Spectrum Software
spacer
Industrial Strength Simulation
select:

divider

 

News:

Spectrum Software has released Micro-Cap 11, the eleventh generation of our SPICE circuit simulator.

For users of previous Micro-Cap versions, check out the new features available in the latest version. For those of you who are new to Micro-Cap, take our features tour to see what Micro-Cap has to offer.

 

divider

 

Smith Chart and Impedance Plots

 

The Smith chart provides a means to view both the complex reflection and the complex impedance of a port. It is most applicable when designing in the RF range for applications involving transmission lines, amplifiers, and antennas among others. One common usage for the Smith chart is to view the input impedance at a port. This article describes the method for correctly plotting the input impedance to a Smith chart in Micro-Cap.

For this example, we will use a simple parallel RC combination since the impedance waveform for that configuration is well known. The initial circuit is displayed below. It consists of the RC combination and a Voltage Source component whose AC magnitude parameter is defined as 1V.

Standard Impedance Measuring Circuit

For a standard Cartesian plot, the V/I equation can be used to plot the impedance. In this case, the impedance would be measured using the following expression:

-V(OUT)/I(V1)

which divides the voltage across the input port by the current going into the port. The negative sign is to account for the fact that the I(V1) is calculated from the positive node to the negative node of the source which would be flowing out of the port. The AC analysis of this plot is displayed below. At low frequencies, the impedance is dominated by the resistance, and at high frequencies, the capacitor impedance dominates. The most common error when trying to plot the impedance in a Smith chart is to use this same technique.

Cartesian Impedance Plot

In order to plot the complex impedance in a Smith chart, the expression that needs to be plotted is the S parameter equivalent. The S11 parameter represents the input impedance and the S22 parameter represents the output impedance. To measure the S11 parameter, the circuit will need to be slightly modified as shown below. A resistor has been added between the voltage source and the impedance to be measured. The value of this resistance will determine the normalization factor that is used when creating the Smith chart.

Smith Chart Impedance Circuit

For this circuit, the S11 parameter is determined by the following equations:

b1 = S11*a1 + S12*a2
a1 = Normalized incident voltage at port 1=(V(Out)+R1*I(R1))/(2*sqrt(R1))
b1 = Normalized reflected voltage at port 1=(V(Out)-R1*I(R1))/(2*sqrt(R1))
a2 = 0 when measuring S11

This reduces the equation to:

S11 = (V(Out)-R1*I(R1)) / (V(Out)+R1*I(R1))

From Kirchoff's law, we determine the voltage loop at the input as:

-V(V1) + R1*I(R1) +V(Out) = 0 where V(V1) is 1 volt for the AC analysis

Plugging this back into the S11 equation, the final expression becomes:

S11 = 2*V(Out) - 1

The resultant Smith chart when plotting this expression is displayed below. Note that this plot has been normalized to the source resistance of 50 ohms. The impedance plot starts approximately at the real, imaginary values of 1,0. It then arcs through the capacitive half and ends at the short circuit point of the Smith chart as would be expected by a parallel RC impedance.

Smith Chart Impedance Plot

 
Return to the main Newsletter page