Smith Chart

Basics of Smith Charts

Coined and developed by Paul Smith, smith charts were essentially deployed to provide electrical, microwave and electronic engineering solutions much before the advent of digital computers. The charts were brought to limelight in the wake of World War II to evaluate the problems associated with the transmission of radio waves.

what is smith chart

Smith Charts

A Smith chart can largely be identified as a diagrammatic illustration revolving around the behavior of transmission lines. It can be most importantly touted as a graphical tool or calculator that assists in displaying and understanding the impedance and frequency values associated with transmission lines with the help of equations.

The chart was acknowledged as a transmission line calculator owing to its prime purpose of use. Gradually, the charts were effectively opted for various other parameters to visualize as well as analyze complexities of functions to derive accuracy and productivity in results.

Smith charts play an integral part to evaluate the impedance values of transmission lines in circuits associated with high frequency.

The chart is a basically circular structure constituting of two major circles or arcs, namely the Constant R Circles and the Constant X Circles that help to visually define the shape and the data values incorporated in the chart.

In simple terms, the graph can be considered a collection of circles, where each of the circle is placed at different locations in the plot area. Each of the circular structure either denotes the constant resistance or constant reactance.

impedance smith chart
Example: Impedance Smith Chart (Image Source:

Impedance matching is the chief and consistently used offering from Smith charts along with designing, tuning and validation of similar networks. Additionally, parameters like admittance, scattering values, analysis of mechanical vibrations, noise figure circles, and reflection coefficients can be simultaneously exhibited with the help of the charts.

Formula for reflection coefficient

On a more technical perspective, a smith chart incorporates a polar plot of complex reflection coefficient (symbolized by Γ) and is implemented by inspecting the load whose impedance must be matched. The reflection coefficient value can be generated from the equation as below;

reflection coefficient formula smith chart

Here, Z0 is the value for the impedance of the transmitter, and ZL represents the impedance of the load.

In cases where the impedance cannot be considered directly, the reflection coefficient (symbolized by ΓL) of parameters like admittance, gain, as well as trans-conductance can be used to characterize the load. The reflection coefficient value is specifically essential when working with RF frequencies.

Types of Smith charts

Smith charts are plotted on a coefficient plane constituting of two dimensions, namely the Z and the Y-axis and can be distinguished as the impedance smith chart or the Z-smith chart, the admittance smith chart or the Y-smith chart and lastly the immittance smith chart or the YZ charts.

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Impedance charts or normal smith charts are common and widely used out of all three categories. Impedance smith charts are related to impedance and show excellent efficiency of results in impedance matching with regard to the load data that is made up of series components and is the most sought after type of smith chart.

Admittance charts are rarely used as they employ the distribution of load data in the form of parallel components, and the most popular applications of smith chart demand the arrangement in a series format.

As admittance can be addressed as the inverse parameter of impedance, its importance can be recorded in many scenarios to cut down the complexity of the former mentioned popular smith chart.

While the immittance charts are availed when both the series components (in impedance charts) and parallel components (in admittance charts) are involved and bring in a lot of complexity.

Applications of Smith charts

Taking insight from the various categories of charts enumerated above, the important applications of smith charts can be identified in its extensive use in calculating admittance and impedance on a transmission line along with impedance matching for relative data.

All these computations impose a lot of complexity owing to the calculations and concrete structures of the charts.

Results for impedance matching can be estimated by simply reading and analyzing the sequence of values along with the multiple circles, which can be accounted for one of the major advantages derived from smith diagrams.

Estimations associated with the distances and lengths of transmission lines in short circuits that offer the necessary capacitive or inductive reactance is another feather in the use of smith charts.

The charts are additionally deployed to determine the values related to Voltage Standing Wave Ratio or VSWR of transmission lines as well as wave-guides in electronic units.

Smith charts can be crafted and constructed with the help of the value derived from the standard reflection coefficient formula and later manipulating it to generate the equations concerning the multiple circles of various radii.


The main disadvantage of deploying smith charts is the complexity of the resulting graphical structure embedded with mathematical equations which makes it hard to perceive at a glance. Another prominent hindrance is that there is no presence of a frequency axis which arouses intricacy of interpretation at a glance or two.

As the circuit associated with the transmission lines matches the values at the centre frequency and thrust the same quantity of discrepancy at the edge frequencies, the efficiency of the results can be hampered to a considerable extent.

Easy construction of the charts imposes a good perception and high-level knowledge of the basics of algebra and complex numbers. To procure the complete understanding of the charts, a user needs to be familiar with a primary understanding of impedance and its associated variables in electronic circuits.


Owing to its massive support in predicting and obtaining results for the values of impedance, admittance and immittance among various other benefits it provides, fabrication of smith charts can be attributed as an efficient method and analogy to solve numerous RF design problems.

The charts have been employed since the 1930s and are still extensively used besides being the only podium to generate accurate results effectively without the need of any calculator.

They are reliable for analyzing and generating complex as well as multifaceted solutions apart from determining the circuit fundamentals and parameters.

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