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### Design Notes

**NDF Measurement vs. K and B1 **

**(from 1994 workshop by Platzker and Struble)**

This project demonstrates the use of the NDF measurement, and its effectiveness at detecting instability when stability factors K and B1 do not. The circuit is a simple one that was used in reference [1], see below.

__Overview__

The circuit has one real and 2 complex parameters (R1, Ys, and Y1), and four different sets of parameter values are simulated (rows in "Table 1" in [1]). The circuit is unstable for the first 3 combinations of parameter values, and stable for the last one. However, K falsely indicates stability in the first case, and instability in the last. Please refer to [1] for a detailed discussion.

__Schematic and Data File__

"Table_1" text data file contains the values from "Table 1" in [1].

"PWS1" schematic is the same as the circuit in "Figure 4" of [1]. Equations are used to calculate and set the values of the 3 parameters by "pulling" values from the text data file. For parallel conductance and inductance pairs in the table, the YL(x) function converts the specified inductance value to the appropriate frequency dependent imaginary conductance, which is then added to the specified real conductance. The row index is swept from 1 to 4, so all four simulations are performed in sequence.

After simulation, open the tuner. One slider will choose the set of parameter values (row) for the NDF measurements in the polar and rectangular graphs ("NDF Polar..." and "NDF AngU..."). The other slider will choose the row for the K and B1 measurements.

__Simulation Plots__

"NDF Polar Tune to Select Row" graph shows the NDF measurement for positive frequencies (corresponds to figures 6, 9, and 10 in [1]). After simulation, use the tuner to select the combination of parameter values (the row in Table 1 in [1]).

"NDF AngU Tune to Select Row" graph shows the unwrapped phase of NDF, which is an easy way to monitor encirclements of the origin. The same tuner bar as for "NDF Polar..." will select the row for this measurement.

"K and G11 Row 1" and "K and G11 Row 2" correspond to figures 5 and 7 in [1].

"K and B1 Tune to Select Row" shows the more conventional stability measurements. A different tuner bar is used to select the row for these measurements.

[1] From "Rigorous Determination of the Stability of linear N-Node Circuits from Network Determinant and the Appropriate Role of the Stability Factor K of Their Reduced Two-Ports" by Aryeh Platzker and Wayne Struble, Raytheon Co. Research Div.. 131 Spring Street, Lexington, MA 02173 (NDF Platzker stabWorkshop 1994.pdf)