# Understanding Swr By Example-Books Pdf

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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.

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