Application of an NVNA-Based System and Load-Independent $X$-Parameters in Analytical Circuit Design Assisted by an Experimental Search Algorithm

Design of injection‐locked oscillator circuits using an HBT X‐parameters™‐based model

“…In [5] the optimum load impedance for maximum output power for our HBT was calculated to be Z ref = 34 + 9.6 j , and a corresponding X‐parameters model was extracted at Z ref , by using a mixed passive–active load‐pull LSNA‐based measurement system. As demonstrated in previous papers by the authors [4, 5–14, 15], the model is able to correctly interpolate and extrapolate at other (close) output fundamental impedances around Z ref . This is very important for oscillator design, since depending on the design or the targeted figures of merit the optimum output impedance will change.…”

“…1 the Smith Chart region, which is covered by the load‐pull extraction procedure performed for both models, is shown. Moreover, the simulated maximum power contours at 1 dB compression (obtained from a non‐linear table‐based model also extracted by the authors [16], and similar to the measured ones [15]) are shown. It can be seen that there is a large Smith Chart region in which differences in power are minimum.…”

“…This optimum impedance may change depending on the compression level we choose, as described in [5]. To obtain Z ref and hence, an accurate X‐parameters model around that impedance termination, we used the measurement‐based search algorithm described in [14, 15], which couples X‐parameters model extraction from measurements with analytical expressions based on X‐parameters to predict power load‐pull contours. In fact, we take advantage of the accuracy of the X‐parameters measurements to predict load‐pull contours to quickly locate the appropriate oscillator impedance design space on the Smith Chart, hence, speeding up the design.…”

“…3 shows its flowchart) can be briefly described as follows: Step 1: Selection of a potentially unstable biased transistor able to provide the desired oscillation frequency and output RF power compatible with the specifications of the oscillator circuit. Step 2: Finding the output impedance space. Selection of the appropriate transistor terminating (output reference) impedance, Z ref , using the search iterative process described in [14], and experimentally validated in [15]. This impedance value is obtained in this procedure using measured X‐parameters and load‐pull power contours analytically computed from those measurements. Step 3: Extracting the behavioural model.…”

“…Step 2: Finding the output impedance space. Selection of the appropriate transistor terminating (output reference) impedance, Z ref , using the search iterative process described in [14], and experimentally validated in [15]. This impedance value is obtained in this procedure using measured X‐parameters and load‐pull power contours analytically computed from those measurements.…”