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syntfil[MakeRealL] - set the quality factors of the inductors in an LC ladder structure to a finite value

Calling sequence:

MakeRealL(blocks, Q, f)

MakeRealL(blocks, Q, f, f1)

Parameters:

blocks - table with LC ladder description

Q - quality factor of inductors (It can be also entered as a list of individual quality factors: [Q1,Q2,...,Qn], where n is count of inductors in filter.) [-]

f - frequency corresponding to quality factor [Hz]

f1 - (optional parameter) if given, then the geometric average will be computed from both frequencies f and f1 for further computation [Hz]

Parameters Q , f and f1 must be positive numbers where f < f1 . If parameter Q is entered as a list, then the count of elements in the list must correspond to the count of inductors in the filter.

Description:

This function adds the serial resistors to the inductors in an LC ladder structure according to the entered quality factors and the entered frequency.
Index type in table is changed from LC_XX_YY to LC_XX_YY_Q .
Given frequency (thrird parameter f ) corresponds to a cutoff frequency in lowpass and highpass filters or to a passband geometric cetre in bandpass and band-rejection filters. If the fourth parameter is entered, then the both parameters f and f1 correspond to the lower and upper cutoff frequency in bandpass and band-rejection filters.
The serial resistors are computed according to following rules: .

Info level:

Setting of variable infolevel[syntfil] can be used to get more detailed results.

infolevel[syntfil] =

2 - print type of filter, terminating resistors and LC ladder branches on separate lines with description.

Example:

> with(syntfil):

Cutoff frequency of lowpass filter (LP)

> fp:=1000;

Table with LP filter description

>    elem_lp := table([
  1 = table([Z = 1/(s*C1), elements = {C1 = .3214929850e-5}, orientation = shunt]),
  2 = table([Z = s*L1,     elements = {L1 = .1582000134e-1}, orientation = direct]),
  3 = table([Z = 1/(s*C1), elements = {C1 = .3214929850e-5}, orientation = shunt]),
R2 = 100.00, R1 = 100.00, type = LC_LP_common]):

Quality factor

> Q:=100;

> elem_lpQ:=MakeRealL(elem_lp,Q,fp);

$elem_lpQ := TABLE([1 = TABLE([Z = 1/(s*C1), elements = {C1 = .3214929850e-5}, orientation = shunt]), 2 = TABLE([Z = Rs1+s*L1, elements = {L1 = .1582000134e-1, Rs1 = .9939999999}, orientation = direct])...$
$elem_lpQ := TABLE([1 = TABLE([Z = 1/(s*C1), elements = {C1 = .3214929850e-5}, orientation = shunt]), 2 = TABLE([Z = Rs1+s*L1, elements = {L1 = .1582000134e-1, Rs1 = .9939999999}, orientation = direct])...$
$elem_lpQ := TABLE([1 = TABLE([Z = 1/(s*C1), elements = {C1 = .3214929850e-5}, orientation = shunt]), 2 = TABLE([Z = Rs1+s*L1, elements = {L1 = .1582000134e-1, Rs1 = .9939999999}, orientation = direct])...$
$elem_lpQ := TABLE([1 = TABLE([Z = 1/(s*C1), elements = {C1 = .3214929850e-5}, orientation = shunt]), 2 = TABLE([Z = Rs1+s*L1, elements = {L1 = .1582000134e-1, Rs1 = .9939999999}, orientation = direct])...$
$elem_lpQ := TABLE([1 = TABLE([Z = 1/(s*C1), elements = {C1 = .3214929850e-5}, orientation = shunt]), 2 = TABLE([Z = Rs1+s*L1, elements = {L1 = .1582000134e-1, Rs1 = .9939999999}, orientation = direct])...$

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