Impedance matching is an engineering procedure employed in circuit design for matching unequal source and load impedances. Impedance matching is required in order to optimize the power delivered to the load from the source. Impedance matching is accomplished by inserting matching networks into a circuit between the source and the load. A simple example might involve matching unequal source and load resistances with an inductance(L)-capacitance(C) circuit, or perhaps optimizing the gain of an amplifier. In this model, Smith Charts are used to visualize the interactive process of impedance matching.

Using this interactive impedance matching model, you can experience using a Smith Chart and s-parameters to optimize transmitted power in simple circuits. Simple series/shunt, inductance/capacitance matching networks are used, and you can interactively adjust the values of corresponding L and C components. Adjusting the matching network components changes the reflectance of the overall circuit. The reflectance of each part of the circuit is indicated on the Smith Chart as a red or blue ball.

As you adjust the sliders and modify the component values, the model calculates new values for the circuit reflectance and moves the red and blue balls on the Smith Chart. The goal of each excercise is to move the reflectance point from the center of the Smith Chart, which represents either the load or source, into the appropriate red and blue colored rings which represent the desired matching condition. You can select three different impedance matching problems of increasing difficulty by clicking on one of the three labeled tabs included in the model.

Description of Exercises

The first exercise lets you experience using the Smith Chart to perform basic impedance matching between a resistive source and a resistive load. A simple series-inductance shunt-capacitance network is used to match the 50 ohm source to the 300 ohm load. The source reflectance of the circuit looking from the load toward the source is represented by the red ball , while the 300 ohm load is indicated by the stationary red ring .

The objective of the exercise is to interactively match these two impedances by adjusting the L and C sliders. The model will provide graphical feedback by moving the red ball indicating circuit reflectance on the Smith Chart. Adjust the series L and shunt C sliders to move the reflectance point from the center of the Smith Chart to the matching impedance position inside the red ring. You can study the Smith Chart Circuit Element Paths below for hints on how different circuit elements change circuit reflectance on the Smith Chart.

Smith Chart Circuit Element Paths

The second exercise provides the impedance matching experience of optimizing the transducer power gain of a transistor amplifier. Matching the 50 ohm source to the input reflectance of the transistor, s*₁₁, and matching the 50 ohm load to the output reflectance of the transisitor, s*₂₂, optimizes the power delivered from the source, through the transisitor, to the load. You are required to match both the input red ball and output blue ball of the transistor separately. Adjust the component values to move both reflectance points to their proper positions within the red and blue rings.

The third part of the interactive impedance matching model is a collection of exercises involving a modular circuit. You begin by constructing a circuit with either one or two modular drag-and-drop matching network components. Once the matching networks have been added to the circuit, the sliders will become active and allow you to adjust the component values. Then you will engage in impedance matching for the circuit you have just created! There are 8 different circuits you can construct and there are 5 different value pairs for s*₁₁ and s*₂₂ on the Smith Chart, altogether 40 impedance matching exercises. You will find that not all matching networks will work! For some of the circuits you will be able to constuct, you will not be able to position the red ball within the red ring or the blue ball within the blue ring. To determine in advance which matching networks will work, take a close look at the Forbidden Regions of the Smith Chart below. There are 5 different location pairs for s*₁₁ and s*₂₂ corresponding to different frequencies that can be matched. Use the frequency indicator to select an operating frequency, and then drag-and-drop appropriate matching networks into the circuit and adjust the component values to move both reflectance points to their proper positions within the red and blue rings.

Forbidden Regions of the Smith Chart

Smith Chart Circuit Elements Paths
The graphs below demonstrate how the various shunt and series L and C components change the circuit reflectance on the Smith Chart. Assuming the given component is the last component in the matching network, the circuit reflectance will move as indicated along constant resistance or constant conductance circles.

You can think of impedance matching using the Smith Chart as driving a car to a specific destination in Smith Town - a city were none of the streets are straight! By adjusting circuit components in appropriate order, we can constrain the circuit reflectance to paths along constant resistance or constant conductance circles. Just like road signs can direct a car along the circular streets of Smith Town, so can we reach the matching impedance condition in a straightforward and deterministic way.

Forbidden Regions of the Smith Chart
For a given load reflectance, only certain L-C matching networks will be capable of transforming the source impedance to the load impedance. In fact, for any load reflectance, exactly two of the four possible L-C matching networks in the Transistor Amplifier-II model above will be able to do the matching job. But which two?

The charts below can be used to determine which matching networks will work in a given load situation. If the load reflectance lies within the forbidden region of the Smith Chart for the indicated matching network, then that network cannot perform the required matching operation. You cannot drive your car into the forbidden neighborhoods of Smith Town! They are unpaved!

Use these charts to determine which matching network should be used. First, visually locate the position of the load reflectance from the Transistor Amplifier-II model above on each of the four color Smith Charts below. Then, eliminate the two networks whose forbidden regions overlap the reflectance point, and use one of the remaining two networks to perform the impedance match.