Simulation Setup

There are three main parameters to set when doing an HB simulation: Frequency, Order, MaxOrder. Additionally, two simulation setup parameters will be determined automatically (and in an optimal manner) by the simulator. These are Convergence mode and Solver. If convergence is achieved and accurate results are obtained, then you don't need to go further. If the circuit does not converge, see Solving Convergence Problems.

Setting Frequency

The Frequency parameter is found on the HB controller's Freq tab. It appears as Freq[i] on schematic, where i=1,...,number of tones (sources) in the circuit. For a single tone HB simulation, set the Frequency to the fundamental frequency of the source used in the circuit. For example, in a circuit with input source at 850 MHz, set Freq[1]=850 MHz.

When doing a multitone simulation, additional Frequencies need to be set on the controller corresponding to the fundamental frequencies of the additional sources. It is strongly recommended to set Freq[1] to the most nonlinear tone. The most nonlinear tone is typically the one with the largest power. For example, consider a two tone HB analysis to determine mixer conversion gain with an LO source at 1850 MHz, and an RF source at 2.1 GHz. Since the LO is the more nonlinear tone, it should be set to be the first fundamental, i.e., Freq[1]=1850 MHz, while the RF should be set to Freq[2]=2.1 GHz. Next consider a mixer intermodulation distortion analysis (same LO at 1850 MHz and RF at 2100 MHz). In this case, use a VAR component to define FrqSpacing=100k, and set the HB controller with Freq[1]=L0, Freq[2]=RF+FrqSpacing/2, Freq[3]=RF-FrqSpacing/2. An example of these circuits and simulations can be seen in Harmonic Balance for Mixers.

If the frequency of the input source is not the fundamental or a related harmonic of a Frequency parameter on the controller, then the frequency of the input source is not used in computing the steady state solution. For example, in a circuit with three sources (1 GHz, 900 MHz, and 940 MHz) in which only two of the three are specified on the HB controller (1 GHz and 900 MHz), the third source is turned off. When this occurs, the following warning message is generated:

Warning detected by HPEESOFSIM during HB analysis `HB1'. For source `SRC1', 
(1xfreq[3])=9.4e+08 is 4e+07 Hz away from the closest analysis frequency at 
9e+08. The maximum frequency difference for analysis time step is 900 Hz. 
This spectral component is turned off for this simulation.

Setting Order and MaxOrder

The Order parameter is found on the Freq tab, and it determines the number of harmonics used in the truncated Fourier series representation of the HB solution. The Order and Frequency parameters are set at the same time. The default value for Order is 3. For a single tone simulation, set the Order to the desired level of Fourier series truncation. The Order needs to be sufficiently large so that the HB simulator can compute its solution waveforms to an adequate degree of accuracy. For example, in the circuit with input source at 850 MHz and Order set to 3, the following three harmonics will be used in HB: 850 MHz, 1700 MHz, and 2550 MHz. However, three harmonics are sufficient only for mostly linear circuits generating sinusoidal-like signals. For mildly nonlinear circuits, the Order should be set to 7 or more. Highly nonlinear circuits with waveforms containing sharp edges and spikes will require many more harmonics (sometimes in the hundreds).

For multitone simulations, the Order needs to be specified for each tone. It is recommended to use a higher Order for the more nonlinear tones. For example, in the above mixer example, the Order for the LO tone should be at least 7, while the RF Order can be left at 3.

The parameter Maximum mixing order (MaxOrder on schematic), also found on the Freq tab, determines how many mixing products are to be included in a multitone simulation. A mixing term, or mixing product, is a combination of two or more fundamentals or their successive harmonics. Mixing products will occur when there are multiple sources in a circuit. Since the number of mixing terms can grow very large, it is limited in ADS by the following:

where k _j is the harmonic for the j ^th tone in the circuit. The Maximum mixing order can be set when there are two or more frequencies in the simulation. This parameter does not affect a single tone simulation, and is therefore disabled on the Freq tab. The table below gives a specific example with the first fundamental at 1.9 GHz with Order[1]=K ₁ =4, the second fundamental at 2.1 GHz with Order[2]=K ₂ =5, and Maximum mixing order=3. The DC term is always included as one of the simulation frequencies; however, it is not listed in the table.

This can also be represented in a plot of k ₂ vs. k ₁. Consider the same two-tone case as above with K ₁ =4 and K ₂ =5, and Maximum mixing order=3. The HB simulator uses a diamond truncation method to determine which spectral components it will retain and use for simulation. This can be seen in the following figure. Note that all of the points in the plot of k ₂ vs. k ₁ will be used in the simulation for those particular values of Order and Maximum mixing order. The dashed lines are there to emphasize the diamond shape.

If Maximum mixing order is 0 or 1, no mixing products are simulated. If Maximum mixing order is not given, then it will be set to the smallest fundamental order, e.g., a diamond truncation is used to determine the mixing products. Make certain that in a multi-tone simulation, the tones are not defined more than once. For example, a 1 GHz tone with 3 harmonics (Order set to 3) means that 2 GHz and 3 GHz are already defined. In a multi-tone environment, such as one with a 1 GHz tone and 200 MHz tone, each with Order set to 3 and Maximum mixing order set to 5, mixing products at 1.2 GHz, 1.4 GHz, and 1.6 GHz are already defined. None of these should be redefined as fundamental frequencies in the Harmonic Balance controller. When tones are redefined, the simulator still runs and gives a warning message in the status window:

More than one mixing term has landed on frequency *,

where * is the value of the mixed frequency.

Initial Guess Selection

By default, the Harmonic Balance simulator uses a DC solution as an initial guess when starting the simulation. However, a transient initial guess can provide a much better starting point for harmonic balance. This is especially true when simulating circuits that are highly nonlinear and contain sharp-edged waveforms (such as dividers). In this case, a transient simulation often provides a good initial guess for the starting point of harmonic balance. It is recommended to use a transient initial guess when simulating frequency dividers.

Automated TAHB

Transient assisted harmonic balance is automated and will be used if the simulator detects a divider in the circuit. By default, if the simulator does not detect a divider, then it will not use TAHB. It can also be turned on or off from the Initial Guess tab on the Harmonic Balance simulation controller. In this case, select the box labeled On, and the simulator will generate its own transient initial guess. The transient simulator will use intelligent defaults and determine a steady state solution as the initial guess for harmonic balance. It is not required to set any of the transient parameters on the Initial Guess tab. However, you may set the transient parameters only when TAHB is set to On. In that case, the settings can be activated from the Advanced Transient Settings dialog. Transient assisted harmonic balance can be turned off by selecting Off on the Initial Guess tab. For more details on setting the additional transient parameters, see Transient Assisted Harmonic Balance - TAHB.