Editor's Note: This post includes excerpts from a new white paper from AWR Corp. Follow this link to download the entire paper.
Harmonic balance (hB) analysis is a method used to calculate the nonlinear, steady-state frequency response of electrical circuits. It is extremely well-suited for designs in which transient simulation methods prove acceptable, such as dispersive transmission lines in which circuit time constants are large compared to the period of the simulation frequency, as well as for circuits that have a large number of reactive components. In particular, harmonic balance analysis works extremely well for microwave circuits that are excited with sinusoidal signals, such as mixers and power amplifiers...
The limitation of traditional harmonic balance analysis occurs when it is used to solve large circuits with many different signal sources because it requires long computational times and large amounts of computer memory. To make harmonic balance analysis viable when analyzing such circuits, AWR has developed a multi-rate harmonic balance (MRhB) technology within its APlAc family of harmonic balance and time-domain simulators. MRhB overcomes the aforementioned limitations, significantly reducing the solution time as well as the computer memory required when applied to frequency-rich nonlinear systems that have multiple signal sources. The capabilities provided with MRhB make it possible to solve entire complex subsystems such as mobile phone transceivers in a practical amount of time.
This white paper traces the use of harmonic balance in solving microwave problems, describes MRhB technology, and provides examples of its effectiveness when compared with traditional harmonic balance simulators...
An innovative new approach: MRhB
To understand the sea change enabled by MRhB, it is important to remember its core concept: that operational blocks such as mixers, filters, and amplifiers in an RF system modify the frequency content. As traditional harmonic balance techniques assume that the relevant frequency content will be the same at every part (or block) in the circuit, it is essentially "out of sync" with how the circuit actually functions. Rather than perpetuating this concept, MRhB enables the designer to allow different parts of the circuit to have different dominating frequencies, and takes into consideration that some frequencies are important to solve while others are not. This intelligent, frequency-selective technique makes it possible to solve very complex circuits such as receivers with multiple stages of downconversion, multi-band power amplifiers, and complex high- frequency digital designs, an order of magnitude faster than with traditional harmonic balance.
MRhB dynamically forms its equations to solve for the multi-tone, multi- harmonic content of the circuit, adding the contribution of each element (block) only at the desired frequencies, which dramatically reduces the number of equations that must be solved.
The analysis information is transferred from one element (block) to another via the shared frequencies, as illustrated in the simple example in Figure 1 in which a circuit has been divided into two blocks, each with single-tone frequency set. The first part (the red block) has eight harmonics and the second one (the blue block) has four.
This simple, three-node circuit has two blocks with different frequency settings, both of which are single tone. Block 1 (red) has eight harmonics and Block 2 (blue) has four.
Communication between these two circuits occurs via the five frequencies they share, DC, and four harmonics. The first part is solved at all nine frequencies, which actually makes the results more accurate because of the greater number of harmonics.
While the solution of such simple circuits generally achieves little by reducing frequency content at some parts of the circuit, many circuits require one of their nonlinear parts to be simulated more accurately. MRhB does not force this local accuracy requirement to affect the simulation of other parts of the circuit, so if a frequency divider requires more than 2,000 harmonics for a single-tone analysis, it can be simulated locally with a large single-tone frequency set without detrimentally impacting the two-tone frequency set used in the same simulation for the mixer.
In short, MRhB presumes that by intelligently addressing the fact that dominating frequencies differ in the various parts of a circuit, it is possible to realize more efficient, yet highly accurate harmonic balance analysis of the entire circuit. This remarkable feat is accomplished while at the same time consuming less memory and less simulation time than traditional harmonic balance techniques.
Follow this link
to download the entire paper.