matlab-model-si-channel

Signal Integrity Channel Modeling

Build SI channel models by cascading measured S-parameter blocks (nport), lossy frequency-dependent transmission lines (txlineWRLGC, txlineWtable), and lumped parasitic elements (resistor, capacitor, inductor) in RF Toolbox circuit objects. Extract insertion loss, return loss, and crosstalk, then bridge to time-domain analysis via rational fitting.

When to Use

• Building channel models from cascaded nport S-parameter data (connectors, packages, PCB traces)
• Modeling frequency-dependent loss with txlineWRLGC or txlineWtable
• Analyzing differential and multi-port networks with port termination
• Combining lumped parasitics, transmission lines, and measured S-parameter blocks
• Extracting insertion/return loss from mixed lumped-distributed topologies

When NOT to Use

• Loading or plotting S-parameter data -- use matlab-manage-sparameters
• Cascading or de-embedding standalone S-parameter blocks -- use matlab-deembed-rf-cascade
• Composing general-purpose RF circuits (not SI-focused) -- use matlab-compose-rf-circuit
• Fitting rational models or computing TDR -- use matlab-fit-rational-model
• Designing impedance matching networks -- use matlab-design-matching-network

Workflow

1. Load blocks — Create nport elements from Touchstone files and transmission line models
2. Build channel — Wire blocks, parasitics, and terminations in a circuit object
3. Extract S-parameters — Call sparameters(ckt, freq) to get channel response
4. Analyze — Plot insertion/return loss, convert to mixed-mode, or fit for time-domain analysis

Lumped Parasitic Elements

Primitive R/L/C elements model vias, bond wires, pad capacitance, and termination resistors in SI channels. Each has terminals p (positive) and n (negative):

r = resistor(50, 'Rterm');        % 50 Ohm termination
c = capacitor(0.1e-12, 'Cvia');   % via pad capacitance
l = inductor(0.5e-9, 'Lvia');     % via barrel inductance

Gotcha: Primitive constructors are positional only: resistor(100, 'R1'). Name-value syntax like resistor('Resistance', 100) is not supported.

Handle semantics: Changing a property after adding to a circuit immediately affects the circuit -- no need to re-add.

Via Model (Lumped Subcircuit)

via = circuit('Via');
add(via, [1 2], inductor(0.5e-9, 'Lvia'));
add(via, [2 0], capacitor(0.1e-12, 'Cvia'));
setports(via, [1 0], [2 0]);

ESD/Decoupling Parasitic

esd = circuit('ESD');
add(esd, [1 0], capacitor(0.3e-12, 'Cesd'));
add(esd, [1 0], resistor(1e6, 'Resd'));    % parallel RC to ground
setports(esd, [1 0]);                       % 1-port shunt element

nport Elements in Circuit

Embed measured or simulated S-parameter data (Touchstone files) as circuit elements. This is the primary building block for SI channel models -- connectors, packages, PCB segments, and fixtures are all characterized as S-parameter data.

2-Port nport

np = nport('connector.s2p');
np.Name = 'ConnIn';

ckt = circuit('Simple');
add(ckt, [1 2 0 0], np);               % 4 nodes: p1+->1, p2+->2, p1-->0, p2-->0
add(ckt, [2 3], inductor(0.5e-9, 'L1'));
setports(ckt, [1 0], [3 0]);

A 2-port nport has 4 terminals (p1+, p2+, p1-, p2-), so add takes a 4-element node vector.

4-Port nport

A 4-port nport has 8 terminals. Two node-mapping forms:

np4 = nport('device.s4p');
np4.Name = 'Dev4P';

% Explicit 8-node form: [p1+ p2+ p3+ p4+ p1- p2- p3- p4-]
add(ckt, [1 2 3 4 0 0 0 0], np4);     % all negatives grounded

% Shorthand N-node form: negatives implicitly grounded
add(ckt, [1 2 3 4], np4);              % same result

Port Selection and Termination

Use setports on the circuit to select which nport ports become external ports. Unexposed ports are left open-circuited -- add explicit resistors for proper termination:

s4 = sparameters('device.s4p');
Z0 = s4.Impedance;
np4 = nport(s4);
np4.Name = 'Dev4P';

ckt = circuit('PortSelect');
add(ckt, [1 2 3 4 0 0 0 0], np4);

% Terminate unused ports 2 and 4 with matched loads
add(ckt, [2 0], resistor(Z0, 'Term2'));
add(ckt, [4 0], resistor(Z0, 'Term4'));

% Expose only ports 1 and 3 as a 2-port network
setports(ckt, [1 0], [3 0]);

freq = s4.Frequencies;
s = sparameters(ckt, freq);    % S21 here equals S31 of original 4-port

Gotcha: Without explicit termination on unused ports, extracted S-parameters will differ from the original -- open-circuit reflections alter the network response.

Differential Port Mapping

For differential signaling, use the full 2N-node form with non-grounded negative terminals:

np4 = nport('diffpair.s4p');
np4.Name = 'DiffChan';

ckt = circuit('DiffAnalysis');
add(ckt, [1 2 3 4 5 6 7 8], np4);  % non-grounded negatives
setports(ckt, [1 5], [3 7]);        % differential: (p1+,p1-) -> (p3+,p3-)

Critical: every negative terminal must have a current path. Each nport port requires current to flow in through pi+ and return through pi-. If a negative terminal is mapped to a node that is not connected to anything (not grounded, not used as a port reference, not connected to another element), the current path is broken and the nport produces zero transmission (~-260 dB). There are three valid approaches:

1. Ground all negatives (simplest): add(ckt, [1 2 3 4 0 0 0 0], np) — all returns share node 0
2. Use negatives as port references: setports(ckt, [1 5], [3 7]) — the port definition itself closes the loop through pi-
3. Connect negatives to other elements: tie them to resistors, other nport terminals, etc.

Never leave negative terminals on isolated floating nodes.

Circuit Differential Ports vs s2sdd

The circuit approach (setports with differential node pairs) and the s2sdd function are not equivalent:

• setports(ckt, [1 3], [2 4]) with grounded negatives creates a physical voltage measurement between two single-ended nodes that each have their own ground return. This is effectively a series combination — it gives results like 2× the single-ended loss.
• s2sdd performs a mathematical modal decomposition of the full S-matrix. It algebraically separates differential and common modes without requiring a physical current path.

For extracting the true differential-mode response from a 4-port file, use s2sdd on the extracted S-parameters rather than trying to replicate it with differential setports. The circuit setports differential form is appropriate when ports physically correspond to differential terminals (e.g., a balanced amplifier with explicit + and - pins).

After extracting sparameters, convert to mixed-mode for differential/common-mode analysis:

s = sparameters(ckt, freq);
sdd = s2sdd(s.Parameters, 2);   % 2x2xK differential array
% Wrap in sparameters with doubled impedance (differential Z0 = 2x single-ended)
sDiff = sparameters(sdd, s.Frequencies, 2*s.Impedance);

Multi-Port Channel Extraction

For a 4-port channel (e.g., near-end and far-end crosstalk):

np4 = nport('coupled_traces.s4p');
np4.Name = 'Traces';

ckt = circuit('CoupledChannel');
add(ckt, [1 2 3 4 0 0 0 0], np4);
setports(ckt, [1 0], [2 0], [3 0], [4 0]);   % full 4-port extraction

s = sparameters(ckt, freq);
% S21 = through, S31 = NEXT, S41 = FEXT (depending on port assignment)

Frequency-Dependent Transmission Lines

txlineWRLGC and txlineWtable model lossy transmission lines with frequency-dependent parameters. Both are 2-port/4-terminal elements that work in circuit and rfbudget.

txlineWRLGC -- W-Element RLGC Model

Models frequency-dependent loss using an analytic formula (Djordjevic-Sarkar wideband model):

tw = txlineWRLGC;
tw.Lo = 350e-9;       % inductance per unit length (H/m)
tw.Co = 130e-12;      % capacitance per unit length (F/m)
tw.Ro = 2.0;          % DC resistance (Ohm/m)
tw.Rs = 5e-4;         % skin-effect resistance coefficient (Ohm/m/sqrt(Hz))
tw.Go = 0;            % DC conductance (S/m)
tw.Gd = 1e-11;        % dielectric loss conductance (S/m/Hz)
tw.LineLength = 0.05;  tw.Name = 'PCBTrace';  % 50 mm

Property	Default	Description
Lo	1e-9	Inductance per unit length (H/m)
Co	4e-13	Capacitance per unit length (F/m)
Ro	0	DC series resistance (Ohm/m)
Rs	0	Skin-effect resistance coefficient
Go	0	DC shunt conductance (S/m)
Gd	0	Dielectric loss conductance
DielectricFrequency	1e9	Reference frequency for Gd (Hz)
Nline	1	Number of signal conductors
LineLength	1	Physical length (m)
StubMode	'NotAStub'	'NotAStub', 'Series', or 'Shunt'
Termination	'NotApplicable'	'NotApplicable', 'Short', or 'Open'

Typical parameter ranges for common PCB technologies (50-Ohm single-ended):

Technology	Lo (nH/m)	Co (pF/m)	Ro (Ohm/m)	Rs	Gd (S/m/Hz)
FR4 microstrip (outer layer)	300-400	100-140	1-5	3e-4 to 8e-4	5e-12 to 2e-11
FR4 stripline (inner layer)	350-450	120-160	2-8	4e-4 to 1e-3	1e-11 to 5e-11
Low-loss (Megtron6, Rogers)	300-400	100-140	1-4	3e-4 to 6e-4	1e-12 to 5e-12

These are approximate starting points. For accurate models, extract RLGC parameters from a 2D field solver (e.g., Ansys Q2D, Cadence Sigrity) matched to your actual stackup geometry.

txlineWtable -- Table-Based Frequency-Dependent Model

Specifies R, L, G, C at discrete frequency points with interpolation. Use when you have extracted or measured per-unit-length parameters at specific frequencies:

wt = txlineWtable;
fpts = [1e8 1e9 10e9];
wt.R = [0.5 1.0 2.0];   wt.Rfreq = fpts;   % Ohm/m
wt.L = [260 250 248]*1e-9; wt.Lfreq = fpts; % H/m
wt.C = [100 100 99]*1e-12; wt.Cfreq = fpts; % F/m
wt.G = [0 1e-4 1e-3];   wt.Gfreq = fpts;   % S/m
wt.Lhf = 248e-9;  wt.Chf = 99e-12;         % HF asymptotes
wt.LineLength = 0.1;  wt.Name = 'MeasuredTrace';

When to Use Each

Model	Use Case
txlineRLCGLine	Constant RLCG -- quick estimates, frequency-independent loss
txlineWRLGC	Analytic frequency-dependent loss -- PCB traces, cables with skin effect
txlineWtable	Measured/extracted RLCG data at discrete frequencies

Using in Circuit

All transmission lines have 4 terminals (p1+, p2+, p1-, p2-):

ckt = circuit('TraceLoss');
add(ckt, [1 2 0 0], tw);     % 4-node mapping
setports(ckt, [1 0], [2 0]);
s = sparameters(ckt, linspace(1e8, 20e9, 500));

Mixed Topology Channel Models

Combine lumped elements, nport S-parameter blocks, and transmission lines in a single circuit -- the core pattern for SI channel modeling:

Connector-Trace-Via-Connector Channel

np_conn = nport('connector.s2p');
np_conn.Name = 'ConnIn';

trace = txlineWRLGC(Name='PCBTrace');
trace.Lo = 350e-9;  trace.Co = 130e-12;
trace.Ro = 2.0;     trace.Rs = 5e-4;
trace.Gd = 1e-11;   trace.LineLength = 0.05;

via = circuit('Via');
add(via, [1 2], inductor(0.5e-9, 'Lvia'));
add(via, [2 0], capacitor(0.1e-12, 'Cvia'));
setports(via, [1 0], [2 0]);

ckt = circuit('Channel');
add(ckt, [1 2 0 0], np_conn);          % input connector
add(ckt, [2 3 0 0], trace);            % PCB trace
add(ckt, [3 4 0 0], via);              % via transition
add(ckt, [4 5 0 0], clone(np_conn));   % output connector (cloned)
setports(ckt, [1 0], [5 0]);

freq = linspace(1e8, 10e9, 500);
s = sparameters(ckt, freq);

figure; tiledlayout(1, 2);
nexttile; rfplot(s, 2, 1); title('S21 -- Insertion Loss');
nexttile; rfplot(s, 1, 1); title('S11 -- Return Loss');

Differential Channel with Package

sPkg = sparameters('package.s4p');
Z0 = sPkg.Impedance;
pkg = nport(sPkg);   pkg.Name = 'Package';
chan = nport('diffpair.s4p'); chan.Name = 'DiffTrace';

ckt = circuit('DiffChannel');
add(ckt, [1 2 3 4 0 0 0 0], pkg);
add(ckt, [2 4 5 6 0 0 0 0], chan);     % ports 2,4 of pkg feed into channel

% Terminate unused package port 3 (near-end crosstalk victim)
add(ckt, [3 0], resistor(Z0, 'TermNEXT'));

% Expose: pkg port 1 -> channel port output
setports(ckt, [1 0], [5 0], [6 0]);    % 3-port: input, thru, FEXT

s = sparameters(ckt, sPkg.Frequencies);

Multi-Path Analysis (Clone + Different Ports)

The clone() + different setports() pattern lets you analyze multiple signal paths through the same topology without rebuilding:

% Build an RC interconnect with crosstalk coupling
base = circuit('Interconnect');
add(base, [1 2], resistor(50, 'R1'));
add(base, [2 0], capacitor(1e-12, 'C1'));
add(base, [2 3], resistor(50, 'R2'));
add(base, [3 0], capacitor(1e-12, 'C2'));
add(base, [2 4], resistor(100, 'Rxtalk'));
add(base, [4 0], capacitor(2e-12, 'Cxtalk'));

% Main signal path
cktMain = clone(base);
setports(cktMain, [1 0], [3 0]);

% Crosstalk path
cktXtalk = clone(base);
setports(cktXtalk, [1 0], [4 0]);

freq = linspace(1e6, 10e9, 500);
sMain = sparameters(cktMain, freq);
sXtalk = sparameters(cktXtalk, freq);

Time-Domain Analysis

For time-domain channel characterization (TDR, impulse response, step response, eye diagrams), fit the extracted S-parameters with a rational model, then compute time responses. See the matlab-fit-rational-model skill for full details.

s = sparameters(ckt, freq);
fit = rational(s);                          % AAA algorithm (preferred over rationalfit)
[resp, t] = stepresp(fit, 1e-12, 10000, 50e-12);  % (Ts, N, Trise)

% Multi-port fits return cell arrays for BOTH resp and t, indexed {output, input}
figure; plot(t{2,1}*1e9, resp{2,1});  % S21 step response
xlabel('Time (ns)'); ylabel('Voltage'); title('Channel Step Response');

Alternatively, convert to a voltage transfer function first, then fit the scalar result:

tf21 = s2tf(s);          % S21 voltage transfer function (default)
fit21 = rational(tf21);
[h, t] = impulse(fit21, 1e-12, 10000);

Gotchas

1. nport node count: min N, max 2N -- an N-port nport needs at least N nodes (negatives implicitly grounded) and at most 2N nodes. Fewer than N errors. For clarity, prefer the explicit 2N form with 0 for grounded negatives.
2. Unexposed nport ports are open-circuited -- when using setports to expose only some ports of a multi-port nport, unused ports are left open. Add explicit resistor(Z0) terminations (where Z0 matches the S-parameter reference impedance, e.g., s.Impedance) for correct S-parameter extraction.
3. nport.Input/Output are for rfbudget only -- these numeric port indices select the through-path for rfbudget. In circuit, use node mapping and setports instead.
4. LineLength not Length -- all transmission line objects use LineLength for physical length. Using Length errors.
5. txlineWtable needs multi-point RLCG data in circuit -- scalar R/L/G/C values (single frequency point) error with "number of data points should be equal to the number of frequency points" when extracting sparameters from a circuit. Provide at least 2 frequency points in each RLCG table.
6. txlineWRLGC/txlineWtable constructors don't accept StubMode/Termination -- set these as properties after construction. Only RLGC, length, and name parameters are accepted in the constructor.
7. txlineWRLGC Nline>1 with matrix Lo/Co -- multi-line coupled extraction has a sparameters bug in R2026a. Workaround: extract each line individually.
8. Elements cannot be shared across circuits -- always clone() before reusing an element or subcircuit in a second circuit.
9. setports/setterminals can only be called once -- plan your topology before defining terminals.
10. Primitive constructors are positional -- resistor(100, 'R1'), not resistor('Resistance', 100).
11. Element Name must be a valid MATLAB identifier -- no spaces, no leading digits.

Conventions

• Use tiledlayout/nexttile for multi-panel channel analysis plots
• Always label axes with units (dB, GHz, ns) and include figure titles
• Name elements descriptively for readable topology: 'ConnIn', 'PCBTrace', 'Lvia', 'Cpad'
• Use clone() liberally -- it deep-copies all nested elements and subcircuits
• Plot both S21 (insertion loss) and S11 (return loss) for channel characterization
• For differential channels, convert to mixed-mode S-parameters with s2sdd after extraction

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