Slight review and trap dipole principle

In a resonant half wave dipole, the voltage and current enter the antenna at the center, travel to the ends and get reflected. The current reflection is out of phase so the currents at the ends cancel. There is always zero current at the ends. (There is always zero current at the end of a an open wire. The voltage is also reflected but is not reversed in polarity like the current, so the voltage at the end is pretty much twice the original voltage. Due to the fact that the voltage and current vary with time, the actual currents and voltages that are set up on the antenna (these are called standing waves) varies or oscillates between two values. At the center the current varies at any given instant between a maximum positive value and a maximum negative value. As you move toward either end the current varies between two limits of decreasing value until at the end the two values go to zero. The voltage and current at the antenna terminals will be in phase. That means when the voltage peaks the current peaks. When the voltage is zero the current is zero. This is just like current and voltage in a pure resistor. When the radio frequency voltage is first applied at the transmitter end of a feed line current will flow (in a ratio of voltage to current determined by the characteristic impedance of the line) Lets look at the current first. The current reaches the terminals then flows to the end, gets reflected (out of phase) and flows back to the center. When it gets to the center it is exactly in phase with the current from the next cycle (remember this is only true for a resonant condition). These two currents then simply add together. Now lets think about the voltage. The voltage signal enters the antenna and travels down the wire to the end where it is reflected but the phase is not reversed. By the time it gets back to the terminals, the voltage is out of phase with the voltage of the next cycle. This reflected voltage tends to cancel the incoming voltage much like happens to current at the ends of the antenna. We should call the voltage and current that comes up the transmission line the initial voltage and current. We can also call it the incident voltage and current. These are the voltages and currents existing before things get muddy due to the reflections, standing waves and all that. The current and voltage waves that are set up on the antenna are standing waves of voltage and current. Initial voltage and current are in phase. Like they would be in a pure resistance. If the antenna is resonant the resulting current will still be in phase with this terminal voltage. The resonant antenna will act like a pure resistance. Now if the antenna is long or short, the resulting standing waves set up on the antenna will be a bit different and will cause the resulting current at the antenna terminals to be slightly out of phase with the applied voltage which will cause the antenna to not act like a pure resistance. The antenna will act like it has a coil or capacitor connected in series with it, even though it does not. It just acts like it does. That’s why we say the antenna is capacitive if it is short and inductive if it is long.
We can take a center fed dipole that is resonant and make it longer. We can also take a center fed dipole and add a coil to both sides. If we pick the right size coil, you will not be able to tell the difference at the antenna terminals. The same goes for making the antenna shorter or adding a capacitor. You will not be able to tell the difference. You can take a short antenna and add a coil to make it “appear” to be longer. You can take a long antenna and add a capacitor and make it appear shorter. This is the principle behind trap antennas. The trap is designed so that it makes the antenna appear to be longer or shorter so that the voltage and current at the terminals will be in phase and of a low enough impedance to be a good match to a coax transmission line.