matlab-analyze-rf-amplifier

RF Amplifier Analysis

Evaluate stability, power gain, matching, and quality of active RF devices using S-parameter data.

When to Use

Evaluating unconditional stability via Rollett K-factor or Edwards-Sinsky mu
Computing maximum available gain (Gmag), maximum stable gain (Gmsg), or transducer gain
Computing input/output reflection coefficients for matching design
Checking passivity and causality of S-parameter data
Simultaneous conjugate match analysis with gammams/gammaml

When NOT to Use

Loading or plotting S-parameter data -- use matlab-manage-sparameters
Fitting rational models or computing TDR -- use matlab-fit-rational-model
Designing impedance matching networks -- use matlab-design-matching-network
Defining amplifier elements for rfbudget -- use matlab-create-rfbudget-elements

Workflow

Load device data — Load amplifier S-parameters (see matlab-manage-sparameters skill)
Check passivity/causality — Confirm data quality; active devices are expected to be non-passive
Evaluate stability — Compute K-factor and/or mu across frequency
Compute gain — Select appropriate gain metric based on stability and application
Analyze matching — Compute reflection coefficients for impedance matching design

Passivity and Causality

Passivity

A passive network cannot produce energy. Active devices (amplifiers) are expected to fail passivity — that is normal.

[isPass, idxNonPass] = ispassive(s);
if ~isPass
    fprintf('Non-passive at %d of %d frequencies\n', numel(idxNonPass), numel(s.Frequencies));
    sFixed = makepassive(s);            % Enforce passivity
end

Gotcha: makepassive(sparametersObj) directly modifies S-parameter data point-by-point to force passivity — it does not optimize. This is different from makepassive(fitObj) on a rational fit, which performs an optimization over the fit residues (see matlab-fit-rational-model skill). Only use makepassive on S-parameter data for small numerical violations (e.g., measurement noise on passive devices). It is NOT appropriate for active devices — the result will not represent the original network.

Causality

if iscausal(s)
    disp('S-parameters are causal');
end

Stability Analysis

Rollett Stability Factor (K)

The classic two-condition test for unconditional stability:

[k, b1, b2, delta] = stabilityk(s);
% Unconditionally stable when K > 1 AND |delta| < 1
isUnconditional = (k > 1) & (abs(delta) < 1);

fprintf('K range: %.3f to %.3f\n', min(k), max(k));
fprintf('Unconditionally stable at %d of %d frequencies\n', ...
    sum(isUnconditional), numel(k));

Output meanings:

k — Rollett stability factor (unconditionally stable when K > 1)
b1 — Auxiliary stability measure: 1 - |S11|^2 - |S22|^2 + |delta|^2. Sign of b1 indicates which stability circle (source or load) contains the Smith chart center. Positive b1 means the stable region for the source includes the center.
b2 — Same as b1 but for the load plane: 1 - |S22|^2 - |S11|^2 + |delta|^2 (symmetric formula)
delta — Determinant of the S-matrix: S11*S22 - S12*S21. Unconditional stability requires |delta| < 1 in addition to K > 1.

Edwards-Sinsky Stability Factor (mu)

Single-condition test — preferred because one parameter suffices:

mu = stabilitymu(s);
% Unconditionally stable when mu > 1

figure;
plot(s.Frequencies/1e9, mu, 'LineWidth', 1.5);
yline(1, 'r--', 'Stability Boundary');
xlabel('Frequency (GHz)'); ylabel('\mu');
title('Edwards-Sinsky Stability Factor'); grid on;

Power Gain

Gain Metrics

Function Call	Metric	Description
`powergain(s, 'Gmag')`	Maximum available gain	Valid only when unconditionally stable (K > 1)
`powergain(s, 'Gmsg')`	Maximum stable gain	Use when conditionally stable (K < 1)
`powergain(s, Zs, Zl, 'Gt')`	Transducer gain	Actual gain with specific source/load impedances
`powergain(s, Zs, 'Ga')`	Available gain	With specific source impedance
`powergain(s, Zl, 'Gp')`	Operating power gain	With specific load impedance

Gotcha: The gain type string must be the last argument. powergain(s, 'Gt', 50, 50) errors — use powergain(s, 50, 50, 'Gt') instead.

gmag = powergain(s, 'Gmag');           % Maximum available gain
gmsg = powergain(s, 'Gmsg');           % Maximum stable gain

gt = powergain(s, 50, 75, 'Gt');       % Transducer gain (Zs=50, Zl=75)
ga = powergain(s, 50, 'Ga');           % Available gain (Zs=50)
gp = powergain(s, 75, 'Gp');           % Operating power gain (Zl=75)

Gotcha: powergain returns linear gain, NOT dB. Convert with 10*log10(g) (power gain uses 10×, not 20×).

Gotcha: Gmag returns NaN at frequencies where the device is conditionally stable (K < 1). Use Gmsg at those frequencies.

Gotcha: Gmsg returns Inf when S12 approaches zero (unilateral device). Guard with isfinite(gmsg) before converting to dB.

Combined Gain Plot Pattern

gmag = powergain(s, 'Gmag');
gmsg = powergain(s, 'Gmsg');

figure;
plot(s.Frequencies/1e9, 10*log10(gmag), ...
     s.Frequencies/1e9, 10*log10(gmsg), '--', 'LineWidth', 1.5);
xlabel('Frequency (GHz)'); ylabel('Gain (dB)');
title('Maximum Available / Stable Gain');
legend('Gmag', 'Gmsg'); grid on;

Reflection Coefficients

For impedance matching design — compute the reflection coefficients needed for simultaneous conjugate match or for given termination impedances.

gin  = gammain(s, zl);                 % Input reflection coefficient (given load Zl)
gout = gammaout(s, zs);                % Output reflection coefficient (given source Zs)
gms  = gammams(s);                     % Source match for simultaneous conjugate match
gml  = gammaml(s);                     % Load match for simultaneous conjugate match

Converting Gamma to Impedance

To convert a reflection coefficient to impedance (e.g., for matching network targets):

Z0 = 50;
Zs = Z0 * (1 + gms) ./ (1 - gms);    % Source impedance for conjugate match
Zl = Z0 * (1 + gml) ./ (1 - gml);    % Load impedance for conjugate match

Frequency Interpolation

If the desired analysis frequency is not in the S-parameter data, interpolate first:

sInterp = rfinterp1(s, targetFreq);   % Interpolate to specific frequency
gms_f0 = gammams(sInterp);            % Now compute at exact frequency

See matlab-manage-sparameters for full rfinterp1 usage.

Circuit Implementation of Matching Networks

After computing gammams/gammaml, translate to matching network circuits using matlab-design-matching-network (for lumped/stub synthesis) or matlab-compose-rf-circuit (for assembling txlineMicrostrip stubs with nport amplifier blocks). Key points for circuit assembly:

Use matlab-compose-rf-circuit for the nport + transmission line + setports workflow
Call setports only once per circuit, after all elements are add()ed and wired
If combining sub-circuits (e.g., input match + amplifier + output match), build each as a separate circuit object, then compose them in a parent circuit using setterminals

Noise Parameters

The noiseParameters object stores noise data (minimum noise figure, optimum reflection coefficient, equivalent noise resistance) that accompanies amplifier S-parameter data.

Constructor

np = noiseParameters(fmin, freq, z0);
% fmin: minimum noise figure (linear, not dB) at each frequency
% freq: frequency vector in Hz
% z0: reference impedance for Rn normalization

Rn Normalization Convention

The Rn property (equivalent noise resistance) is normalized to z0:

% If measured Rn data is in ohms (absolute):
np = noiseParameters(fmin, freq, 1);   % z0=1: Rn values ARE resistance in ohms
np.Rn = measuredRn_ohms;

% If Rn data is normalized to 50 ohm:
np = noiseParameters(fmin, freq, 50);  % z0=50: Rn = Rn_actual/50
np.Rn = measuredRn_normalized;

Many datasheets give Rn in ohms, so z0=1 is more intuitive for direct entry.

Gotcha: z0 only affects Rn normalization — it does NOT affect Fmin or GammaOpt. Do not confuse noise reference impedance with S-parameter reference impedance.

Gotchas

powergain gain type string must be the last argument -- powergain(s, 'Gt', 50, 50) errors. Use powergain(s, 50, 50, 'Gt').
powergain returns linear gain, not dB -- Convert with 10*log10(g) (power gain uses 10x, not 20x).
Gmag returns NaN when conditionally stable -- At frequencies where K < 1, Gmag is undefined. Use Gmsg at those frequencies instead.
Gmsg returns Inf for unilateral devices -- When S12 approaches zero, Gmsg blows up. Guard with isfinite(gmsg) before converting to dB.
Do not apply makepassive to amplifiers -- Active devices are expected to be non-passive. makepassive(sparametersObj) modifies data point-by-point and does NOT represent the original active device.
makepassive on S-parameters vs rational fits -- makepassive(sparametersObj) is a crude point-by-point fix. makepassive(fitObj) on a rational fit runs an optimization over residues (see matlab-fit-rational-model skill). Only use on S-parameter data for small numerical violations on passive devices.
setports can only be called once per circuit -- If you get "terminals already set", you are calling setports on a circuit that already has ports defined. Build all elements and wiring first, then call setports once at the end. See matlab-compose-rf-circuit for the full circuit assembly workflow.
gammams/gammaml return complex values -- Convert to impedance with Z = Z0*(1+gamma)./(1-gamma). Convert to magnitude/angle with abs(gamma) and angle(gamma)*180/pi.

Conventions

Use tiledlayout/nexttile for multi-panel stability/gain figures
Always label axes with units (GHz, dB) and include figure titles
Plot a yline(1, 'r--') stability boundary on mu plots for visual clarity
Active devices are expected to be non-passive — do not apply makepassive to amplifiers