1. INTRODUCTION Power Point Presentation on Amateur Radio Transmission Lines and Antennas. By Alton Higgins, W4VFZ Copyrighted © 2013 by Alton Higgins, Hiawassee, GA

2. Or, how to get what you input from here… To go through here… And pass through here… Or here… To get to here… And end up here… Or here… TRANSMISSION LINES & ANTENNAS

3. Objective: To obtain maximum efficiency by minimizing losses of power in any components between the Transceiver and the energy radiated by the antenna. Typical Amateur Radio Station:

4. The more power your transmitter puts out, the greater the distance your signal can be received! FACT : A 100 watt transmitter can actually provide greater “DX” communications than a 1,500 watt (legal limit) transmitter, IF there are “mismatches” in “Impedance” in the 1,500 watt transmitter, along the path of its RF signal! The “Bottom Line” is, what is the ultimate ERP (Effective Radiated Power) at the antenna of the station? We’ll next discuss the issues involved in getting the maximum ERP from your station, by the correct selection of transmission lines and antennas. MAJOR MISCONCEPTION:

5. Impedance is an important factor along the “highway” by which our RF signal travels from the Transmitter to the Antenna and is then “radiated” into the atmosphere. “Impedance” is defined as the “Net AC resistance or “reactance” of a group of components in a circuit to an AC voltage or current applied to that circuit. But for simplicity, let’s first talk about the transfer of DC (Direct Current) energy in a circuit. IMPEDANCE:

6. In the circuit shown, note that the battery has an “internal resistance” of 2 ohms! This is due to the resistance of the materials that make up the plates and conductors within the battery. ALL batteries have some internal resistance, which WILL enter into the calculations of current flow through the battery. Note that the Lamp also has a resistance of 2 ohms. Thus the total resistance of the circuit is 4 ohms, and the current is: I = E/R or 2.5 amperes. DC Circuits:

7. Referring again to the DC circuit, the Power in the Lamp is: P = I 2 R or 25 watts. Note that the Resistance of the Source is equal to that of the Load or Lamp! Now, let’s decrease the resistance of the lamp to 1 ohm! The current will now be 3.333 amperes and the power in the lamp will be 11.11 watts, or less than 25 watts! Correspondingly, if we increase the lamp to 3 ohms, the current will be 2 amperes and the power in the lamp will be 12 watts, again less than 25 watts. Power in the Lamp or “Load”:

8. One can continue this “exercise” with different values of resistance in either or both the battery and the load, and the maximum power in the load will always be maximum ONLY when the resistance of the load and the battery (or any power source) are EQUAL! Let’s next see how this compares with AC circuits, or ones containing a “reactance”. This will first require some discussion of “reactance”. Moral: The Resistance of the Load MUST be equal to the Resistance of the Source for maximum power in the Load!

9. There are TWO types of Reactance: Inductive and Capacitive. Capacitive Reactance, refers to the AC resistance to current flow through a CAPACITOR, while Inductive Reactance refers to the AC resistance to current flow through an INDUCTOR. Reactance is expressed in “Ohms”, the same unit of measure used for resistors in DC circuits. Capacitors:Inductors: REACTANCE:

10. A capacitor may be compared to an un- inflated balloon. If we apply air pressure to the input of the balloon (compare this to the application of a voltage across a capacitor), a small amount of pressure (voltage) will result in a large flow or air (current) into the balloon. Thus the flow of air (current) LEADS the pressure (voltage) in the balloon (capacitor). Analogy of a CAPACITOR:

11. Thus as the balloon fills with air, the flow diminishes, and the balloon is “fully charged” with air. In our “analogy” the balloon now has pressure (compared to Voltage), which is in the form of stored or potential energy,

12. Thus a capacitor can store energy, it is essentially charged like a battery. But let’s now take another look of the capabilities of a capacitor. Consider a “conductor for the flow of air” in a pipe, or, for our example, a “conductor for the flow of electrons” in a wire. In the case of the “conductor for the flow of air” in a pipe, let’s place a flexible diaphragm cross a section of the pipe. As the air pressure is applied, it will exert a force on the diaphragm, and cause it to “bulge”, BUT, once maximum pressure is applied, there will be NO more flow of air. Next, lets replace the molecules of air with electrons.

13. Refer to the figure below, the diaphragm is “stressed”, and flow ceases. BUT, if we alternately reverse the pressure or Voltage an alternating current will flow!

14. Thus, a CAPACITOR BLOCKS DC CURRENT, BUT PASSES AC CURRENT. Additionally, the current always LEADS the Voltage applied across a capacitor! AND, in a sine wave, the current (red trace) always LEADS the voltage (blue trace) by an angle of 90 degrees, as shown to the right:

15. A capacitor is made up of two, insulated plates. The insulation (dielectric) can be air or other insulating materials. Electric Fields in a Capacitor.

16. “Rolling” a tubular capacitor. Finished tubular capacitor. Construction of a tubular capacitor.

17. An Inductor may be compared to a mechanical flywheel. If we apply a “turning” force to a flywheel (compare this to the application of a voltage across an inductor), a large amount of force (voltage) will be required to cause the flywheel to start to turn or to flow (current). Thus the flow or motion (current) LAGS the pressure (voltage) in the flywheel (inductor). Analogy of an INDUCTOR.

18. “Phase Shift" in an Inductor: As in the capacitor, there is a “phase shift” between the applied “pressure” (voltage) and the resulting “flow” (current). And, again, it is 90 degrees, BUT in an Inductor, the Current LAGS the applied Voltage! Now, here’s an easy way to remember this rule: ELI the ICE man! In this expression: E = applied Voltage. I = the resulting Current. L = an Inductor. C = a Capacitor.

19. Remember that reactance is expressed in Ohms, and is the resistance to the flow of AC current in an Inductor or Capacitor. Reactance is represented by X. The Reactance of a Capacitor is defined: The Reactance of an Inductor is defined: Where: = 3.14 = Frequency in Hz. C = Capacitance in Farads. REACTANCE FORMULA:

20. INDUCTANCE & CAPACITANCE IN SERIES. If an Inductor and Capacitor of EQUAL REACTANCE at a specific frequency, and a 10 ohm resistor, are wired in series, then what do you suppose would happen to the net phase relationship between the Voltage and Current flowing in the circuit? (Refer to the circuit, below.) Hint: Remember which way each device shifts the current phase!

21. The answer: The net current will be in phase with the applied voltage! BECAUSE, as the Reactance of both the Capacitor and the Inductor are the same, but in the Capacitor, the current LEADS by 90 degrees, and in the Inductor, the current LAGS by 90 degrees, then they CANCEL OUT their respective phase shifts, and thus the IMPEDANCE of the circuit is purely RESISTIVE, or simply 10 ohms! Now here’s another interesting fact about what happens to a series (OR even a parallel) circuit in which both the inductive and capacitive reactance are EQUAL!

22. Resonant Frequency of a “Tuned Circuit”. IF in a series or parallel LC circuit, the reactance of both elements are equal, they not only cancel each others reactance, BUT they will resonate or be tuned to a very specific frequency! This is the very principle that is used to designed the Tuned Circuits of a radio receiver or transmitter! AND, the formula for that resonant frequency is: Also, note that in the above formula, the resonant frequency will be the one at which the reactance of both the Inductor and Capacitor are equal!

23. Parallel and Series “Tuned Circuits”. In a SERIES tuned circuit, the IMPEDANCE (series AC “resistance”) is minimum at its resonant frequency. In a PARALLEL tuned circuit, the IMPEDANCE (parallel AC “resistance”) is maximum at its resonant frequency.

24. Coordinate Graphing System In order to produce “graphic” representations of how currents and voltage relate to each other, we use something called the “Coordinate” system. In the example, right, the horizontal line is called the “X” axis, while the vertical line is called the “Y” axis. Here we’ve shown both a linear and a nonlinear function.

25. BREAK TIME It’s time to take a break, and digest what we’ve covered to this point. As a “Review”, we’ve discussed: Effective Radiated Power out versus Impedance. DC circuit power. Source versus Load Resistance and Reactance. Analogies of a Capacitor and an Inductor. The formulas for Reactance in a Capacitor and an Inductor. Series and Parallel Resonance, Tuned Circuits. Coordinate Graphing System. In the next session, we’ll discuss the “Impedance Triangle” and Transmission lines.

26. PART TWO TRANSMISSION LINES, IMPEDANCE MATCHING, AND ANTENNAS.

27. THE IMPEDANCE TRIANGLE

28. LET”S TAKE THIS ONE STEP AT A TIME! First, determine the total Inductive and Capacitive Reactance. Then subtract the Smaller Reactance from the Larger Reactance to get the NET REACTANCE.

29. CONTINUING: Next, determine the Total RESISTANCE. Then draw the “Rectangle” with the Ordinate and Abscissa sides, and with one corner at the 0 point of the axis. The IMPEDANCE is shown in the figure.

30. CONTINUING: Finally, using the Pythagorean Theorem,determine the length of the Hypotenuse, whose length is equal to the square root of the sum of the squares of the other two sides.

31. SOME TRIGNOMETRY: The Pythagorean Theorem is the easiest way to determine Impedance. HOWEVER, using some Trigonometry, we can determine the ANGLE (from the Resistance axis), or the Phase Shift angle caused by having a NET REACTANCE or IMPEDANCE of a Network. Using most calculators, is the easiest way to perform Trigonometric functions, but below is listed the basic “Trignometry Functions: BUT, don’t worry, you won’t need to memorize these functions!

32. SO WHERE ARE WE NOW? We have learned that for maximum power from a Source to a Load, requires that the RESISTANCE or IMPEDANCE of both the SOURCE and the LOAD MUST BE EQUAL! Since the Output Impedance of most of today’s Amateur Transmitters/Transceivers is a “SINGLE ENDED, UN- BALANCED, COAXIAL OUTPUT”, designed for connection to a 50 OHM COAXIAL CABLE which then feeds the ANTENNA (or Antenna Tuner, if used). This is compared to a BALANCED (Twin Line), UNGROUNDED OUTPUT.

33. TYPICAL TRANSCEIVER OUTPUTS. Note that the lower end of the Output Link, and the chassis side of the Coax Connector are grounded, in the Single Ended (standard) configuration, while the Output Link is floating in the Balanced configuration.

34. TRANSMISSION LINES: For the moment, we’ll discuss only single ended, 50 ohm, coaxial outputs and transmission lines, as they are the most common in use today. CONSTRUCTION: Let’s first consider the construction of coaxial cable: A: Vinyl outer jacket. B: Copper braided shield, could include aluminum foil wrap. C: Foam or other insulation. D: Copper center conductor, or copper coated steel, single or multiple strand..

35. TYPES OF COAXIAL CABLE: The Outer Jacket, A, is generally black, and made of vinyl. But other colors can be used, and special materials, such as UV resistant, direct burial (often including armored jacket), etc.. The shielding can be single or multiple layers of braid, made of either bare or tinned copper, or aluminum. It may also include a solid aluminum foil between the braid and insulating foam, C. The center conductor is made of copper or copper coated steel, may be stranded, or a single strand. With stranded wire, there is less chance of failure due to breakage as if a single strand of wire were used.

36. Below is a photo of a coaxial cable with a single strand (copper coated steel), foam dielectric, aluminum foil shield, braided and tinned copper shield, and vinyl jacket. DOUBLE SHELDED COAX:

37. HOW DOES THE NUMBERING SYSTEM WORK? In a typical “designation” such as “RG58/U” or “RG58A/U” The “R” refers to “Radio Guide” (application). The “G” refers to “Government Specification”. The “58” is an assigned number. The “U” refers to “Universal Specification”. The “A” refers to an “Enhanced version.” There are literally a “jillion” different types of coaxial cables, with different manufacturers using different numbering systems.

38. TABLE OF A FEW CABLE TYPES: TYPE: IMPEDANCE: DIELECTRIC: O.D.(Inches) SHIELD: RG8/U 52 Ohms PE 0.405 Braid RG8A/U 52 Ohms PE 0.405 Braid (NOTE: The letter “A” in the TYPE designation indicates an enhanced version of the cable). RG58/U 52 Ohms PE 0.195 Braid RG58A/U 52 Ohms PE 0.195 Braid RG170DB 75 Ohms ST 0.125 Dbl. Braid RG213 50 Ohms PE 0.405 Braid RG316 50 Ohms ST 0.102 Braid The Dielectric Types include: PE = Polyethylene (Solid or Foam) ST = Solid Teflon

39. COAXIAL CABLE CONNECTORS: BNC PL259 TNC N Mating connectors: PL259 SO239

40. “HELIAX” CABLE All coaxial cable has “losses”, which can be reduced by choice of the dielectric material. A uniquely constructed cable, “Heliax”, employs a flexible, solid outer “tube” (replaces the shielding in conventional cable), which is “ribbed” to allow bending, and the center conductor is of similar construction. The dielectric is a spiral wound material, with air being the primary dielectric.

41. CHARACTERISTICS OF COAXIAL CABLE The “Characteristic Impedance” of Coaxial Cable (50 ohms for most ham radio applications) is defined the by following formula: Where: Zo is the characteristic impedance (ohms). L is the inductance per unit length. C is the capacitance per unit length. Below is the “equivalent circuit” for a length of coax:

42. A COAX CABLE CIRCUIT: For maximum power transfer from the Source (Transmitter) to the Load (Antenna), through the Coax Cable, the Impedance of all must be equal. Why was 50 ohms chosen for Amateur radio applications? Because the approximate feed (input) impedance of a Dipole antenna is between 50 and 75 ohms. More on Dipole antennas later.

43. DOES ALL THE ENERGY REACH THE ANTENNA? ‘fraid not! ANY conductor has “losses” (unless they are operated at a temperature of “absolute zero”, or –459.67 ° F!). So even with proper matching impedances in a coaxial system, there ARE losses of power along the transmission line. Let’s take a look at how to determine the loss along a section of coaxial cable (usually specified by manufacturers in dB per 100 ft.).

44. MEASURING COAXIAL LOSSES: Step 1, hook up equipment as shown below, set the transmitter at a fixed output power, measure the power into the coax/dummy load. This is termed “P1”. Step 2, hook up the system as shown above, and take a second power reading. This is termed “P2”.

45. NOW COMES THE CALCULATION: We want to measure the “goes into” and compare it with the “comes outta”! Expressed in dB. Note that we’re comparing the difference in the two power measurements (P1-P2), and dividing by the original power In (P1), then taking the Log of the results and multiplying it by 10, to get the answer in dB, the common value for measuring RF power. But there’s yet another “Loss”, called SWR!

46. SWR (Standing Wave Ratio) In our previously discussed DC Circuits, the maximum power transfer from a source to a load, required equal Source and Load resistance. HOWEVER, with an AC (RF) circuit, any Inductance or Capacitance will result in Reactance in the circuit, causing a phase shift in the current flowing in the circuit. Thus, if the Load (Antenna) for a RF Transmitter, does NOT look like an Impedance of 50 ohms, then some of the energy sent down the coax will be reflected back toward the Source (Transmitter).

47. WHAT IS “REFLECTED POWER”? When we get into the discussion about Antennas, you’ll see how current is actually “reflected” backwards into the transmission line from a “mis-matched” antenna! This results in “canceling” some of the forward current going to the antenna, which in turn, results in loss of actual power being “radiated” by the antenna, and if excessive, reflected current can damage the Transmitter if not properly “tuned out”. The “unique” characteristic of this phenomenon, is that that, due to phase shift of the reflected current, the result will be “Standing Waves” along the transmission line!

48. EXAMPLE OF “STANDING WAVES”. If the “Reflected Wave” is equal in amplitude to the “Transmitted Wave”, it will produce a steady pattern, as shown below.

49. “TRAVELING” STANDING WAVES. BUT, If the Amplitude of the Reflected Wave is less than that of the Transmitted Wave, it will move along or “Travel” down the transmission line.

50. WHAT IS SWR? The term “Standing Wave Ratio” is just that, a Ratio between the Transmitted Power and the Reflected Power. It is expressed, mathematically as: OR, simply the ratio between the Maximum Amplitude and the Minimum Amplitude of the resulting wave along the transmission line!

51. WEB SITES FOR COAXIAL CABLE LOSSES, AND ANTENNA DATA. This web site includes a calculator for coaxial cable loss for different types, lengths and frequencies of some common coax types: http://timesmicrowave.com/calculator/ Here’s a good site for antenna theory and “do it yourself” antenna projects: http://www.ac6v.com/antprojects.htm Take a look at the multi-band, directional “Hex Beam” antenna described on the above site.

52. VSWR The wave forms we’ve been discussing are generally referred to as the Current waveforms. But in certain applications, such as Microwave guides, they could also refer to the Voltage waveforms along the wave guide. They are referred to as VSWR or Voltage Standing Wave Ratio, pronounced “vis-war”.

53. ANTENNAS: But before we further study SWR and reflected power, let’s first take a look at typical antennas, to learn how energy is “reflected” back down the coax cable (or ANY type of feed line, including “Open Line” or “Window Line”). But that’s enough for this session, we’ll continue next time with a discussion on different antennas, how they “match” a feed line, and what happens if the antenna does NOT have a proper Impedance Match to the feed line.

54. BREAK TIME! So take a break, have a cup of Java, and we’ll continue next time!

55. PART THREE ANTENNAS Basically, an “Antenna” is a conductor used to transmit or receive radio signals. Transmitted radio frequency currents are “coupled” into the conductive element(s) of the antenna, through a “Transmission Line”. As previously discussed, the “Transmission Line” may be either a coaxial cable (unbalanced) or an Open Line or Window Line cable pair. For the moment, we’ll continue this discussion, using coaxial cable.

56. WHAT QUALIFIES AS AN ANTENNA? Technically speaking, an antenna is any device that will radiate or receive radio signals. For receiving radio signals, virtually and length of just “plain old wire” will do, and generally the longer the length, the more “sensitive” will the antenna be in order to receive these radio signals. BUT, for transmitting a radio signal, the “efficiency” of the antenna depends on matching its impedance to that of the “feed line” connected to the antenna. Let’s next discuss some typical Transmitting antennas.

57. THE DIPOLE ANTENNA. While there are many types and configurations of antennas, one of the most common type is the “Center Fed, Half Wave Dipole”. This antenna consists of two wires, fed with a trans- mission line. The Input Impedance of a typical Half Wave Dipole in “free space” is about 72 ohms. So if the Input Impedance of the Center Fed, Half Wave antenna is 72 ohms, why use 50 ohm coax? Studies show that the maximum “efficiency” for a coax antenna feed cable is around 32 ohms, so the 50 ohm value was chosen as a comprise between these two values.

58. CONSTANT IMPEDANCE? While 72 ohms is considered the typical impedance of the Half-Wave Dipole (in “free” space), it can be seriously changed by nearby objects, both metallic (roof gutters, masts, etc.) and and non-metallic (tree branches, wooden structures, etc.). Any antenna should be “tuned” for the specific frequency used, and all antennas will have one specific resonant frequency. It may well, however, have a number of resonance frequencies, but there should be only ONE major resonant frequency. This resonance frequency is dependent upon the length of the radiating elements.

59. TYPICAL HALF WAVE DIPOLE Below is shown a typical Half Wave Dipole antenna. Note that the total length of the antenna is one half wavelength of its design frequency. To determine the full length of this antenna, use the formula:

60. CALCULATING ANTENNA LENGTH HOWEVER, to make things simpler, let’s determine the length of each leg or arm of the antenna: OR, simply:

61. WHAT IS THE ORIGIN OF THE NUMBER 468? It is related to the speed of the travel of the electrons in the antenna wire, which is close to the speed of light. We’ll discuss that a bit later. But let’s first discuss the construction of the Half Wave Dipole antenna.

62. CONSTRUCTION Refer again to the figure, below. Each end of the antenna is insulated from any support mechanism (rope, wire, etc.) by an insulator, such as the ceramic ones shown. The center of the antenna also contains an insulator to separate the two, equally distant “arms” of the antenna, and has a provision for supporting the antenna’s center.

63. Note that the shield of the coax is connected to one “arm” (it does not matter which one), and the center conductor of the coax is connected to the other arm. The arms are equal in length, and the total length is one-half the wavelength of the operating frequency. The “exposed” end of the coax should be sealed with some sort of insulating, waterproof material.

64. Finely, the antenna wire itself may be solid or stranded, and can also be insulated. One type of commonly used antenna wire is “Copper Weld” wire. This type of wire is made of steel (for strength) and coated with copper for better conductivity (skin effect) of RF energy. The gauge of the wire can be virtually any gauge strong enough to support the system, BUT the larger the wire diameter, the greater the bandwidth.

65. WIDE BAND WIDTH ANTENNA Remember that RF energy travels mostly in the outer layer of a conductor, the so-called “skin effect”. The higher the frequency, the less the current will penetrate into the core of the wire. Thus multi- stranded wire will actually have more “surface area’ for conduction of RF energy! Also, the larger the wire diameter, the wider the bandwidth – remember that the antenna is “tuned” to a very specific frequency, BUT has a limited bandwidth to either side of that frequency.

66. Below is shown a scheme for increasing the bandwidth of an antenna by effectively increasing the “diameter” of the wire! By stringing a group of standard size wires through insulating “rings” at each end of the leg of the antenna, its bandwidth is increased, simulating the effect of a single wire with the same large diameter.

67. TUNING AN ANTENNA As mentioned earlier, surrounding materials, height above ground, and other factors affect the resonant frequency of an antenna. The proper way to build an antenna is to make it a bit longer than specified by the formula (given earlier in this presentation), then find its resonant frequency and bandwidth with a good antenna analyzer. Finally, you’ll “trim” the (initially too long) antenna wire to achieve the desire resonant frequency.

68. One procedure for tuning an antenna (ONLY after being installed at the desired location and height) is as follows: (1) Cut each “leg” per the formula (but add a few % in length for “tuning”). (2) Erect the antenna and determine the actual Resonate Frequency. (3) Use this formula to determine YOUR “number” (x) for the equation: or

69. (4) Use the “x” in the original formula to determine the actual length required for your frequency: (5) Cut your antenna to the new length, reinstall it, and check the resonate frequency. Resonate frequency of an antenna can be determined by using a variety of instruments and techniques, such as an “Antenna Analyzer” or a “Grid Dip Meter”, such as shown to the right.

70. FIELDS AROUND AN ANTENNA Let’s take a look at the type of fields that surround the conducting wire of an antenna, as shown below. There are two types of fields created by current (AC or DC) flowing through a conductor: The “B” or magnetic field and the “E” or electrostatic field. They surround the conductor as shown, but it is the “B” field that actually radiates.

71. These Magnetic Fields are what actually enable radio transmissions. The current flow which is oscillating back and forth along the antenna’s radiating elements (the “arms” of the Dipole antenna), creates these two fields, the electromagnetic and the magnetic fields. The electrostatic field dissipates a short distance from the antenna, but the magnetic field, which, either by “direct” or “ground” wave or a “reflected” (from the ionosphere) or “sky” wave, induces a current flow into a receiving antenna, much in the way the primary of a transformer induces current into its secondary.

72. ANTENNA FIELD PATTERNS Let’s look at the “radiation patterns” of a typical, horizontal, “long wire” antenna (or a leg of a Dipole Antenna). The “axis” of the radiating wire goes “into” the page, and the “pattern” is reflected by the surface of the earth, as a function of the height above ground.

73. Let’s take a closer look at just one example, where the antenna is ¼ of a wavelength above the earth. For the 80 meter band, this would be 20 meters or about 66 feet. The “rings” are the “relative field intensity” for different angles above the earth’s surface. At ¼ wavelength, there is a single, almost circular “lobe”. At a height of 1.75 wave length, multiple “lobes” exist, as shown to the left.

74. HORIZONTAL PATTERNS. The upper figure shows a “top” view of the 0 dB point (intensity) of the pattern around a dipole antenna, with the antenna lying along the 90 degree axis. Note that the pattern resembles an apple cut in half! The lower figure is a 3 D figure of the field pattern, with the antenna along the axis line drawn through the figure.