Harmonic Balance Simulations and Load Lines

[fourierpwn]

Hi all,

I've been doing some reading about large signal stability analysis where the traditional methods make use of a small current perturbation injected at a given node of a circuit. Then a harmonic balance (HB) simulation is performed with the frequency of the current source being swept in order to obtain the frequency response of the circuit, then through differing methods the transfer function is obtained. From here it's simple stability theory by observing the pole-zero plot to determine any positive real poles (instabilities).

For a given power amplifier, you have a load line (DC or dynamic, doesn't matter) where the DC bias of the device is being swung around. HB simulations are a periodic steady state simulation, so how can this be used to ensure stability at all possible DC bias points of operation? Am I missing something here?

[David Hess]

The stability test is run at selected operating points with enough coverage that the worse case is revealed.

In linear circuits, transconductance changes with collector/drain current which typically leads to problems at low currents where phase margin is reduced.  Switching power supplies have problems in discontinuous conduction mode where gain within the loop varies with output.

[fourierpwn]

The stability test is run at selected operating points with enough coverage that the worse case is revealed.

I'm not sure what you mean by "selected operating points".

In linear circuits...

This is non-linear stability analysis.

How can a steady state (HB) simulation be used for non-linear (transient) analysis like the literature suggests?

[David Hess]

The stability test is run at selected operating points with enough coverage that the worse case is revealed.

I'm not sure what you mean by "selected operating points".

When you sweep the DC operating point (DC bias), then you are selecting the operating point.

In linear circuits...

This is non-linear stability analysis.

How can a steady state (HB) simulation be used for non-linear (transient) analysis like the literature suggests?

I just used that as an example.  Non-linear transient analysis is a large signal phenomena so the stimulus is larger.

[fourierpwn]

Sure, running the simulation at different DC operating points is needed for complete analysis, however, each DC operating point will produce a different load line. For the case of a PA, the device will be "taken" at any given point along the load line (red or blue curve below). Therefore, to ensure complete stability, one must cover all load line states.



The non-linear stability analysis methods state that the response is linearised about the large-signal (HB) periodic steady state (PSS) response. The literature states that the HB simulation takes into account all the various states along the load line (see below). How it does this is one of my questions. The follow figure illustrates all possible load line states used in the PSS analysis.



This is all fine, though the pole-zero identification method used in non-linear stability analysis determines the closed-loop transfer function of the circuit. How can this be achieved when you have multiple load line states, as shown above. Is there not a separate transfer function for each state along the load line?