ahkab.symbolic

This module provides the functionality needed to perform a small-signal symbolic simulation.

The principal method is symbolic_analysis(), which performs the symbolic circuit solution.

Note

This module is geared towards setting up and running the symbolic simulation. Typically, it should be used in conjunction with ahkab.results.symbolic_solution, the symbolic solution class, which holds several convenience methods to extensively manipulate, simplify, post-process and analyze the simulation results, complementing the functionality offered by the Sympy module itself.

Reference

calculate_gains(sol, xin, optimize=True)

Calculate low-frequency gain and roots of a transfer function.

Parameters:

sol : dict

the circuit solution

xin : Sympy symbol

the input variable

optimize : boolean, optional

If optimize is set to False, no algebraic simplification will be attempted on the results. The default (optimize=True) results in sympy.together being called on each expression.

Returns:

gs : dict

A dictionary with as keys the strings <key>/<xin> and as values dictionaries with keys 'gain', 'gain0', 'poles', 'zeros'.

generate_mna_and_N(circ, opts, ac=False, subs=None, verbose=3)

Generate a symbolic Modified Nodal Analysis matrix and N vector.

Only elements that have an is_symbolic attribute set to True (the default) are considered symbolically. Simply set the attribute to False to employ the numeric value. This allows to simplify and speed up the work of the symbolic solver.

The formulation can be performed using conductances or resistances. The choice is made setting the global options.symb_formulate_with_gs value to True. A formulation done in terms of resistors, may result in many separate \(1/R\) terms in the matrices. Historically, sympy choked on those, because of a long-standing bug in polys. Now the issue seems to have been solved and the two computations should be symbolically equivalent albeit computationally different (as expected). The option value options.symb_formulate_with_gs is provided to restore the old functionality in case you use an old version of sympy.

Parameters:

circ : circuit instance

The circuit.

opts : dict

The options to be used for the generation of the matrices. As of now, the only supported option is 'r0s' which can be set to either True or False, and selects whether the equivalent output resistance of the transistors should be taken into account or not.

ac : bool, optional

Flag to trigger the inclusion of frequency-dependent elements. Defaults to False currently (but may change).

subs : dict, optional

The substitution dictionary, composed by mappings of <symbol>:<sympy expression>.

verbose : int, optional

Verbosity flag, from 0 (silent) to 6 (very logorrhoic). Defaults to 3.

Returns:

mna, N : Sympy matrices

The MNA matrix and the contant term of symbolic type.

subs_gs : dict of symbols

In case the formulation of the MNA is performed in terms of conducatances, this dictionary is to be used to substitute away the conducatances for the resistor symbols, after the circuit is solved but before the results are shown to the user. sympy‘s sub() can take care of that for you. If not necessary, this dictionary is empty.

Note

Setting opts['r0s'] = True, ie considering all the transistors output resistances, can significantly slow down – or even prevent by consuming all available memory – the solution of complex circuits with several active elements.

We recommend a combination of the following:

• setting the above option in simple circuits only,
• inserting explicitely the \(r_0\) you wish to consider at circuit level,
• beefing up your machine with extra RAM and extra computing power,
• being patient.

get_roots(expr)

Given the transfer function expr, returns poles, zeros.

get_variables(circ)

Get a sympy matrix containing the circuit variables to be solved for.

Parameters:

circ : circuit instance

The circuit

Returns:

vars : sympy matrix, shape (n, 1)

The variables in a column vector.

s = s

the Laplace variable

symbolic_analysis(circ, source=None, ac_enable=True, r0s=False, subs=None, outfile=None, verbose=3)

Attempt a symbolic, small-signal solution of the circuit.

Parameters:

circ : circuit instance

the circuit instance to be simulated.

source : string, optional

the part_id of the source to be used as input for the transfer

function. If None, no transfer function is evaluated.

ac_enable : bool, optional

take frequency dependency into consideration (default: True).

r0s : bool, optional

take transistors’ output impedance into consideration (default: False)

subs: dict, optional

a dictionary of part IDs to be substituted. It makes solving the circuit easier. Eg. subs={'R1':'R2'} - replace the resistor R1 with R2.

outfile : string, optional

output filename - 'stdout' means print to stdout, the default.

verbose: int, optional

verbosity level 0 (silent) to 6 (painful).

Returns:

sol : symbolic solution

The solutions.

tfs : symbolic solution

The transfer functions, only if requested. Otherwise tfs is a None object.