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Adding Reactance to the Picture, In the main article I used several examples of SWR. based on a resistive load A resistive load is the easiest. to visualize calculate and understand but it s not the. most common type of load In most cases loads have, some reactive impedance as well That is they contain. a resistive part and an inductive or capacitive part in. combination For instance your antenna might appear. as a 50 resistor with a 100 nH inductor in series or. perhaps some capacitance to ground In this situation. the SWR is not 1 1 because of the reactance Even, antennas that show a perfect 1 1 SWR in mid band. will typically have some larger SWR at the band edges. often due to the reactance of the antenna changing with. frequency Fortunately a given SWR behaves the same. on a transmission line whether it s reactive or resistive If. you have a handle on understanding the resistive case. the concept will get you pretty far, To explore SWR further it s useful to look at the. reactive load case or what happens under the condition. that loads are not simply resistive Complex imaginary. number math is the routine way to analyze the SWR, of complex loads and can be done if you have access.

to a calculator or computer program that will handle it. Even so the math gets tedious in a hurry Fortunately. there s a very easy way to analyze complex loads using. graphical methods and it s called the Smith Chart See. The concept behind the Smith Chart is simple There. is a resistive axis that is down the middle of the chart Figure A The normalized Smith Chart ready to simplify. left to right and a reactive axis along the outer edge of transmission line analysis. the chart s circumference Inductive loads are plotted. in the top half of the graph and capacitive loads in the. bottom Any value of resistance and reactance in a, series combination can be plotted on the chart Then. with a ruler and compass the SWR can be determined. Advanced users of the chart can plot a load and use. graphic techniques to design a matching structure or. impedance transformer without rigorous math or com. puter It s a very powerful tool Here s a simple example. showing how to determine SWR from a known load, using the chart. Suppose you have just measured a new antenna, with an impedance bridge and you know that the input. impedance is 35 in series with 12 reactive The, coax cable feeding it has a Z0 of 50 What is the SWR. at the antenna end of the coax, This impedance can be written as the complex num.

ber Z 35 j12 5 The j is used to indicate the reac, tive part from the real part and they can t simply add. together To use a normalized Smith Chart we divide. the impedance by 50 to normalize the impedance, Smith Charts are also available designed for 50 with. 50 at the center instead of the 1 0 that we show for the. normalized chart Ed We now have Z 0 7 j0 25, Smith Chart numbers are normalized which means that. they have been divided by the system impedance before. being plotted In most cases the system impedance, is the transmission line impedance and is represented. on the chart by the dot in the center Now plot Z on the. chart Along the horizontal line nd the 0 7 marker and. move upward inductors or positive reactances are, upward capacitors or negative reactances are down Figure B An impedance of 35 j12 5 normalized to 0 7 j0 25.

to use on the normalized chart, From November 2006 QST ARRL. ward from center until you cross the 0 25 reactance line. see Figure B Draw a point here that notes your imped. ance of 35 j12 5 Next draw a line from the center, dot of the chart to your Z point Measure the distance of. that line then draw the same length line along the bot. tom SWR scale From here you can read the SWR for, this load The SWR is 1 6 1. Another useful attribute of the Smith Chart is called. a constant SWR circle The SWR circle contains all, the possible combinations of resistance and reactance. that equal or are less than a given SWR The circles. are drawn with a compass by using the distance from. the SWR linear graph at the bottom and drawing a, circle with that radius from the center of the chart or.

use the numbers along the horizontal axis to the right. of the center point For instance where you see 1 6 on. the horizontal line a circle drawn with radius distance. from the center to that point is SWR 1 6 1 as shown in. Now any combination of impedance on the circle will. be equal to SWR 1 6 1 and anything inside the circle will. be less than 1 6 1 The example impedance that was, plotted before should lie on the 1 6 1 circle. Also useful is to know that rotating around the outer. diameter of the Smith Chart also represents a half. wavelength of distance in a transmission line That is as. you move along the outer circle it s the same as moving. along a transmission line away from the load One time. around the circle and you re electrically 2 away This. is also very powerful feature of the chart since it allows. Figure C A circle of constant SWR drawn through the impedance you to see how your load impedance changes along a. of Figure B The SWR is 1 6, transmission line again without doing the math. Here s another example If your coax cable has a, 1 6 1 terminating SWR as you move along the trans. mission line away from the load you move along the. constant SWR circle on the chart Remember from the. article text that a 1 6 1 SWR can be equal to either. 80 or 31 resistive 1 6 80 50 or 50 31 From the, Smith Chart where the SWR circle crosses the hori. zontal axis the impedance is purely resistive Where. the circle crosses 1 6 it s equal to 80 and crossing at. 0 62 it s equal to 31 This is the basis of how imped. ance transformers work Remember to multiply any, numbers from the chart by your working impedance.

50 in this example to get their actual value, Where do these purely resistive points lie on the. transmission line From the chart looking at the line. extended from the center dot through our Z point nd. where it crosses the wavelengths toward generator, curve on the outside of the chart as shown in Figure D. The line crosses at approximately 0 07 wavelengths on. the chart which will be the starting point Note that the. 80 point 1 6 is at 0 25 and the 31 point 0 62 is, at 0 50 on the chart Subtracting the starting point of. 0 07 the chart is telling us that at 0 18 0 25 0 07. from the load the impedance is 80 and at 0 43, away it s 31. To nd the distance in a real piece of cable multiply. the chart wavelengths by the free space wavelength by. the cable velocity factor For example if your frequency. is 144 MHz then a full wavelength in air would be, 300 144 2 08 meters Multiplying by the velocity fac.

tor of 80 gives 1 67 meters Multiplying by the chart. Figure D A line drawn from the chart center through the. impedance of Figure B to the edge showing the distance from the wavelengths and then at 30 cm you d nd 80 and at. pure resistive points on the line 72 cm it s 31, From November 2006 QST ARRL. wave At some places on the cable the reflec, tied voltage adds to 133 percent and others. it subtracts to 66 percent of the matched, transmitter output The voltage ratio is. 133 66 or 2 0 That voltage ratio defines the, SWR The fact that the voltage along the line. changes with position and is different from, what the transmitter would produce is called.

a standing wave Standing waves are only, present when the line is mismatched. Does Higher SWR Lead to Lower, Power Being Transmitted. Not always so dramatically Believe it or, not 100 percent of the power is actually trans. mitted in both of the previous examples In the, first case with a 50 antenna it s easy to see. how all the power is transferred to the antenna, to be radiated since there are no reflections.

In the second case the 33 percent voltage, reflection travels back down to the transmitter. where it doesn t stop but is re reflected from, the transmitter back toward the antenna along. with the forward wave The energy bounces, back and forth inside the cable until it s all. radiated by the antenna for a lossless trans, mission line An important point to realize. is that with extremely low loss transmission, line no matter what the SWR most of the.

power can get delivered to the antenna A later, example will show how this can happen. Is High SWR Bad or Not, Now that you have a sense of what SWR. is a few examples can show why under, some conditions high SWR can lead to less. power radiating and in other cases it s no, big deal The easiest way to see how SWR. affects an antenna system is to use a set of, charts Figures 1 and 2 are taken from The.

ARRL Handbook in the chapter discussing, transmission lines There is much more. theory in the Handbook than I m presenting, here so if you want to be an expert on trans. mission lines that s one place to learn more, In the previous examples the transmis. sion line had no loss and all our power, was being delivered to the antenna That s. a nice way to visualize what is happening, with the reflections but it doesn t match the.

real world because all transmission lines, Figure 2 A graph showing the actual SWR at an antenna based on measured SWR at. the transmitter end of a transmission line with loss have some loss Here s a more practical. straightforward situation This time we have, a length of 50 cable with a total loss of. cable is still 50 The SWR for this setup is reflected for various SWR values 3 dB 50 percent power and a 50 antenna. calculated as 100 50 or 2 1 Now the energy In the case of a mismatched condition SWR is therefore 1 1 Transmitting 1 W. wave hits the antenna and part of it is radi something interesting happens along the would result in 0 5 W applied to the antenna. ated by the antenna but part of it is reflected transmission line Before with the matched Since the SWR is 1 1 there is no mismatch. back down the line toward the transmitter antenna the same voltage existed anywhere loss to worry about A very simple situation. That is the antenna is not matched to the line along the line Now as you move along the and no charts are needed If life were only. so there is a reflection It turns out that for a distance of the line the voltage will change that simple. 2 1 SWR 33 percent of the voltage wave is It now has peaks and valleys The 33 percent Next ry t 100 antenna with he. t he t asme, reflected like an echo back down the line reflection from the antenna alternately adds coax The SWR is then 2 1 at the antenna. Table 1 lists how much voltage and power is to and subtracts from the forward voltage since 100 50 2 0 According to Figure 1. From November 2006 QST ARRL, expect a mismatch loss of 0 35 dB in addi reflections die out in the cable Remember at him because you know that the 4500 of. tion to the cable loss In this case we lose a no reflections looks like a SWR of 1 1 The the antenna will present an SWR of 90 1 on. total of 3 35 dB of our signal and send the value of that virtual resistance in this case is his 50 cable resulting in a mismatch loss. antenna 0 46 W Not much difference from 50 which is the definition of characteristic of 12 dB beyond the 0 25 dB cable loss Sure. a perfect SWR of 1 1 impedance or why some cables are called he can tune his SWR to 1 1 with the tuner. How about a SWR of 3 1 with the same 50 and some are 75 or 300 That num at his radio but guess who will be working. cable According to Figure 1 again we would ber is the impedance the RF would see if the the DX. have an additional loss of 0 9 dB which cable were infinitely long Or it is also the. makes a total loss of 3 9 dB and 0 41 W to resistance of the load needed in order to cause Conclusion. the antenna This is still not a lot of additional no reflected energy and match the cable I hope I have been able to show by. loss even with an SWR of 3 1 Under most The moral of this story is to measure example that SWR can be a serious issue or. conditions a power reduction of 0 9 dB is not the SWR at the antenna especially if you something not so important With the help. noticeable over the air Even at a 3 1 SWR the have a long cable run SWR measurements of the graphs and a little information about. signal it not significantly reduced at the transmitter can be deceiving The your transmission line and antenna it s easy. The SWR vs loss tables make it easy to second moral is to know that when a cable to determine how much of your signal is. figure out what your additional loss might be manufacturer quotes loss numbers they are actually getting on the air or how much is. for any given antenna system as long as you based on an SWR of 1 1 or a perfect match being lost in the transmission line. know the matched cable loss Anything less than a perfect match can cause Darrin Walraven K5DVW has been licensed. additional losses since 1986 at the age of 18 He enjoys DX CW. Is that the Whole Story and SSB He has an engineering degree from. No not exactly There s even more to Why Ladder Line Works for Texas A M University and is employed as an. explore in the world of SWR One very High SWR RF design engineer You may contact him at. strange situation occurs on a long and lossy Open wire line window line or lad k5dvw hotmail com. transmission line which causes your SWR der line has been used since the early days. coveted 1 1 SWR at any cost But why This article is written to help explain what SWR actually is what makes it bad and when to worry about it What is SWR SWR is sometimes called VSWR for voltage standing wave ratio by the technical folks Okay but what does it really mean The best way to easily understand SWR is by example In the