tdr

Characterize impedance discontinuities from S-parameters using TDR

Since R2025a

Description

Use time-domain reflectometry (TDR) to characterize impedance discontinuities from S-parameter data.

Creation

Syntax

tdrObj = tdr(sparam)

tdrObj = tdr(sparam,Name=Value)

Description

tdrObj = tdr(sparam) creates a TDR object from a Touchstone file or an sparameters object specified in sparam to characterize impedance discontinuities in a system.

tdrObj = tdr(sparam,Name=Value) sets properties using one or more name-value arguments. For example, t = tdr(ConvertToDifferential=true) enables differential S-parameter conversion.

Input Arguments

sparam — N-port S-parameters

sparameters object | data file

N-port S-parameters, specified as either an sparameters object or an N-port Touchstone data file.

Properties

Ports — Port definitions for single-ended and differential ports

vector of integers

Port definitions for single-ended and differential ports, specified as a vector of integers.

• Single-ended ports: Define on which ports to perform TDR analysis by specifying the port indices in the vector.

• Differential ports: Define the differential ports pairs by specifying the port indices in a vector of the form [DiffPort1p, DiffPort1n, DiffPort2p, DiffPort2n ...].

Example: [1 2]

ConvertToDifferential — Option to enable differential S-parameter conversion

false or 0 (default) | true or 1

Option to enable differential S-parameter conversion, specified as a logical true (1) or false (0). Set this property to true or 1 to enable differential S-parameter conversion.

Example: true

SampleTime — Time step of TDR step response

1e-12 (default) | positive scalar

Time step of the TDR step response, specified as a positive scalar in seconds. The object uses sample time to define a default input signal and a custom TDR stimulus waveform that you specify using the CustomWaveform property.

Example: 10e-3

RiseTime — Rise time of TDR step stimulus waveform

10e-12 (default) | positive scalar

Rise time of the TDR step stimulus waveform, specified as a positive scalar in seconds.

Example: 10e-12

EndTime — Stop time of TDR step response

10e-9 (default) | positive scalar

Stop time of the TDR step response, specified as a positive scalar in seconds.

Example: 10e-8

CustomWaveform — Custom TDR stimulus waveform

1-D vector

Custom TDR stimulus waveform, specified as a 1-D vector. Use this property to generate a custom TDR stimulus as an alternative to the default stimulus generated by this object. By default, the stimulus generated by this object is a step response with the default sample time, rise time, and end time.

Note

You must specify sample time in the SampleTime property when creating a custom TDR stimulus waveform using the CustomWaveform property.

Example: [zeros(1,16),ones(1,16),zeros(1,128)], pulse response assuming 16 samples per symbol.

RationalOptions — Rational fitting options

structure

Rational fitting options to control the rational object properties, specified as a structure.

This object uses a rational object to perform rational fitting on complex frequency-dependent data. To do this, the object uses a noniterative interpolatory algorithm to construct a fit with complex frequencies. Input the properties and name-value arguments of the rational object to the structure to control the aspect of the fit. For more information on how to set this property, see Plot Differential TDR Response of a Specific Differential Port Pair.

Example: struct('Tolerance',-30,'MaxPoles',500)

Fit — Fit of each TDR response

Read-only: vectors of rational objects

This property is read-only.

Fit of each TDR response, returned as a vectors of rational objects.

ImpedanceTDR — TDR response in units of impedance

Read-only: column matrix

This property is read-only.

TDR response in units of impedance, returned as a column matrix.

VoltageTDR — TDR response in units of volts

Read-only: column matrix

This property is read-only.

TDR response in units of volts, returned as a column matrix.

Time — Time vector of TDR responses

Read-only: vector

This property is read-only.

Time vector corresponding to the TDR responses, returned as a vector.

SParameterQuality — IEEE quality rating

Read-only: struct

This property is read-only.

IEEE quality rating for causality, reciprocity, and passivity for the input S-parameters, returned as a structure.

Label — Port label

Read-only: string array

This property is read-only.

Port label for each TDR response, returned as a string array.

Example: ["Port 1" "Port 2" "Port 3" "Port 4"]

Object Functions

createTDRTable	Return TDR results as MATLAB table
plot	Plot TDR response
tdr.automaticPortOrdering	Display port ordering of S-parameter data
tdr.sParamQuality	Return S-parameter quality metrics

Examples

Plot Differential TDR Response of 4-Port S-Parameter

Create an S-parameter object from a 4-port Touchstone file.

sparam = sparameters('default.s4p');

Create a TDR object and set the ConvertToDifferential property to true. In this example, the ports are not defined using the Ports property. Therefore, the tdr object automatically determines the differential ports.

tdrObj = tdr(sparam,'ConvertToDifferential',true);

Plot the differential TDR response of a 4-port S-parameter. This plot displays the port mapping between single-ended (SE) ports that the object identified as differential (DD) pairs.

plot(tdrObj)

Plot Differential TDR Response of a Specific Differential Port Pair

Use a 16-port S-parameter Touchstone file to plot the TDR response of a differential port pair located at port 1 and 2.

First, create a structure to define the rational fitting parameters. These parameters enable you to control the rational fitting process for complex S-parameters.

rationalOptions = struct('Tolerance',-30,'MaxPoles',500);

Create a TDR object with the differential port pair set to 1 and 2.

tdrObj = tdr('default.s16p',...
    ConvertToDifferential=true, ...
    Ports=[1 2],...
    EndTime=9e-9,...
    RiseTime=10e-12,...
    SampleTime=5e-12, ...
    RationalOptions=rationalOptions);

Plot the differential TDR response of the differential port pair 1 and 2.

plot(tdrObj)

Display Single-Ended TDR of 4-Port S-Parameter Results

Create a TDR object from a 4-port Touchstone file.

tdrObj = tdr('default.s4p');

Plot the single-ended TDR of a 4-port S-parameter in units of impedance.

plot(tdrObj)

Plot the single-ended TDR of a 4-port S-parameter in units of voltage.

plot(tdrObj, Type="voltage", Title="TDR Response (Voltage)")

Plot the single-ended TDR of a 4-port S-parameter with respect to velocity of propagation of the medium. Scale the X-axis of this response in meters.

plot(tdrObj,Vp=3e8/2,Title="TDR Response(m)")

Create a TDR table that displays the time and voltage TDR values for all the ports specified in the TDR object.

T = createTDRTable(tdrObj,tdrType='voltage')

T=10000×5 table
    Time (s)    Port 1 (V)    Port 2 (V)    Port 3 (V)    Port 4 (V)
    ________    __________    __________    __________    __________

          0            1             1             1             1  
      1e-12       1.0062       0.99943        1.0126        1.0087  
      2e-12        1.012       0.99992        1.0237        1.0168  
      3e-12       1.0175        1.0013        1.0335        1.0243  
      4e-12       1.0228        1.0035        1.0421        1.0312  
      5e-12       1.0278        1.0063        1.0498        1.0376  
      6e-12       1.0324        1.0097        1.0565        1.0436  
      7e-12       1.0369        1.0135        1.0625        1.0491  
      8e-12        1.041        1.0175        1.0678        1.0541  
      9e-12       1.0449        1.0218        1.0726        1.0587  
      1e-11       1.0485        1.0263        1.0769         1.063  
    1.1e-11       1.0457        1.0313        1.0682        1.0582  
    1.2e-11        1.043        1.0353        1.0606        1.0536  
    1.3e-11       1.0404        1.0382        1.0542        1.0494  
    1.4e-11       1.0378        1.0402        1.0487        1.0453  
    1.5e-11       1.0353        1.0414         1.044        1.0415  
      ⋮

TDR and Group Delay of Coaxial Transmission Line

This example shows computation of time-domain reflectometry (TDR) and group delay of a coaxial transmission line.

Design Coaxial Transmission Line

Design a 75 $\Omega$ coaxial transmission line.

Z0 = 75;            % Desired characteristic impedance (Ohms)
innerRadius = 0.0005;   % Inner conductor radius (meters)
dc = DielectricCatalog;
ItemsDC = string(dc.Materials.Name);
MaterialType = dielectric(ItemsDC(5)); % Low loss material

Compute the outer radius of the cable from impedance:

$$Z0=\frac{60}{\sqrt{{\epsilon }_r}}*\log \left(\frac{D}{d}\right)$$

outerRadius = innerRadius*exp(Z0*sqrt(MaterialType.EpsilonR)/60);
length = 0.01;        % Conductor length (meters)
mc = MetalCatalog;
Items = string(mc.Materials.Name);
MetalType = metal(Items(2));

Create the coaxial transmission line object.

coaxLine = txlineCoaxial( ...
    'InnerRadius', innerRadius, ...
    'OuterRadius', outerRadius, ...
    'LineLength', length, ...
    'EpsilonR', MaterialType.EpsilonR, ...
    'LossTangent', MaterialType.LossTangent,...
    'SigmaCond', MetalType.Conductivity);

Frequency Sweep

Requirements for frequency sweep:

1. Sweep from DC to very high frequencies to capture details for tdr (frequency to time-domain transformation).

2. Select a step-size such that the resolution of the frequency sweep ensures the unwrapped phase of S21 decreases with frequency.

travel_time = coaxLine.LineLength*sqrt(coaxLine.EpsilonR)/rf.physconst("LightSpeed");
stepSize = 0.9*(1/(4*travel_time));
freq = stepSize/1e6:stepSize:200e9;

Compute Group Delay

Use the groupdelay function to compute the group delay of the transmission line. Compute the group delay of the transmission line.

gd_ns = groupdelay(coaxLine,freq,"Impedance",Z0)*1e9;

Plot the group delay.

plot(freq/1e9, gd_ns)
ylim([floor(min(gd_ns*1e3)) ceil(max(gd_ns*1e3))]./1e3)
ylabel('Group delay (ns)')
xlabel('Frequency (GHz)')

Compute S-parameters

Compute S-parameters of the transmission line for the given frequency sweep and plot S21 phase.

s = sparameters(coaxLine,freq);
rfplot(s,2,1,"angle")

Therefore, we have enough frequency resolution to ensure that the unwrapped phase S21 is decreasing with frequency.

Compute TDR

Use tdr function to plot the TDR.

plot(tdr(s,EndTime=(6*travel_time)))

Overlay the mean value of the group delay on the TDR plot.

hold on
xline(mean(gd_ns), '--', {'mean of the','group delay'}, ...
    'DisplayName','mean(groupdelay)',...
    'LabelVerticalAlignment','middle',...
    'LabelHorizontalAlignment','center');

Conclusion

The TDR delay is the time it takes for a signal to enter the input port of the device under test, propagate to the location of a discontinuity, reflect from that discontinuity and then propagate back to the input port. In this case, the discontinuity is the change from the 75 $\Omega$ impedance of the DUT to the 50 $\Omega$ impedance of the TDR measurement equipment.

Observe that the TDR delay is equivalent to twice the group delay. This observation is generally true for an uniform transmission line, such as a coaxial transmission line, where the:

• RLGC is uniformly distributed across the line,

• dielectric material is lossless, and

• dielectric material has no frequency dependent dispersion.

Therefore, in this study, both TDR delay and group delay represent the time it takes for a signal to traverse the structure, provided the line is uniform and is operating below the multimode threshold.

Version History

Introduced in R2025a