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Best Practices for Efficient and Effective Planar EM Simulation 17 www.cadence.com/go/awr Chapter 4: Simulation Best Practice Tip #7: When results from the AWR AXIEM simulator are used in nonlinear circuit simulations, make sure a DC simulation and enough harmonic frequency simulations are included in the answer. The AWR AXIEM simulator produces S-parameters, which can be viewed in a graph or used in a circuit simulation. The designer places the S-parameters into the schematic as a subcircuit, and the resulting circuit is then simulated using a circuit simulator, most typically harmonic balance (HB), although a time-domain simulator will have the same issues as HB. First, HB simulates at DC enabling the DC bias point for the circuit to be set. Second, HB simulates the circuit at the desired frequency using a Fourier series, which has harmonics in it. Both simulations need the S-parameter file values, in the first case at DC and in the second case at the harmonics of the fundamental frequency being simulated. Problems occur if the S-parameter file does not include these frequency points because S-parameters must be extrapolated down to DC and up to the highest harmonic, which can lead to inaccurate answers. The circuit may not bias properly, and the simulation may not even converge. This problem can be overcome by including a DC value for the S-parameter file and values up at the harmonic frequencies. The designer can add DC to the simulated points in the frequency control panel; the Add Single Point feature in the menu is used to add 0Hz. Similarly, the designer can add frequencies at a few of the harmonics. For example, if the designer is devel- oping an amplifier for 2.0 to 2.2GHz and is using five harmonics, a reasonable frequency range is to set frequencies of 0Hz, a sweep of frequencies from 2.0 to 2.2GHz, and the harmonic frequencies of 4GHz, 6GHz, 8GHz, and 10GHz—the higher frequencies do not usually need to be swept. The point is to give the circuit simulator enough frequency points that it can interpolate to obtain the necessary frequencies. The designer should check the passivity of the S-parameters because non-passive S-parameters can result in HB giving inaccurate answers, or in extreme cases, not even converging. Passivity issues can become more prevalent at the higher harmonic frequencies, where, for example the board thickness is becoming electrically large. The designer might want to enforce passivity for this case, although it should be used with caution. (Best Practice Tip #10 provides more details). Best Practice Tip #8: Understand how frequency interpolation works in the AWR AXIEM simulator. Advanced frequency sweeping (AFS) can be configured to reduce the number of required simulation frequencies while maintaining a specified accuracy over the frequency range. The AWR AXIEM simulator is usually set to run over a frequency range. The designer sets the number of frequencies so that the results can be accurately interpolated to any frequency in the specified range. S-parameters are plotted on graphs with straight-line interpolation between the points. Circuit simulators also interpolate between the frequency points in the S-parameter file; the default interpolation scheme is linear, which can be changed. Typically, enough frequency points are used in the simulation that interpolation between points is not noticed; the problem, however, is that if the software simulates many frequencies, it can take a long time to run. Therefore, it uses AFS, an approximate method wherein only a few of the frequencies requested are simulated and an interpolated answer is given for the others. The user can set an error tolerance for AFS, with the default being -30dB. The settings for AFS are under the AXIEM tab of the EM project options. AFS works by first having AWR AXIEM software simulate the lowest and highest frequencies in the range of frequencies requested. For example, if the designer requests a frequency range of 1 to 10GHz, with 0.1GHz steps (in other words, 99 frequencies), the software simulates at 1 and 10GHz. It then simulates the middle frequency, 5.5GHz, returning results at three frequencies, with the results at the remaining 96 frequencies interpolated using AFS. Two more frequencies are then simulated, and the five known results are now used to interpolate all the frequencies. The results are compared to the original interpolation using three computed frequencies. If all 99 frequency points for the two simulations differ by less than -30dB, the result is considered converged. Otherwise, a new simulation is run at the frequency point where the two results disagree by the largest amount. A new approximation is then generated from the six computed frequency points. This process of refinement is continued until the error criterion is met or all frequencies are simulated. The interpolated S-parameters are calculated by using a rational function pole-zero technique. In this way the properties of the S-parameters stay well behaved with reasonable numerical properties. This would not be the case if the S-parameters were simply fit to a polynomial, that would result in a numerically unstable procedure. Like all approximation methods, it is possible for AFS to fail. The two most difficult cases are when a large frequency range is modeled and when a high-Q resonance response is being modeled. The typical class of problems where a large frequency range is simulated is when the S-parameters are used in an HB simulation of a nonlinear circuit. Best Practice Tip #7 recom- mends that the S-parameter file include a DC simulation point and a few points at the harmonic frequencies being used by the HB simulator, which will result in a large frequency range for AFS to model. The settings for AFS allow it to be used only on

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