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8. Gestblom and E. Noreland
Transmission Methods in Dielectric Time Domain Spectroscopy B. Gestblom and E. Noreland” Institute ofPhysics, University of Uppsala, Box 530, S- 751 2 1 Uppsals, Sweden (Received October 12, 1976) Publlcation costs assisted by the Institute of Physics, University of Uppsala
It is shown how transmission methods can be used in dielectric time domain spectroscopy (TDS)for the evaluation of permittivities over a large frequency range. Graphs, which show the transmission coefficientsunder different conditions, are given, and compared with those for the corresponding reflection methods hitherto used in TDS. The transmission methods are applied to the study of 1-butanol and chlorobenzeneand comparison is made with results from reflection measurements. The permittivities were studied up to 10 GHz. The results show that transmission methods offer an attractive alternative to the reflection methods over the total frequency range within reach in TDS.Direct time domain evaluation of dielectric parameters from thin sample transmission data is illustrated for 1-butanol.
Introduction In dielectric time domain spectroscopy (TDS) the dielectric properties of a sample are determined by its response to an electric pulse with very short rising time.’ The pulse is generated by a tunnel diode and the incident pulse and its response, which are transmitted in a coaxial line, are monitored with a sampling oscilloscope. The method most frequently used is to study the first reflection r ( t ) of the incident pulse ~ ( t )The . ~ sample should here be sufficiently long to allow the reflected pulse to reach a steady state before multiple reflections reach the sampling system. This method may be called the single reflection method. Fourier transformation
F ( o )= :1 f(t)e-Iwt d t
(1)
of the two pulses give the reflection coefficient in the frequency domain
R ( w ) 1 --€*1‘2 V ( 0 ) 1 t e*l/2
p=-=
from which the complex permittivity E* = E’ - jd‘ may be calculated. An alternative approach is to study the totally reflected pulse, including all multiply reflected contributions from a sample of short lengths3 The permittivity can in this case be determined from the solution of the transcendental equation for the reflection coefficient
reference point for the incident pulse and reflected pulse.
A timing error At will cause a phase error in the Fourier transform of wdt. Since the phase shift, e.g., in the single reflection coefficient p, only varies with a few degrees with varying permittivity, it is realized that for frequencies 11 GHz the timing error cannot be allowed to exceed a few picoseconds. An alternative to the reflection methods is obtained by studying the pulses transmitted through a sample. The direct approach here is to study the first transmitted pulse through a long sample, the single transmission method, or the totally transmitted pulse through a short sample, the total transmission method. The transmission coefficient ratio method7uses the ratio of the transforms of the singly transmitted pulses through two samples of different length. The transmission methods create larger phase shift in the transmission coefficients than what is achieved for the reflection coefficients in the reflection methods. Errors in the phase of the experimental transmission coefficients due to inaccuracies in the time reference procedure should therefore be less severe than for the corresponding reflection methods, implying that the TDS transmission methods should offer an attractive alternative to the TDS reflection methods in determination of permittivities. It is the purpose of this paper to show how the single and total transmission measurements can be made and to compare results and accuracies with the corresponding reflection methods.
Single Transmission In the frequency domain the single transmission coefficient for a signal of frequency w through a dielectric sample of length 1 is given by’ Here c is the speed of light and 1 is the length of the sample. This equation has also been used as a basis for thin sample approximations, IwlE*’”/cl
