Time Domain Measurement of Complex Propagation Constant and Impedance of Transmission Lines
Original Publication Date: 1991-Dec-01
Included in the Prior Art Database: 2005-Apr-04
Arjavalingam, G: AUTHOR [+2]
Disclosed is a simple method for the measurement of the attenuation a(f), phase constant b(f), and characteristic impedance Zo(f) of any transmission line system, over a wide frequency range.
Time Domain Measurement of Complex Propagation Constant
of Transmission Lines
a simple method for the measurement of the
attenuation a(f), phase constant b(f), and characteristic impedance
Zo(f) of any transmission line system, over a wide frequency range.
measurement of transmission-line properties by automatic
network analyzers is often limited by its expense and the need to
de-embed the frequency-dependent parasitics of the
instrument-to-sample interface . Time-domain measurements with
step excitations have been used to determine propagation-delay,
risetime degradation, characteristic impedance and crosstalk .
However, the measurement of driving-point impedance, which is a key
parameter of digital interconnections, has the least accuracy due to
interface generated distortions.
In the new
technique, a short electrical pulse is launched onto
two identical transmission lines of different lengths, l1, l2 . In
recent times, such a source can be easily obtained by using
photoconductive switches or simple differentiator networks in line
with high- speed step excitations. The attenuated and dispersed
pulses are detected at the ends of the lines, and the sampled
waveforms are digitized and used for calculating two Fourier
transforms. Time windowing is used to extract only the forward
traveling part of the waveforms and to eliminate unwanted multiple
reflections. The forward term for the line voltage (quasi-TEM
behavior) can be expressed as (2). The ratio of the amplitudes
yields the attenuation constant
while the difference in phase gives the phase constant:
where are the amplitude and phase, respectively, of the Fourier
transforms corresponding to lines l1 and l2 . The effect of
interface discontinuities linearly cancel out in the frequency domain
and laborious de-embedding is not necessary. When dielectric losses
are negligible (GNO), the pr...