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##

`.ac` Line

The ac small-signal portion of *WRspice* computes the ac output
variables as a function of frequency. The program first computes the
dc operating point of the circuit and determines linearized,
small-signal models for all of the nonlinear devices in the circuit.
The resultant linear circuit is then analyzed over a user-specified
range of frequencies. The desired output of an ac small-signal
analysis is usually a transfer function (voltage gain, transimpedance,
etc). If the circuit has only one ac input, it is convenient to set
that input to unity and zero phase, so that output variables have the
same value as the transfer function of the output variable with
respect to the input.

- General Form:

`.ac dec|oct|lin `*np fstart fstop* [dc|
sweep *args*]

- Examples:

`.ac dec 10 1 10k
`

.ac dec 10 1k 100meg

.ac lin 100 1 100hz dc vcc 10 15 5

.ac dec 10 1meg 1g dc vdd 5 7.7 .25

The keyword `dec` specifies decade variation, with *np* the
number of points per decade. The keyword `oct` specifies octave
variation, with *np* the number of points per octave, and `lin` specifies linear variation, with *np* the number of points.
The two parameters *fstart* (the starting frequency), and *fstop* (the final frequency) complete the basic analysis
specification. If this line is included in the circuit file,
*WRspice* will perform an ac analysis of the circuit over the
specified frequency range. Note that in order for this analysis to be
meaningful, at least one voltage or current source must have been
specified with an `ac` value.

There is a subtlety when using `dec` with *fstop*/*fstart* less than 10. *WRspice* will adjust the frequency delta to
hit the final value, if the frequency ratio is integral. This is very
appropriate when *fstop*/*fstart* is a power of two and *np* is 10. The table shows the frequency multiplication factors
without and with correction. Without correction, the frequency
multiplier is the tenth root of 10. The corrected multiplier is the
ninth root of 8. With correction, the binary powers are hit exactly.

**Uncorrected ** |
**Binary Correction** |

1.000000 |
1.000000 |

1.258925 |
1.259921 |

1.584893 |
1.587401 |

1.995262 |
2.000000 |

2.511886 |
2.519842 |

3.162278 |
3.174802 |

3.981072 |
4.000000 |

5.011872 |
5.039684 |

6.309573 |
6.349604 |

7.943282 |
8.000000 |

10.000000 |
10.079368 |

The optional dc sweep is a dc analysis specification which will cause
the ac analysis to be performed at each point of the dc sweep. The
small-signal parameters are reevaluated at every sweep point, and the
output vectors will be multidimensional.

In interactive mode, the **ac** command, which takes the same
arguments as the `.ac` line, can be used to initiate ac analysis.

AC analysis is not available if Josephson junctions are included in the
circuit.

** Next:** .dc Line
** Up:** Analysis Specification
** Previous:** Chained Sweep Analysis
** Contents**
** Index**
Stephen R. Whiteley
2021-01-27