Extraction of Frequency Dependent Transmission Line Parameters Using TDIUTDT Measurements

Transcription

1 IEEE Instrumentation and Measurement Technology Conference Budapest, Hungary, May 21-23,2001. Extraction of Frequency Dependent Transmission Line Parameters Using TDIUTDT Measurements Madhavan Swaminathan', Sreemala Pannala* and Tanmoy Roy* 777, Atlantic Drive, School of Electrical and Computer Engg. + Atlanta, GA , USA * Sun Microsystems, 15 Network Circle, M/S MPK Menlo Park, CA 94025, USA Abstract - This paper discusses a method for extracting the frequency dependent parameters of lossy bransmission lines from TDtUTDT measurements. These parameters were extracted for stripline structures in printed wiring boards. Using short -thru calibration, the transmission line parameters were extracted using a combination of time windowing and rational functions. I. Introduction Time Domain Reflectometry (TDR) and Time Domain Transmission (TDT) measurements provide an alternate method for characterizing interconnections. They provide time windowing capability that is absent in Network Analyzers [I]. This feature can be used advantageously for characterizing transmission lines. A typical set-up for TDR/TDT measurements is shown in Fig 1. In the set-up a fast rising edge is launched onto the Device Under Test (DUT). The digital sampling oscilloscope is used to measure both the reflected and transmitted waveforms, from which the DUT can be characterized. Details on TDR and TDT measurements are available in PI. This paper discusses a method for extracting the transmission line parameters directly from time domain measurements. The novelty of the method is in the use of rational functions to extract the transmission line parameters which can then be used to construct spice models with relative ease. This paper discusses the characterization from DC - 2GHz due to the rise time of the source used. The bandwidth can be increased to 10GHz using commercial sampling heads and high frequency probes. II. Measurement Method The extraction process is based on the use of rational functions, details of which are available in [2]. In [2], rational functions were used to extract the S-parameters of the device under test. In this paper, the method has been extended for extracting the frequency dependent characteristic impedance and propagation constant of transmission lines. SD-24 Digital Sampling SD-24 Sampling Head Sampling Head Oscilloscope Ch -l(trigger) High Speed Pulse Generator CASCADE GSG Fig 1 : Measurement Set-up Attenuator GORE 40 GHz Cables Two calibration structures, namely, a short and a thru have been used in the measurements. The short measurement has been used for setting the reference plane for defining the beginning of the time window. The thru measurement has been used to de-convolve the effect of the step source. The extraction procedure consists of the following steps: i) A short calibration measurement for setting the reference plane. ii) Measurement of the Device Under Test (DUT) and application of the method discussed in [2] for capturing the poles of the system. This requires the use of the Generalized Pencil of Function Method, details of which are available in [2]. iii) A thru calibration measurement to de-convolve the effect of the step source. The thru waveform has been used to update the residues of the system. This measurement and extraction process results in the impulse response of the DUT in the form /01/$ IEEE 1726

2 M H(s) k = - s-sk k= 1 where s=jo, ak are the residues, sk are the poles and M is the number of poles in the approximation. Equation (1) can now be used to compute the frequency response of the device. The measurement method has been used to extract the lossy transmission line parameters for striplines in printed wiring boards. Ill. Test Structures The test structures consisted of transmission lines in a printed wiring board. The lines were stripline structures with two line widths namely, 3.5 mils and 5.5 mils. Each line width consisted of transmission line lengths of 5, 10, 20 and 40. The striplines were optimized for a characteristic impedance of 50Q by controlling the dielectric thickness. The start and end points of the transmission lines contained vias for probing the structure.the 0 test structures are shown in Fig 2. Ground Plane E, Ground w=3.5 mils, 5.5 mils ; D=Dilectric ThicknegAane a) these parameters are a function of the line length. These parameters uniquely determine the propagation and reflection characteristics of lossy transmission lines. A. Propagation Constant Measurement The complex propagation constant of a transmission line can be written as where a(f) and p(f) are the attenuation constant and phase constant, respectively. For a transmission line, the forward transfer function can be written as (3) In the TDT measurement, time windowing was used to eliminate any reflections in the waveform. Hence, the measured waveform corresponds to the forward transfer function of the transmission line. In this paper, a two step process has been used to compute H(s) for the transmission line to minimize the order of the rational functions required. The approximate one way delay T was first measured. This delay was subtracted from the DUT TDT measurement. This is equivalent to shifting the edge of the measured waveform towards the reference plane. The forward transfer function of the transmission line can then be computed as: -jot H(s) = B(s)xe (4) where B(s) corresponds to the risetime degradation which can be computed as: L=5,10,20,40 b) Fig 2 Symmetric Stripline a) Cross Section b) Top View IV. Extraction of Transmission Line Parameters The TDR measurement was used to extract the characteristic impedance ZO(f) and the TDT measurement was used to extract the propagation constant df). Both these parameters are complex and frequency dependent for lossy transmission lines. In addition, neither of Using the extraction method discussed earlier, the impulse response B(s) in equation (5) can be computed. The accuracy of the computed impulse response is shown in Fig 3 where the DUT waveform has been reconstructed from the impulse response and the thru waveform and has been compared to measurements. Using equations (4) and (5), the frequency response of the transmission line has been computed. This can be used to compute the attenuation and phase constant of the transmission line as follows 1727

3 1 py) = --LH(s) 1 (7) where I is the length of the transmission line Approximated " " " " ' I Frequency m Hz x mil and 5.5mil Fig 3: Measured and approximated DUTKDT waveform Using the procedure described, the propagation constant was extracted for the IO", 20" and 40" long lines with line widths of 3.5mil and 5.5mil. The results are shown in Figs 4a and 4b. Fig 4a shows that the 5.5mil wide line has a smaller attenuation constant as compared to the 3.5mil wide. This is expected since the 5.5mil wide line has smaller loss. The 3.5mil wide line has a larger variation as compared to the 5.5mil wide which could be due to larger line width variations. The phase constant in Fig 4b varies linearly with frequency (no dispersion), which is expected from a low loss line. As seen in Fig 4b, the line width has little effect on the phase constant. Since the phase constant contributes to the delay, the time of flight delay is a function of only the material parameters (in this case the dielectric constant of FR4). B. Characteristic Impedance Measurement As in the TDT measurement, a short measurement has been used to set the reference plane for the TDR measurement. In the TDR measurement, the far end of the line was left unterminated. However, the time window was suitably chosen to eliminate the reflection from the Frequency in Hz Fig 4: a) Attenuation constant a(f) in nepershnch b) Phase constant p(f) in degreeshnch far end. In addition, a load calibration measurement was subtracted from the DUT TDR waveform, based on an error correction procedure. The thru waveform was used to de-embed the step source from the DUT TDR waveform. The procedure described in [2] was used to extract the frequency response using rational functions in the form: A4 ak s-sk k= 1 A(S) = - Xl 1728

4 Since, A(s) represents the reflection coefficient (S11) referenced to 50Q and the effect of the far end has been removed, the characteristic impedance ZO(f) of the transmission line can be extracted as follows [3]: 1 + A 0 = 50(1 (9) The accuracy of the approximation in equation (8) is shown in Fig 5 where the DUT TDR waveform has been reconstructed using the rational function and the thru waveform. The initial negative glitch is due to the capacitive discontinuity of the via which is included in the measurement. The approximated waveform has been used to smoothen the response (the DUT TDR waveform contains glitches due to line width variations, bends etc). However, if a more exact fit is desired, more pole-residue pairs can be used to approximate the waveform. 50 $ mil wide lot 01 ' _._.> Frq"@"q x 10' Zo(imag) x Jli-40' J13-40' J16-20' J19-lo' 002t / > C a p ow I / - I J13-40' J16-20' J19-lo' 4 w ' Fig 5: Approximated and measured DUT/ TDR waveform for the 3.5mil wide 40" long line Using equations (8) and (9), the complex frequency dependent characteristic impedance has been extracted, which are shown in Figs 6a and 6b. x 10- I -101 ' > Frequew x 10s (b) Fig 6: a) Real(Zo) Vs Frequency b) Imag(Zo) Vs Frequency C. Extraction of Transmission Line parameters The frequency dependent propagation constant y(9 and characteristic impedance Zo(f) uniquely determine the propagation and reflection characteristics of the lossy transmission line. The frequency dependent RLGC parameters of a low loss transmission line can be extracted from Zo and y using the equations:: G = wctan6 1729

5 V. Conclusion This paper discussed a method for extracting the frequency dependent parameters of transmission lines. These parameters become extremely critical for high speed signal propagation on printed circuit board interconnections. The novelty of the method was in the use of rational functions that provides a path for enabling spice simulation with the extracted data. References [l] Dylan F. Williams and Roger B. Marks, Accurate Transmission Line Characterization, IEEE Microwave Guided Wave Letters, Vol. 3, No. 8, pp , Aug [2]Sreemala Pannala and Madhavan Swaminathan, Extraction of S-Parameters from TDR/TDT Measurements using Rational Functions, / 54th Automatic RF Techniques Group (ARFTG) Conference Digest, pp , Atlanta, Dec [3] Woopoung Kim, Madhavan Swaminathan and Y. L. Li, Extraction of the frequency dependent characteristic impedance of Transmission Lines using TDR measurements, Proceedings of the Electronic Components and Technology Conference, Singapore, Dec