Modeling a High-Speed Backplane (4-Port S-Parameters to Differential TDR and TDT)
This example shows how to use RF Toolbox™ functions to calculate the TDR (Time-Domain Reflectometry) and TDT (Time-Domain Transmission) of a differential high-speed backplane channel.
Read the Single-Ended 4-Port S-Parameters and Convert Them to Differential 2-Port S-Parameters
Read a Touchstone® data file, default.s4p, into an sparameters object. The parameters in this data file are the 50-ohm S-parameters of a single-ended 4-port passive circuit, measured at 1496 frequencies ranging from 50 MHz to 15 GHz. Then, get the single-ended 4-port S-parameters from the data object, and use the matrix conversion function s2sdd to convert them to differential 2-port S-parameters.
filename = 'default.s4p';
backplane = sparameters(filename);
data = backplane.Parameters;
freq = backplane.Frequencies;
z0 = backplane.Impedance;Convert to 2-port differential S-parameters.
diffdata = s2sdd(data); diffsparams = sparameters(diffdata,freq,2*z0);
Calculate and Plot the Differential Time-Domain Reflectometry
TDR is the reflected voltage signal for a step input. First, extract the differential S11 data using the rfparam function, and convert the S11 data to TDR voltage transfer function data [1]. Next, create a rational function of that data using the rationalfit function, then compute the TDR using the stepresp function of the rfmodel.rational object. Lastly, plot the calculated TDR.
s11 = rfparam(diffsparams,1,1); Vin = 1; tdrfreqdata = Vin*(s11+1)/2; tdrfit = rationalfit(freq,tdrfreqdata,'NPoles',350); Ts = 5e-12; N = 5000; % number of samples Trise = 5e-11; % Define a step signal [Vtdr,tdrT] = stepresp(tdrfit,Ts,N,Trise); figure plot(tdrT*1e9,Vtdr,'r','LineWidth',2) ylabel('Differential TDR (V)') xlabel('Time (ns)') legend('Calculated TDR') ylim([0.46 0.55])
Calculate and Plot the Differential Time-Domain Transmission
TDT is the transmitted voltage signal for a step input. Use the rationalfit function to get the rational function object of the TDT voltage frequency data, then use the stepresp function to compute TDT. Lastly, plot the calculated TDT.
delayfactor = 0.98; % Delay factor. Set delay factor to zero if your % data does not have a well-defined delay s21 = rfparam(diffsparams,2,1); tdtfreqdata = Vin*s21/2; tdtfit = rationalfit(freq,tdtfreqdata,'DelayFactor',delayfactor); Ts = 5e-12; N = 5000; % number of samples Trise = 5e-11; [tdt,tdtT] = stepresp(tdtfit,Ts,N,Trise); figure plot(tdtT(1:N)*1e9,tdt(1:N),'r','LineWidth',2) ylabel('Differential TDT (V)') xlabel('Time (ns)') legend('Calculated TDT','Location','best')
References
[1] A. S. Ali, R. Mittra. "Time-Domain Reflectometry using Scattering Parameters and a De-Embedding Application" Technical Report, Electromagnetic Communication Laboratory Report No. 86-4, May 1986.