2.3         Circular waveguide discontinuity

After loading (File-Open) the ..Various/Cwgd/cwgd.pro file into the QW-Editor, we obtain the views of the circular waveguide discontinuity, as shown in Fig. 2.3-1. Pressing the Start  button in the Simulation tab, exports the data, opens QW‑Simulator, and starts the FDTD analysis. Successive operations of the software are reported in the Simulator Log window, as shown in Fig. 2.3-2.

Fig. 2.3-1 A view of the cwgd.pro example in QW-Editor.

Invoke Results window with S-parameters results and power balance in Cartesian coordinates by pressing  button in the Results tab of QW-Simulator. The window will look as in Fig. 2.3-3, with two curves displayed: magnitudes of the reflection coefficient |S11| and power balance PowSK1.

Switching to extended results (by pressing Extended  button inResults tab) adds six curves (phase of propagation constants and absolute value and phase of wave impedance) to the Curves list. Colours and styles of lines and cursors are modified in Edit Line dialogue.

There are three ways of snapping the results specifically at iteration 10000, as in Fig. 2.3‑3:

§  Invoke Suspend from Run tab of QW-Simulator at an earlier stage, then progress the simulation manually by Step  button from Run tab of QW-Simulator. At iteration 10000, invoke Results window or (if the window is already open) refresh the results display by pressing space on keyboard.

§  If the simulation has run beyond 10000 iterations, invoke Stop  in Run tab of QW-Simulator. Invoke Breakpoints dialogue using  button in Run tab, and Add the Suspend breakpoint from the list for Iteration set as 10000. Press Start  button in Run tab. The simulation will run and automatically suspend at iteration 10000, at which point Results window for S-parameters results may be invoked. It is also possible to configure both Suspend and View S Results breakpoints, so that the window will automatically open.

§  From QW-Editor, launch QW‑Simulator using Run  button in Simulation tab. Invoke Breakpoints dialogue and proceed as in the previous bullet case.

Fig. 2.3-2 Simulator Log of QW-Simulator for cwgd example.

Power balance is a way of checking the convergence of calculations. For this lossless circuit, it should stabilise to the flat value of unity since it is defined as:

Pow.Sk1= sqrt[(S₁₁)²+(S₂₁)²+..+(S_N1)²].

In Fig. 2.3-3 the input and output power have been balanced within 0.01% at 20 GHz. Power balance is defined differently with Extended option off and on. For more information regarding power balance calculation refer to Power Balance.

Fig. 2.3-3 Reflection coefficient and power balance of cwgd circuit after 10000 iterations.

Note that the same result as obtained through Power balance option can be produced more laboriously via the Config dialogue. Fig. 2.3-4 shows a window with four operations producing the following curves: square of absolute value of reflection coefficient, square of absolute value of transmission coefficient, their sum, and a square root of this sum. The last curve is equivalent to power balance Pow.Sk1.

Fig. 2.3-4 Customised display of S-parameter results of cwgd circuit after 10000 iterations: squared reflection, squared transmission, their sum, and a square root of this sum.

Fig. 2.3-5 Reflection coefficient of cwgd circuit after 10000 iterations calculated with corrections for imperfect output absorbing boundary (green), and without this correction (blue).

Note that the cwgd circuit has been declared as reciprocal in QW-Editor. Therefore the reflection coefficient at the input port has been corrected for reflections at the output, due to imperfect absorbing boundaries (for more information regarding the applied correction refer to S-parameters). To verify the importance of such corrections, save current simulation results (options available in Export tab of Results window), stop the simulation (Stop button in Run tab), return to QW-Editor (File-Exit), open the S-Parameters dialogue (S button in Simulation tab) and uncheck the reciprocal field, press OK, and launch a new simulation. Fig. 2.3-5 compares the amplitude of S₁₁ produced by the previous and current experiment. We can see discrepancies at lower frequencies. This is because the absorbing boundaries have been optimised for 20 GHz (by the setting of effective permittivity to 0.6063 in the Edit Transmission Line Port dialogue of QW‑Editor), and the effects of dispersion are most pronounced near cutoff.

Note that the S-parameters of the cwgd example have been extracted with excitation from one port, so we obtained six characteristics: S₁₁ and S₂₁ amplitude and phase, and propagation constant amplitudes at the input and output waveguide. The set of results can be extended to phases of the propagation constants and amplitudes and phases of normalised port impedances via Extended button () in Results window for S-parameters results.

To produce the full S-matrix, we should use the Smn post-processing with excitation from both ports. We stop the simulation, return to QW-Editor, open the S-Parameters dialogue, select Smn at reference planes, set Iterations per port to 10000, press OK, and launch a new simulation.

Successive operations of the software are reported in the Simulator Log window of Fig. 2.3-6. After calculating the templates, QW-Simulator applies the excitation for 10000 iterations to the first port and extracts S₁₁ and S₂₁ as previously; then applies the excitation for 10000 iterations to the second port and analogously extracts S₂₂ and S₁₂; then combines the two sets of results, and displays the final characteristics.

Note that now both reflection and transmission coefficients are compensated for imperfect absorbing boundaries at both ports. Therefore, as shown in Fig. 2.3-7, near cutoff there is a slight discrepancy between the amplitudes of S₂₁ produced by Smn and Sk1 post-processing.

It is also possible to run the Smn post-processing without the iteration limit. For that purpose, in S-Parameters dialogue of QW-Editor, the Multi simulator option instead of Sequential should be chosen. For more information regarding Smn regime of S-parameters calculation refer to S-parameters.

Fig. 2.3-6 Simulator Log of QW-Simulator for modified cwgd example with Smn post-processing.

Fig. 2.3-7 Transmission coefficient of cwgd circuit, calculated with Smn (blue) and Sk1 (green) post-processing.