Find Zeros, Poles, and Gains for CTLE from Transfer Function

This example shows how to configure the Specification parameter GPZ Matrix of a CTLE in the SerDes Designer app to use zeros, poles, and gains output by the zpk function, given poles and residues output by the rational function. You can reformat the set of zeros, poles, and gains output by the zpk function to use as a GPZ matrix in a CTLE block.

Import Transfer Function

Import a .csv file containing a transfer function using the readmatrix function.

ctle_transfunc = readmatrix('ctle_transfer_function.csv','Range','A7:E775');
freq = ctle_transfunc(:,1);
ri = ctle_transfunc(:,4:end); 

Convert Transfer Function to Complex Form

To prepare data for use by the rational function, convert the real numbers from the transfer function to complex numbers using the complex function.

data = complex(ri(:,1:2:end),ri(:,2:2:end));

Find Rational of Transfer Function

You can use the rational function to find the best fit to the transfer function. The rational function performs iterations to identify a fit with the lowest error. It is important to set the argument TendsToZero to true to add a pole so that the fit tends to zero as S approaches infinity. This meets the requirement to have one more pole than the number of zeros in the GPZ matrix.

bestfit = rational(freq,data,'Tolerance',-40,'TendsToZero',true,'MaxPoles',8,'Display','on');
nSurrogate=1; reduced to 100.0%
min achievable error=-Inf
Region 1 of 1 init: np=0 errdb=0
Region 1 of 1: np=0 errdb=-3.04769
Region 1 of 1: np=2 errdb=-37.9389
Region 1 of 1: np=4 errdb=-122.215
final: np=4 errdb=-123.386

Convert to Zeros, Poles, Gains from Poles and Residues

The rational function returns poles and residues, but you need to convert these into zeros, poles and gains for a CTLE block. The CTLE can be configured to use Specification parameter GPZ Matrix where the units for gains, poles and zeros are dB, Hz, and Hz, respectively.

[z,p,~,dcgain]=zpk(bestfit);

gpz(1,1) = 20*log10(dcgain);           % Convert to dB
gpz(1,2:2:length(p)*2) = p/(2*pi);     % Convert to Hz
gpz(1,3:2:length(z)*2+1) = z/(2*pi);   % Convert to Hz                            

Configure CTLE Block in SerDes Designer

Launch the SerDes Designer app. Place a CTLE block after the analog model of the receiver. Select the CTLE and from the Block Parameters pane, set the Specification parameter to GPZ Matrix. Then copy the value of the gpz variable and paste it to the Gain pole zero matrix parameter, or type the name of the variable gpz.

Correlate Pulse Response in SerDes Designer to IBIS-AMI Simulation

In the SerDes Designer app, plot the CTLE Transfer Function and Pulse Response from the Add Plots button.

Then click the Export > Make IBIS AMI Model for SerDes System button. The IBIS-AMI model may be loaded into an appropriate EDA tool to plot the Pulse Response from the model. For correlation purposes, you can compare the plots for Pulse Response from the SerDes Designer app and the EDA tool.

See Also

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