Increasingly stringent design constraints imposed by compact wireless devices for telecommunications, defense, and aerospace systems require the miniaturization of antennas. Unlike most electronic components, which benefi t from decreased size, antennas suffer limitations in gain, effi ciency, system range, and bandwidth when their size is reduced below a quarter-wavelength. The electrical size of the antenna is measured by its ka value, where k is the wavenumber ( k = 2 π / λ , λ = wavelength at the operating frequency) and a is the radius of the smallest sphere that circumscribes the antenna. Antennas are considered to be electrically small when ka ≤ 0.5. Recent attention has been directed towards producing radiofrequency identifi cation (RFID) antennas by screen-printing, [ 1 ] inkjet printing, [ 2 ] and liquid metalfi lled microfl uidics [3][4][5] in simple motifs, such as dipoles and loops. However, these fabrication techniques are limited in both spatial resolution and dimensionality; yielding planar antennas that occupy a large area relative to the achieved performance.Omnidirectional printing of metallic nanoparticle inks offers an attractive alternative for meeting the demanding form factors of 3D electrically small antennas (ESAs). We have previously demonstrated that fl exible, stretchable, and spanning silver microelectrodes with features as small as ∼ 2 μ m can be patterned both in and out-of-plane (e.g., spanning arches) on fl at substrates by this approach. [ 6 ] Here, for the fi rst time, we demonstrate the conformal printing of silver nanoparticle inks on curvilinear surfaces to create electrically conductive meander lines. When interconnected with a feed line and ground plane, the resulting 3D ESAs exhibit performance properties that nearly match those predicted theoretically for these optimized designs.Antennas act as effective transducers between free space and guided waves over a range of frequencies, known as their impedance bandwidth. The impedance of most small antennas can be approximated by a single resistor-inductor-capacitor (RLC) circuit, and their bandwidth is inversely proportional to their radiation quality factor ( Q ), defi ned as the ratio of energy stored to energy radiated. [ 7 ] Because of this inverse relationship, a low Q serves to increase bandwidth, and therefore the data rate over a given wireless channel. However, a fundamental relation exists between the antenna size and Q . [ 8 , 9 ] As the maximum dimension decreases below a wavelength, the bound on the minimum attainable Q rapidly increases, a phenomenon commonly referred to as Chu's limit -an important fi gure of merit for antenna performance. While Thal recently derived a more accurate bounding limit, [ 10 ] both limits depend on the electrical size of the antenna. For decades, researchers have sought antenna designs that approach these fundamental lower limits. However, prior efforts, such as those based on genetic algorithms [ 11 , 12 ] lack fl exibility, since their output cannot be modifi ed in a straightfor...
