Network Analysis

Posted on Edited on In

image-20240704212740246

Rational Fit

Matlab/rationalfit

To resolve the convergence problem of s-parameter in Spectre simulator - rationalfit and write Verilog-A

image-20220630224525565

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
filename  = 'touchstone/ISI.S4P';
s4p = read(rfdata.data, filename);
sdd_params = s2sdd(s2p.S_Parameters, 2);
sdd21 = squeeze(sdd_params(2, 1, :));   % s21
freq = s4p.Freq;

% rational fitting
weight = ones(size(sdd21));
weight(floor(end*3/4):end) = 0.2;
weight(2:10) = 0;

[hfit, errb] = rationalfit(freq, sdd21, 'IterationLimit', [4, 16], 'Delayfactor', 0.98, ...
    'Weight', weight, 'Tolerance', -38, 'NPoles', 32);
[sdd21_fit, ff] = freqresp(hfit, freq);

figure(1)
plot(freq/1e9, db(sdd21), 'b-'); hold on;
plot(ff/1e9, db(sdd21_fit), 'r-'); hold off; grid on;
legend('sdd21', 'sdd21\_fit');
xlabel('Freq (GHz)');
ylabel('magnitude (dB)');


ts = 1e-12;
n = 2^18;
trise = 4e-14;
[yout, tout] = stepresp(hfit, ts, n, trise);
figure(2)
plot(tout*1e12, yout, 'b-'); grid on;
xlabel('Time (ps)');
ylabel('V');
title('Step Response');


% write verilog-A
writeva(hfit, 'channel_32poles.va');

Z0

Remember, S-parameters don't mean much unless you know the value of the reference impedance (it's frequently called Z0).

simulator will read sp file's Z0 parameter

image-20220430214052538

image-20220430214136970

image-20220430214419283

The default Z0 exported by EMX is 50

reference

microwaves101, S-parameters (https://www.microwaves101.com/encyclopedias/s-parameters)

Pupalaikis, P. (2020). S-Parameters for Signal Integrity. Cambridge: Cambridge University Press. doi:10.1017/9781108784863

Coelho, C. P., Phillips, J. R., & Silveira, L. M. (n.d.). Robust rational function approximation algorithm for model generation. Proceedings 1999 Design Automation Conference (Cat. No. 99CH36361). doi:10.1109/dac.1999.781313

Cadence IEEE IMS 2023, Introducing the Spectre S-Parameter Quality Checker and Rational Fit Model Generator [https://support.cadence.com/apex/ArticleAttachmentPortal?id=a1O3w000009lplhEAA]

The Complex Art Of Handling S-Parameters: The importance of extraction and fitting to circuit simulation involving S-parameters [https://semiengineering.com/the-complex-art-of-handling-s-parameters]