droppnlp.html

droppnlp.mws

syntfil[DroppNLP] - compute the element values of normalized lowpass (NLP) LC ladder

Calling sequence:

DroppNLP(termination, R, direction, struct, pol, chpol)

DroppNLP(termination, R, direction, struct, pol, chpol, zeros)

Parameters:

termination - termination of NLP ( common , open , short )

R - value of normalized termination resistor (R=1)

direction - direction of processing NLP ( front - from first element, rear - from last element)

struct - structure of NLP ( PI or T ) - structure begins at the front with shunt capacitor PI , direct inductor T

pol - inverse tranfer function

chpol - characteristic function

zeros - (optional) one dimensional array of transfer function's zeros

Parameter R must be positive number. If termination is open then direction must be front and struct must be T for even order filter or PI for odd order filter.
If the termination is short then direction must be rear and struct must be T .

Description:

This function computes the element values of normalized lowpass (NLP) LC ladder by means of consecutive removal from chain matrix. The chain matrix is made up from inverse transfer function and characteristic matrix.

Realization method and resulting structure of filter depends on presence of last parameter zeros . This parameter is necessary to enter for correct NLP realization in case of inverse Chebyshev or Cauer approximation.

Return value of function is table with filter description. This table has following indices: type , R1 , R2 and 1..n , where n is equal to filter order ( order of approximation).

Index type can have following values: LC_NLP_common , LC_NLP_open a LC_NLP_short in dependence on termination.

Indices R1 , R2 depends on parametru R and on termination. If termination is open then R2 is infinity and R1 is R . If termination is short then R1 is zero and R2 is R . If termination is common then R1 is R and R2 can be equal to R1 , but in some cases it can be either greater or less than R1 . It depends on the approximation type used.

Indices 1..n describes connection of individual branches of filter in consecutive sequence which corresponds with index number in direction from voltage source. These indices have type table with following indices: Z , elements a orientation .

Index orientation determines branch orientation and it can have values: direct or shunt . These values alternate. If one branch is direct then the next branch is shunt and vice versa.

Index elements is made up of set and it contains branch elements and their values.

Index Z is equal to branch impedance in symbolic form. It determines the connection of branch elements listed under index elements . The impedance can have following values (if variable in inverse transfer function and characteristic function is s):

for direct inductor, Z = 1/(s*C1)

for shunt capacitor, Z = s*L1+1/(s*C1)

for shunt serial resonant circuit and Z = 1/(1/(s*L1)+s*C1)

for direct parallel resonant circuit.

Info level:

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

infolevel[syntfil] =

2 - print resulting reminder chain matrix, NLP type, values of termination resistors and individul branches of NLP

3 - as level 2 + print initial chain matrix

4 - as level 3 + print interim chain matrices that are made up after removal of two individual branches of ladder structure

5 - as level 4 + print element values of individual branches of ladder structure

Example:

> with(syntfil):

Inverse transfer function and characteristic function for normalized Butterworth approximation

> pol,chpol:=s^3+2*s^2+2*s+1,s^3;

> DroppNLP(common,1,front,T,pol,chpol);

Compute inverse Chebyshev approximation

> G,Phi,zeros:=InvChebyshev(3,1.4,1,s);

> elems_nlp:=DroppNLP(common,1,front,PI,G,Phi,zeros);

$elems_nlp := TABLE([1 = TABLE([elements = {C1 = .4980605765}, Z = 1/(s*C1), orientation = shunt]), 2 = TABLE([elements = {L1 = .9961201436, C1 = .3841434827}, Z = 1/(1/(s*L1)+s*C1), orientation = direc...$
$elems_nlp := TABLE([1 = TABLE([elements = {C1 = .4980605765}, Z = 1/(s*C1), orientation = shunt]), 2 = TABLE([elements = {L1 = .9961201436, C1 = .3841434827}, Z = 1/(1/(s*L1)+s*C1), orientation = direc...$
$elems_nlp := TABLE([1 = TABLE([elements = {C1 = .4980605765}, Z = 1/(s*C1), orientation = shunt]), 2 = TABLE([elements = {L1 = .9961201436, C1 = .3841434827}, Z = 1/(1/(s*L1)+s*C1), orientation = direc...$
$elems_nlp := TABLE([1 = TABLE([elements = {C1 = .4980605765}, Z = 1/(s*C1), orientation = shunt]), 2 = TABLE([elements = {L1 = .9961201436, C1 = .3841434827}, Z = 1/(1/(s*L1)+s*C1), orientation = direc...$
$elems_nlp := TABLE([1 = TABLE([elements = {C1 = .4980605765}, Z = 1/(s*C1), orientation = shunt]), 2 = TABLE([elements = {L1 = .9961201436, C1 = .3841434827}, Z = 1/(1/(s*L1)+s*C1), orientation = direc...$

Compute transfer function from table with filter description

> MakeH(elems_nlp);

MakeH, ElemsLP, ElemsHP, ElemsBP, ElemsBP2, ElemsBPm, ElemsBP2m, ElemsBS, ElemsBSm