Smith Chart Primer

The Smith chart is a graphical tool that displays impedance, admittance, and reflection coefficient all in one circular plot. Originally invented in 1939 by Philip Smith, it remains the most powerful visualization tool for RF impedance matching. The NanoVNA-H displays your measurements directly on a Smith chart, making impedance analysis intuitive.

Why the Smith Chart?

Impedance is a complex number (R + jX), which normally requires two separate graphs---one for resistance and one for reactance. The Smith chart cleverly maps this two-dimensional data onto a single circular plot where:

• Every point represents a unique impedance
• Distance from center represents magnitude of reflection (SWR)
• Angle from center represents phase of reflection
• Circles represent constant resistance or constant reactance

Normalized Impedance

The Smith chart uses normalized impedance (z = Z/Z0). For a 50 ohm system, z = 1 means 50 ohms, z = 2 means 100 ohms. This makes the chart universal for any reference impedance.

The Coordinate System

Constant Resistance Circles

Horizontal lines of constant resistance on a rectangular plot become circles passing through the right edge of the Smith chart:

flowchart LR
  subgraph Smith Chart
      direction TB
      A((Center<br/>R=1))
      B((Right Edge<br/>R=infinity))
      C((Left Edge<br/>R=0))
  end

• Center point: z = 1 (50 ohms in a 50 ohm system)
• Right edge: z = infinity (open circuit)
• Left edge: z = 0 (short circuit)
• Each circle: All impedances with that resistance value

The firmware renders these circles in plot.c:

static bool smith_grid(int x, int y) {
  // Constant Resistance Circle: 1 : R/2
  d = circle_inout(x - P_RADIUS/2, y, P_RADIUS/2);
  if (d > 0) return 0;
  if (d == 0) return 1;

  // Constant Resistance Circle: 1/3 : R*3/4
  if (circle_inout(x - P_RADIUS/4, y, P_RADIUS*3/4) == 0) return 1;

  // Constant Resistance Circle: 3 : R/4
  d = circle_inout(x - 3*P_RADIUS/4, y, P_RADIUS/4);
  // ...
}

Constant Reactance Arcs

Vertical lines of constant reactance become arcs touching the right edge:

• Top half: Inductive reactance (+jX)
• Bottom half: Capacitive reactance (-jX)
• Horizontal axis: Pure resistance (X = 0)

Region	Reactance	Component Behavior
Upper half	+jX (positive)	Inductive (antenna too long)
Horizontal axis	jX = 0	Purely resistive (resonance)
Lower half	-jX (negative)	Capacitive (antenna too short)

Reading the NanoVNA Display

When you enable the Smith chart trace on your NanoVNA-H:

Finding Key Points

Point Location	Impedance	Meaning
Center	50 + j0 ohms	Perfect match
Right edge	Open circuit	Total reflection, 0 degree phase
Left edge	Short circuit	Total reflection, 180 degree phase
On horizontal axis	R + j0	Purely resistive
Top of chart	0 + j50 ohms	Pure inductance (normalized)
Bottom of chart	0 - j50 ohms	Pure capacitance (normalized)

VSWR Circles

Circles centered on the chart center represent constant SWR:

Distance from center = |S11| = (SWR - 1) / (SWR + 1)

Circle Radius	SWR	Return Loss
0 (center)	1:1	infinity
0.20	1.5:1	14 dB
0.33	2:1	10 dB
0.50	3:1	6 dB
1.0 (outer edge)	infinity	0 dB

Mental Picture

Imagine the Smith chart as a target. The center is a bullseye (perfect match). The farther from center, the worse your match. Your goal in antenna tuning is to move the trace point toward the center.

Practical Interpretation

Antenna Tuning Example

You connect your 40m dipole and see the measurement point at the 7.1 MHz marker:

Case 1: Point in upper right quadrant

• Above horizontal axis = inductive
• Right of center = resistance > 50 ohms
• Fix: Antenna is too long. Shorten it to reduce inductance.

Case 2: Point in lower left quadrant

• Below horizontal axis = capacitive
• Left of center = resistance < 50 ohms
• Fix: Antenna is too short. Lengthen it to reduce capacitance.

Case 3: Point on horizontal axis, right of center

• On axis = resonant (X = 0)
• Right of center = resistance > 50 ohms
• Fix: Antenna is resonant but high impedance. Add matching network or adjust height/configuration.

Frequency Sweep Pattern

As you sweep frequency across a band, the trace moves around the Smith chart:

flowchart LR
  A[Low Freq<br/>Capacitive] --> B[Resonance<br/>On Axis]
  B --> C[High Freq<br/>Inductive]

A typical antenna trace forms a clockwise arc as frequency increases:

1. Below resonance: Capacitive (lower half)
2. At resonance: Crosses the horizontal axis
3. Above resonance: Inductive (upper half)

Admittance Chart

The NanoVNA-H can also display the admittance chart (Y = 1/Z = G + jB):

• Admittance chart is the Smith chart mirrored horizontally
• Useful for designing parallel matching networks
• Conductance (G) circles and Susceptance (B) arcs

The firmware draws this by mirroring the x-coordinate:

static void cell_admit_grid(int x0, int y0, int w, int h, pixel_t color) {
  // offset to center (note: x is mirrored)
  x0 = P_CENTER_X - x0;
  y0 -= P_CENTER_Y;
  for (y = 0; y < h; y++)
    for (x = 0; x < w; x++)
      if (smith_grid(-x + x0, y + y0)) cell_buffer[y * CELLWIDTH + x] = color;
}

Using the Smith Chart for Matching

Series Components

Adding a series component moves along constant resistance circles:

• Series inductor: Move clockwise (up) along resistance circle
• Series capacitor: Move counter-clockwise (down) along resistance circle

Shunt (Parallel) Components

Adding a shunt component moves along constant conductance circles (use admittance chart):

• Shunt capacitor: Move clockwise (down on admittance chart)
• Shunt inductor: Move counter-clockwise (up on admittance chart)

L-Match Design

To match an impedance to 50 ohms:

1. Plot your load impedance on the Smith chart
2. Choose series or shunt component to move toward 50 ohm point
3. Add complementary component to complete the match
4. Calculate component values from reactance and frequency

LC Match Function

The NanoVNA-H includes a built-in LC matching calculator. Enable it via Display > Measure > LC Match to see suggested component values automatically.

Key Smith Chart Features

The Unit Circle

The outer edge (|S11| = 1) represents total reflection:

• All points on this circle have SWR = infinity
• Open and short circuits both lie on this circle
• They differ only in phase (0 vs 180 degrees)

The Real Axis

The horizontal diameter represents purely resistive impedances:

• Center = 50 ohms (normalized 1.0)
• Left of center = less than 50 ohms
• Right of center = greater than 50 ohms

Rotation with Transmission Line

Adding transmission line length rotates the point clockwise:

• Half wavelength (180 degrees) returns to same point
• Quarter wavelength (90 degrees) inverts impedance
• This is the basis of quarter-wave matching transformers

Summary

Chart Region	Impedance Character	What to Do
Center	50 + j0 (perfect match)	Nothing - you are done
Upper half	Inductive (+jX)	Add series capacitance
Lower half	Capacitive (-jX)	Add series inductance
Right half	R > 50 ohms	Use matching transformer
Left half	R < 50 ohms	Use matching transformer
On outer edge	Open or short	Check connections

Next Steps

Now that you can read the Smith chart, learn more about Impedance and Q Factor to understand what resistance and reactance mean for your components.