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# HP ADS SIMULATION EXAMPLE – Basic Harmonic Balance Simulation for Large Signal Steady State AC Simulation

HP ADS SIMULATION EXAMPLE – Basic Harmonic Balance Simulation for Large Signal Steady State AC Simulation.

Background:

• Harmonic Balance (HB) simulation is used to find the steady state response of a circuit, which contains nonlinear components. The basic HB analysis is usually applied to a single periodic source. The periodic source can be sinusoidal or non-sinusoidal.
• The HB method works by assuming the steady state response of a circuit being driven by a periodic source is also periodic. Fourier series can represent the periodic voltages and currents in the circuit, i.e. as a summation of harmonics.
• Each voltage and current harmonic in the circuit must fulfill the Kirchoff Voltage and Current Laws.
• The HB method works for a circuit that can be separated into linear and nonlinear portion.
• An error function for the circuit is obtained using circuit laws.
• Initial solution is proposed for the harmonics of voltage or current of the linear network. The voltage and current of the nonlinear portion is unknown.
• The frequency domain representation is then converted to time domain, and the nonlinear voltage or current values for a nonlinear component is obtained from the time domain equation.
• The time domain current and voltage of the nonlinear portion are than converted into the respective harmonics. Now all the voltage and current harmonics of the circuit are available, and these are fed into the error function.
• If the error function value is larger than the threshold value, iterative methods such as conjugate gradient or Newton-Raphson methods are used to find the successive approximation voltage and current harmonics. The cycle is repeated until the error function is less than the threshold value.

Figure 1 – The basic schematic. This is a CE amplifier operating under large signal condition (notice the source voltage level is 0.5Vpp).

The Simulated Data:

Figure 2 – The magnitude of the output voltage harmonics at the load.

Figure 3 - The phase of the output voltage harmonics at the load.

# Reference

You can find out more about the Harmonic Balance method from this classic book:

S.A. Maas, “Nonlinear microwave circuits”, IEEE Press, 1997.

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May 2004 F. Kung