What a vector network analyzer really measures

A vector network analyzer supplies a swept single-frequency RF signal and compares complex receiver channels referenced to the same coherent source. Its directional sampling distinguishes waves incident on and leaving a calibrated port, including both magnitude and relative phase. This differs from a conventional spectrum analyzer, which primarily measures signal spectral power.

The incident and outgoing wave amplitudes depend on an explicit reference impedance and measurement plane. A VNA cannot directly identify a microscopic material parameter without a model, cannot distinguish every unmeasured radiation channel, and requires linear steady-state DUT behavior for ordinary small-signal S-parameter interpretation.

With one real-positive R0 reference and its current entering the positive DUT terminal, define $a_1=\frac{V_1+R_0I_1}{2\sqrt{R_0}}$ and $b_1=\frac{V_1-R_0I_1}{2\sqrt{R_0}}$. A corrected one-port experiment reports the complex ratio $S_{11}=\frac{b_1}{a_1}$ under its calibration assumptions.

The reflection contains the interaction of the DUT termination with the selected reference plane. A negative complex S11 is not automatically an active response; it may merely indicate a phase inversion. Moving a probe or cable reference plane rotates the reflection phase even when the physical DUT stays unchanged.

To measure the forward transmission coefficient S21, drive port 1 and arrange the port-2 external environment so a2=0. This means that the receiver or termination sends no incident wave back toward the DUT. The DUT may still send an outgoing b2 and have nonzero V2 and I2.

Driving the other direction with a1=0 yields S12 and S22. The measured matrix describes a specific port and wave normalization, not a loaded transistor voltage gain under an arbitrary output impedance. Bias, calibration, linearity and frequency must be documented for active components.

For a purely resistive load connected to a lossless real R0 port, $\Gamma=\frac{Z_L-R_0}{Z_L+R_0}$. A load ZL=$75\,\Omega$ at R0=$50\,\Omega$ gives Γ=+$0.2$; 20% of the voltage amplitude is reflected but only 4% of the incident power.

Return loss is $\mathrm{RL}=-20\log_{10}|\Gamma|\approx13.98\,\mathrm{dB}$, while $\mathrm{VSWR}=\frac{1+|\Gamma|}{1-|\Gamma|}=1.5$. Do not confuse return loss with insertion loss or assume |Γ| gives its phase. Finite calibration directivity is especially important for small reflections.

An ideal $25\,\Omega$ resistance in series between two real $50\,\Omega$ wave-reference ports has $\begin{pmatrix}A&B\\C&D\end{pmatrix}=\begin{pmatrix}1&25\,\Omega\\0&1\end{pmatrix}$ Its scattering coefficients are $S_{11}=S_{22}=0.2$ and $S_{12}=S_{21}=0.8$, independent of frequency only in the ideal lumped model.

For a1 incident with a2=0, reflection takes $0.2$²=4% of incident power, and transmission $0.8$²=64%. The remaining 32% is dissipated in the resistance. Its insertion loss is $-20\log_{10}(0.8)\approx1.94\,\mathrm{dB}$, a different quantity from return loss ≈$13.98\,\mathrm{dB}$.

Place a one-port load at $z=0$ and the source on the negative-z side with AoN exp(+jωt). An ideal lossless line section of outward length d=−z moves the reflection phase by $-2\beta d$. For $S_{11}=0.4\angle30^\circ$ and $d=\frac{\lambda_g}{8}$, the new phase is −60° with unchanged magnitude.

For a two-port, extending reference planes outward by d1 and d2 shifts S21 phase by −(β1d1+β2d2). Real cables can attenuate, disperse and drift thermally, so raw S phase comparisons require identical calibrated planes. Group delay $\tau_g=-\frac{\mathrm d\arg S_{21}}{\mathrm d\omega}$ is meaningful where transmission remains finite and phases can be unwrapped.

A common one-port receiver-error model writes measured m as $m=E_D+\frac{E_R\Gamma}{1-E_S\Gamma}$, with directivity E_D, reflection tracking E_R and source match E_S. These parameters describe systematic errors at the chosen planes, not intrinsic properties of the device being measured.

Solve algebraically for $\Gamma=\frac{m-E_D}{E_R+E_S(m-E_D)}$; the denominator may become ill-conditioned. Calibration requires characterized standards including their delays and parasitics, and additional terms appear in two-port calibrations. De-embedding the DUT fixture is a separate operation.

Begin by recording instrument model and firmware, sweep range, RF source level, IF bandwidth, point count, averaging, connector and cable state, and DUT bias or temperature. Calibrate at clearly identified planes using the correct characterized standards; then check with a verification device that was not used to derive the calibration.

Measure complex S11 and S21 for an accessible well-terminated $25\,\Omega$ series resistor network and compare against $0.2$ and $0.8$ only over a frequency span where parasitics are demonstrably negligible. Archive Touchstone with units and port order, report uncertainty and repeat cable connections. Never substitute simple $50\,\Omega$ textbook equations for the specifications of a particular compact VNA.

1. Explain what a coherent VNA ratio receiver measures and how this differs from a spectrum analyzer.
2. Derive S11 from peak V/I waves at a real R0 reference plane.
3. Explain what a2=0 means for a forward S21 test and why b2 can be nonzero.
4. Calculate Γ, RL, VSWR and reflected-power fraction for a 75 Ω load on a 50 Ω port.
5. Calculate all S for an ideal 25 Ω series resistor at two 50 Ω ports.
6. Compute the resistor's dissipated-power fraction using both S and physical I²R.
7. Translate S11=0.4∠30° outward by λg/8 and identify the new phase.
8. Invert the three-term VNA one-port error model to solve for Γ.
9. Explain why finite directivity and calibration noise matter near perfect matching.
10. Draft a verification experiment using a VNA, archive fields and repeatability checks.

Next: calibration reference planes, systematic error boxes and the difference between calibration and fixture de-embedding.