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       Algorithm for Single-Tone Y-parameters Evaluation of Nonlinear Systems           

Algorithm for Single-Tone Y-parameters Evaluation of Nonlinear Systems

For single-tone bandpass analysis, it is assumed that a nonlinear element’s measurements are obtained when both the source and load have a 50 termination and the input is a bandpass single-tone signal. The measurements obtained are directly related to the large signal S-parameters of the two-port nonlinear element and the power available at the input and output ports.

For a given single-tone input, we can refer to large signal S-parameters as the operating point of the nonlinear two-port element when operating independently and terminated in 50. One would certainly expect this operating point to change when this nonlinear element is embedded in a nonlinear topology system (as in Figure 1) composed of linear and nonlinear components.

The new operating point (i.e., large-signal S-parameters) is determined for each nonlinear element using an iterative algorithm where the levels of the incident powers at both ports are interpolated iteratively until the algorithm converges to the actual operating point. This nonlinear frequency domain iterative algorithm accounts for all nonlinearities and inter-stage mismatches in the system.

For the multi-channel nonlinear topology in Figure 1, it is always assumed that parallel nonlinear channels connected to the same linear electrical subsystem are not coupled (i.e., non-interacting). This, in simple terms, implies that signals traveling in one nonlinear path do not spill over into the other nonlinear path (by virtue of the S-parameters describing the linear electrical subsystem).

This effectively implies that the signals in nonlinear channels are not coupled, and as a result, the impedances Zs_n, Zin_n, Zout_n, and Zl_n for the n^th nonlinear element () in Figure 1 are well defined. With that important assumption, the iterative algorithm used for evaluating the operating point for each nonlinear element proceeds as follows (refer to Figure 1):

1. Assume an initial guess of for the first iteration () for the n^th nonlinear element ().

2. Calculate the power-dependent S-parameters for the n^th nonlinear element () at the k^th iteration (). For the first iteration (), this would basically yield the n^th nonlinear element small signal S-parameters since the initial estimate for the incident powers is zero.

3. Calculate the entire system’s Y matrix, the impedances shown in the above figure Zs_n(k), Zin_n(k), Zout_n(k), and Zl_n(k), and the nodal voltages at the input and output ports of the n^th nonlinear element at the k^th iteration.

4. Recalculate the incident powers at each port with () and () according to

P1_n(k + 1) = The power available at the input port of the n^th nonlinear element at the k^th iteration when the output port is terminated in Zl_n(k).

and

P2_n(k + 1) = The power available at the output port of the n^th nonlinear element at the k^th iteration when the input port is terminated in Zs_n(k).

5. Form the error function

The algorithm is assumed convergent if the condition is met. If this convergence condition is not satisfied, steps 2-5 above are repeated until the algorithm converges. If the algorithm fails to converge after 30 iterations, an error in analysis message will be displayed.

Upon completion of the fundamental analysis discussed above, the measurements for single-tone frequency domain analysis may be obtained in the Sweep, Budget, Spectral and Time domains. These domains are discussed next.

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