matlab-design-matching-network

Impedance Matching Network Design

Design, evaluate, and optimize 1-port impedance matching networks. The matchingnetwork object and matchingNetworkDesigner app match a source impedance to a load impedance — they do not yet design 2-port (e.g., filter-style) matching. The object generates candidate topologies, ranks them by performance, and exports as circuit objects.

When to Use

• Designing L, Pi, or Tee impedance matching networks
• Matching a source impedance to a frequency-dependent load (antenna, filter)
• Ranking candidate topologies by return loss or transducer gain
• Converting lumped matching designs to transmission line stubs via Richards transformation
• Evaluating component tolerance sensitivity in matching networks
• Importing custom matching circuits for comparison

When NOT to Use

• Building general-purpose RF circuits with arbitrary topologies -- use matlab-compose-rf-circuit
• Composing rfbudget cascade elements -- use matlab-create-rfbudget-elements
• Analyzing amplifier stability or gain circles -- use matlab-analyze-rf-amplifier

Workflow

1. Define impedances — Set source and load impedances (scalar, S-parameter object, or function handle)
2. Create network — Construct matchingnetwork with center frequency, bandwidth, and topology
3. Evaluate — Add evaluation parameters, inspect candidates with circuitDescriptions
4. Export — Extract best circuit with exportCircuits for use in larger designs

Creating a Matching Network

mn = matchingnetwork( ...
    'SourceImpedance', 50, ...
    'LoadImpedance', 75 + 20i, ...
    'CenterFrequency', 2.4e9, ...
    'Bandwidth', 200e6, ...
    'Components', 2);

Properties

Property	Default	Description
SourceImpedance	50	Source impedance (see formats below)
LoadImpedance	50	Load impedance (see formats below)
CenterFrequency	1e9	Design frequency (Hz)
Bandwidth	100e6	Target bandwidth (Hz)
LoadedQ	10	Loaded Q factor
Components	2	Topology: 2, 3, 'L', 'Pi', 'Tee'
Circuit	(auto)	Read-only array of generated circuits

Bandwidth and LoadedQ Are Coupled

LoadedQ = CenterFrequency / Bandwidth. Setting one updates the other. If both are specified, Bandwidth takes precedence.

Components / Topology Options

Value	Circuits Generated
2 or 'L'	2 L-section designs (series-L/shunt-C and series-C/shunt-L)
3	8 three-element designs (all permutations)
'Pi'	4 shunt-series-shunt designs
'Tee'	4 series-shunt-series designs

Gotcha: Maximum is 3 components. Components = 1 or Components = 4 error.

Impedance Source Formats

Both SourceImpedance and LoadImpedance accept:

% Scalar (constant impedance)
mn.LoadImpedance = 75 + 20i;

% S-parameter object (frequency-dependent, 1-port)
sAnt = sparameters('antenna.s1p');
mn.LoadImpedance = sAnt;

% Z-parameter or Y-parameter object
mn.LoadImpedance = zparameters(sAnt);

% Touchstone file path
mn.LoadImpedance = 'antenna.s1p';

% 1-port circuit object (must have setports called)
ckt = circuit('Load');
add(ckt, [1 0], resistor(75, 'RL'));
add(ckt, [1 0], capacitor(1e-12, 'CL'));
setports(ckt, [1 0]);
mn.LoadImpedance = ckt;

% Function handle (frequency in Hz)
mn.LoadImpedance = @(f) 50 + 30i*(f/1e9);

Inspecting Candidate Designs

[topology, performance] = circuitDescriptions(mn);
disp(topology);       % Component types and values for each design
disp(performance);    % Pass/fail, tests failed, performance score

The topology table columns: circuitName, component1Type, component1Value, component2Type, component2Value, etc. Component types are "Series L", "Series C", "Shunt L", "Shunt C".

The performance table columns: circuitName, evaluationPassed ("Yes"/"No"), testsFailed, performanceScore. Designs are ranked by score (descending). The performanceScore is a weighted composite — higher is better, but the scale depends on your evaluation parameters (it is not a fixed 0–100 range). Use it for relative ranking between candidates, not as an absolute quality metric.

Use component1Type/component2Type columns in the topology table to identify which topology each auto-generated design represents (e.g., "Series L" + "Shunt C" vs "Series C" + "Shunt L").

Evaluation Parameters

Add performance goals to rank and filter designs. Only two parameter types: 'gammain' (input reflection) and 'Gt' (transducer gain).

% Require return loss below -15 dB in-band
addEvaluationParameter(mn, 'gammain', '<', -15, [2.3e9 2.5e9], 2);

% Require insertion loss above -1 dB
addEvaluationParameter(mn, 'Gt', '>', -1, [2.3e9 2.5e9], 1);

% View current evaluations
params = getEvaluationParameters(mn);
disp(params);

% Remove an evaluation by row index
clearEvaluationParameter(mn, 1);

Arguments: (mn, parameter, comparison, targetdB, [fLow fHigh], weight)

A default automatic evaluation (Gt > -3 dB over [CenterFrequency - Bandwidth/2, CenterFrequency + Bandwidth/2]) is always present. Clear it with clearEvaluationParameter(mn, 1) if the automatic entry is at row 1.

Gotcha: Only 'gammain' and 'Gt' are supported — no S11, S21, VSWR, or other parameters.

Exporting Circuits

ckt = exportCircuits(mn);            % Best-ranked circuit only
ckts = exportCircuits(mn, [1 3]);    % Specific designs by index

Returns circuit objects containing inductor and capacitor elements. These can be used directly with sparameters(ckt, freq), embedded in larger circuits via add(), or cascaded.

Visualization

Frequency Response

rfplot(mn);                          % All designs, auto frequency range
rfplot(mn, freq);                    % Custom frequencies
rfplot(mn, freq, [1 3]);             % Specific designs

Plots two panels: input reflection coefficient (gammain) and transducer gain (Gt) in dB. Overlays evaluation goal lines.

Smith Chart

smithplot(mn);                                        % Best design
smithplot(mn, 'CircuitIndex', 2, 'Z0', 50);          % Specific design

Shows the impedance transformation path from source to load.

Gotcha: smithplot(mn) works directly on the matchingnetwork object. To plot an exported circuit's S-parameters on a Smith chart, use the S-parameter object form:

ckt = exportCircuits(mn);
s = sparameters(ckt, linspace(1e9, 3e9, 201));
smithplot(s, 1, 1);                                   % Plot S11

Do not pass the circuit object directly to smithplot — it only accepts matchingnetwork, sparameters, or numeric data.

S-Parameters

s = sparameters(mn);                       % Best design, auto frequency
s = sparameters(mn, freq);                 % Custom frequencies
s = sparameters(mn, freq, Z0);             % Custom reference impedance
sArr = sparameters(mn, freq, Z0, [1 3]);   % Multiple designs -> array

The 4-argument form sparameters(mn, freq, Z0, circuitIndex) extracts S-parameters directly without needing exportCircuits first. Use gammain(s) or powergain(s, 50, 50, 'Gt') on the result for analysis (see matlab-analyze-rf-amplifier).

Richards Transformation (Lumped → Stubs)

Convert lumped L/C matching elements to transmission line stubs:

txCkt = richards(mn, 2.4e9);              % Best design at 2.4 GHz
txCkts = richards(mn, 2.4e9, [1 2]);      % Specific designs

Returns circuit objects with txlineElectricalLength stub elements. Each stub has:

• Z0 — characteristic impedance (from original element)
• LineLength — electrical length in radians (pi/4 for quarter-wave)
• ReferenceFrequency — the operating frequency argument
• Termination — 'Short' for inductors, 'Open' for capacitors
• StubMode — 'Series' or 'Shunt' matching the original topology

Stub element names get a _tx suffix: C becomes C_tx, L becomes L_tx.

Tolerance Analysis

Evaluate matching network sensitivity to component value variations:

% Default 5% tolerance on all components
toleranceAnalysis(mn);

% Custom tolerances per component
toleranceAnalysis(mn, [0.05 0.02 0.10]);    % 5%, 2%, 10% for each component

% Custom frequency range and specific circuit
toleranceAnalysis(mn, 0.05, linspace(0.5e9, 2.5e9, 500), 1);

Arguments: (mn, tolerances, freqList, circuitIndices) — all optional after mn. Plots the nominal and perturbed responses showing the spread due to component variations.

Custom Matching Networks

Import user-designed circuits for comparison alongside auto-generated designs:

% Build a custom matching circuit
custom = circuit('MyMatch');
add(custom, [1 2], inductor(3.3e-9, 'Ls'));
add(custom, [2 0], capacitor(0.8e-12, 'Cp'));
setports(custom, [1 0], [2 0]);

% Add to matchingnetwork for evaluation
addNetwork(mn, custom);    % Appears as "user_1" in circuitDescriptions

% Remove a custom network by name
deleteNetwork(mn, 'user_1');

% Suppress auto-generated designs to evaluate only custom circuits
disableAutomaticNetworks(mn);

% Re-enable auto-generated designs
enableAutomaticNetworks(mn);

Custom networks appear as "user_1", "user_2", etc. in circuitDescriptions.

Gotcha: Custom circuits must be 2-port with setports called, and contain only R/L/C elements. Other element types produce -Inf performance scores.

Matching Network Designer App (R2021a+)

Interactive GUI for designing and comparing matching networks:

matchingNetworkDesigner              % Launch empty
matchingNetworkDesigner(mn)          % Pre-loaded with existing design

The app provides visual comparison of topologies, interactive evaluation parameter setup, and Smith chart visualization. Configure programmatically with matchingnetwork, then open in the designer for interactive exploration.

Handle Class Behavior

matchingnetwork is a handle class. These methods mutate in-place (no output argument):

• addNetwork, deleteNetwork
• disableAutomaticNetworks, enableAutomaticNetworks

Use copy(mn) for independent deep copies.

Gotchas

1. Property is Bandwidth (lowercase 'w') — not BandWidth as some help text suggests.
2. Components range is 2–3 only — Components = 1 or Components = 4 error.
3. Only 'gammain' and 'Gt' evaluation parameters — no S11, S21, VSWR. All 6 positional arguments are required: (mn, parameter, comparison, targetdB, [fLow fHigh], weight).
4. Handle class — addNetwork/deleteNetwork mutate in-place. Assigning their output errors ("too many output arguments").
5. Custom circuits must be 2-port RLC only — other element types produce warnings and -Inf scores.
6. Default automatic evaluation always present — Gt > -3 dB over bandwidth. Clear explicitly if unwanted.
7. Bandwidth takes precedence over LoadedQ when both are specified.
8. smithplot only accepts matchingnetwork or sparameters objects — do not pass a circuit object directly. For exported circuits, call sparameters(ckt, freq) first, then smithplot(s, 1, 1).
9. performanceScore is relative, not absolute — use it to rank candidates against each other, not as a fixed quality metric. The scale depends on your evaluation parameters and weights.

Conventions

• Use tiledlayout/nexttile for multi-panel matching analysis plots
• Show smithplot alongside rfplot for matching network analysis
• Always inspect circuitDescriptions to compare candidates before selecting
• Label axes with units (GHz, dB) and include figure titles

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