## 2 Nonlinear Switch Characterization
### Measurements  
Extensive measurements of S- and X-parameters of diode MA4 AGBLP912 were performed in the 1-50 GHz range, using different biasing levels. Note that in the case of the PIN diode, the biasing current \(IDC_{1}\) is equivalent to the \(DCS_{q}\) term (part of the LSOPS) in the X-parameters notation. Measurements of \(S_{11}\) from 45 MHz to 50 GHz are shown in Figure 3. From this figure, it is clear that in the forward bias condition varying DC level has an important impact on the diode behavior. Likewise, it can be observed that for biasing currents higher than 15 mA the diode achieves a stable behavior. Therefore, \(0,1\) and 20 mA bias are taken as representative of the diode \"OFF\", \"NL\" (nonlinear) and \"ON\" states. Measurement  
Figure 2: X-parameters measurement setup. results are validated against S-parameter files provided by the manufacturer (up to 30 GHz) ascertaining a very good agreement. One-port X-parameter measurements were carried out at different biasing levels \(I_{b}=\{0,1,2,5,10,20\}\) mA. For each of these DCS a power-frequency grid for \(|A_{11}|\) is defined, varying input power in the range \(P_{in}=\{-10,-6,-2,2,6,10\}\) dBm and sweeping fundamental frequency from 1 to 16 GHz with \(n_{f}=16\) points, considering up to the third harmonic (total frequency expanding from 1 to 48 GHz). That is, in total there are 6 sets of measurements each with a total of 3 X parameters over a \(6\times 16\times 3\) sampling grid. In contrast, a conventional S-parameter measurement would only contain 6 sets of \(n_{f}\) points each. To ease the comparison of X parameters for the different diode biasing levels, slices of \(X_{1m}^{(FB)}\), \(X_{11,1n}^{(S)}\), and \(X_{11,1n}^{(T)}\) can be taken either at fixed frequencies or input powers of the fundamental \(A_{11}\). For example, slices representing the variation with input power at a fundamental frequency \(f_{1}=5\) GHz are illustrated in Figure 4 for the diode \"ON\" and \"OFF\" states. Valuable information about the nonlinearity of the DUT can be extracted from the variation with RFS power of the large signal response \(X_{1m}^{(FB)}\), represented in Figure 4a, where it can be observed that for the \"OFF\" and \"ON\" states the fundamental and the harmonic tones linearly increase with input power. This figure also demonstrates that the diode is not driven into a high nonlinearity region for the powers used in the model extraction, as in both cases the second and third harmonics are at least 40 dB below the fundamental level. Besides, the \(X_{1m}^{(FB)}\) terms allow an estimation of the Third Harmonic Intercept Point (IP3) that is \(\sim\)35 dBm in the case of the \"OFF\" state, and \(\sim\)43 dBm for the \"ON\" state. Another common approach to estimate the nonlinearity of the DUT is by defining the nonlinear transition as the input power resulting in the 1 dB CP of the reflected fundamental wave; this value can be extracted directly from Figure 4a or by representing the large signal reflection coefficient \(X_{11,11}^{(S)}\equiv X_{11}^{(FB)}/|A_{11}|\). In the diode case, it is apparent that for the input powers used, compression does not occur for the \"OFF\" nor the \"ON\" states. In contrast, for the case of the \"NL\" state, 1 dB CP occurs at around 6 dBm. On the other hand, the variation with input power of the set of functions \(X_{11,1n}^{(S)}\) illustrated in Figure 4b and \(X_{11,1n}^{(T)}\) illustrated in Figure 4c, indicate a small contribution of the reflected second and third harmonics to the total response at fundamental for both the \"OFF\" and \"ON\" diode states. Figure 3: Measured S-parameter (de-embedded) vs. Bias. The X parameters convergence to the S parameters in the small-signal regime is verified for both the \"ON\" and \"OFF\" states. Direct S-parameter measurements are compared to X-parameter reduced to S parameters using circuit simulation in Keysight ADS.