How a Vector Network Analyzer Measures S-Parameters

What a VNA actually measures

A vector network analyzer (VNA) does not report "how much power came out." It reports how one wave compares with another wave, in both magnitude and phase. Each result is a complex number.

For a two-port device, four waves matter. The wave a1 travels into port 1, and b1 travels out of port 1. The wave a2 travels into port 2, and b2 travels out of port 2. With the incoming wave a2 at port 2 equal to zero, the two forward parameters are:

Swap the roles of the ports and you get S22 and S12. The condition a2 = 0 is not a detail. S-parameters are defined with every unused port terminated in the reference impedance, usually 50 ohm. A perfect termination reflects nothing, so no wave comes back into port 2.

The blocks inside a two-port VNA

A two-port VNA has four kinds of blocks.

• Source. A swept or stepped signal generator. It supplies the stimulus at one frequency at a time.
• Switch. It routes the source to port 1 or to port 2, so the instrument can measure all four parameters.
• Directional couplers or bridges. One sits at each port. They tap off a small part of the wave travelling in a chosen direction.
• Receivers. They convert the tapped signals into numbers that keep both amplitude and phase.

Each port has a reference receiver that samples the incident wave and a test receiver that samples the wave coming back or passing through. The VNA divides one reading by the other. That division is the S-parameter.

Why couplers can separate the waves

At a test port, the incident and reflected waves share the same connector and the same conductor. A plain voltage probe sees only their sum. It cannot tell them apart.

A directional coupler solves this. It passes a small, known fraction of the forward or reflected wave to a receiver. Depending on how the coupled port is arranged, the receiver sees either the forward wave or the reflected wave, not the sum. A bridge does the same job with a resistive network instead of a coupled-line structure.

Because the coupled fraction is small, most of the signal continues to the device under test. Because it is known, the VNA can correct for it. Calibration also removes the remaining imperfections of the couplers, cables and switch, which is why a VNA result is only as good as its calibration.

Why the VNA reports ratios and phase

Consider what happens if the source power changes by a factor k in amplitude. Both a1 and b1 scale by k, so their quotient does not change. The same holds for b2/a1. S-parameters are therefore dimensionless and do not depend on the absolute source power, provided the receivers stay linear.

This is the main reason a VNA works with ratios. The device is described by what it does to a wave, not by how strong the wave was. Source drift, cable-to-cable differences in the signal level, and small changes in output power cancel in the division, because the reference receiver sees the same change as the test receiver.

Phase is kept for a similar reason. A ratio of two complex numbers has a magnitude and an angle. The angle tells you the delay and the reactive part of the match. A scalar power meter throws that information away. With magnitude and phase together, you can compute impedance, plot a Smith chart, or transform the data to the time domain.

The linearity condition matters. If the source is so strong that a receiver compresses, the reading no longer scales with the wave, and the ratio is no longer correct. The same applies if the device under test itself is driven into compression. The result is then not the small-signal S-parameter.

Worked example: a reflection of 0.1

Suppose the reference receiver reads an incident wave a1 and the test receiver reads a reflected wave b1 that is one tenth as large in amplitude, with port 2 terminated in 50 ohm. Then:

Convert to decibels with the 20 log10 rule for amplitude ratios:

Power goes as the square of amplitude, so the reflected power is 0.1² = 0.01 of the incident power. That is 1 percent. The return loss is the same number with the sign flipped, 20 dB.

Now double the source amplitude. Both a1 and b1 double, and the ratio is still 0.1. The display still reads -20 dB. That is the practical meaning of "ratios, not absolute power."

What keeps the numbers valid

Three conditions carry most of the weight:

1. Every unused port is terminated in the reference impedance, usually 50 ohm.
2. The receivers stay linear, so the ratio does not depend on signal level.
3. The calibration plane sits where you want the measurement to start, which is normally at the connector of the device under test.

When one of these fails, the VNA still prints a trace. It is simply the answer to a different question. For definitions of the four parameters, see the page on S11, S21, S12 and S22. For how reflection and transmission map to loss figures, see the page on return loss and insertion loss.

In plain words · for students and beginners

Measuring S-parameters in plain words

An everyday picture

Shout into a canyon and listen. Some of your voice goes on, and some bounces back as an echo. If you compare the echo with your shout, you learn about the canyon. You do not need to know how loud you shouted. A VNA does this with radio waves: it sends a test signal into a device and compares what comes back, and what comes out the other side, with what went in.

The picture breaks down in one way. A canyon echo is only about loudness. A VNA also records timing, called phase, which tells you how the wave was delayed or shifted.

The same example in simple steps

1. The VNA sends a test signal into port 1. Call its size "1" (in units of amplitude).
2. A small tap on the cable, called a directional coupler, sends a tiny copy of the outgoing wave to one receiver and a tiny copy of the returning wave to another.
3. The returning wave is one tenth the size of the outgoing wave.
4. The VNA divides: 0.1 / 1 = 0.1. This is the reflection ratio.
5. It converts to decibels: 20 × log10(0.1) = -20 dB.
6. Turn the source up to twice the size. Both waves double, and 0.2 / 2 is still 0.1. The answer does not change.

Mistakes beginners make

• Thinking the VNA shows power. It shows a ratio. Ask a power meter if you need watts.
• Leaving the other port open. The unused port must be connected to a 50 ohm termination. An open or wrong load sends an extra echo into the device and spoils the result.
• Driving too hard. If the signal is so strong that a receiver or the device overloads, the ratio is no longer true.
• Ignoring calibration. Cables and connectors add their own reflections and delays. Calibration removes them from the answer.

Remember

• A VNA measures ratios of waves, such as S11 = b1/a1, with the other port terminated.
• A directional coupler lets the VNA tell the outgoing wave from the returning one.
• A ratio of 0.1 is -20 dB, and it stays the same when the source power changes, as long as the receivers stay linear.

Related pages on RF View

• S11, S21, S12 and S22 Explained for a Two-Port
• Return Loss vs Insertion Loss: What Each Number Tells You