matlab-deembed-rf-cascade

Cascade and De-embed S-Parameter Networks

Chain RF components in series (cascade) and remove fixture effects from measurements (de-embed) using cascadesparams and deembedsparams.

When to Use

Chaining RF components in series to compute end-to-end S-parameters
Removing fixture effects from measured DUT data (de-embedding)
Performing through calibration or round-trip verification
Building signal chains from individually measured blocks

When NOT to Use

Loading or plotting S-parameter data -- use matlab-manage-sparameters
Converting between network parameter types -- use matlab-convert-network-parameters
Composing arbitrary RF circuits with node wiring -- use matlab-compose-rf-circuit
Building channel models from transmission lines and nport blocks -- use matlab-model-si-channel

Workflow

Load networks — Load all S-parameter blocks (see matlab-manage-sparameters skill)
Align frequencies — Interpolate all networks to a common frequency grid with rfinterp1
Cascade or de-embed — Chain networks or remove fixtures
Verify — Compare results against expectations; round-trip cascade+de-embed to check accuracy

Prerequisite: Frequency Alignment

All networks must share the same frequency vector and reference impedance. This is the most common source of errors.

% Find overlapping frequency range
fCommon = linspace(max(s1.Frequencies(1), s2.Frequencies(1)), ...
                   min(s1.Frequencies(end), s2.Frequencies(end)), 500);

% Interpolate all networks to the common grid
s1i = rfinterp1(s1, fCommon);
s2i = rfinterp1(s2, fCommon);

Gotcha: cascadesparams and deembedsparams require identical frequency vectors. If you skip rfinterp1, you get a dimension mismatch error or silently wrong results. Always interpolate first.

Gotcha: Networks must share the same reference impedance. If impedances differ, re-normalize with newref before cascading: s2i = newref(s2i, s1i.Impedance).

Gotcha: rfinterp1 interpolates the real and imaginary parts independently (like interp1), not magnitude and angle. This can produce artifacts near sharp resonances or rapid phase transitions.

Cascading Networks

Connect networks in series — output ports of one feed into input ports of the next.

% Two networks
sTotal = cascadesparams(s1i, s2i);

% Three or more networks
sChain = cascadesparams(s1i, s2i, s3i);

Gotcha: cascadesparams assumes standard port ordering: ports 1:N are inputs, N+1:2N are outputs. If your ports follow a different convention, use snp2smp (from matlab-convert-network-parameters skill) to reorder before cascading.

Identifying Input vs Output Ports

To determine which ports are inputs and which are outputs, inspect the S-parameter matrix at the lowest frequency: off-diagonal elements closest to unity (0 dB) are the through connections.

s4 = sparameters('device.s4p');
S = s4.Parameters(:,:,1);          % S-matrix at lowest frequency
disp(abs(S));                       % Through paths have magnitude ≈ 1
% If S(2,1) ≈ 1 and S(4,3) ≈ 1, then ports 1,3 are inputs and 2,4 are outputs

For typical 4-port differential pairs: through paths are S21 and S43, meaning ports 1,3 are near-end (input) and ports 2,4 are far-end (output). To use with cascadesparams, reorder so inputs are first:

% Reorder from [1,2,3,4] to [1,3,2,4] so ports 1,2=input and 3,4=output
sReordered = snp2smp(s4, [1 3 2 4]);
sCascade = cascadesparams(sReordered, sReordered);
% Reorder result back to original convention
sCascade = snp2smp(sCascade, [1 3 2 4]);

Multi-Port Cascading

cascadesparams supports networks of different sizes when you specify how many ports connect via the third argument:

% Default (no 3rd arg): both must be 2N-port, connects last N to first N
sTotal = cascadesparams(s2a, s2b);      % Two 2-port -> 2-port result

% With connection count (3rd arg): works with different-sized networks
sTotal = cascadesparams(s4, s2, 1);     % 4-port + 2-port, connect 1 port
% Result: (4 + 2 - 2*1) = 4-port

The third argument specifies how many ports connect between the networks. The last M output ports of the first network connect to the first M input ports of the second. The result has (N1 + N2 - 2*M) ports.

For complex topologies where cascadesparams port ordering doesn't match your physical setup:

Use snp2smp to reorder ports before cascading
Or use the circuit object for full topology control (see matlab-compose-rf-circuit skill)

De-embedding Fixtures

Remove fixture (test fixture, adapter, cable) effects from a measured DUT to recover the true device response.

Gotcha: deembedsparams always requires 3 arguments: deembedsparams(sMeasured, s1, s3) where s1 is the port-1 fixture and s3 is the port-2 fixture. Calling with only 2 arguments errors with "Not enough input arguments." For one-sided de-embedding, pass an ideal thru for the unused side.

Two-Sided De-embedding

% Measured: fixture1 + DUT + fixture2
% Goal: extract DUT S-parameters
sDUT = deembedsparams(sMeasured, sFixture1, sFixture2);

One-Sided De-embedding

To de-embed only one side, construct an ideal thru for the other side:

nf = numel(sMeasured.Frequencies);
thruData = zeros(2, 2, nf);
thruData(1,2,:) = 1;
thruData(2,1,:) = 1;
sThru = sparameters(thruData, sMeasured.Frequencies, 50);

% Remove only the left fixture
sDUT = deembedsparams(sMeasured, sFixture1, sThru);

% Remove only the right fixture
sDUT = deembedsparams(sMeasured, sThru, sFixture2);

Verification Pattern

Cascade then de-embed to verify round-trip accuracy:

% Build chain
sChain = cascadesparams(sFixture, sDUT, sFixture);

% Recover DUT
sRecovered = deembedsparams(sChain, sFixture, sFixture);

% Check error
origS21 = rfparam(sDUT, 2, 1);
recS21 = rfparam(sRecovered, 2, 1);
maxErr = max(abs(origS21 - recS21));
fprintf('Round-trip S21 max error: %.2e\n', maxErr);

Gotchas

Frequency alignment is required -- cascadesparams and deembedsparams require identical frequency vectors. Always rfinterp1 to a common grid first, or you get dimension mismatch errors or silently wrong results.
deembedsparams always requires 3 arguments -- deembedsparams(sMeasured, s1, s3) where s1 is the port-1 fixture and s3 is the port-2 fixture. Calling with only 2 arguments errors. For one-sided de-embedding, pass an ideal thru for the unused side.
rfinterp1 interpolates real/imag independently -- Not magnitude and angle. Can produce artifacts near sharp resonances or rapid phase transitions.
cascadesparams assumes standard port ordering -- Ports 1:N are inputs, N+1:2N are outputs. If your ports follow a different convention, use snp2smp to reorder before cascading.

Conventions

Always interpolate to a common frequency grid before cascading or de-embedding
Use tiledlayout/nexttile when comparing original vs. cascaded/de-embedded results
Label plots clearly to distinguish standalone vs. cascaded responses
Verify de-embedding accuracy by round-tripping when fixture data is available