Example 4.1: Harmonic Balance simulation of the test circuit

The same test set-up as in the previous example is now simulated using HB. Obtaining a result for this circuit is trivial for HB: there is no feedback in the circuit, so no non-linear optimisation steps are required to obtain the steady-state response. The static non-linear part of the circuit is evaluated in the time-domain and the obtained spectrum is passed through the elliptic filter by a simple multiplication in the frequency domain. The obtained solution will therefore be exact when the correct frequency grid is provided to the HB simulation.

The circuit is unchanged, so the same $\aleph=12$ is used as before in the transient simulation. Because the used multisine is a bandpass multisine which excites $k_{\mathrm{tones}}\!=\!41$ tones around $10\mathrm{GHz}$ which are spaced $5\mathrm{MHz}$ apart, the HB simulator is given two frequencies $f_{\mathrm{res}}=5\mathrm{MHz}$ and $f_{\mathrm{center}}=10\mathrm{GHz}$ with orders $O_{ f_{\mathrm{res}}}=252$ and $O_{f_{\mathrm{center}}}=12$ respectively. The maximum mixing order is set to $O_{ f_{\mathrm{res}}}$. This results in a spectrum that consists of $6157$ frequencies. The obtained spectrum for the output of the non-linear block is shown below:

Figure 4.3 Full output spectrum of the Harmonic Balance simulation

Note that the numeric noise floor in the HB simulations in ADS lies considerably lower than in the transient simulation. To be completely correct, a higher $\aleph$ should be used in this simulation, but the obtained error in this simulation is already so low that the added accuracy will be negligible. The spectra at the input and output of the elliptic filter, zoomed in around $f_{\mathrm{center}}$ are shown below:

Figure 4.4 Input output spectrum in the HB simulation

Again, these spectra are used to estimate the FRF of the elliptic filter. The obtained result is shown below

Figure 4.5 Estimated frequency response of the filter

The FRF of the filter obtained with the HB coincides perfectly with the FRF obtained with an AC simulation. This is as expected, because the linear parts in the circuit are evaluated in the frequency domain during the HB simulation.