# Statements Relating AC Analysis

The small-signal frequency-domain analysis is a sequence of individual analyses at a set of discrete excitation frequencies. Since the excitation frequency is monotonically increased from the starting frequency to the stopping frequency, this sequence of analyses is usually called the "swept AC analysis", or "AC analysis with swept frequencies". The excitation frequency of the first analysis is set to "start_freq". In each subsequent analysis, the excitation frequency is increased according to the "sweep_type" and "n_pt" parameters. The sequence of analyses is stopped when the excitation frequency exceeds the parameter value of "stop_freq". At each of the excitation or analysis frequencies, periodic small-signal stimuli having the same frequency as the analysis frequency are applied to excite the system around its operating point or equilibrium. The response of the system at this analysis frequency is then measured. The analysis frequencies are defined through an analysis statement and the small-signal stimuli are defined through device statements. In addition, you have the option of analyzing the system in either the continuous domain or the discrete domain by using an option statement.

In this topic:

## .AC Analysis Statement

The .AC analysis statement instructs SIMPLIS to carry out the SIMPLIS-FX Small-Signal Frequency-Domain analysis. The format of the .AC statement is:

`.AC  sweep_type  n_pt  start_freq  stop_freq`
where
 .AC is the three-character keyword ".AC", standing for small-signal frequency-domain analysis. sweep_type is either the three-character keyword "DEC", the three-character keyword "OCT", or the three-character keyword "LIN". n_pt is a positive integer. If "sweep_type" is set to "DEC", the frequency of analysis will be swept in a logarithmic manner and n_pt represents the number of points per decade in the swept frequency. If "sweep_type" is set to "OCT", the frequency of analysis will be swept in a logarithmic manner and n_pt represents the number of points per octave in the swept frequency. If "sweep_type" is set to "LIN", the frequency of analysis is swept in a linear manner and n_pt represents the total number of points in the linear frequency sweep. If "sweep_type" is set to be "LIN", n_pt must be an integer larger than one. start_freq is a positive floating-point number representing the starting frequency of the sweep. stop_freq is a positive floating-point number representing the stopping frequency of the sweep.
The .AC statement can be specified in any one of the three formats shown. Just like any other analysis statement, the .AC statement can only appear within the scope of definition of the main circuit. There can be no more than one .AC statement in an input file. Since the SIMPLIS-FX Small-Signal Frequency-Domain analysis is specifically designed for the small-signal analysis of switching piecewise-linear systems around its periodic operating point, the periodic operating-point (POP) analysis must be carried out before the small-signal analysis can be applied. Therefore, the .POP statement must appear before the .AC statement in the input file. If both the time-domain transient analysis and the small-signal frequency-domain analysis are specified in an input file, the .AC analysis statement for the small-signal frequency-domain analysis must appear before the .TRAN analysis statement for the time-domain transient analysis.

## Option Statement Associated with AC Analysis

There is one option statement associated with the SIMPLIS-FX small-signal frequency-domain analysis. The format of this option statement is:

`.OPTIONS FREQ_DOMAIN=D`
where
 .OPTIONS is the eight-character keyword ".OPTIONS" indicating this is an option statement. FREQ_DOMAIN= is the 12-character keyword "FREQ_DOMAIN=" D is either the character 'S' indicating the continuous domain or the character 'Z' indicating the discrete domain.
By default, a frequency-domain analysis is carried out in the continuous domain. The statement:
`.OPTIONS FREQ_DOMAIN=Z`

will override the default and instruct SIMPLIS-FX to analyze the system using discrete domain techniques. If the continuous domain is chosen, the waveform of each small-signal stimulus will be a continuous sinusoidal function of the time variable. If the discrete domain is chosen, the waveform of each small-signal stimulus as a function of the time variable is equal to the result of applying the sample and hold to a continuous sinusoidal function of the time variable. See Synopsis of Small-Signal AC Analysis for a more detailed explanation of the difference between using the different domains in a small-signal frequency-domain signal analysis.

## Statement Defining a Small-Signal AC Source

A small-signal stimulus is defined via a small-signal AC voltage or current source. The formats for defining small-signal AC voltage and current sources are:

`Vname>  n+  n-  AC  amplitude  phase`
and
`Iname  n+  n-  AC  amplitude phase`
where
 V is the one-character element keyword "V" indicating a voltage source. I is the one-character element keyword "I" indicating a current source. name is the individual name of the device. n+ is the name of the positive node, and is a nonnegative integer. n- is the name of the negative node, and is a nonnegative integer. AC is the two-character keyword "AC" to signify that this is a small-signal AC source. amplitude is a positive floating-point number representing the amplitude of this small-signal AC source relative to any other specified small-signal AC sources. The specification of the amplitude parameter is optional. A default value of 1.0 (unit) will be used if no value is specified. phase is a floating-point number representing the relative phase of this small-signal AC source in degree. The specification of phase is optional. If the phase parameter is to be specified for a certain source, the amplitude parameter must also be specified. The default for phase is 0.0 degree.
Since device statements can appear within the scope of definition of any general circuit, the small-signal AC voltage/current sources can be defined in the main circuit as well as in any subcircuit. For a more detailed explanation of the "amplitude" and the "phase" parameters, see Synopsis of Small-Signal AC Analysis.