Introduction to Smith Charts

• Presentation delivered at VHF Amateur Radio Conference (Oct 2018)
• Focus on basics of Smith charts

What is a Smith Chart?

• Graphical tool for plotting and computing:
  • Complex impedance
  • Complex reflection coefficient
  • Voltage standing wave ratio (VSWR)
  • Transmission line effects
  • RF matching network design

Normalized Impedance

• Definition: Actual measured impedance divided by system impedance (Z0), typically 50 ohms.
• Example:
  • Measured impedance: 37 + J55
  • Normalized impedance (Z'): (37/50) + j(55/50) = 0.74 + J1.1
• Usable for various system impedances (600 ohms, 75 ohms, etc.)

Regions of the Smith Chart

• Center Axis: Purely resistive axis
• Above Axis: Inductive components
• Below Axis: Capacitive components
• Key Points:
  • Center point = system impedance (50 ohms)
  • Right end = open circuit (infinity)
  • Left end = short circuit (0 ohms)

Constant Resistance and Reactance Circles

• Constant resistance circles: Tangent to the infinity axis
  • Example values: 1.0, 1.2, 1.4, etc.
• Constant reactance arcs: Emanate from open circuit position
  • Inductive: Positive J values
  • Capacitive: Negative J values

Plotting Complex Impedance

• Example: 25 + J40 (inductive, above center axis)
• Normalize: (25/50) + j(40/50) = 0.5 + J0.8
• Find intersection of resistance circle (0.5) and reactance circle (0.8) to plot on Smith chart.

Designing RF Matching Networks

• Adding Elements: Move along Smith chart circles:
  • Series Inductors: Move clockwise along constant resistance circles
  • Series Capacitors: Move counterclockwise along constant resistance circles

Admittance

• Definition: 1/impedance; conductance is 1/resistance, susceptance is 1/reactance.
• Admittance curves: Rotate Smith chart 180 degrees to visualize.
• Combining Smith Charts: Use combo charts for easier admittance calculations.

Tips for Adding Inductors and Capacitors

• Inductor Addition:
  • Series: Elevate through real axis along constant resistance circles.
  • Parallel: Move along constant conductance circles.
• Capacitor Addition:
  • Series: Crash down through real axis along constant resistance circles.
  • Parallel: Move down on constant conductance circles.

Radially Scaled Parameters

• Parameters visible along the bottom axis of the Smith chart:
  • Voltage Standing Wave Ratio (SWR)
  • Return Loss (.1 dB)
  • Power Reflection Coefficient (0.155)

Standing Wave Ratio and Transmission Lines

• Impedance transformation occurs at multiples of 1/2 wavelength in transmission lines.
• 1/4 wavelength transformations:
  • Open circuit behaves as a short circuit and vice versa.

Practical Application Example

• Measured impedance: 75 - J60 ohms.
• Normalize: 1.5 - J1.2.
• Use shunt inductor followed by series capacitor for matching network.
• Calculate values for inductance and capacitance based on movement on the Smith chart.

Conclusion

• Smith charts simplify complex impedance matching and transmission line problems.
• Encouragement to explore tools like SimSmith for automated calculations.
• Additional resources and tutorials available online.