Data Analysis on a Set of S-parameters for an RF Filter

This example shows how to perform statistical analysis on a set of S-parameter data files. First, read twelve S-parameter files representing twelve similar RF filters into the MATLAB workspace and plot them. Next, plot and analyze the passband response of these filters to ensure they meet statistical norms.

Read in S-parameters from Filter Data Files

Use built-in RF Toolbox functions for reading a set of S-Parameter data files. For each filter, collect and plot the S21 raw values and S21 dB values. The names of the files are AWS_Filter_1.s2p through AWS_Filter_12.s2p. These files represent 12 passband filters with similar specifications.

numfiles    = 12;
filename    = "AWS_Filter_"+(1:numfiles)+".s2p"; % Construct filenames
S           = sparameters(filename(1)); % Read file #1 for initial set-up
freq        = S.Frequencies; % Frequency values are the same for all files
numfreq     = numel(freq); % Number of frequency points
s21_data    = zeros(numfreq,numfiles); % Preallocate for speed

% Read Touchstone files
for n = 1:numfiles
    S   = sparameters(filename(n));
    s21 = rfparam(S,2,1);
    s21_data(:,n) = s21;
end
s21_db = 20*log10(abs(s21_data));

figure
plot(freq/1e9,s21_db)
xlabel('Frequency (GHz)')
ylabel('Filter Response (dB)')
title('Transmission performance of 12 filters')
axis on
grid on

Filter Passband Visualization

In this section, find, store and plot the S21 data from just the AWS downlink band (2.11 to 2.17 GHz).

idx             = (freq >= 2.11e9) & (freq <= 2.17e9);
s21_pass_data   = s21_data(idx,:);
s21_pass_db     = s21_db(idx,:);
freq_pass_ghz   = freq(idx)/1e9;    % Normalize to GHz    

plot(freq_pass_ghz,s21_pass_db)
xlabel('Frequency (GHz)')
ylabel('Filter Response (dB)')
title('Passband variation of 12 filters')
axis([min(freq_pass_ghz) max(freq_pass_ghz) -1 0])
grid on

Basic Statistical Analysis of the S21 Data

Perform Statistical analysis on the magnitude and phase of all passband S21 data sets. This determines if the data follows a normal distribution and if there is outlier data.

abs_S21_pass_freq   = abs(s21_pass_data);

Calculate the mean and standard deviation of the magnitude of the entire passband S21 data set.

mean_abs_S21        = mean(abs_S21_pass_freq,'all')

mean_abs_S21 = 0.9289

std_abs_S21         = std (abs_S21_pass_freq(:))

std_abs_S21 = 0.0104

Calculate the mean and standard deviation of the passband magnitude response at each frequency point. This determines if the data follows a normal distribution.

mean_abs_S21_freq   = mean(abs_S21_pass_freq,2);
std_abs_S21_freq    = std (abs_S21_pass_freq,0,2);

Plot all the raw passband magnitude data as a function of frequency, as well as the upper and lower limits defined by the basic statistical analysis.

plot(freq_pass_ghz,mean_abs_S21_freq)
hold on;
plot(freq_pass_ghz,mean_abs_S21_freq + 2*std_abs_S21_freq,'r')
plot(freq_pass_ghz,mean_abs_S21_freq - 2*std_abs_S21_freq,'k')
legend('Mean','Mean + 2*STD','Mean - 2*STD')
plot(freq_pass_ghz,abs_S21_pass_freq,'c','HandleVisibility','off')
grid on
axis([min(freq_pass_ghz) max(freq_pass_ghz) 0.9 1]);
ylabel('Magnitude S21')
xlabel('Frequency (GHz)')
title('S21 (Magnitude) - Statistical Analysis')
hold off

Plot a histogram for the passband magnitude data. This determines if the upper and lower limits of the data follow a normal distribution.

histfit(abs_S21_pass_freq(:))
grid on
axis([0.8 1 0 100])
xlabel('Magnitude S21')
ylabel('Distribution')
title('Compare filter passband response vs. a normal distribution')

Calculate the phase response of the passband S21 data, then the per-frequency mean and standard deviation of the phase response. All the passband S21 phase data is then collected into a single vector for later analysis.

pha_s21         = angle(s21_pass_data)*180/pi;
mean_pha_S21    = mean(pha_s21,2);
std_pha_S21     = std(pha_s21,0,2);
all_pha_data    = reshape(pha_s21.',numel(pha_s21),1);

Plot all the raw passband phase data as a function of frequency, as well as the upper and lower limits defined by the basic statistical analysis.

plot(freq_pass_ghz,mean_pha_S21)
hold on
plot(freq_pass_ghz,mean_pha_S21 + 2*std_pha_S21,'r')
plot(freq_pass_ghz,mean_pha_S21 - 2*std_pha_S21,'k')
legend('Mean','Mean + 2*STD','Mean - 2*STD')
plot(freq_pass_ghz,pha_s21,'c','HandleVisibility','off')
grid on
axis([min(freq_pass_ghz) max(freq_pass_ghz) -180 180])
ylabel('Phase S21')
xlabel('Frequency (GHz)')
title('S21 (Phase) - Statistical Analysis')
hold off

Plot a histogram for the passband phase data. This determines if the upper and lower limits of the data follow a uniform distribution.

histogram(all_pha_data,35)
grid on
axis([-180 180 0 100])
xlabel('Phase S21 (degrees)')
ylabel('Distribution')
title('Histogram of the filter phase response')

ANOVA Analysis of the S21 Data

Perform ANOVA analysis on both the magnitude and phase passband data.

anova1(abs_S21_pass_freq.',freq_pass_ghz);

ylabel('Magnitude S21')
xlabel('Frequency (GHz)')
ax1 = gca;
ax1.XTick = 0.5:10:120.5;
ax1.XTickLabel = {2.11,'',2.12,'',2.13,'',2.14,'',2.15,'',2.16,'',2.17};
title('Analysis of variance (ANOVA) of passband loss')
grid on

anova1(pha_s21.',freq_pass_ghz);

ylabel('Phase S21 (degrees)')
xlabel('Frequency (GHz)')
ax2 = gca;
ax2.XTick = 0.5:10:120.5;
ax2.XTickLabel = {2.11,'',2.12,'',2.13,'',2.14,'',2.15,'',2.16,'',2.17};
title('Analysis of variance (ANOVA) of passband phase response')
grid on

Fit the Phase Data to 1st-Order Polynomial

Perform a curve fit of the S21 phase data using a linear regression model.

phase_s21_fit = fit(repmat(freq_pass_ghz,numfiles,1),all_pha_data,'poly1')

phase_s21_fit = 
     Linear model Poly1:
     phase_s21_fit(x) = p1*x + p2
     Coefficients (with 95% confidence bounds):
       p1 =      -310.8  (-500.9, -120.6)
       p2 =       665.3  (258.3, 1072)

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