Lesson 6 derived the reflection coefficient from the boundary condition at the load, and Lessons 10 through 13 put it on the Smith chart, where the matched load is the center, the short is the left edge, and the open is the right edge. Every measurement today lands on one of those points or on a curve you can predict from them.

A VNA describes a device by its scattering parameters, or S-parameters, which are ratios of waves rather than of voltages and currents. The subscripts name the receiving port and then the sending port, so \(S_{21}\) is the wave received at port 2 when port 1 transmits. With a single load connected to port 1, the reflected wave over the incident wave is exactly the reflection coefficient of Lesson 6, so \(S_{11} = \Gamma\). Lesson 16 uses \(S_{21}\) as well. The NanoVNA displays four traces at once: \(\vert S_{11}\vert\) in dB in yellow, \(\vert S_{21}\vert\) in dB in blue, the phase of \(S_{11}\) in magenta, and \(S_{11}\) on a Smith chart in green.

The analyzer measures wave amplitudes, which are voltages, so it converts the magnitude of \(\Gamma\) to decibels with \(20\log_{10}\), not \(10\log_{10}\). A load that reflects everything reads \(0\) dB. A perfect match reads \(-\infty\) dB, which no real measurement reaches: a good \(50\ \Omega\) resistor reads somewhere between \(-30\) and \(-50\) dB, and the floor is set by how well you calibrated. The \(1\ \text{k}\Omega\) value comes from \(\Gamma = \frac{1000 - 50}{1000 + 50} = 0.905\).

Between the analyzer’s port and the load sit a cable, an SMA-to-BNC adapter, and a pair of clip leads. Lesson 7 showed that a length of line transforms the impedance at its end, so without correction the VNA would report the load as seen through all of that hardware, not the load itself. Calibration fixes this. You connect three loads whose reflection coefficients are known exactly, the open, the short, and the \(50\ \Omega\) load, at the exact point where the device will go. From the three measurements the VNA solves for the error the hardware introduces at each frequency, and it removes that error from every later measurement. The correction holds only for the hardware and the frequencies you calibrated with.

A capacitor stores energy and dissipates none, so Lesson 6 predicts \(\vert\Gamma\vert = 1\). To get the phase, we multiply the numerator and denominator by \(j\). The numerator becomes the complex conjugate of the denominator, so the ratio has magnitude one and a phase of minus twice the denominator’s angle. At low frequency \(X\) is large, \(\phi\) is small, and the capacitor looks like an open. As the frequency rises, \(X\) falls and the phase grows more negative, so on the Smith chart the measurement traces the outer circle clockwise from the open toward the short.

The packet asks you to fill in the expected impedance of the 470 pF capacitor at ten frequencies from 50 kHz to 5 MHz and plot them on the Smith chart before the lab. The table shows four of them, worked with the result of the previous frame. At 5 MHz, for example,

so \(\Gamma = 1\angle -72.9^\circ\). Work the other six the same way. Over the band you will measure, the capacitor covers only the upper quarter of the Smith chart’s outer circle; its reactance would equal \(50\ \Omega\) at 6.8 MHz, just above the top of the sweep.

The second mismatched load puts a resistor and a capacitor in series, so it has both a real and an imaginary part. Its impedance at 2 MHz is the resistor plus the capacitor’s reactance from the previous frame. In the numerator the two \(50\ \Omega\) terms cancel, which leaves only the reactance. Dividing the magnitudes, \(169/196.6 = 0.861\), and subtracting the angles, \(-90^\circ - (-59.4^\circ) = -30.6^\circ\), gives \(\Gamma\). The resistance equals \(Z_0\) at every frequency, so on the Smith chart the trace rides the \(r = 1\) circle, starting near the open at 50 kHz and moving toward the center as the reactance shrinks. The packet asks you to work this before the lab and to explain the path in the lab.

Today you measured loads you already understood, which tests the instrument and your calibration as much as the theory. Lesson 16 reverses the roles. The device under test is a filter with its label taped over, and you identify what it is, where its cutoff falls, and whether it looks capacitive or inductive in each part of its band, using only the analyzer.

Before Lesson 16, read Measurement 6 of the lab packet.