# How to Use a Smith Chart for Impedance Matching

### Key Takeaways

• There are many methods for impedance matching in your circuits.

• One popular method for plotting impedance and determining impedance matching is to use a Smith chart.

• Once impedance matching requirements are determined, the results can be simulated in a SPICE-based simulation application. Impedance matching in this PCB can be determined using a Smith chart

High speed and high frequency systems need impedance matching to ensure efficient power transfer and prevent reflections. In many cases, you need to measure and carefully simulate the appropriate impedance required to ensure impedance matching and prevent power reflection. In some cases, such as with transmission line stub matching in RF circuits or input impedance matching to a feedline’s characteristic impedance, a graphical representation of impedance can aid impedance matching.

A Smith chart provides just such a graphical representation of impedance, and it is a useful tool for understanding how impedance varies in different systems. Using a Smith chart might seem complicated to new designers, and one might question why it is any more or less useful than a graph in Cartesian coordinates. Smith charts are a standard tool used by many RF engineers, so it pays to know how to use a Smith chart for impedance matching.

## What Is a Smith Chart?

A Smith chart is a type of graph used to plot the normalized impedance of a circuit, a circuit element, or an interconnect. This unique type of chart was developed by Philip Smith at Bell Telephone's Radio Research Lab in the 1930s. As a graphical method for performing impedance matching, it was very useful before the time of graphical computers and simulation tools for plotting impedance. However, some commercial applications and simulation tools will display impedance data in a Smith chart.

### Reading Impedance From a Smith Chart

To start working with a Smith chart for impedance matching, we need to normalize our load component that requires impedance matching to the desired system impedance. The system impedance might be a 50 Ohm transmission line. Suppose our unmatched load impedance is Z = 60 - i35 Ohms; if the system impedance is 50 Ohms, then we divide the load and system impedances, giving a normalized impedance of Z = 1.2 - i0.7 Ohms.

The image below shows an example Smith chart used to plot the impedance Z = 1.2 - i0.7 Ohms. In this plot, the distance along the horizontal axis is used to denote the real part of the impedance. By tracing out a circle (shown in red) passing through the resistance axis, we are saying that all points on that curve have the same resistance. Next, the reactance is determined by looking at the values along the outside of the chart. By tracing the curve back to the right-most origin, we find an intersection between the reactance curve and the resistance circle. This point (shown in blue) is the impedance we want to plot. There is also a phase angle with respect to the origin of -110°. Impedance matching in this PCB can be determined using a Smith chart

While this may seem like a very involved way to show an impedance value, there is more that can be determined from looking at a Smith chart. Determining impedance matching from a Smith chart requires comparing the plotted impedance to the source impedance. By measuring the required shift in the reactance and resistance, you can determine how large and what type of components are needed in a matching network.

### Determining Impedance Matching From a Smith Chart

By adding some components, we can move the blue point, shown above, around the Smith chart until it sits at our desired impedance value:

• Adding series L and C values shifts the point along constant resistance circles.

• Adding parallel L and C values shifts the point along constant reactance curves.

• Adding R expands or decreases the radius of a constant resistance circle.

In our example, suppose we need to match to a system impedance of 50 Ohms. First, we need to shift the impedance back to the resistance axis by adding a series inductor with reactance of i0.7. Finally, we can shift the normalized impedance back to Z = 1 + i0 by adding a resistor in parallel to shift the equivalent parallel resistance to 50 Ohms.

## Verifying Impedance Matching Results

Once an appropriate impedance match has been determined from a Smith chart, a designer often needs to perform a simulation to verify the results. Doing this in a simulation environment is useful, as it is easy to spot calculation errors and it might eliminate a board spin. There are two principle options available:

• SPICE simulations: Using a frequency sweep in a SPICE simulation for a matching circuit allows impedance matching to be simulated directly. The goal is to simulate the input impedance of the (matching + load) arrangement to ensure there is sufficient impedance matching in your desired frequency band.

• Post-layout network parameter extraction: If the goal is to match the impedance of a transmission line to a driver and receiver, the network parameters should be extracted from the physical layout. Design software with integrated field solver tools can extract and display impedances, which can then be compared with Smith chart results to determine sufficient matching.

For more complex circuits, like a nonlinear circuit, maximum power transfer may not occur with perfect impedance matching. This is where specialty simulation methods are normally used, such as load-pull analysis in power amplifiers. The best design tools will include options to perform a range of analyses for validating Smith chart results.

Once you’ve used a Smith chart for impedance matching and you’ve determined the input impedance required in your circuits, you can simulate your system and create a physical layout with PCB design and analysis software. Cadence provides a powerful set of software tools that help automate many important tasks in systems analysis, including frequency sweeps and transfer function analysis to determine impedance matching requirements in your system.