Plotting

• Plotting
• Smith Charts
• Smith Chart Circles
• Plot Options
• Rectangular Plots

The core of the plotting functionality in Marconi comes from the PGFPlotsX backend. This library allows for publication-quality graphics with complete configurability of the layout itself.

The functions within the plotting library merely contextualize the Network object or other parameters into a PGFPlotsX plot object.

It is highly recommended to thoroughly read the docs for PGFPlotsX to make the post of its plotting capability.

Smith Charts

To start plotting on Smith Charts, it generally is a good idea to start with an empty SmithChart axis object from PGFPlotsX.

using Marconi
using PGFPlotsX
sc = SmithChart()

This object is an Axis which can accept Plots objects as well as PGFPlotsX.Options.

To push plot objects into this circle, one can use either plotSmithData! or plotSmithCircle!.

These functions create a Plot object out of Network data and adds them to an existing Axis object.

Lets add some data to this axis

bpf = readTouchstone("BPF.s2p")

2-Port Network
 Z0 = 50.0
 Frequency = 10.0 MHz to 5.0 GHz
 Points = 236

This is a network object of a BFCG-162W+ filter from MiniCircuits

We can now simply call plotSmithData! to write this data to the chart. The third argument is a tuple of the parameter we want to plot. For this data, we want S(1,1), so we pass in the (1,1) tuple.

plotSmithData!(sc,bpf,(1,1))

This is the same behavior as if we constructed the axis and plotted simultaneously with plotSmithData.

plotSmithData(bpf,(1,1))

To add labels to any plot, we just call any of the plotting functions with the label kwarg.

plotSmithData(bpf,(1,1),label="S(1,1)")

Plotting with Equation-Driven Networks

To plot with an EquationNetwork, we must also provide the frequencies to plot. This is done with the additional kwarg freqs. We can also pass in arguments to our functions with the args kwarg.

function inductorAndResistor(L=1e-9,R=30;freq,Z0)
    z = R + im*2*pi*freq*L
    return (z-Z0)/(z+Z0)
end
RL = EquationNetwork(1,50,inductorAndResistor)

ax = plotSmithData(RL,(1,1),freqs=range(100e6,stop=10e9,length=201))
plotSmithData!(ax,RL,(1,1),freqs=range(100e6,stop=10e9,length=201),args=(1e-9,50))

Smith Chart Circles

As anyone who has read Microwave Transistor Amplifiers would know, drawing circles on a Smith Chart could be very useful. In Marconi, use cases such as stability circles and gain circles are explored in RF Analysis.

The plotSmithCircle! function behaves similarly to plotSmithData as it accepts a SmithChart object, x and y center coordinates, and a radius.

These coordinates are referenced to the unit circle $\Gamma$ plane, so $-1 \leq x \leq 1$ and $-1 \leq y \leq 1$.

This plot can also accept the opts kwarg.

sc = SmithChart()
style = @pgf {"color" = "cyan", "very thick"}
plotSmithCircle!(sc,0.3,0.75,0.3,opts = style)

Plot Options

As these plots and axes are fundamentally PGFPlotsX objects, we can pass in options using the opts kwarg. Additionally, the plotSmithData function can take a axopts kwarg to pass in options specific to the axis such as title and size.

style = @pgf {color = "red", "thick"}
sc = plotSmithData(bpf,(1,1),opts = style)

The return of plotSmithData is a SmithChart axis object, so we can set variables after the fact as well just like every other PGFPlotsX object.

sc["title"] = "My Smith Chart"

"My Smith Chart"

Finally, the width and tick mark density is all related as per the PGFPlots manual.

Check it out here

When creating a SmithChart axis by itself, there is no kwarg for options.

axis_style = @pgf {width = "15cm",title = "Medium Smith Chart"}
sc = SmithChart(axis_style)

Rectangular Plots

To plot on a rectangular axis, we call the plotRectangular and plotRectangular! functions.

These operate similar in functionality to the smith chart plotting utilities as plotRectangular accepts a network object and the parameter to plot. Additionally, plotRectangular requires a function to apply to make 1-D data. This could be dB or dB20 for 20log10 as supplied by this library, real, imag, or some other function. Finally, one could plot any network parameter, be it S, Z, Y, or T.

Same as plotSmithData, plotRectangular! accepts an opts kwarg as well as an axopts kwarg for plotRectangular as it is creating an axis object.

amp = readTouchstone("Amp.s2p")
ax = plotRectangular(amp,(1,1),dB,label="S(1,1)")
plotRectangular!(ax,amp,(2,1),dB,label="S(2,1)")
ax["ylabel"] = "dB"

Also, instead of supplying a tuple for the parameter to plot, one can supply a function to reduce a network to an array. There are several in this library for calculating stability, gain, and otherwise.

plotRectangular(amp,testK,label="K Stabilty")

To apply another function, such as dB, real, or otherwise; supply that function after the network function.

ax = plotRectangular(amp,testMSG,dB,label="MSG")
ax["ylabel"] = "dB"

Plotting with Equation-Driven Networks

Plotting rectangular plots with equation-driven networks works much the same as plotting with smith charts. All of the other functionality for plotting is conserved as well of course.

function inductorAndResistor(L=1e-9,R=30;freq,Z0)
    z = R + im*2*pi*freq*L
    return (z-Z0)/(z+Z0)
end
RL = EquationNetwork(1,50,inductorAndResistor)

ax = plotRectangular(RL,(1,1),freqs=range(100e6,stop=10e9,length=201))
plotRectangular!(ax,RL,(1,1),freqs=range(100e6,stop=10e9,length=201),args=(1e-9,50))