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: 36 Poles: [36x1 double] Residues: [2x2x36 double] DirectTerm: [2x2 double] ErrDB: -40.8708

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: -0.7603

resp5 = freqresp(r5, S.Frequencies); plot(S.Frequencies, real(rfparam(S, 1, 1)),...S.Frequencies, real(squeeze(resp5(1,1,:))))

加强目标精度

Redo the fit, asking for a tighter tolerance (-60dB), Notice that the fit is significantly improved, particularly in the stopbands of the sawfilter.

rgood = rational(S, -60)

rgood = rational with properties: NumPorts: 2 NumPoles: 101 Poles: [101x1 double] Residues: [2x2x101 double] DirectTerm: [2x2 double] ErrDB: -54.4408

respgood = freqresp(rgood, S.Frequencies); plot(S.Frequencies, real(rfparam(S, 1, 1)),...S.Frequencies, real(squeeze(respgood(1,1,:))))