Vectorfitting

This is a from scratch pure python implementation of the fast relaxed vectorfitting algorithm for MIMO frequency domain data. Different modes (standard VF, relaxed VF and fast relaxed VF) are implemented. Matrix shaped frequency domain data is supported, and a model with common poles is fitted

$$\mathbf{H}_{fit}(s) = \mathbf{D} + s \cdot \mathbf{E} + \sum_{k=1}^{n} \mathbf{R}_{k} \cdot \frac{1}{s - p_k} $$

where $\mathbf{D}$ is the constant term, $\mathbf{E}$ is the linear term and $\mathbf{R}_{k}$, $p_k$ are the (possibly complex) residues in matrix form and poles.

Example

importnumpyasnpimportmatplotlib.pyplotasplt# plt.style.use('dark_background')cycle=plt.rcParams['axes.prop_cycle'].by_key()['color']
fromvectorfittingimportVecFit, RelaxedVecFit, FastRelaxedVecFitfromvectorfitting.parsersimportread_touchstone

#load data from snp fileFreq, H, *_=read_touchstone(r"example_data/3port.s3p")
#initialize vectorfitting engine

#or initialize vectorfitting engine directly from touchstone fileVF, H, Freq=FastRelaxedVecFit.from_touchstone(
filepath=r"example_data/3port.s3p",
n_cpx=6,
n_real=1,
smart=False,
autoreduce=False
)
#run fitting procedureVF.fit(tol=2e-3, max_steps=15, debug=True)

debugging status : iteration step number (step) : 0
model order (n_real, n_cpx) : 7, 3
fitting relative error (mean, max) : 0.0001708429691544018, 0.0023363418460802367
debugging status : iteration step number (step) : 1
model order (n_real, n_cpx) : 3, 5
fitting relative error (mean, max) : 9.409935882693254e-05, 0.0008016668878070043
<vectorfitting.transferfunction.TransferFunction at 0x229ef6a8140>

#evaluate fit in the frequency domainH_fit=VF.TF.evaluate(Freq)
#compute relative errorerr_rel= (H-H_fit) /H#dB helperdB=lambdax: 20*np.log10(abs(x))
#plot resultsfig, ax=plt.subplots(nrows=1, ncols=1, figsize=(10,6), tight_layout=True, dpi=100)
N, n, m=H.shapeforiinrange(n):
forjinrange(m):
ax.plot(Freq, dB(H[:,i,j]), "-d", color=cycle[0], markevery=15, markersize=5, label="H"ifi==j==0elseNone)
ax.plot(Freq, dB(H_fit[:,i,j]), "--", color=cycle[1], lw=2, label="H_fit"ifi==j==0elseNone)
ax.plot(Freq, dB(err_rel[:,i,j]), ":", color=cycle[2], lw=2, label="err_rel"ifi==j==0elseNone)
ax.set_xlabel("freq [Hz]")
ax.set_ylabel("mag in dB")
ax.grid(True)
ax.legend(loc="lower right")
fig.savefig("Figures/test_freq.png", dpi=300)

#evaluate location of polespoles=VF.TF.Polesprint("poles :", poles)
#plot resultsfig, ax=plt.subplots(nrows=1, ncols=1, figsize=(6,6), tight_layout=True, dpi=100)
ax.scatter(poles.real, poles.imag, marker="x", s=60, color=cycle[0], label="poles")
ax.set_xlabel("Real")
ax.set_ylabel("Imag")
ax.grid(True)
ax.legend(loc="lower right")
fig.savefig("Figures/test_poles.png", dpi=300)

poles : [-1.72203113e+12+0.00000000e+00j -1.83467749e+11+0.00000000e+00j
-5.17583220e+09+0.00000000e+00j -9.25175278e+10+1.32482288e+12j
-9.25175278e+10-1.32482288e+12j -7.61051335e+11+3.86841214e+11j
-7.61051335e+11-3.86841214e+11j -3.68806617e+10+6.37226049e+11j
-3.68806617e+10-6.37226049e+11j -1.75281196e+11+9.13374927e+10j
-1.75281196e+11-9.13374927e+10j -1.13430812e+10+7.73637981e+08j
-1.13430812e+10-7.73637981e+08j]

References

[1] Gustavsen, B. and Adam Semlyen. “Rational approximation of frequency domain responses by vector fitting.” IEEE Transactions on Power Delivery 14 (1999): 1052-1061.

[2] B. Gustavsen, "Improving the pole relocating properties of vector fitting," in IEEE Transactions on Power Delivery, vol. 21, no. 3, pp. 1587-1592, July 2006, doi: 10.1109/TPWRD.2005.860281.

[3] D. Deschrijver, M. Mrozowski, T. Dhaene and D. De Zutter, "Macromodeling of Multiport Systems Using a Fast Implementation of the Vector Fitting Method," in IEEE Microwave and Wireless Components Letters, vol. 18, no. 6, pp. 383-385, June 2008, doi: 10.1109/LMWC.2008.922585.

!jupyternbconvert--ClearMetadataPreprocessor.enabled=True--ClearOutput.enabled=True--tomarkdownREADME.ipynb

[NbConvertApp] Converting notebook README.ipynb to markdown
[NbConvertApp] Support files will be in README_files\
[NbConvertApp] Making directory README_files
[NbConvertApp] Writing 4401 bytes to README.md