Deembeding of the Taper-fed CPW and Microstrip Lines Characteristic Impedance with Probe-tip Calibrations

Abstract

A procedure allowing systematic determination of the characteristic impedance of the taper-fed CPW and microstrip lines and deembedding the influence of the feeding discontinuities is presented. The procedure is based on the measurement technique of two different on-wafer line standards. An initial off-wafer LRM or TRL calibration with standard calibration substrate is assumed. The feeding structure consists of a coplanar pad configuration suited for probe-tip feeding and via-based or taper-based transitions to microstrip or CPW configurations, respectively. The procedure consists of two steps. In the first step the probe–tip discontinuity only is deembedded. For this purpose we use our new chain matrix formulated calibration comparison technique based on the measurements of two on-wafer CPW line standards of the same geometry as the feeding pads. Our onwafer CPW standards stay the same for all measured microstrip lines. This allows to perform only one probe-tip deembeding valid for all of the measured microstrip lines. The second step is deembeding of the CPW-microstrip line or CPW-taper-CPW transition and determination of the characteristic impedance of measured lines. The first novelty is the formulation of the whole extraction problem in terms of the ABCD chain matrix. It allows us to omit one of the limitations of the true traveling waves based S-matrix [3] asymmetry of the general CPW-microstrip line and CPWtaper-CPW transitions. This limitation is a difference between complex characteristic impedances of CPW and microstrip or different CPW lines. On the contrary, the symmetry of its admittance matrix or equivalently the determinant AD-BC of its chain matrix is not influenced by this effect. The next novelty lies in the modeling of these transitions. We assume that it can be approximated by a symmetric model. Its chain matrix fulfills the condition A=D. This, in turn, allows to extract the characteristic impedance of the lines based on two line measurements without using of any fixed transition model. Such a formulation takes automatically into consideration even a distributed nature of the transition, which can be of importance at mm-wave frequencies. The complex propagation constants and characteristic impedance of wide CPW lines on fused silica substrate exceeding the pitch of the probes have been determined from the measurements. We have also analyzed the extraction procedure of different CPWmicrostrip geometries on GaAs and MCM-D substrates up to 70GHz. We have compared different transition models: simple series inductance, cascade of parallel capacitance and series inductance, cascade of series inductance and parallel capacitance and our box model with its chain matrix fulfilling the condition A=D. The latter model outperforms the others, esp. at higher mm-wave frequencies. We have also investigated different topologies of the transition for MCM-D to find the optimum one. The best extraction accuracy can be achieved if the microstrip GND extends under the CPW feeding part. The equivalent model elements are extracted for every frequency point. Thus their frequency behavior can be investigated and the possible validity of the model (constant equivalent element values) proved. I. General Waveguide Theory In the course of the paper reading we will always refer to the definition of S-matrix based on general waveguide theory (mentioned in the abstract), namely true traveling or pseudowaves S-matrix. More detailed information on the definition and properties of these intensities can be found in our second paper, which is to be published in the SPI 2002 proceedings (“ S Matrix versus ABCD Chain Matrix Formulation in the Probe-tip Calibrations“ ) or in [3]. II. Existing methods versus our problem formulation The general two-port measurement problem is shown in Fig.1. Losses and phase delays caused by the connectors, cables, transitions and switching as well as isolation errors of the VNA have been accounted for by the initial off-wafer calibration. Also probe-tip discontinuities have already been deembedded in the first step of the procedure in a way described in the abstract. Hence the error boxes on both sides of the DUT represent CPW-microstrip line or CPW-taperCPW transition and are equal. Such that only error box denoted as RA is to be determined (measurement problem is symmetric).