Understanding VNA and S-parameters

A vector network analyzer can fully characterize components by deriving their scattering parameters.

In earlier parts of this series, we looked at analog spectrum analyzers (part 1 and part 2) and vector signal analyzers (part 3), both of which monitor unknown signals, whether emanating from a system, device under test (DUT), or an enemy’s transmitter in an electronic-warfare scenario. Yet another analyzer is the vector network analyzer (VNA). Unlike the other analyzers, it comes with its own variable-frequency signal generator, and it determines how a DUT responds to the signals it generates.

How does it work?

In Figure 1, the VNA source drives a splitter, which divides the signal into two equal parts. One part goes to a reference-receiver input (labeled Ref), and the other, labeled a₁, goes to the DUT’s port 1 (P1). A portion of that signal (b₂) will emerge from the DUT’s port 2 (P2) and be transmitted to a load, typically equal to the test system’s characteristic impedance Z₀. From an earlier post on insertion loss and return loss, we know that DUT impedance mismatches will cause some portion of the signal to reflect back toward the source (b₁). Directional couplers DC1 and DC2 connect the reflected and transmitted signals b₁ and b₂, respectively, to the VNA’s test receivers T1 and T2, and the VNA calculates the DUT’s scattering-parameter (S-parameter) matrix and displays the results, often in the form of a Smith chart, which we looked at in an earlier series.

VNA diagram — Figure 1. A VNA applies an incident signal (blue) to a DUT and measures the transmitted (red) and reflected (orange) signals.

Why S-parameters, not voltages, currents, and impedances?

Voltage and current are difficult to measure at high frequencies. Figure 2 helps illustrate why. At the top, we have a DC circuit with point sources and loads and ideal wires, and we can locate our voltmeters and ammeters at various locations and still get consistent readings. Granted, real wires can have IR drops at high currents and long lead lengths, but we can compensate using, for example, a four-wire measurement technique that adds the sense wires shown in red.

VNA S-paramater ports — Figure 2. Meters distributed throughout a DC circuit provide consistent results (top), but that’s not the case for high-frequency circuits (bottom).

At high frequencies, the situation is completely different. As shown at the bottom, our wires are infinite series of infinitely small impedance elements, and measurement results depend on where we make the measurements. Cables are often shielded, but even if we could penetrate the shield to connect voltmeters or ammeters, we wouldn’t know exactly where to probe, and the meter leads would become stubs that degrade the signal we are trying to measure. What we can do is accurately measure power at cable connectors and device ports. S-parameters are simply ratios of power measurements.

How are the S-parameters calculated?
For the Figure 1 setup, the calculation proceeds as follows:

Insert Eq1 here

where s₁₁¬ equals the reflection coefficient and s₂₁ equals the transmission coefficient.

Figure 3 illustrates a point about S-parameter notation. Counterintuitively, the first digit of the subscript refers to the DUT port from which energy emanates, and the second digit refers to the port to which energy is applied.

Figure 3. S-parameter notation can be counterintuitive.

Do the two S-parameters completely characterize our DUT?
No. The number of S-parameters for an n-port network is n2, so our two-port network has four S-parameters. We could simply turn the DUT around to measure the other two, but that’s error-prone and inconvenient, requiring recalibration. Alternatively, we can choose a VNA configured as shown in Figure 4, where a switch reroutes the signal-source output (a2) to P2. (Additional poles of the switch connect and disconnect load Z0 as required.) Then, DC1 and DC2 route the transmitted (b1) and reflected (b2) signals to the VNA receivers, and the VNA calculates the remaining two S-parameters.

VNA switch port — Figure 4. A switch connects the source to P2.

Figure 5 shows a simplified diagram of the forward and reverse paths through the DUT along with the full set of four S-parameters, where s22¬ and s¬12 represent the reverse reflection coefficient and reverse transmission coefficient, respectively.

VNA two-port network — Figure 5. A two-port network has four S-parameters, representing forward and reverse reflected and transmitted signals.

How many ports can a VNA have?

You can buy a one-port VNA. Often called a reflectometer, it measures s11. There is no theoretical upper limit to the number of ports. Versions configured with 24 ports are commercially available, and you can use RF switching matrices to add ports to a VNA you already have.

Do VNAs have applications outside of electronics?
Yes, VNAs find use in applications ranging from healthcare to agriculture.

Where can I learn more?
See these resources: