Why do we need an Admittance Smith Chart?

The standard Impedance (Z) Smith Chart is perfect for series components. If you add an inductor in series, you simply move clockwise along a constant resistance circle. But adding components in parallel (shunt) is mathematically cumbersome in impedance, requiring you to invert the impedance to admittance (Y = 1/Z), add the parallel component's admittance, and invert back. The Admittance (Y) Smith Chart maps conductance (G) and susceptance (B) directly. When you add a shunt capacitor, you simply move clockwise along a constant conductance circle. By having an admittance chart, parallel matching networks can be designed visually without doing any complex reciprocal mathematics.

How is the Y-chart related to the Z-chart?

The Admittance chart is exactly the Impedance chart rotated by 180 degrees. On a Z-chart, the open circuit (infinite impedance) is on the far right, and the short circuit (zero impedance) is on the far left. Constant resistance circles converge on the right. On a Y-chart, a short circuit has infinite admittance, so it sits on the far right. An open circuit has zero admittance, so it sits on the far left. Constant conductance circles converge on the far left. In practice, designers use a combined Z-Y chart (often called an immittance chart), which superimposes the red Z-grid and the blue 180-degree-rotated Y-grid on the same paper. This allows instant visual conversion between impedance and admittance for any point.

How do you use it for stub matching?

Stub matching almost exclusively uses the Admittance chart. You start with an unmatched load, find its admittance, and rotate around the center (moving toward the generator along the transmission line) until you hit the 1+jb circle (the unit conductance circle). At this physical location on the line, the real part of the admittance perfectly matches the characteristic admittance of the line. However, there is leftover imaginary susceptance (+jb). You then place an open or shorted transmission line stub in parallel (shunt) at that exact location. The stub's length is chosen so that its input susceptance is exactly minus jb. The stub cancels out the imaginary part, leaving you precisely at the center of the chart (matched). Because the stub is in parallel, working on the Y-chart makes the addition trivial.

Simulation & Design

Admittance Smith Chart

Designing a matching network requires combining series and parallel components. If you only have a standard Impedance (Z) Smith Chart, adding a series inductor is trivial: just move up the constant resistance circle. But adding a parallel capacitor requires a nightmare of complex math: you must invert your current impedance (Z) to find admittance (Y = 1/Z), mathematically add the parallel capacitor's susceptance, and invert the result back to Z to plot it. The Admittance (Y) Smith Chart solves this geometry problem elegantly. It is simply the Z-chart rotated 180 degrees. The circles now represent conductance (G) and susceptance (B). Adding a parallel capacitor means simply moving clockwise along a constant conductance circle. By superimposing the Z and Y grids into a single "Immittance" chart, RF engineers can seamlessly zigzag between series and parallel components, designing complex matching networks visually without ever picking up a calculator.

Category: Simulation & Design

Alias: Y-Chart

Usage: Shunt component mapping

Impedance vs. Admittance Chart Mechanics

Action	Impedance (Z) Chart	Admittance (Y) Chart
Add Series Inductor	Move clockwise along constant R	Requires Z-Y conversion
Add Series Capacitor	Move counter-clockwise along constant R	Requires Z-Y conversion
Add Shunt Inductor	Requires Z-Y conversion	Move counter-clockwise along constant G
Add Shunt Capacitor	Requires Z-Y conversion	Move clockwise along constant G
Open Circuit Location	Far right (infinity)	Far left (zero)
Short Circuit Location	Far left (zero)	Far right (infinity)

Admittance definition:
Y = 1 / Z = G + jB
G = Conductance (Real part, Siemens)
B = Susceptance (Imaginary part, Siemens)

Shunt component susceptance:
Capacitor: B = ωC (Positive susceptance, upper half of Y-chart)
Inductor: B = −1/(ωL) (Negative susceptance, lower half of Y-chart)

Transformation rule:
To convert any normalized Z point to normalized Y, draw a straight line through the center to the exact opposite side of the chart (180° rotation).

Common Questions

Frequently Asked Questions

Why do we need an Admittance chart?

The standard Z-chart makes adding series components easy but parallel (shunt) components difficult, requiring complex 1/Z math. The Y-chart makes shunt components easy. Adding a parallel capacitor is just a clockwise rotation along a constant conductance circle. Combining both into a Z-Y chart allows visual matching network design.

How are the Z and Y charts related?

The Y-chart is the exact same geometry as the Z-chart, just rotated 180 degrees. On a Z-chart, open circuit (infinite impedance) is on the right. On a Y-chart, open circuit (zero admittance) is on the left. To convert an impedance point to admittance, simply draw a line through the origin to the opposite side.

How is it used for stub matching?

Stub matching puts a transmission line stub in parallel with the main line. You plot the load, rotate on the chart to find where the line hits the unit conductance circle (G=1), and read the remaining susceptance (+jB). You then add a parallel stub cut to a length that provides exactly -jB susceptance, bringing you to the perfectly matched center.

Related Terms

← Active Load Modulation Amplitude Imbalance →

Matching Networks

Interactive Immittance Chart

Plot load impedances, add series and parallel components in real-time, and watch the trajectory zigzag across the combined Z-Y Smith chart to hit your exact matching target.

Launch Y-Chart Tool