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Who improved the early spark-gap transmitter design allowing much higher levels of radio-frequency power output?

Some historians credit Reginald Fessenden in 1900 for making improvements to the earliest spark-gap transmitters allowing significantly higher levels of radio-frequency energy to be concentrated into a damped or partially damped wave of a single frequency.  Other scholars say it was Ferdinand Braun performed in a hastily improvised demonstration in September 1898.

In reality, Nikola Tesla revealed the basic techniques for improving transmitter performance with a series of U.S. patents, starting with his "System of Electric Lighting" Patent No. 454,622, dated June 23, 1891, the accompanying drawing of which clearly shows an energy storage capacitor and a discharge device on the primary side of a resonance transformer.  This radio-frequency power supply circuit was used in a demonstration of what might be considered the world's first practical wireless transmitter at an 1893 meeting of the National Electric Light Association in in St. Louis.

"In the transmitter group on one side of the stage was a 5-kva high-voltage pole-type oil-filled distribution transformer connected to a condenser bank of leyden jars, a spark gap, a [Tesla] coil, and a wire running up to the ceiling.

"In the receiver group at the other side of the stage was an identical wire hanging from the ceiling, a duplicate condenser bank of Leyden jars and coil�but instead of the spark gap, there was a Geissler tube that would light up like a modern fluorescent lamp bulb when voltage was applied.  There were no interconnecting wires between transmitter and receiver.
" [Tesla�Man Out of Time]

His patent "Means for Generating Electric Currents" No. 514,168 of February 6, 1894 describes a variation of this same circuit.  Between September 15, 1896 and November 18, 1898 no fewer than 17 patents were granted for equipment directly related to the production of powerful high-frequency electrical currents.  It was during that same period, on September 2, 1897, that Tesla filed his first application which was directly related to wireless transmission and reception, resulting in two patents that were subsequently issued as "System of . . ." and "Apparatus for Transmission of Electrical Energy," dated March 20 and May 15, 1900 respectively.  On July 1, 1898 another wireless-related application was filed for the radio-controlled boat resulting in the patent, "Method of and Apparatus for Controlling Mechanism of Moving Vessels or Vehicles" issued November 8, 1898.  All of these patents are presented in the book Dr. Nikola Tesla � Complete Patents.

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