Basics of Smith Chart

The Smith chart is a straightforward method for designing matching networks to deliver maximum power from the source to the load. There are some important feature of Smith chart needed to be considered first.

  • The upper half of the Smith chart is inductive, while the lower half is capacitive.
  • The center point of the circle is 50 ohm.
  • On the far right, the impedance is at its maximum and the Current (I) is zero (open circuit). Left side impedance is zero and the Current (I) is at its maximum (short circuit)
  • Any upward movement shows the addition of an inductor, while any downward movement shows the addition of a capacitor.

The red circles and curves illustrated below and started from right side represent impedance (𝑍 = 𝑅 + π‘—πœ”πΏ). The circles are resistance (real part of impedance), whose values increase as they move to the left, and the curves are for imaginary part of impedance. Notably, movement on these circles/curves will add a series component to the matching network.

The blue circles and curves started from left side demonstrate admittance (π‘Œ = 1/𝑍) and the real part of admittance (circles) getting bigger as going towards right side. The movement on these circles/curves will add a parallel component to the matching network.

Given that the load impedance is 50 ohm, a matching network is required to match the input impedance to the load impedance. The second scenario is when a 50-ohm source must be matched to a non 50-ohm load with a matching network.

The reflection coefficient (|Π“|βˆ βˆ…) is defined as the ratio of the powerΒ  reflected to the power inserted. This value is 1 on the open circuit side of the Smith chart and -1 on the short circuit side. At the center, where 50 ohm impedance is available, maximum power will be delivered with minimal reflection (|Π“|=0).

For working on the Smith chart, the following steps must be taken:

  1. The impedance values must be normalized to the characteristic impedance (Z0=50 ohms);
  2. Locate load and source impedance values on the Smith chart.
  3. We must move on the circles/curves (from load to source or vice versa).
  4. If we move from the bottom to the top of the smith chart, inductance will be added to our matching network; if we move from the top to the bottom, capacitance will be added.

Example:


We start with the mentioned 4 steps:
1. Normalized the impedance values to 50 ohmΒ 

2. Determine the place of load and source impedance values on the Smith Chart

3. We have to move on the circles/curves (from load to source)

4. For this example, the initial move is on the admittance circle, which represents a parallel component. As we ascend, the inductor will become the necessary component. As the next movement is toward the bottom, the capacitor will be chosen; as this movement is on the impedance circle, the capacitor must be positioned in series within the matching network.

 

Tell us where to send your free copy:

"*" indicates required fields

Consent