 MHz into your radio, make sure the offset is set to 5 MHz and select – as the offset direction. You can verify that your radio is programmed correctly if you see 447.725 MHz displayed during receive, which should change to 442.725 MHz when you push the transmit button. Tone – For most repeaters, you will need to transmit a CTCSS tone to access the repeater. (CTCSS is Continuous Tone Coded Squelch System.) Repeaters with carrier access do not require a tone, so you can skip this step. This is normally a two-step process: set the tone frequency and then enable the tone. Sometimes this is done with one selection (with “Off” being an option for the tone frequency). Some radios have separate settings for the transmit tone and receive tone. For now, just leave the receive tone off, since it can be a source of confusion. The tone that you need to set is your transmit tone. Most radios display a “T” somewhere on the display when the tone is enabled. Again, check your operating manual. Kerchunk At this point, you should be ready to try accessing the repeater. After listening on frequency for a minute, transmit and identify using your callsign. On most repeaters, you will hear a short transmission coming back from the repeater along with a courtesy beep. A courtesy beep is just a short audio tone or tone sequence that occurs after someone finishes transmitting. If you hear the beep, then you accessed the repeater. Congratulations! Go ahead and make a call and see if someone will come back to you. Troubleshooting What if you don’t hear the repeater coming back to you? Then we need to go into troubleshooting mode. If the radio is new, you might wonder if it is even working properly. The quality level of today’s equipment is quite good, so most likely your radio is just fine. Still, you may want to check it out. First, you can check to make sure your radio is receiving properly. In the US, a good way to do this is to tune into your local NOAA weather transmitter. These transmitters are on the air continuously, operating on 162.400, 162.425, 162.450, 162.475, 162.500, 162.525 or 162.550 MHz. These frequencies are outside of the 2m ham band but most ham transceivers are able to listen to these frequencies. You’ll want to set this frequency as simply as possible…use the keypad or VFO mode to enter it directly. In most cases, you can just try the short list of frequencies until you hear the transmitter in your area. Next, you might want to know that your radio is able to transmit a signal. The best way to do this is find a local ham nearby that can run a simplex check with you. By nearby, I mean within 5 miles or so, because we want someone so close that there is no question about whether they should be able to contact us. Program your radio to a 2m simplex frequency such as 146.52 MHz (the National 2m FM Simplex Frequency). For this test, we do NOT want the transmit offset turned on…the radio needs to be set to simplex. You can double check this by looking at the display when transmitting—it should show 146.52 MHz (transmit frequency is the same as the receive frequency). For this test, we don’t care about the transmit tone…it can be on or off. Have the other ham give you a call and see if you can contact him. If you happen to have a second transceiver, you can try this test yourself – just see if each radio can hear the other one. One warning: do this on a simplex frequency. Trying to go through a repeater can really confuse things because you may not have the offset and tone set properly. Even more confusing is that one radio can “de-sense” the other radio, which means that the other radio’s receiver will be overloaded and not able to receive the repeater’s signal. Using simplex keeps things simple. The final thing to check is whether your signal is able to reach the repeater. Well, that is a bit of a challenge! For starters, are you sure you are within range of the repeater? Have you ever heard a signal from this repeater, and was it full scale on your S meter? You may want to ask local hams about whether you should be able to hit the repeater from your location with the radio you are using. For that matter, you might want to check if the repeater is actually on the air – they do go down from time to time. This brings us to an important point about the use of handheld transceivers. They are really, really handy. How else can you carry a complete ham radio station in your hand? Well, the tradeoff is that an HT operates with relatively low power (5 watts or less) and has a compromised antenna. (The standard rubber duck antenna on an HT is a very convenient crummy antenna.) You may need to add some extra umph to your signal by improving the antenna. Some good dual-band choices are a longer whip such as the Diamond RH77CA, SRH77CA, or SRJ77CA or a magnetic-mount mobile antenna placed on a vehicle or on other metal object. Summary In this article, I’ve tried to provide some assistance in figuring out why you aren’t hitting the repeater. The most common problem for newly acquired radios is getting them programmed (remember FOT: Frequency Offset and Tone). Once you have that right, it is usually just making sure that you have enough signal to make it to the repeater. For some additional background information on repeaters, see the Ham Radio School article: Introduction to UHF/VHF FM Repeaters. 73, Bob K0NR

You’ve got that shiny new HF transceiver out of the box and on the shelf in your shack. You have a nice DC power supply ready to provide 13.8 volts. You’ve even got the rig components properly grounded! Now, what do you need to do with that dipole antenna to get on the air? This is a common scenario for many new aspiring HF operators. As Bob KØNR mentions in his article, Your First Dipole Antenna, erecting an antenna for HF operations is perhaps the most challenging aspect of establishing a basic HF station. The horizontal wire, half-wave dipole antenna is one of the simplest HF antennas to set up, it offers very good performance, and that makes it a very popular choice for hams. Let’s see how trimming a dipole antenna, and following a few other guidelines, can make it glimmer like an RF gem! To get the best performance from your dipole you’ll want to follow a few simple guidelines. Try to keep the dipole away from other conductors, especially long, linear ones like household rain gutters, or at least try to avoid aligning the dipole parallel with such conductors. A dipole will provide low take-off angles for good over-the-horizon skip propagation when it is approximately one-half wavelength above the ground. At lower heights the radiation pattern will become more vertically directed and more omnidirectional. The strongest signals radiate broadside to the antenna, or at right angles to the orientation of the dipole’s wire, and you may want to establish your dipole so that those strongest signals are pointed in desired propagation directions. Be sure to seal up any connectors that will be exposed to the elements to avoid water penetration into your coaxial feed line. Finally, trimming your dipole antenna for the band and frequency range you intend to operate on is critical! Trimming a dipole antenna refers to the adjustment of antenna length to operating frequency. The total length of the dipole should be just under one-half wavelength for the operating band. When the dipole is properly trimmed for an operating frequency the antenna feed point will present an impedance that is closely matched to the feed line impedance. When feed line and antenna feed point impedances match, your antenna system will have effective power transfer and will radiate efficiently. If the trim is poor for the operating frequency the impedances will not be well matched and some of your transmitter’s power will be reflected back down the feed line instead of being radiated as RF energy. SWR: Nearly all antenna systems will have at least a little power reflection due to mild impedance mismatch at the antenna feed point. The standing wave ratio (SWR) is a comparison of the forward power in your antenna system with the reflected power. A low SWR indicates little power reflection and efficient power transfer to the antenna, while higher SWR values indicate greater reflection and less efficient power transfer. Generally, you should strive for a low SWR in your antenna system. You can judge the proper trim for your dipole by measuring the SWR as you adjust the antenna length. Measurement Instruments: How do you measure SWR in your new dipole? You’ll need a measurement instrument. Two very popular instruments for trimming a dipole antenna are the SWR meter and the antenna analyzer. These two instruments work differently, so let’s briefly review the functioning of each. The SWR meter is positioned into the feed line between the transmitter and antenna. Most hams will place the SWR meter into the feed line immediately after the transmitter so the readings are viewable in the shack while transmitting. The SWR meter evaluates feed line voltages in the forward and reflected directions and displays the SWR computation for the operator. So, you have to actually transmit a signal for the SWR meter to take a reading, and you must read the SWR value during the transmission. The antenna analyzer requires the feed line to be connected to it, but no connection to the transmitter is needed. The analyzer generates its own signals for the antenna system, computes SWR, and displays it to the user alongside frequency. It is very common for an antenna analyzer to allow the user to dial through a range of frequencies while observing the SWR readout, and some will display a graph of SWR across a frequency range, similar to the SWR curve plots depicted below. This way the user can see where along the frequency range the SWR value dips to its minimum value, and thereby see the precise frequency range for which the antenna is currently trimmed. Step-by-Step: With those measurement devices in mind, let’s consider the big picture practical steps of trimming a dipole antenna: Determine the band and frequency range for which you desire the antenna trimmed. For example, you may want to trim a 20-meter band dipole for the General Class phone frequencies of 14.225 MHz to 14.350 MHz. Compute the approximate antenna length for the center frequency of the range for which you are trimming. In our example that would be a trim for about 14.287 MHz, or a dipole length of about 32.75 feet (32 feet, 9 inches). Cut the dipole wire to be a little longer than the computed length – it’s easier to cut wire than to extend it. So, perhaps you would cut your 20-meter dipole length to be about 34 feet long, with each of the two segments at about 17 feet. (17 x 2 = 34) If possible, erect the dipole into the desired position to make SWR measurements. You might accomplish this by anchoring the center point of the dipole in its intended elevated position, while using lengths of cord to temporarily “pull up” the ends near their intended permanent anchor points. The specific methods used will depend on your dipole configuration (flattop, inverted V, or sloper) and its height above ground, as well as the type of anchor points being used. Note: Getting the dipole into its approximate operating position and height above ground will provide the most accurate SWR measurements, especially if other unavoidable conductors are within a wavelength of the dipole’s operating position. Note: If you cannot erect the dipole near its final operating position, approximate it as closely as possible and elevate the antenna above the ground to the extent possible for measurements. Use one of the measurement instruments to determine the frequency at which the lowest SWR is achieved. (See SWR Measurement Techniques that follow.) Given the extra-long length of wire left on the dipole segments, the SWR should bottom out at a frequency below the desired operating frequency. In our example let’s suppose you measured a minimum SWR of 1.2:1 at 14.100 MHz. To raise the frequency of minimum SWR, trim the antenna shorter. Cut each of the dipole’s segments by equal amounts so that the two halves maintain equivalent lengths. If the minimum SWR is minimized at a higher frequency than desired, you must lengthen the wire segments. This is usually a very rare circumstance, but to avoid it you should trim carefully and trim often rather than taking only a couple of giant chunks of dipole length at once! Physically trim the wires shorter – lower the antenna ends to accomplish this if you erected the dipole near its operating position. You may trim in one of two ways: Either cut the wire or wrap the wire back along itself toward the center feed point. Be sure the wire is routed through the insulating anchor before wrapping, and you may wish to use a combination of cutting and wrapping to carefully trim into just the right frequency without having an excessive wire wrap. Reposition the dipole and make another SWR measurement to see what effect your trim has had. Likely you’ll find the frequency of lowest SWR has been raised closer to your desired center point frequency, but not yet there. Repeat the trim action in small adjustments until you achieve lowest SWR near the desired frequency. Once you have your antenna trimmed satisfactorily for your desired operations, tie it up permanently and get on the air! It’s a good idea with dipoles to provide a little strain relief for the wire, and a little slack or droop in the wires will not impact performance significantly. Especially if you are using trees as anchor points, be sure to provide some slack and strain relief to avoid snapping a wire when the trees move around with wind. Some operators prefer to hang a weight over a pulley or over a tree limb with the cord attached to the horizontal dipole wire. When the tree moves the cord and weight will keep the wire taught without over-straining it. SWR Measurement Techniques: Before we wrap up, let’s chat about SWR measurement techniques. We’ll start with the antenna analyzer, since it is usually more convenient than the SWR meter. It is easy to dial across frequencies to find the lowest SWR with an analyzer. You can measure, adjust the trim, and measure again in quick cycles. However, you may want to plot an SWR curve rather than just identifying the lowest SWR frequency. The SWR will be lowest at just one frequency position, and it will rise gradually for frequencies above and below this center point. An SWR curve is typically a U-shaped or V-shaped curve with frequency plotted horizontally and SWR plotted vertically. Such a curve tells you more about your dipole’s performance across the frequency band on which you are operating. A common metric of antenna performance is SWR bandwidth, and this is often defined as the bandwidth for which the SWR is at a value of 2:1 or less. At SWR values greater than 2:1, most modern transmitters will begin to automatically reduce transmit power to avoid high power reflections returning into the transmitter circuits. An SWR curve is pretty easy to plot with an antenna analyzer. Simply record the SWR readings every few thousand kilohertz as your dial across the frequencies with the analyzer. Then, plot the SWR values against frequency with graph paper or using a spreadsheet utility on a computer. As noted above, some analyzers will display an SWR plot directly, reducing the necessity to record individual frequency-SWR pairs for manual plotting. Plotting an SWR curve using an SWR meter requires slightly more effort. As noted, the SWR meter is read while transmitting with the meter inserted between the transmitter and the feed line/antenna system. You must change your transmitter frequency and take multiple SWR readings across the frequency band. Again, tune your transmitter in steps across the band and record the SWR readings with each transmission, and then plot your results as described above. Be sure that you do not transmit in sub-bands for which you do not have privileges! Stay within your license class sub-bands. You can “move” your SWR curve up or down the frequency band by changing the length of your dipole. Your performance with your dipole should be quite satisfactory within the 2:1 SWR bandwidth that you measure with these techniques, and with an antenna tuner you will probably get somewhat reduced, but still quite operable, performance well outside of your 2:1 bandwidth. Multi-band Dipoles: And remember, there are several different varieties of dipole antennas, some of which can help you get onto multiple bands with a single antenna and feed line. The fan dipole, or multi-element dipole, is a good choice for the amateur who wants to have access to three, four, or even more HF bands with a single antenna. The trap dipole offers similar multi-band performance. See our General License Class book for more about these options. I hope this helps you get off to a great start with a dipole antenna on the HF bands. I’ve used one for years, stealthily positioned in high pine trees near my home. Good luck, 73. Stu WØSTU

The 2023-2027 General License question pool seeks the length of a Yagi antenna's driven element: G9C02: What is the approximate length of the driven element of a Yagi antenna? A. 1/4 wavelength B. 1/2 wavelength C. 3/4 wavelength D. 1 wavelength The Yagi antenna, also known as the Yagi-Uda antenna, was designed by Japanese inventors Shintaro Uda and Hidetsugu Yagi in 1926. Although Uda was the principle inventor with his colleague Yagi in a lesser role, the name Yagi became more associated with the antenna design due to Yagi’s filing of a patent without Uda’s name included, the subsequent transfer of that patent to the UK Marconi Company, and Yagi’s publication of the first English language description of the antenna design in 1928. The Yagi antenna is a directional antenna, or beam antenna. It differs from the ideal isotropic emitter that theoretically radiates equally in all spherical directions from a point source, and it differs from the omni-directional antenna that radiates equally in all radial (horizontal) directions. A directional antenna such as the Yagi sacrifices radiated power in most directions to emit more powerfully in a single direction. The greater radiated power in the singular direction is called the main lobe of the antenna’s radiation pattern. When a comparison is made between the directional antenna’s main lobe signal strength and a reference antenna such as the ideal isotropic radiator, the ratio resulting from the comparison is the directional antenna’s gain, usually expressed in decibels (dB). If the comparison antenna is the isotropic ideal case the comparison will usually be indicated with dBi. When a comparison is based upon the common half-wave dipole antenna reference instead, the gain is indicated as dBd. The Yagi directional antenna produces gain in its main lobe by careful positioning of parasitic elements. A parasitic element is an antenna element that is not directly energized by the transmitter via a feedline. A Yagi antenna will include a single driven element, the element to which the feedline is attached and that is energized during transmissions. Parasitic elements are positioned parallel to the driven element, both behind and in front of the driven element. A parasitic element behind the driven element (opposite the direction of the main lobe of radiation) is called a reflector element. A parasitic element in front of the driven element (same direction as the main lobe) is called a director element. In addition to the driven element, a Yagi antenna may have a reflector only, or a reflector plus one or more director elements. A parasitic element will be electrically energized by the RF radiation of the driven element during transmissions, and it will re-radiate RF due to this energizing. These parasitic elements are designed with specific lengths and spacing along the Yagi’s boom so that the combined radiated and re-radiated wavelengths cancel one another in the direction opposite the main lobe and reinforce one another in the forward direction. This wave reinforcement creates the increased power in the main lobe direction at the expense of rear and side direction radiation. The spacing and number of parasitic elements in a Yagi help to determine the shape of the main lobe of radiation. Generally, a single reflector is implemented in a design, and as additional directors are added the radial angle of the main lobe will become narrower, increasing gain and directionality of the Yagi. But, no matter the specifics of a particular Yagi design’s parasitic elements, it will have a single driven element that by itself is a commonly used antenna type. The Yagi employs a half-wave dipole as the driven element, and the parasitic elements manipulate and shape the radiated pattern of the half-wave dipole into the directional pattern of the main lobe. Of course, as the name indicates, a half-wave dipole is about one-half wavelength long. The answer to General Class question G9C02, “What is the approximate length of the driven element of a Yagi antenna?” is “B. ½ wavelength.” -- Stu WØSTU

One of the more advanced topics in amateur radio electronics, and one that is often difficult for students to fully grasp, is complex impedance and the phase angle between voltage and current in AC circuits that helps define the behavior of the circuit. This topic is all cluttered up with inductive reactance, capacitive reactance, and resistance, in addition to some heady trigonometric concepts like the sine of angles, polar coordinates, and even those kooky imaginary numbers! Well, let’s see if we can keep it real, ham hipster, and disentangle this testy topic with some common sense consideration and explanations. Big Picture: This article is part 1 of a planned three-part discussion of complex impedance in AC circuits. But let’s lay out the big picture so that you can put the parts and pieces together as you read them separately. Some of the items below may not have very clear meaning to you now, but as you work through this series of articles you can return to these with new understanding and allow them to help you glue together the interesting and complex picture of impedance. At some point the big light bulb is apt to illuminate your scalp. Voltage and current applied to AC circuits are each represented by smoothly changing sine waveforms of equal frequency, depicting the regular reversals of direction and smoothly changing magnitudes of each. The applied voltage and current sine waves often get out of step with one another so the two representations no longer oscillate together, as if one sine wave is shifted ahead or behind the other in time, or phase. The amount of deviation between the voltage and current sine wave signals in a circuit is described by a phase angle between the two signals, in units of degrees. Phase angle shifts between voltage and current are imposed by a type of opposition to current flow called reactance in AC circuit components, specifically inductive reactance and capacitive reactance, measured in units of ohms. Inductive and capacitive reactances combine in a complex way with resistance in a circuit to determine the overall impedance of the circuit. Complex impedance is described with both a magnitude in ohms and a phase angle in degrees, and there are two primary shorthand methods of representing complex impedance in writing. Impedance magnitude and phase angle impact the behavior of AC circuits, particularly with respect to power transfer and resonance, as in RF antenna circuits, oscillator circuits, matching networks, power supply circuits, and many others. We will explore these enumerated facets of complex impedance, reactance, and phase angles in more detail for some in-depth understanding of these electrical principles. We start with some simple facts about voltage and current in AC circuits and build from there. Press on, intrepid reader! Voltage and Current: I’m sure you’re already familiar, but just to be safe let’s state a couple of things that are probably obvious. Current is the motion or flow of electric charges in the circuit. You may think of this as negatively charged free electrons flowing through the wires and components. Keep in mind that in AC circuits the current reverses direction on a regular basis. Back and forth motion. And that is key to understanding phase angles. Voltage is the difference in electric potential between two points in the circuit. Using the water analogy of a circuit from the HamRadioSchool.com books, potential difference is like water pressure differences in a plumbing circuit. The pressure may be great in advance of driving a load like a waterwheel (or an electric appliance), and since some of the potential energy is expended on the load the pressure beyond it is reduced. Measure the pressure before and after the load and you’ll get a pressure difference, or a potential difference, expressed as a voltage. Sometimes you’ll hear this difference characterized as a “voltage drop.” In an AC circuit the electric potential or voltage also reverses on a regular basis, with the same frequency as the current reversals. Again, a key concept for really getting the phase angle topic. Sine Waves: The most common alternation of current and of voltage in AC circuits may be depicted as a sine wave, that smoothly curving wave image you have probably seen many times. You may ask, “Why is the sine wave so common?” and that is a great question, but a question for another lesson altogether. I will ask for now that you simply accept as fact the lovely sine wave variation of current and voltage is common and perhaps easiest to deal with among other alternating waveforms. The most common form for AC signals is the sine wave. What the sine wave is representing is the regularly varying magnitude and direction of current flow or of potential difference over time in a circuit. For current, the upward portion of the waveform indicates the magnitude of current flowing in the positive direction in the circuit, smoothly increasing over time, peaking, and then decreasing in magnitude over time as measured in units of amperes. The bottom half of the current sine wave depicts a similar cycle of current magnitude, only in the other (negative) direction of flow. For voltage, the sine waveform indicates an analogous cycle of voltage, with potential difference increasing, peaking, and decreasing in the positive direction, or more correctly stated, “with positive polarity” (the potential drop from high to low between two measured points is in the positive direction). This is followed from the zero voltage line by an identical cycle of voltage magnitude in the opposite (negative) direction, or polarity, in which the potential drop direction is reversed. If you are not a student of trigonometry you may now inject, “But, what is sine?” That, too, is a great question that we’ll try to get at graphically for a little better understanding. Imagine a wheel rotating about is center axis, and one rotation is a standard 360 degrees of angular measure. Put a mark on the outside edge of the wheel, and let’s say the wheel has a radius of 1 unit. (That may be one inch, one foot, or one mile. It doesn’t matter. It is one unit from the axis to the edge, or “one radius.”) Place the mark to the right as shown in the diagram and designate that location the 0 degree position of the wheel. Now rotate the wheel counter-clockwise. The mark on the wheel moves up, and let’s stop it at a 30-degree angle above the 0 degree position. If you measure the height of the mark above the 0 degree position in units of the wheel’s radius, you will find that the mark is exactly one-half of a radius, or 0.5. The sine of a 30 degree angle is 0.5. Continue rotating the wheel counter-clockwise until the mark is at the 45 degree position and again measure its height above the 0 degree position. The mark is 0.707 radiuses high. The sine of 45 degrees is 0.707. You get the idea. Every angle around the 360 degree circle from the 0 degree rotational start point will have an associated height relative to the radius of the circle, and that is the sine of the angle. Notice that at the 90 degree point the sine is 1.0. At the 150 degree point the sine is again 0.5. At the 180 degree point the sine is zero, same as the 0 degree angle sine. Notice also that the graphic depiction of sine above for 30 degrees and 45 degrees forms a right triangle, and the value of sine for any rotational angle of the wheel is computed as the opposite side of the triangle (side opposite the angle in question) divided by the radius “mark” side of the triangle. In our case, the radius “mark” side is always a value of 1. But for any right triangle the sine may be computed as the value of the triangle side opposite the angle divided by the side across from the right angle, the longest side called the hypotenuse. Sine is “opposite over hypotenuse” for any angle in a right triangle. Sine is calculated as the angle’s opposite side divided by the hypotenuse. As you continue to rotate the wheel and increase the angle beyond 180 degrees the sine values become negative values, as indicated by a distance below the 0 degree line. At 225 degrees the sine is -0.707. At 270 degrees sine is -1.0. At 315 degrees sine is again -0.707, and so on. With a scientific calculator set to use degrees for angular values (in lieu of radians), simply enter the angle value in degrees and press the sine button to see the exact sine value of the angle. Try it! You can see now that a sine wave is a continuous plot of the mark’s vertical distance from the 0 degree position (the sine of the angle) as the wheel rotates at a constant rate over time. In fact, the positions along the horizontal time axis of the sine wave plot are identified by the circular angles. For instance, the first upper peak of a standard up/down cycle of a sine wave (one full rotation) is the 90 degree point of the sine wave. The point at which the sine wave decreases and crosses the zero line again is the 180 degree position. The downward pointing peak position is 270 degrees, and so on. There is a one-to-one relationship between the angle of rotation of the wheel and positions across the sine waveform. A sine wave is a continuous repeating plot of the value of sine as the value of the angle cycles from 0 to 360 degrees. Consider that if you spin the wheel faster you obtain a higher frequency sine wave, with more cycles per unit of time. Slower rotation yields a lower frequency wave. Once again, the most common AC signals you will encounter, whether oscillating electrons in a circuit or oscillating electromagnetic fields in a traveling RF wave, are accurately characterized by the sine wave variations of magnitude and direction. Further, in common AC electric circuits both the voltage and the current follow the sine form with equivalent frequency of oscillation. Phase Relationships: So, we have two sine waveforms to work with in an AC circuit, one for voltage and one for current, and they are of equal frequency. Imagine that each of these two waveforms is derived from its own rotating wheel, as described above. The voltage wheel and the current wheel must rotate at the same rate for the frequencies to be equal between the two waveforms. Imagine the two wheels begin rotation at exactly the same instant in time. The two sine waves that result will be perfectly in-step with one another. Each wave will peak at the same point on the time axis, each will cross the zero line at the same position, and so on. Nice. (Although there is no required equivalency of amplitude, as shown.) But what if one of the wheels is delayed in starting as compared to the other wheel? What if one wheel begins rotating before the other? Then the two sine waves will no longer be perfectly in-step with one another. Instead, the waveforms will reach peaks and cross the zero line at different times, at different positions along the time axis. The size of the disparity between the two out-of-step waveforms is determined by the difference in the start time of wheel rotation. Remember, each position on a sine wave has an angle analog from the wheel rotation in units of degrees. So, you may describe the extent to which the two waveforms are out-of-step with one another in units of degrees. For example, in the graph below evaluate the degree position of the earlier waveform (black dashed) that is matched up with the zero degree starting point of the later waveform (blue solid). In this graphic the later waveform begins its cycling when the earlier waveform is already at its 90 degree position (the upper peak position of any full cycle). We may state that these two waveforms are 90 degrees out of phase. Further, we can state that the earlier (black-dashed) wave leads the later (blue-solid) wave by 90 degrees, or that the later wave (blue-solid) lags by 90 degrees. Any two sine waves of identical frequency have a phase relationship. The phase relationship is a description of how much the two waves are out-of-step with one another, as described above, in units of degrees (or radians). The phase angle describes the time disparity between the voltage and current sine waves in a circuit. However, notice that when a waveform position is specified with an angle, such as the 90 degree position, that also specifies a time or duration as measured from the time of the zero start point of rotation. As the time axis implies, time and angle of the waveform depiction are rigidly related. That is, as the wheel turns at a constant rate the angle of the mark changes constantly with it, and every angle around the wheel is associated with a unique amount of time required for the mark to rotate around to it from the 0 degree starting point. The difference between the two waveform times or phases, as stated in units of degrees, is called the phase angle. The voltage and current phase angle is important because it affects the behavior of the AC circuit, particularly with respect to characteristics of resonance and power transfer. We will get around to the topics of resonance and power transfer, including the notion of how phase angle impacts circuits in these arenas. But for now, let’s consider how AC circuit components produce phase variations between voltage and current. Continued... Complex Impedance Part 2: Reacting Nicely Complex Impedance Part 3: Putting It All Together -- Stu WØSTU

Putting together a small solar power system to power your transceiver is quite simple with modern components, and it is affordable with most budgets. This article provides some general background and guidance on building a simple solar power system, and these concepts can be applied to construct systems across a range of power capacities. Components: A solar power system typically consists of three main components that can be purchased separately or in packages. Individually purchased components can be mixed and matched to construct systems of different powering capability. As illustrated in Figure 1, the three main components are: Photovoltaic panels (solar panels) - These are arrays of individual solar cells that convert sunlight into electrical power. Typically, numerous individual 0.5-volt cells are connected in series to raise the panel output voltage to a higher value, and multiple sets of series cells are connected in parallel to provide increased current. The power of a panel, in units of watts, is determined by the product of voltage x current. Commercially available panels can produce 100 watts or more in bright sunlit conditions. Combinations of panels can produce much more power. Charge controller - A charge controller receives the output of the photovoltaic panel(s) and conditions it for the purpose of safely charging a battery that will store the energy produced by the panels. A solar charge controller keeps the battery from overcharging, avoiding damage. It also blocks current from flowing in reverse, from the battery to the panels. The charge controller varies the voltage and current required by the battery chemistry type as the battery charge begins to approach its maximum. PWM Charge Controller - An older type of charge controller is the pulse width modulation charge controller. It gradually reduces the current to the battery during charging by reducing the duration of pulses of applied voltage. PWM controllers are less efficient than the newer MPPT controllers because they operate at a constant voltage. Excess voltage produced by the panels cannot be converted into increased current for charging and is wasted. MPPT Charge Controller - A maximum power point tracking charge controller is more efficient than the PWM type of controller because it does convert excess panel voltage into charging current. The MPPT controller allows the panel to produce power at its maximum power point of current and voltage, converting this power into a safe and optimized charging profile for the battery chemistry type. MPPT controllers are generally more expensive than PWM controllers, but they provide reduced charging times. Battery - Often one or more deep cycle cells, the battery or battery bank stores the energy produced by the panel. The most common battery chemistries used today are lithium-ion (or the very similar lithium iron phosphate) and lead-acid. Each chemistry type has unique charging profile requirements, and the charge controller should be set to match the battery chemistry. A wide range of battery capacities are available, expressed in amp-hours, and higher capacity cells will be more expensive than lower capacity cells. Cables & Connectors: Most solar panels will use photovoltaic (PV) cables with MC4 connectors. The MC4 means "multi-contact, 4 mm diameter." The MC4 comes in male-female pairs, and they have a locking clip to prevent accidental disconnection. They are sealed, weather proof connectors that provide excellent conductivity and represent an industry standard promoting interoperability among separately purchased components. Most photovoltaic panels will provide short leads of PV cable with MC4 connectors from the back of the panel. Longer PV cables are connected to the short leads with the MC4, leading to the charge controller. Typically, a charge controller will have input ports requiring pigtail termination of the PV cables rather than an affixed MC4 connector. Heavy gauge wire is used from the output of the charge controller to the battery terminals. Heavy ring connectors crimped or soldered to the heavy gauge wire are convenient for many battery terminal connections. For most small solar power systems, 12 AWG or 10 AWG insulated wire is recommended for the controller-to-battery connections. A good safety practice is to install an in-line fuse in the positive connection rated for the maximum output current of the charge controller. Connection of the transceiver to the battery should use transceiver manufacturer-recommended wire gauge, or the manufacturer-provided power cable. Ring clamps may also be convenient for this battery connection, and including in-line fuses near the battery in both positive and negative connections is a good safety precaution. Since you may want to easily disconnect your transceiver from the battery, the use of quick disconnects such as Anderson Powerpole® connectors is recommended for the battery leads. Example System: Figure 3 shows an example of a small solar power system used by the author to power a portable 100-watt transceiver along with various camping equipment such as LED area lighting, a small refrigerator, and a device recharging station. The system is comprised of two 100-watt photovoltaic panels connected in parallel using two PV Y-cables and feeding an MPPT controller mounted in the top of a dual-storage cell holding box. The controller is connected to two lithium-ion deep cycle storage cells housed in the box and connected in parallel to provide 85 amp-hours capacity and 13.8 volts output. A Powerpole® connector distribution bus is connected across the two storage cells, with various fuse ratings among the eight available outputs. A separate (green wire) battery recharging connection is seen extending to the left of the battery box for an alternative AC recharging connection. Figure 4 shows the back of the solar panels. The panels are hinged together and close in a clamshell approach that stores the PV cables and aluminum props used to stand the panels at desired angles to the sun. The PV Y-cables are visible that connect the two 100-watt panels in parallel and join to the two PV cables that lead to the battery (red & black). This example system provides continuous power for the camping needs and 100-watt radio operations when at least modest sunlight is available to recharge the storage cells. In bright sunlight, recharging the storage cells from 50% capacity to 100% capacity is accomplished in about 7 hours (~42 amp-hours). Daily recharging of 10% (8.5 amp-hours) or less of the storage capacity is usually accomplished in under 2 hours, even with irregular sunlight. Recently, the two rigid 100-watt photovoltaic panels were replaced with an integrated set of folding panels weighing 18 pounds and rated at 200 watts. These make transportation and storage of the solar system much easier and efficient. The products used in the rigid panel example are: Renogy 100 watt, 12 volt, monocrystalline PV panels (2) Renogy RoVER 30 amp MPPT charge controller (1) Renogy PV extension cables, 20' (+/- pair) BougeRV solar connector Y branch parallel adapter cables (2) Renogy 30 amp ANL fuse and fuse holder (1) Ionic 50 ah lithium ion deep cycle storage cell (1) Ionic 35 ah lithium ion deep cycle storage cell (1) Chunzehui F-1005 9-port 40A connector power splitter distributor (1) Anderson Powerpole® connectors (various) 10 AWG and 12 AWG insulated wire (various) Be sure to do your homework before purchasing components to ensure compatibility and desired feature sets, as well as the desired power capacities. But a DIY solar power system can be constructed easily from the components highlighted in this article that provides excellent long-term power for your portable station. Stu WØSTU

Ham Radio School's new General License Course 2023-2027 offers many updates and improvements over the previous edition. In this article we highlight some of those improvements and provide a little behind-the-scenes insight on Ham Radio School's developments and plans. The New General Question Pool: The new 2023-2027 NCVEC General License Question Pool goes into effect for exams issued July 1, 2023 or later. The committee made a significant change to the question pool, reducing the number of questions from 454 to 429. Several new question topics were added to the pool, including questions related to: FT8 and other popular digital modes The concepts of link budget and link margin Good amateur practices Propagation assessment with automated receiving stations Impedance definition Station lightning grounding and protection RF exposure evaluations And more Many other question topics were deleted, and numerous question tweaks and shifts of specific questions on legacy topics were also made, rounding out a substantially updated new General question pool. Improved Chapter & Section Structure: The new General License Course 2023-2027 explains each of the 429 questions in the new pool with the proven Ham Radio School method. Using our keep-it-simple explanations, high-quality explanatory graphics, and a logical building block approach to concepts, the course provides the background and conceptual support necessary to understand each question and its correct response. The new question pool drove some restructuring of the book chapters and sections, and other structural updates were accomplished for improved sequencing and more concise presentation. Most notably: Old Chapter 2, Operating Your Radio, was parsed into two chapters. The digital modes content of this chapter were combined with new digital mode question pool concepts to form a new Chapter 3, Digital Modes. The digital modes content was completely rewritten for improved presentation and sequencing of concepts in the new Chapter 3. Old Chapter 4, How Radio Works, was completely restructured, rewritten, and renamed Chapter 5, Processing Signals. These updates are more consistent with our Technician and Extra License Course approaches and resulted in a more concise and logical treatment of the topics. Multiple individual sections within chapters were rewritten or substantially edited to improve topic presentation sequences, to improve the narrative, and to provide more concise treatment of topics. New & Improved Instructional Graphics: Overall, the new General License Course book includes more than 150 instructional and informative graphics. Many graphics have been improved, and many new graphics have been incorporated. A few older graphics have been retired, particularly where related to questions deleted from the pool. Here are just a few examples of the many new or improved graphics: You can see more of the revised book and new graphics with our online Try Before You Buy preview. New Online Support Materials: In addition to new and updated content in the General License Course book, we have revised and added to the online support materials for the course. The supplemental General Learning Media have been updated with many new items, section by section with the book. These include video, audio, articles, and links that provide greater depth and detail on the topics covered in each section. Of course, we have updated our online Section Quizzes that provide the full question pool items in an interactive quiz of all the items explained within a book section. These quizzes are bite-sized review opportunities for each section that help prepare for the exam with a topical focus and comprehension. In addition to the section quizzes, we have provided a set of full 35-question practice exams that cover the entire question pool in interactive review. Each exam is properly weighted by question pool sub-element composition so that each is representative of the question topic mix found in the real exams. These exams help to gauge readiness for the real thing. New Instructor Resources: For our registered instructors, we have totally overhauled our General License Course Instructor Resources. The revisions represent a big step up in the quality of our classroom instructional materials, and include: Content restructuring consistent with the new book structure Numerous new and improved full-color graphics Updated branding to our new logo, colors, and stylistics Updated classroom presentation quizzes, section by section Imbedded video and animations for enhanced presentation And more What's Next? We are planning the development of a video edition of the General License Course with a release date in the latter half of 2023. Modeled after our popular Technician License Course Video Edition, the video lesson course will be instructed by Stu WØSTU and will follow the same sequence as the General License Course book version. There may even be some cameo appearances of Bob KØNR! Look for our announcement about this video edition in the coming months. Wrap Up: Our new Ham Radio School General License Course is a significant improvement over the predecessor. We're very proud to offer it to our patrons with a fresh stamp of quality assurance and superb exam preparation, second to none in the ham radio world! You can order yours today, directly from us: General License Course 2023-2027. I hope you'll give it a try for your upgrade or for your license class offering. Drop us a note if we can answer any questions for you. info@HamRadioSchool.com

The Technician and General license exams emphasize the concept of impedance matching to achieve maximum power transfer. This is often described as making sure the 50 Ω output of your transceiver drives a 50 Ω transmission line that connects to a 50 Ω antenna. In this article, we will go a little deeper to understand the role that phase plays in power transfer. Figure 1 shows a resistive source and resistive load connected with the aim of transferring power from the source to the load. Most signal sources such as your transmitter have an internal resistance shown as RS in the figure. The load resistance, RL might represent the antenna or dummy load. The maximum power transfer principle can be stated as: “Maximum power is transferred when the internal resistance of the source equals the resistance of the load, when the external resistance can be varied, and the internal resistance is constant." Figure 1. Circuit diagram showing a resistive source connected to a resistive load. Figure 2 shows how the power to the load varies as a function of RL/RS. Power delivered to RL depends on both the current through the load and the voltage across the load. Large values of RL increase the voltage (EL) but starve the current (IL). Similarly, small values of RL increase the load current but diminish the load voltage. A bit of math can show that maximum power occurs when RL = RS. Figure 2. The plot of PL vs. RL/RS shows maximum power to the load when RL/RS =1. Complex impedance Now consider the AC case where the impedances are complex, as shown in Figure 3. The source impedance is ZS = RS + jXS and the load impedance is ZL = RL +jXL. The maximum power transfer occurs when ZL is the complex conjugate of ZS, which means RL = RS and XL = –XS. This is sometimes referred to as complex conjugate matching. As expected, if XS =0, the situation reduces back to the resistive case. Figure 3. Circuit diagram showing a source connected to a load where both have complex impedances. It's all about the phase Interestingly, when XL = –XS, the voltage source, ES sees a pure resistance (RS + RL), which means the current out of the voltage source is in phase with the voltage. This is not a coincidence; the phase between the voltage and current waveforms plays an important role in the average power in the load. Let's examine the time domain representations of instantaneous voltage, current, and power for a complex impedance. Instantaneous power is given by p (t )= e(t )i (t ) Assuming e(t ) and i (t ) are both sinusoids where ϴ is the phase difference between the voltage and current waveforms. Figure 4 shows the time domain waveforms e(t ), i (t) and p(t ) for the case ϴ = 45°. Figure 4. Plots of e (t ), i (t ) and p (t ) for the case ϴ = 45°. We will skip the math, but the power equation can be reduced to: The expression for p (t ) is made up of a constant term and a cosine function at twice the original frequency. We are often interested in the average power in a waveform, which we can find by integrating p(t ) over one waveform period. The double frequency cosine term will average to zero, leaving only the constant term, so that The plot of p(t ) in Figure 4 shows that the instantaneous power varies sinusoidally and even goes negative for part of the cycle. This is going to happen for all cases where ϴ does not equal zero. Also notice from the plot the average value of p(t ) is positive, indicating that power is delivered to the load. Power engineers use the concepts of True Power and Apparent Power to quantify the effect that phase has on power. True Power represents the actual power transferred, which includes the effect of the phase between e and i , measured in units of Watts. Apparent Power is a more simplistic concept of just the raw current times the voltage, measured in units of Volt-Amps or VA to distinguish it from True Power. Power engineers also use the concept of Power Factor (PF), And it turns out that for sinusoidal waveforms, PF is equal to the cosine of the phase angle between the voltage and current waveforms. Power Factor is a straightforward way to describe how much of the apparent power is being translated into useful (true) power. If ϴ = 0, then True Power and Apparent Power are the same and PF =1. When ϴ = ±90°, the True Power drops to zero and PF = 0. The example shown in Figure 4 with ϴ = 45°, PF = 0.707, which means that the True Power is 70% of the Apparent Power. Wrap up We’ve reviewed the basics of maximum power transfer and the importance of phase relationships, tying it together with the power engineering concepts of power factor, true and apparent power. I intentionally ignored any discussion of transmission lines but these power transfer concepts have a lot in common with the usual transmission line concepts (standing wave ratio, return loss, reflection coefficient).

The 2019-2023 General License exam pool requires some calculations of equivalent component values, such as a single component that is equivalent to multiple resistors in a parallel circuit arrangement. The details of this type of calculation are beneficial for the advanced Technician License student as well, who should understand how series and parallel circuit arrangements impact both voltage and current flow in circuits: G5C04: What is the total resistance of three 100-ohm resistors in parallel? A. .30 ohms B. .33 ohms C. 33.3 ohms D. 300 ohms The General License Course section 6.3 is all about parallel and serial electronic components and the concept of equivalent component values. Based on Kirchoff’s Laws for electrical current and voltage, multiple electronic components such as resistors, capacitors, and inductors arranged in either parallel or serial connections in a circuit may be “replaced” by a singular equivalent component. Multiple General License exam pool questions test your mathematical skill in calculating the value of the equivalent component, or put another way, the equivalent value provided by the multiple components. Each of the three component types mentioned above may be arranged in either series or parallel circuit configurations, and one of two general equation forms applies for calculating the equivalent component value depending on the type of component and the type of circuit arrangement. The calculations themselves are rather trivial once properly set up, so the real challenge of these questions boils down to applying the appropriate equation form among the six possible combinations of components and configuration. Let’s consider the two general forms of the two equations involved, using a generic “X” component indicator. The X component in these equations may be replaced by R for resistance, C for capacitance, or L for inductance. (In no way is X intended to imply reactance, in these cases.) Sum of Components form: ...and so on for the number of components Reciprocal of Reciprocals form: ...and so on for the number of components So, which of these two equations applies to each of the six combinations of component and connection types? Here’s how that shakes out: Notice that resistors and inductors have identical equation form application, while capacitors are the opposite from those two. Keep this table of relationships in mind and you can’t go wrong in applying the proper equation to the scenario defined in the exam question. Now, let’s apply the proper equation form to the question at hand, G5C04: What is the total resistance of three 100-ohm resistors in parallel? Here’s how that simple circuit arrangement may be depicted. Referencing the table above we see that parallel resistors’ equivalent resistance value is calculated using the reciprocal of reciprocal equation form, like this: From an intuitive standpoint, perhaps considering a ‘water flowing in pipes’ analogy to the circuit depiction above, this makes sense. In the parallel arrangement the total resistance to current flow offered by three equivalently sized pipes will be less than the resistance of any single pipe of the same size. If the three resistors were instead arranged in series, one behind the other and each offering additional resistance to the current flow in a single loop, the resistor values would add in accordance with the Sum of Components equation form above. [In the series arrangement scenario, total resistance would be 100+100+100 = 300 ohms.] The answer to General Class question G5C04, “What is the total resistance of three 100-ohm resistors in parallel?” is “C. 33.3 ohms.”

How would you answer this request from your local civic club leader, school principle, or police chief? “Say… You’re one of those ham radio guys, right? Well, could you and your buddies help us out with some communications problems we’ve got with a big event that’s coming up? We need a way to keep everything coordinated across a large area, like a bunch of folks with radios. Is that the kind of thing you do?” For several years on July 4th in my little home town, a group of young amateur radio operators from the local boy scout troop volunteered to provide radio communications for the civic club that runs the town’s Independence Day Parade. It’s a big parade for a small town, usually with well over 100 parade units. Getting it all lined up and keeping it all running smoothly and safely on narrow streets crowded with families, dogs, and bicycles is a real challenge. These young amateurs provided the communications glue that held the whole operation together. In these parades they have helped ensure the event stayed on schedule, served as the eyes of local law officers for automobile traffic flow dangers and emergencies, expeditiously found lost children, and provided seamless distributed communications to coordinate parade operations along the several miles of the route. How did they do it all? These scouts had honed their skills as tactical radio net operators, learning to listen, transmit, and distribute information with remarkable efficiency even under busy and stressful conditions. Their skilled volunteerism provided a valuable service to our community, and you can do the same for your local area along with your radio club or informal group of volunteer hams. Let’s introduce you to some of key characteristics of a tactical net and define some important related terms. Radio Net: Several stations on the same frequency following some agreed procedures, and usually directed by a single net control station. A net can be a general social forum or convened for a specific purpose. Tactical nets usually are convened for a specific purpose or function. Net Control Station: A single station that moderates or directs the net transmissions and discussion, ensuring prioritization of transmissions and reducing simultaneous transmissions by net stations. The net control may be relaxed in some “open nets” where communications are sparse, allowing stations to freely call directly to one another. Tactical nets are usually heavily “directed nets,” in which strict control is enacted, and every station must receive permission from net control before transmitting or “passing traffic.” A busy tactical net, heavy with communications needs, must be a directed net with disciplined operators. A skilled net control station is a must for effective operations. Tactical Call Signs: A tactical net will use tactical call signs to designate specific station positions or functions. For example, the parade net mentioned above uses tactical call signs associated with station positions along the parade route, such as Parade Start, Parade End, Announcer’s Booth, and 2nd Street Rover. Combined with this are tactical call signs of stations shadowing parade officials or civil officials, such as Parade Marshall and Fire Chief. Each station must also comply with FCC identification requirements, and the easiest way to do this is to simply tack on your FCC call sign at the end of your last transmission in a series of transmissions. Operating Efficiently: Critical to the success of a busy tactical net is efficient transmission. Learning to be efficient takes some practice and experience, but you can do it if you think first, formulate your message, and only then push-to-talk. Do not ramble and consume valuable frequency air time. This is where developing good radio skills and maintaining good discipline becomes important. Follow these simple principles for efficient tactical net operations: Keep your transmissions brief and to the point – be succinct. Avoid making unnecessary transmissions. Push-to-talk only when you have something relevant to contribute to the net. Speak clearly and distinctly using common language appropriate to the net’s purpose in order to avoid confusion or the need to retransmit your traffic. Answer questions directly and succinctly. Do not include unnecessary elaboration, details, or explanations. If such information is needed, net control or other stations will ask for it. If you have not been monitoring net traffic temporarily due to side duties or conversations, listen for several seconds before transmitting to ensure you are not interrupting other traffic flow. Avoid overuse of FCC call signs and language not directly associated with the net, such as stating “clear” after transmissions. (But be sure to comply with FCC call sign identification requirements.) Before keying your microphone to respond to a call, pause for about one second to allow any potential higher priority or emergency traffic to be injected, if needed. Don’t consume air time on the frequency nonstop, as other traffic may be urgent. Allow opportunities for important calls to break in. Stay alert! Keep your ear to your radio and respond to calls promptly. Calling Net Control: When you have traffic to report to the net you should call net control for permission to report it. All you do is briefly transmit your tactical call sign and perhaps include very brief information about your traffic. For instance: “Parade End, emergency,” or “Parade Marshall, announcement.” Net control will respond to you with directions to transmit or to stand by. For instance, net control may say, “Parade End, go,” meaning that Parade End tactical position should transmit its emergency traffic. Doubles: In spite of strict control and discipline on a tactical net, sometimes stations will transmit simultaneously. For example, you and another station may call at the same time for net control recognition. You will not hear the other station, so you may be unaware of the double transmissions. Be sure you receive net control permission before continuing with your traffic report, and do not assume that net control must have just confused your tactical call sign when he is responding to the other station with which you doubled. You’ll only make worse the doubled transmissions by continuing without proper permission. Calling Other Net Stations: Do not call directly to another station without net control permission. Contact net control and request permission to “go direct” with the other station, and await net control confirmation that you may do so. Then, call for the other station just with its tactical call sign followed by your own, and firmly establish two-way contact before any additional transmissions. The other station should confirm contact with only a brief response. Third Party Traffic: Many times it may be more efficient to allow third parties to speak on the radio than to try and relay third party traffic yourself. While the frequency should not be tied up for an extended time with a lengthy chat between third party communicators, it is often more efficient to allow an individual with special knowledge of a situation to speak on your radio to relay traffic of a specialized nature. If You Must Leave Your Station: Be sure to notify net control before you leave your station, even temporarily. When you return, check in again with net control. This will avoid net control wasting time attempting to contact you with multiple calls. Local public service opportunities are a great way to get introduced to tactical nets. Tactical nets are also used for emergency response operations, such as RACES and ARES activations. While the character, intensity, and seriousness of tactical nets can vary widely, it is a good idea to develop the skills so you can put them to use when your community calls. Check out your local club, RACES or ARES organization, and get started honing your tactical net skills. -- Stu WØSTU

When AC voltage and current waveforms are not in phase with one another, the power delivered to a circuit will be only a portion of the power computed by multiplying voltage (E) and current (I). The fraction of powered delivered to the circuit is determined by the phase angle between voltage and current waveforms. The delivered power is called the real power. Real power is computed as: P(real) = EI cos Θ where Θ (theta) is the phase angle between voltage and current waveforms. The value of cos Θ will be between 0 and 1, and this fractional value is called the power factor. Power Factor (PF) = cos Θ. To determine the real power, simply complete the multiplication of the three terms: voltage x current x cosine Θ. Voltage and current values are trivial, but let's see how to get a value for cosine Θ, or power factor, using a common scientific calculator. Mathematically, cosine values vary between -1 and 1 depending on the angle. Some cosine and angle values are: Notice the cyclical nature of the cosine values. They vary between -1 and 1 as the angle cycles through 360 degrees. The cosine function is determined by the vertical, or y axis value, of a point on a circle as the interior angle of the circle rotates about the 360-degrees of the circle, as illustrated in this graph: Cosine values are easily obtained with a scientific calculator as follows: Make sure the calculator mode is set to degrees. (Not radians.) Enter the angle in degrees. Select the trigonometry function "cos" for cosine. Suppose we want to compute the power factor for an RL circuit that produces a 45-degree phase angle between voltage and current. The following video illustrates calculation of cosine using a scientific calculator. Cosine 45 degrees = 0.707 (rounded). (PF = 0.707 for a 45-degree phase angle between E and I.)

Everyone wants to know how their signal sounds on the air and often the best way to find out is a signal report from other ham radio operators. The standard signal reporting method for amateur radio is the RST (Readability-Signal Strength-Tone) system (see below). The best signal report for CW operation is RST 599. The T, or tone factor, refers to the sound qualities of the received CW signal. On phone, we drop the reading for Tone and just give RS reports, so a perfect signal on phone is RS 59 or just “five nine.” On the HF bands, you’ll typically hear something like this: “your signal report is five nine in central Kansas.” If you are good copy, you will usually get a Five for Readability (which means "Perfectly Readable"). A Four indicates "Readable with practically no difficulty" and Three means means "Readable with considerable difficulty." Most signal reports are R3 to R5, else the signal is not very readable. (See the scale listed below.) The Signal Strength usually reflects what the operator is seeing on the S-Meter of his receiver. Of course, with both CW and SSB, the S-Meter will be bouncing around a bit, so some interpretation is required. More importantly, there is considerable variation in S-Meter calibration, so signal reports can vary from radio to radio. (S9 is commonly defined as 50 µV at the receiver input, with each S unit representing a 6 dB change in signal strength.) A 55 or 57 report indicates that the signal is very readable but the signal strength is not as strong as a 59 signal. Most S Meters show an extended scale above S9 that is listed in terms of decibels. The scale may be marked with +10 dB, +20 dB, etc. indicating that the signal strength is that much stronger than S9. You’ll hear radio amateurs say something like “you are 5 9 plus 20 dB.” Or they may just say “you are 20 dB over.” It is common for DX and contest stations to give out “rubber stamp” signal reports. Basically, they are trying to work as many stations as fast as possible and don’t want to be bothered with accurate signal reports, so everyone gets a 59 or 599 report. CW operators may extend this further by substituting the letter N for 9, sending the report 5NN. (In Morse Code, N is a much shorter character than 9.) In fact, there is a collection of “cut numbers” that CW contesters often use to shorten things up: 0 is replaced by T, 5 is replaced by E, etc. An RST 599 report might be sent as ENN. On VHF FM, signal reports are often given in terms of FM quieting. A strong FM signal is said to “quiet the receiver” since there is virtually no noise present in the received audio. As the signal strength is decreased, noise starts to appear on the received signal. At some signal level, the noise increases dramatically and the signal becomes unreadable. This dramatic increase is called the threshold effect, meaning that FM signals do not gradually fade out, they suddenly crash into the noise. The key idea here is that you want your signal to be strong enough to be above this noise threshold. In terms of a signal report, a strong signal may result in a “full quieting” report. If the signal is less than full quieting, you may hear a report like “90 percent quieting” or “you have about 10% noise”, which both describe the amount of noise present in the signal. If the signal is really noisy, the report might be “50% quieting.” You will also hear the classic Five Nine signal report on FM, which is basically saying “excellent signal.” While S Meters are often inconsistent on CW/SSB transceivers, they are almost universally poor on FM rigs. Most FM radios just give you an unlabeled bar graph that is only a relative indicator of signal strength. Usually, these are not labeled in terms of S units, so don’t try to interpret them as such. If all of the bars are lit up on your meter, then you might give a report of “your signal is full scale.” For FM repeater operation, keep in mind that the signal you are receiving is coming from the repeater and not from the other station. So if the other radio ham is fiddling around with his antenna and asking for signal reports, the repeater signal strength is going to remain the same. You may notice that the other station’s signal into the repeater gets more or less noisy, so giving a report on how well he is hitting the repeater is helpful. “Joe, you are full quieting into the repeater.” This is another reason why FM signal reports tend to be in terms of receiver quieting…in linked systems, the signal strength at the transceiver is less important. One final note is that sometimes the operator on the other end is looking for a more critical evaluation of his signal quality. If he says something about “checking out this new microphone” or “have been working on solving an audio problem”, that may be the clue to spend a little extra time really listening to the signal and providing more comments on how it sounds. For most of us, we don’t actually get to hear our own signal on the air, so it’s very helpful to get quality feedback from other radio amateurs. -- Bob KØNR The RST system as listed on the ARRL web site, Quick Reference Operating Aids: Readability 1 – Unreadable 2 – Barely readable, occasional words distinguishable. 3 – Readable with considerable difficulty. 4 – Readable with practically no difficulty. 5 – Perfectly readable. Signal Strength 1- Faint signals, barely perceptible. 2- Very weak signals. 3- Weak signals. 4- Fair signals. 5- Fairly good signals. 6- Good signals. 7- Moderately strong signals. 8- Strong signals. 9- Extremely strong signals. Tone 1- Sixty cycle a.c or less, very rough and broad. 2- Very rough a.c., very harsh and broad. 3- Rough a.c. tone, rectified but not filtered. 4- Rough note, some trace of filtering. 5- Filtered rectified a.c. but strongly ripple-modulated. 6- Filtered tone, definite trace of ripple modulation. 7- Near pure tone, trace of ripple modulation. 8- Near perfect tone, slight trace of modulation. 9- Perfect tone, no trace of ripple or modulation of any kind.