High-sensitivity picosecond time-domain reflectometry

Abstract

The combination of a time-domain reflectometer, signal averager, and lock-in amplifier is shown to increase the amplitude sensitivity of the reflectometer by a factor of about 200 for observing small, multiple transmission line reflections. Replacing the signal averager by a second lock-in amplifier increases the sensitivity further by a factor of 10, but this method is only suitable for measuring reflections from a single point. In the latter case, the minimum, detectable shunt capacitive discontinuity (signal-to-noise ratio of unity, Z <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> = 50 Ω) is about 5 aF (1 aF = 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−6</sup> pF); the corresponding value for a series inductive reflection is 10 fH (1 fH = 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−3</sup> pH). The time window drift must be very low to achieve such sensitivity. Methods are described which reduce the intrinsic drift by about a factor of 500 to 20 fs. In precision 7-mm coaxial line, relatively pure shunt “capacitors,” below 0.5 fF, and series “inductors,” below 1 pH, have been constructed and measured using these techniques.