Smith chart
| Smith chart | |
|---|---|
| What it is | A circular graph of impedance used to solve transmission-line and matching problems |
| Inventor | Phillip H. Smith (1905–1987), of Bell Telephone Laboratories |
| First published | Electronics magazine, January 1939 |
| Improved version | Electronics, January 1944 |
| Reading it | |
| Plots | Normalized impedance on the plane of the reflection coefficient |
| Center | A perfect match (50 + j0 on a 50-ohm chart) |
| Upper half | Inductive reactance |
| Lower half | Capacitive reactance |
| Outer edge | Pure reactance; all power reflected |
| One full turn | Half a wavelength of transmission line |
| Found on | Vector network analyzers such as the NanoVNA; RF design software |
The Smith chart is a circular graph that shows impedance in a way that makes transmission-line and matching problems easy to solve by eye. Every passive impedance, from a short circuit to an open circuit, fits inside one circle, with a perfect match at the center.[1] The chart was devised by Phillip H. Smith, an engineer at Bell Telephone Laboratories, and published in 1939.[2] Computers now do the arithmetic, but the chart remains the standard way to picture impedance, and many antenna analyzers and network analyzers display their measurements on it.
History
Phillip Hagar Smith (1905–1987) built his own amateur radio stations as a young man and joined Bell Labs' radio research department in 1928, after graduating from Tufts College.[3] His work involved many measurements of standing waves on transmission lines, and the calculations were slow and tedious. He drew a first graphical solution, on a rectangular grid, in 1931, and kept refining it.[3] The circular chart appeared as a "Transmission Line Calculator" in the January 1939 issue of Electronics, and an improved version followed in the same magazine in January 1944.[2] Smith spent 42 years at Bell Labs[3], and his chart became one of the best-known tools in radio engineering.
Reading the chart
The chart is normalized: each impedance is divided by the characteristic impedance of the system, usually 50 ohms for ham radio.[4] A normalized value of 1 + j0 is the center point. On a 50-ohm chart, 100 + j50 ohms is plotted as 2 + j1.
- Resistance circles. Each full circle marks a constant resistance; all of them meet at the far right point of the chart. The horizontal center line carries pure resistance, from zero at the far left to infinity at the far right.
- Reactance arcs. Curves fanning out from that same point mark constant reactance. Arcs above the center line are inductive (positive reactance); arcs below are capacitive (negative reactance).[1]
- The edge. The outer circle is pure reactance with no resistance, where all the power is reflected. The far left point is a short circuit and the far right an open circuit.[1]
Behind the grid, the chart is a polar plot of the reflection coefficient, the fraction of the signal voltage that bounces back from a mismatched load. The distance from the center gives the size of the reflection, and the angle gives its phase.[4] All points at the same distance from the center have the same SWR, so a circle drawn around the center is a constant SWR circle. Where it crosses the right half of the center line, the normalized resistance there equals the SWR.
Using the chart
- Feed lines. Adding length of lossless feed line moves a point around its SWR circle: clockwise when moving from the load toward the transmitter, and once all the way around for every half wavelength of line.[1] This shows why the impedance an analyzer reads at the shack end of the coax can differ greatly from the impedance at the antenna, while the SWR stays the same. Real cable loss makes the point spiral slowly inward, which is why a lossy line can make a poor antenna look good.
- Matching networks. Adding a series inductor or capacitor moves a point along its resistance circle.[4] Shunt components are easier to handle on the companion admittance chart, which is the impedance chart rotated by 180 degrees; many printed charts overlay both.[4] A designer finds a route from the load to the center in two or three such moves, and each move gives the value of one component. An L-network antenna tuner does the same job with one series and one shunt component.
- Stubs. A short length of line, open or shorted at the far end, acts as a pure reactance. The chart shows where along a feed line to connect such a stub, and how long to make it, so that it cancels the reactance and leaves a match.[1] Smith himself applied for a patent on a single-stub matching network in 1932.[3]
In the shack today
Inexpensive vector network analyzers such as the NanoVNA measure both the size and phase of the reflected signal and show the result on a Smith chart as they sweep a band. A well-matched antenna appears as a curve passing close to the center at its working frequency. Programs such as SimSmith, written by AE6TY,[5] let hams design matching networks by placing components on the chart and watching the point move.
See also
References
- ↑ 1.0 1.1 1.2 1.3 1.4 Smith Chart Basics, Microwaves101.
- ↑ 2.0 2.1 Transmission Line Calculator, January 1939 Electronics Magazine, RF Cafe.
- ↑ 3.0 3.1 3.2 3.3 Lianne Frith, Phillip Smith: From Amateur Radio Operator to Creator of the Smith Chart, All About Circuits, August 2023.
- ↑ 4.0 4.1 4.2 4.3 Impedance Matching and Smith Chart Impedance, Analog Devices.
- ↑ Smith Charts, AE6TY.