#Smith chart vswr series
Z ( d ) = 25 + j 100 Ω © Amanogawa, 2000 - Digital Maestro Series The chart provides directly the magnitude and the phase angle of Γ(d) Example: Find Γ(d), given 4.įind the circle of constant normalized resistance r Find the arc of constant normalized reactance x The intersection of the two curves indicates the reflection coefficient in the complex plane. Z (d ) R X = + j = r+ j x z (d ) = Z0 Z0 Z0 2. ⇒ Find Γ(d) and Z(d) Given Γ(d) and Z(d) ⇒ Find ΓR and ZR X=0 x = - 0.5 © Amanogawa, 2000 - Digital Maestro Seriesīasic Smith Chart techniques for loss-less transmission linesįind dmax and dmin (maximum and minimum locations for the voltage standing wave pattern)įind the Voltage Standing Wave Ratio (VSWR) The result for the imaginary part indicates that on the complex plane with coordinates (Re(Γ), Im(Γ)) all the possible impedances with a given normalized reactance x are found on a circle withĪs the normalized reactance x varies from -∞ to ∞, we obtain a family of arcs contained inside the domain of the reflection coefficient | Γ | ≤ 1. The result for the real part indicates that on the complex plane with coordinates (Re(Γ), Im(Γ)) all the possible impedances with a given normalized resistance r are found on a circle withĪs the normalized resistance r varies from 0 to ∞, we obtain a family of circles completely contained inside the domain of the reflection coefficient | Γ | ≤ 1. Multiply by x and add a quantity equal to zero Z ( d ) = Re ( z ) + j Im ( z ) = r + jx Let’s represent the reflection coefficient in terms of its coordinates The normalized impedance is represented on the Smith chart by using families of curves that identify the normalized resistance r (real part) and the normalized reactance x (imaginary part) Z(d ) 1 + Γ (d ) z( d ) = 1 − Γ (d ) Z0 © Amanogawa, 2000 - Digital Maestro Series In order to obtain universal curves, we introduce the concept of normalized impedance It is obvious that the result would be applicable only to lines with exactly characteristic impedance Z0. To do so, we start from the general definition of line impedance (which is equally applicable to the load impedance)ġ + Γ (d ) V (d ) = Z0 Z( d ) = 1 − Γ (d ) I (d ) This provides the complex function Z( d ) = f that we want to graph. The goal of the Smith chart is to identify all possible impedances on the domain of existence of the reflection coefficient. This is also the domain of the Smith chart. The domain of definition of the reflection coefficient is a circle of radius 1 in the complex plane. © Amanogawa, 2000 - Digital Maestro Series
![smith chart vswr smith chart vswr](http://hl1lua.com/wp-content/uploads/2014/02/SQ11new_S11_VSWR.png)
From a mathematical point of view, the Smith chart is simply a representation of all possible complex impedances with respect to coordinates defined by the reflection coefficient. The chart provides a clever way to visualize complex functions and it continues to endure popularity decades after its original conception. Smith Chart The Smith chart is one of the most useful graphical tools for high frequency circuit applications.