Electronic devices may be provided with antennas. An antenna may be formed from conductive antenna structures that include a frequency-dependent distributed capacitor. The antenna may include an antenna ground and an antenna resonating element that are separated by a gap. A low pass filter circuit may bridge the gap. The antenna resonating element may have antenna resonating element conductive structures that serve as first and second electrodes for the distributed capacitor. The second electrode may have first and second conductive elements coupled by a filter. The filter may be a low pass filter implemented using an inductor. The inductor may have a first terminal coupled to the first conductive element and a second terminal coupled to the second conductive element. A first antenna feed terminal may be coupled to the first conductive element and a second antenna feed terminal may be coupled to the antenna ground.