Harmonic Balance (HB) Simulation - Chapter 3

Chapter 3

Harmonic Balance (HB) Simulation

PathWave Advanced Design System (ADS)

Harmonic balance basics

Harmonic balance is a frequency-domain analysis technique for simulating distortion in nonlinear circuits and systems. It is well-suited for simulating analog RF and microwave problems since these are most naturally handled in the frequency domain. You can analyze power amplifiers, frequency multipliers, mixers, modulators, and many more designs under large-signal sinusoidal drive.

Harmonic balance simulation enables the multi-tone simulation of circuits that exhibit inter-modulation frequency conversion. This includes frequency conversion between harmonics. Not only can the circuit itself produce harmonics, but each signal source (stimulus) can also produce harmonics or small-signal sidebands. The stimulus can consist of up to 12 non-harmonically related sources. The total number of frequencies in the system is limited only by such practical considerations as memory, swap space, and simulation speed.

The harmonic balance method is iterative. It is based on the assumption that for a given sinusoidal excitation there exist steady-state solutions that can be approximated to satisfactory accuracy by means of a finite Fourier series. Consequently, the circuit node voltages take on a set of amplitudes and phases for all frequency components. The currents flowing from nodes into linear elements, including all distributed elements, are calculated by means of a straightforward frequency-domain linear analysis. Currents from nodes into nonlinear elements are calculated in the time-domain. Generalized Fourier analysis is used to transform from the time-domain to the frequency-domain.

The Harmonic Balance solution is approximated by truncated Fourier series and this method is inherently incapable of representing transient behavior. The time-derivative can be computed exactly with boundary conditions, v(0)=v(t), automatically satisfied for all iterations.

The truncated Fourier approximation + N circuit equations results in a residual function that is minimized.

N x M nonlinear algebraic equations are solved for the Fourier coefficients using Newton’s method and the inner linear problem is solved by:

• Direct method (Gaussian elimination) for small problems.

• Krylov-subspace method (e.g. GMRES) for larger problems.

Nonlinear devices (transistors, diodes, etc.) in Harmonic Balance are evaluated (sampled) in the time- domain and converted to frequency-domain via the FFT.

For a successful HB analysis

1. Add the Harmonic Balance simulation component to the schematic and double-click to edit it. Fill in the fields under the Freq tab.

• Enter at least one fundamental frequency and the number (order) of harmonics to be considered in the simulation.
• Make sure the frequency definitions are established for all of the fundamentals of interest in a design. For example, mixers should include definitions for RF and LO frequencies.
• If more than one fundamental is entered, set the maximum mixing order. This limits the number of mixing products to be considered in the simulation. For more information on this parameter, see “Harmonics and Maximum Mixing Order” section under PathWave Advanced Design System (ADS) HB Simulation documentation.

2. You can use previous simulation solutions to speed the simulation process. For more information, see “Reusing Simulation Solutions” under PathWave ADS documentation of Harmonic Balance.

3. You can perform budget calculations as part of the simulation. For information on budget analysis, see the chapter “Using Circuit Simulators for RF System Analysis” in the Using Circuit Simulators documentation.

4. You can perform small-signal analysis. Enable the Small-signal option and fill in the fields under the Small-Sig tab. For details, see Harmonic Balance for Mixers.

5. You can perform nonlinear noise analysis. Select the Noise tab, enable the Nonlinear noise option, and fill in the fields in the Noise (1) and Noise (2) dialog boxes.

6. If your design includes NoiseCon components, select the Noise tab, enable the NoiseCons option and fill in the fields.

7. If your design includes an OscPort component, enable Oscillator and fill in the fields under the Osc tab. Harmonic Balance for Oscillator Simulation focuses specifically on simulating oscillator designs.