## 4 Measurements  
On-wafer measurements were performed with a broadband VNA from 0.5 GHz to 110 GHz. One hundred micrometer (100 \(\upmu\)m) pitch wafer probes and a commercial impedance standard substrate (ISS) CS-5 (GGB industries, Inc.) were used. On CS-5, there are short, open match standards, and 50 \(\Omega\) lines of multiple lengths, required by multiline thru-reflect-line (MTRL) calibration [27]. The calibrations proposed in this work are compared with MTRL calibration in order to assess their accuracy. The line lengths are 200 \(\upmu\)m, 500 \(\upmu\)m, 550 \(\upmu\)m, 1000 \(\upmu\)m, 1500 \(\upmu\)m, and 6000 \(\upmu\)m. The on-wafer short standards are used as the short for the calibrations, but open is realized by lifting the wafer probes in air. The different match standards have DC resistances ranging from 12.5 \(\Omega\) to 100 \(\Omega\). An LRM calibration was performed with the 200 \(\upmu\)m line, open, and a pair of 50 \(\Omega\) loads. An LRMM calibration was performed with the 200 \(\upmu\)m line, open, and a 50 \(\Omega\) load at port 1 and a 100 \(\Omega\) load at port 2. An LRRM calibration was performed with the 200 \(\upmu\)m line, on-wafer short, open, and a 50 \(\Omega\) load at port 1. The reference plane for these calibrations is at the probe-tip.  
Since LRM and LRMM calibrations require known match standards, the match standards are first characterized using on-wafer MTRL. Figures 4 and 5 show the measured match impedances of the 50 \(\Omega\) and 100 \(\Omega\) loads, respectively.  
In Figures 4 and 5, the measured load impedances are fitted to a physical load model which takes into account the parasitic inductance and capacitance of shunt loads [26]. The close agreement between the measured (circles) and fitted (squares) values shows that the physical model is sufficient in describing the dispersion in the match impedances up to 110 GHz. The fitted match impedances are used as match definitions for LRM and LRMM calibrations. The triangles in Figure 4 indicate the extracted load impedances from LRRM calibrations. They also show a close match with the impedances from MTRL calibrations, which proves the validity of the proposed LRRM in terms of shunt load characterization.  
The LRM, LRMM, and LRRM calibrations are compared with on-wafer MTRL calibrations using the calibration comparison technique [28]. Calibration comparison is a known method for comparing two calibrations. The method calculates the maximum deviation in calibrated \(S\)-parameters (\(\max\mid\Delta\text{S}_{\text{i, j}}\mid\text{i}_{\text{, j=1 or 2}}\)) of an arbitrary passive DUT. The error boxes [\(T_{10}\)] and [\(T_{23}\)] are transformed into the cascade matrices defined in [6] and then compared with the error boxes from MTRL calibrations. The calibration comparison results of LRM and LRRM are shown in Figure 6a. The proposed LRM and LRRM calibrations show relatively low deviations from MTRL calibration, compared to the repeatability of MTRL calibration. Figure 6b shows the comparison between the LRMM, TRM, and MTRL calibrations. The proposed LRMM gives exactly the same calibration coefficients as the state-of-the-art TRM method [14], and shows small deviation from the reference MTRL. As a conclusion, LRM, LRMM, and LRRM all show good accuracies up to 110 GHz.  
Figure 4: Real (**a**) and imaginary (**b**) part of the 50 \(\Omega\) match impedance. “MTRL meas.” denotes the impedance measured with multiline thru-reflect-line (MTRL) calibration, “MTRL model” denotes the impedance fitted from “MTRL-meas.”, and “LRRM model” denotes the load impedance determined by LRRM calibration.  
Figure 5: Real (**a**) and imaginary (**b**) part of the 100 \(\Omega\) match impedance. “MTRL meas.” denotes the impedance measured with MTRL calibration, and “MTRL model” denotes the impedance fitted from “MTRL-meas.”