Smith_Chart - Smith Chart Application

A Smith Chart Application

Keith Greiner

This text describes how a reading from a NanoVNA can be used to determine the component values of an L-network. There is much specific information that refers to the images and mathematical formulas, so a slow reading is recommended.

Below is an image from an NanoVNA that is connected to a 75-ohm RG6U coaxial cable that is connected to the NanoVNA Port1, at one end, and to a magnetic loop antenna tuned on the other end. The magnetic loop is tuned to 14.040 Mhz.

Figure 1. NanoVNA-F V2 analysis of 20 Meter magnetic loop antenna.

The VNA display shows several layers of information that are written on top each other on the display. The large blue/white “V” shape is the SWR scan of frequencies from 13.0 MHz to 15.0 MHz. The V dip indicates the resonant frequency of the antenna. There is a blue icon at the bottom of the V and numbered “1”. The large circles are the Smith Chart, and the yellow circle shows the Smith Chart values for the complete frequency scan. In the top right cell, and the cell that is three down and one to the left there is the number 1.99. that is actually part of a statement of “1.0/1.99” and indicates the SWR at the point at the bottom of the V.

On the top left, there is yellow text that says “S11 SMITH 92.3 21.9j”. That tells us the impedance is 92.3 ohms resistive (R = 92.3) and 21.9 ohms reactive (Xj = 21.9) at the frequency of 14.04 MHz. The Z value may be found using the Pythagorean theorem.

Z = (R^2 + Xj^2)^0.5.

In words, Z is equal to the square root of the sum of R squared plus X squared. Plugging in the values from the VNA we find that, Z = 94.86.

In the middle of the above screen, there is blue/white text that tells us what values of capacitors and inductors that will match the cable to a 50-ohm transmitter. I've enlarged that section below.

Figure 2. VNA image selection.

The table shows us that the following L/C values match the source device that has an impedance, Z0, of 50.0 ohms. In the second line there are three columns with headings “Src shunt”, “Series”, and “Load shunt”. There is no information in the Src shunt column. In the columns for Series and Load shunt, there are two important rows. Thin those rows, three and 4 from the top of the screen selection there are values for inductance and capacitance values for each of the two solutions. This follows the circuit system topology from left to right with transmitter on the left, followed by Src shunt, then Series, then Load shunt, then the RG6U cable, and then the antenna. In some cases, the output can be connected directly to the antenna. In one of my systems, there is an L-network between the transmitter and the RG6U, and another between the RG6U and the antenna.

So, in this situation there are two solutions to the calculation, which also means we have two ways to create the match. Option 1, is to connect a 552nH (0.552 µH) inductor in series, and then connect a 140pF capacitor in shunt (parallel, aka. From the center wire of the coax to ground). We can also connect a 232pF capacitor in series and a 1.50µH inductor in shunt. The order of the components is important. From left to right, goes from transmitter through the matching network and then to the coax. If there were a shunt component at the transmitter, it would be listed under the column “Src shunt”.

Let’s enter the R=92.3 and Xj = 21.9 values into this online 50-Ohm Smith Chart. Press “enter” to perform the calculation and discover the L-network components. Following is the table that shows the same values as the VNA. In this display, the components are labeled as L for inductance and C for capacitance.

Figure 3. Selection from Smith Chart tool..

Now, let’s confirm these values by using the Will Kelsey onlinesmithchart.com .

The following two images show how I entered the results from the VNA and from my Smith Chart into the Will Kelsey online chart. The two images that follow show how I entered the values into the online chart tool. What’s not shown in this image is that just below the circular chart there is a place to enter the frequency. Be sure that is set correctly as the default will cause the tool to return values that are far away from correct. Here, we see that both solutions are verified because the connecting lines both end in the center of the chart where the impedance 50 ohms is indicated. The R and X values from the VNA are entered into the dialog boxes below the image labeled "Black Box". Then the L-network components are added as specified by the 50-ohm calculator program at this site. The two solutions are shown in the two images that are below. From that process, you will see that the blue dot is in the same location on the Smith Chart, as is shown in the calculator on this site. Then you'll see an orange line and a green line that describe the changes in impedance that occur when each of the components is added. Put the two together, and the result is a green dot in the center of the chart where the "50-ohms" resistive value is represented. Be sure you have entered the frequency correctly, below the circular chart, and the goal of 50-ohms as the final desired value, also shown below the circular chart. If you have entered everything correctly, the beginning blue dot should be in the same location as shown on this calculator, and the final green dot should be on the 50.

Make note of the following, as it is very important. Output from this Smith Chart calculator and the image shown above, has components in the following sequence: transmitter/source, then source-side capacitor or inductor, and then series component , and in the most right position, the load-side component, and finally the complex value from the NanoVNA. The input fields on https://onlinesmithchart.com, are in the opposite direction. On that site, the box described as “Black Box” is the Load, and contains the measured value that you record from the NanoVNA, and type into the tool.

Figure 4. Selection #1 from oneline Smith Chart.

and ....

Figure 5. Selection #2 from oneline Smith Chart.

Let’s see how this can fit into a practical project. I like to build antenna tuners. They are simple to build and can be custom created to fit most any situation. Since I use inexpensive 75-ohm coax there is a need to provide a match where the transmitter is connected to the coax, and another match where the coax is connected to the antenna. There is a common misunderstanding among amateur radio operators that all coaxial cable must be 50 ohms. That's not true. If you add the appropriate matching network at the beginning, and another appropriate matching network at the end, the cable or feed line in-between can be most anything. On this site, there is a calculator that is set-up to calculate values if the load is 50-ohms, 75-ohms, or 300-ohms. There is a fourth calculator where you can add any load value and obtain component values for an L-network. For WSPR operation, my transmitter is connected to an L-network tuner and that is connected directly to the antenna. There is no feed line. In that case, it is important to put an L-network between the transmitter and the antenna, for proper match, minimum SWR, usually 1:1, and maximum output from the 200 mw transmitter. With that combination, the signal has been heard all over the globe.

The L-network is a simple two-component tuner. With the inductance in series and the capacitance in shunt, it serves as a low pass filter and that’s a good thing because it surpresses above-frequency harmonics. Below is a circuit diagram of a versatile circuit that can serve as up to three configurations. When S1 is closed and S2 is open, the L-network has the sequence of shunt-capacitor series inductor. When S1 is open and S2 is closed, the sequence is series inductor shunt capacitor. If both S1 and S2 are closed, it serves as a pi network.

Figure 6. Two L-networks -- optionally a pi network.

What we know about the VNA measurements can inform the component selections. My flea market find of a matched pair of capacitors has a range of 20 pf to 350 pf and works very well. My toroid that is wound with 10 turns with ten taps run through a rotary switch has values of 0 µH to ~40µH. So, the inductor is barely used, but is available to provide greater values in another situation. Since we know that the solution calls for a 0.552 µH inductance but the first step in the variable capacitor goes from 0µH to 4µH, perhaps the design could be improved if there were a second inductor that has a variable range that would cover a range of values between 0µH to 4µH. It would be nice to have the whole device be a roller coil. If you use an auto-tuner and it fails because can't find the settings needed for a match, check the values that come from your NanoVNA and this program, and make adjustments that bring the load closer to a 1:1 match on the load side, before connecting the auto-tuner.