So it's with some interest that I hear they're working on a program to miniaturize Very Low Frequency antennas. Actually, miniaturize is too weak a word. See, antennas work best when they're a significant portion of a wavelength long (the wavelength times the frequency is always the speed of light: c = f*l). As a rule of thumb, most amateur antennas are longer than 1/8 wavelength, and some are several or many wavelengths long.
For example, a relationship lots of hams know is that the length (in feet) to start working on a 1/4 wavelength antenna is 234/f where f is in MHz. That says an AM radio antenna 1/4 wavelength long at 1.000 MHz (near the middle of the AM broadcast band) is 234 ft long. DARPA wants to miniaturize that antenna to fit in a teacup, with room to spare. They want antennas 1/10,000 of a wave long. That turns the 234 foot tall antenna into 1.12 inches tall.
“At these frequencies, free‐space electromagnetic (EM) field wavelengths are measured in tens of kilometers, resulting in very large transmitter structures when employing conventional antenna approaches. Electrically‐small antennas are defined as having dimensions much smaller than the EM wavelength, with examples in the literature of antenna‐sizes as small as 1/10th of the EM wavelength. DARPA is seeking innovation to bring that size below 1/10,000 of the EM wavelength or by at least a factor of 103 smaller than the current state of the art (SOA).”Unlike the world that car commercial writers live in, nobody can “break the laws of physics”, so nobody is going to come up with a way to treat those antennas to make them behave just like a full-sized antenna. The laws of physics not can't be broken, nor are they up for negotiation. On the other hand. they can be dealt with. There may ..may ... be tricks that can be done to make a system work effectively with antennas that small.
Such a tremendous reduction in size is impossible to achieve through traditional antenna design so DARPA said it is looking to gather information “in the areas of materials, mechanical actuation, and overall transmitter architectures to address impedance matching, power handling, signal modulation, scalability, and other system level considerations.”
The main problem is going to be the impedances required. An electrically tiny antenna is barely distinguishable from an open circuit; they're a very, very high impedance. Full sized antennas have much lower impedances, and most transmitter and receiver systems are designed around a 50 ohm standard impedance. If you go buy virtually any amateur HF base station radio made in the last 50 years, that's what they'll be designed for. Your cheap, Chinese VHF/UHF radio will be designed around a similar value. (Cable TV systems, which don't transmit, are designed around 75 ohms for their cable ports rather than 50 ohms; car radio antennas are electrically quite small for AM radio, but not DARPA 1/10,000 wave "quite small", and they're high impedance).
Half and quarter wave antennas are the impedance they are because of the physics. They can be thought of as matching the impedance of the transmitter to the impedance of free space which is just under 377 ohms and any antenna has to match its impedance to 377 ohms. The output impedance of the power device in the transmitter isn't 50 ohms just because the antenna is 50 ohms, and impedance matching is one of the very basic skills of an RF designer (impedance matching been berry berry good to me!). The impedance of the output stage depends on the circuit configuration and device. A convenient way to approximate the output impedance is the voltage squared over 2 times the power output ((Vcc^2)/(2*Po)) That means the higher the voltage and the lower the output power, the higher the output impedance.
In a transmitter, low output power is rarely something desirable (I never, ever, had anyone ask me or anyone else I was ever around for less transmitter power). Modern power transistors can run at hundreds of volts, but it seems to me that we'd be looking at even higher voltages to get the impedances they're looking for. High voltage brings its own problems: notably arcing and corona, but high voltage is handled in the business.
The biggest problems here are the antenna efficiencies. An open circuit can only be tuned so far to look like an antenna. It may require so many parts or be so narrowband that it becomes a useless antenna. Component quality is going to be a big concern; it will likely require huge, heavily silver-plated coils and capacitors with vacuum dielectrics. I don't know that the antenna can work. It may turn out that the combination of extremely inefficient antennas, forcing higher powers to be used, forcing ever higher voltages into the circuits is simply insurmountable.
I always used to say that the company that can turn the land requirements for an AM broadcaster from "many acres" down to "a store in a strip mall" will never run out of money. The typical AM broadcaster uses three quarter wave tall monopoles (verticals), spaced around a quarter wave from each other, because they need to carefully recreate an antenna pattern they're authorized to use, so they'd need three of these magic antennas. Once the radio waves leave that antenna, it's still a full-sized EM wave. I just don't see how they can do it, but that's what DARPA is for.
The "Trideco" antenna tower array at the US Navy's Naval Radio Station Cutler in Cutler, Maine, USA. The central mast is the radiating element, while the star-shaped horizontal wire array is the capacitive top load. About 1.2 miles in diameter, it communicates with submerged submarines at 24 kHz at a power of 1.8 megawatts, the most powerful radio station in the world. If scaled the way DARPA is targeting, that 979.5 foot tall tower becomes 11.75 inches. It's currently 1/10 wave long; 11.75 inches reflects shrinking it by 1/1000.