Sketching Current on the Antenna

I may be repeating a few things as we go along, but I think the important principles of radio and antenna theory need to be reinforced. I have found over the years that current, voltage, impedance and standing waves were among the most misunderstood concepts in radio or electronics. I think everyone has heard the term SWR (Standing Wave Ratio). I have been talking about standing waves on antennas. These are both standing waves of voltage and standing waves of current.
The ratio of voltage to current is the impedance at that point. When dealing with transmission likes, the common SWR is not a voltage to current ratio, but a ratio of two voltages measured at two different places on a line (VSWR). It could also be the ratio of two currents measured at different places on the line (ISWR). In fact there are numerous methods that can be used to measure transmission line SWR. I will eventually get around to explaining that. Right now I want to get the concept of antenna current and voltage down first. That really comes first and is a direct cause of the transmission line SWR.
There are a couple things that we need to know about antennas. First we want them to radiate as high a percentage of the power we supply to them as possible. (We want the transmission line to deliver as high a percentage of the transmitter power to the antenna as possible.) In order for the antenna to be able to accept all the power from the feed line we must have an antenna whose impedance matches that of the feed line. There are numerous physical things that will determine this ‘feed point” impedance. Almost all of these things are within our control, but we must have a basic understanding of them and how they work in order to control them. Otherwise it is just by trial and error.
The most important thing is to know approximately what the current and voltages are on an antenna. In order to start we need to pick a frequency and determine the wavelength and half wavelength. I always sketch the antenna then note some ballpark information about the current standing wave at various points along the wire. What do we know about the current at an open end? (It will be zero) Then I put a dot a quarter wave back from every end. What do we know about current at this point? (Current will be a maximum.) Continue on away from the end another quarter wave (if the wire is long enough). What do we know about the current here? It will be zero or a minimum. The reason it is not zero is that some of it is radiated as it travels along the wire to and from the ends, and when it crosses “fresh” current, there is not enough of it to completely cancel out the “fresh” current.
You should be able to sketch a half wave wire and draw a smooth curve representing the current. It should look like the first half of a sine wave. The curve representing current should start at zero on one end, rise like a sine wave to a maximum in the center and down to zero at the other end. If the wire is one wave long, we draw that current curve the same for the first half wave (going from left to right) then the second half wave is drawn below the line down to a maximum negative value, then back up to zero at the end. The current above the curve represents positive current and below the line represents negative current. It does not really matter which way the first arrow goes, what does matter is that the current in the first half wave flows one way and the current in the second half wave flows the opposite way. Another way to illustrate can be seen if you draw a long line from left to right. Divide it into four equal segments. So you can follow what I am doing, number the segments left to right 1, 2, 3 and 4. Over segments 2 and 4 draw an arrow pointing right. Over segments 1 and 3 draw an arrow pointing left. The currents in segments 2 and 4 are in phase; the currents in 1 and 3 are also in phase with each other but out of phase with currents in segments 2 and 4. To start to analyze any antenna, you can draw a sketch. Divide the wire into half wave segments and draw arrows over each half-wave segment, being sure to change the direction of the arrows in each adjacent half-wave segment.
Once you have drawn the sketch, you immediately know where the current is zero (at the ends) and where the current is a maximum (between the zero points). You also know that the points where the impedance is low are at the same place where the current is a maximum. These are the most likely places that you would want to connect a coaxial feed line. (There are exceptions, but we will deal with the exceptions one at a time later. For now, be advised that there seems to always be an exception to everything)
The impedance is different at different points on the wire. The voltage to current ratio at the ends is very high. Voltage is at its highest. We say the current is zero. You cannot really divide something like 100 or 200 volts by zero. You have to divide by almost zero, and get a close answer. In math or physics we always seem to run into problems where we want to divide by zero. If you divide by zero you get infinity. Not a good answer. So what we do is usually try and figure out what the limit is as we approach zero. We divide by smaller and smaller numbers to approximate dividing by zero. You might think of it a instead of dividing by zero, dividing by 1/1000 amps or maybe 1/1,000,000 amps. Sometimes you get close enough to the right answer that no one can ever tell it is not exactly the right number! In our case it is almost always good enough to say that the impedance at the end of an antenna wire is very high and leave it at that. I do. Funny things happen in the real world when you try and work with impedances like at the end of a wire where they are real high. There are situations where things become unstable and unpredictable. There are cases where impedances rise very fast to an extremely high inductive value and then like you would flip a switch, they change to a very high capacitive value. For most of us, we need only know that such conditions do exist, recognize when they may exist, understand that it is best to avoid them! I will try and help you with that. I just rambled some. Let me back up and start again.
The impedance is different at different points on the wire. The voltage to current ratio is very high at the ends and this ratio goes down as you move away from the end. The impedance reaches a minimum at the middle of each half-wave section. You can connect cut the wire and connect a feed line anywhere. In the center you will get a good match to 50 or 75 ohm coax. Somewhere between the center and the end you may find a point that is a close match for 300-ohm line. No matter where you choose to connect a transmission line on any length wire there will be an impedance at that point that is acting like either a pure resistance, or a resistance in series with a coil (inductor) or capacitance. If the impedance is not a good match for the chosen feed line, you have several choices. First you can change the point of connection. That sometimes works. Second you can change the type of feed line. Third you can add a matching circuit or matching network to transform the impedance of the antenna to the value of the transmission line. Fourth you can change the length of the antenna (longer or shorter). Lastly, you can do nothing. That means you accept the additional loss due to the mismatch. We normally do not accept much of a mismatch when using coax. However, when using open wire or parallel wire transmission line, typically 300 or 600-ohm lines, we find that the increased losses due to a rather large mismatch are not significant and we can live with that small loss.