using rational object to fit s-凯发k8网页登录

create rational object

read in the sparameters, and create the rational object from them. the rational function automatically fits all entries of the s-parameter matrices.

s = sparameters('sawfilter.s2p')

s = 
  sparameters: s-parameters object
       numports: 2
    frequencies: [334x1 double]
     parameters: [2x2x334 double]
      impedance: 50
  rfparam(obj,i,j) returns s-parameter sij

r = rational(s)

r = 
  rational with properties:
      numports: 2
      numpoles: 24
         poles: [24x1 double]
      residues: [2x2x24 double]
    directterm: [2x2 double]
         errdb: -40.9658

with the default settings on this example, the rational function achieves an accuracy of about -26 db, using 30 poles. by construction, the rational object is causal, with a non-zero direct term.

compare fit with original data

generate the frequency response from the rational object, and compare one of the entries with the original data.

resp = freqresp(r, s.frequencies);
plot(s.frequencies, real(rfparam(s, 1, 1)), ...
    s.frequencies, real(squeeze(resp(1,1,:))))

limit number of poles

redo the fit, limiting the number of poles to a maximum of 5. the rational object may use fewer poles than specified. notice that the quality of the fit is degraded as opposed to the original 30-pole fit.

r5 = rational(s, 'maxpoles', 5)

r5 = 
  rational with properties:
      numports: 2
      numpoles: 4
         poles: [4x1 double]
      residues: [2x2x4 double]
    directterm: [2x2 double]
         errdb: -1.7376

resp5 = freqresp(r5, s.frequencies);
plot(s.frequencies, real(rfparam(s, 1, 1)), ...
    s.frequencies, real(squeeze(resp5(1,1,:))))

tighten target accuracy

redo the fit, asking for a tighter tolerance (-60 db), notice that the fit is significantly improved, particularly in the stopbands of the saw filter.

rgood = rational(s, -60)

rgood = 
  rational with properties:
      numports: 2
      numpoles: 188
         poles: [188x1 double]
      residues: [2x2x188 double]
    directterm: [2x2 double]
         errdb: -53.6397

respgood = freqresp(rgood, s.frequencies);
plot(s.frequencies, real(rfparam(s, 1, 1)), ...
    s.frequencies, real(squeeze(respgood(1,1,:))))