3D Smith Chart

The most recent article on the 3D Smith chart ( November 2016) can be found in IEEE Transactions on Microwave Theory and Techniques Journal

Extended Capabilities of the 3-D Smith Chart With Group Delay and Resonator Quality Factor

Electronics Letters (2014) - called Apollonius unilateral transducer power gain on 3D Smith charts while a new capability of it is pointed out in October 2015 Electronics Letters journal.
The initial articles can be found in IEEE Microwave and Wireless Letters and Microwave Journal back in 2011 and 2012



3D Smith Chart

Is a new 3d telecommunications design tool with applications mainly in high frequency engineering

An unprecedented  desktop version is starting  November 2013 online for download!

A free demo version from January 2013 is available free on the site!

A new feature that allows visualizing specific contour plots in 3D was integrated into the tool on 17 June 2014

The 3D Smith was most recently presented on 19 November 2013 at ARMMS Conference, Wyboston Lakes, UK .

novel application of the 3D Smith chart was presented at Asia-Pacific Microwave Conference  on 7 December 2012- Kaohsiung, Taiwan

The free 3D Smith chart Java demo generalizes the Smith chart on circles on the unit sphere (thus just on the surface- sphere= surface of the unit ball)

It is intented to be a complete and compact  Smith chart that includes both the entire reflection coefficient and impedance planes,                                                                                          

one may switch to the other through a rotation

It is desired to be  a design tool for both passive and active circuits                                                                                                                                                

Amplifiers, Oscillators, Active filters, lossy matchings designs are eased.

An important visual feature is the capability to plot stability circles in a compact manner                                                                                                                               

All possible situations for stability circles are included on the 3D Smith chart                 

an impossible thing on an extended 2D Smith chart.  Some examples are plotted below

The main mathematical "trick" of the 3D Smith chart  was used by Escher in his arts and by Mandelbrot in the fractal theory too                                                                                                                                                                                       

Tool: It uses just circles on the surface of the unit sphere

The north hemisphere is only for passive circuits.The south hemisphere is for active circuits

Watch the demo videos:


or try the

3D Smith Chart Demo


You can support the development with any amount you consider appropriate.
Thank you!


The West of Greenwich meridian is made of capacitive circuits. The East of Greenwich is made of inductive circuits                                                                                                                                                               
The perfect matching point is the north pole of the sphere
The infinite mismatch is in the south pole of the sphere
One has to get to the north pole in order to obtain the matching
Moving along a transmission line is represented by the movement on a latitude circle- for the lossless case
Movie presents a 3D Smith chart demo tool
Stability circles are very easy to be seen in a compact manner on the 3D Smith chart.

In the last years several attempts were done to develop a 3D Smith chart suitable for both active and passive design. The 3D Smith chart presented here is based on the June 2011 MWCL journal article "A 3D Smith chart based on the Riemann sphere for active and passive microwave circuits" The article uses for the first time inversive geometry on the Riemann sphere (used sometimes without knowledge in arts too) and unifies the active circuits and passive circuits design generalizing the Smith chart. Latitude and longitudes become the important 3D Smith chart tool options in designing-while the theory behind is from pure mathematics-South pole = mapping of infinity. Important details can be found in the IEEE June 2011 MWCL  and in the July 2012 Microwave Journal articles

 The 3D Smith chart  tool  was presented in premiere at European Microwave Week, special event " Microwave fundamentals"  on 13 October 2011 - Manchester

( tks to prof T.J. Brazil, University College Dublin, Ireland and to Stepan Lucyszyn- EUMC chairman)
Stability circles on the 3d Smith chart ( left a simplified representation in the reflection plane)
3D Smith chart stability circles: input and output stability circles at a sepcific frequency of an amplifier - both graphs show the same phenomenon
3D Smith chart stability circles:  different representations of the same amplifier- the last chart includes the extended impedance plane too since the 3D Smith chart
inculdes both entire reflection and entire impedance planes- note also the position of the circles (the green one for example in the capacitive part of the  Smith chart thus it is mapped west of Greenwich, the orange circle is in the inductive part thus it is mapped East of Greenwich. When the circles enter the Smith chart  this seen on the 3D Smith chart as an entering of the North hemisphere
Power wave reflection coefficient for inverters with complex port impedances 
Voltage reflection coefficient for inverters with complex port impedances
Smith chart random circuits
One of the basic ideas of the extension:
Andrei - in the RHP of the impedance plane
Andrei- under the Smith chart mapping
The Smith chart is placed in the equatorial plane, thus Andrei is "sent" in the North hemisphere- since he was in the RHP of the impedance plane thus inside of the classical Smith chart
A lossy line on the 3D Smith chart in the reflection coefficient's plane, voltage and power wave reflection coefficients ( complex  ports)
A lossy line in the impedance plane ( one rotates the sphere and gets the entire impedance plane) the orange circles are constant abs(z) circles
The 3D Smith chart tool can plot also stability circles and do lossy matchings in different approaches
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