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A library that renders impedance charts that include capacitance and inductance grids.

Project description

RLC Chart

Author:

Ken Kundert

Version:

0.0.0

Released:

2021-03-21

What?

rlc_chart is library that renders impedance charts in SVG with the normal impedance versus frequency log-log grids, but they also include capacitance and inductance grids. They can be used to directly read component values from a plot of impedance.

Consider the impedance of a capacitor that has series resistance and inductance parasitics along with a shunt resistor as represented by the following circuit:

figures/leaky-cap-schematic.svg figures/leaky-cap-chart.svg

You can use the various grids on this graph to determine the values of the various components: C = 1 nF, L = 10 μH, Rs = 2 Ω, Rp = 500 kΩ, and f₀ = 1.6 MHz. You can do this in other ways, but they involve manual calculation. In addition, an RLC chart is a convenient way of sharing or publishing your findings.

Using an RLC chart is often enough to allow you to build a linear model for common two terminal components.

How?

Here is an example of how to use rlc_chart:

from rlc_chart import RLC_Chart
from math import log10 as log, pi as π

fmin = 1
fmax = 1e8
zmin = 1
zmax = 1e6
mult = 10**((log(fmax) - log(fmin))/400)
f = fmin
freq = []
impedance = []
resistance = []
reactance = []

while(f <= 1.01*fmax):
    z1 = 2 + 1/(2j*π*f*1e-9) + 2j*π*f*10.0e-6
    z2 = 5e5
    z = z1 * z2 / (z1 + z2)
    freq += [f]
    impedance += [abs(z)]
    f *= mult

with RLC_Chart('lcr-chart.svg', fmin, fmax, zmin, zmax) as chart:
    chart.add_trace(freq, impedance)

Most of the code builds the two arrays that represent the trace. The impedance array is expected to contain real values. In this case it is the magnitude that is being plotted, though it is also common to call add_trace twice to show both the real and imaginary parts of the impedance.

If you use the Spectre circuit simulator, you can use psf_utils with rlc_chart to extract models from simulation results. For example, here is the model of an inductor given by its manufacturer:

subckt MCFE1412TR47_JB (1 2)
    R1 (1 7) resistor  r=0.036
    L5 (2 8) inductor  l=20u
    C2 (7 8) capacitor c=10.6p
    R2 (8 2) resistor  r=528
    C1 (7 9) capacitor c=28.5p
    R5 (9 2) resistor  r=3.7
    L0 (7 3) inductor  l=0.27u
    L1 (3 4) inductor  l=0.07u
    L2 (4 2) inductor  l=0.11u
    L3 (3 5) inductor  l=0.39u
    L4 (4 6) inductor  l=0.35u
    R3 (5 4) resistor  r=3.02158381422266
    R4 (6 2) resistor  r=43.4532529473926
ends MCFE1412TR47_JB

This model is overly complicated and so expensive to simulate. It requires 13 extra unknowns that the simulator must compute (7 internal nodes and 6 inductor currents). The impedance of this subcircuit is extracted by grounding one end and driving the other with a 1 A magnitude AC source. Then, the RLC chart for this subcircuit can be generated with:

from psf_utils import PSF
from inform import Error, os_error, fatal
from rlc_chart import RLC_Chart

try:
    psf = PSF('MCFE1412TR47_JB.ac')
    sweep = psf.get_sweep()
    z_ckt = psf.get_signal('1')
    z_mod = psf.get_signal('2')

    with RLC_Chart('MCFE1412TR47_JB.svg', 100, 1e9, 0.01, 1000) as chart:
        chart.add_trace(sweep.abscissa, abs(z_ckt.ordinate), stroke='red')
        chart.add_trace(sweep.abscissa, abs(z_mod.ordinate), stroke='green')

    with RLC_Chart('MCFE1412TR47_JB.rxz.svg', 100, 1e9, 0.01, 1000) as chart:
        chart.add_trace(sweep.abscissa, abs(z.ordinate.real), stroke='green')
        chart.add_trace(sweep.abscissa, abs(z.ordinate.imag), stroke='orange')
        chart.add_trace(sweep.abscissa, abs(z.ordinate.real), stroke='blue')
        chart.add_trace(sweep.abscissa, abs(z.ordinate.imag), stroke='red')

except Error as e:
    e.terminate()
except OSError as e:
    fatal(os_error(e))

The RLC chart shows that the above subcircuit can be replaced with:

subckt MCFE1412TR47_JB (1 2)
    L   (2 2) inductor l=442.24nH r=36mOhm
    C   (2 2) capacitor c=27.522pF
    R   (2 2) resistor r=537.46_Ohm
ends MCFE1412TR47_JB

This version only requires one additional unknown, the inductor current.

Here is the RLC chart of both showing the difference, which are inconsequential.

figures/MCFE1412TR47_JB.svg

The differences are a bit more apparent if the real and imaginary components of the impedance are plotted separately.

figures/MCFE1412TR47_JB.rxz.svg

The differences are significant only in the loss exhibited above resonance, which is usually not of concern.

The Details

RLC_Chart

The RLC_Chart class constructor takes the following required arguments:

filename:

Path to the output SVG file.

fmin:

The minimum frequency value (left-most value on the chart). This value is always rounded down the next lower multiple of 10. So for example, if you give 25 Hz as fmin, then 10 Hz is used.

fmax:

The maximum frequency value (right-most value on the chart). This value is always rounded up the next higher multiple of 10. So for example, if you give 75 MHz as fmax, then 100 MHz is used.

zmin:
The minimum impedance value (bottom-most value on the chart). This value is

always rounded down the next lower multiple of 10. So for example, if you give 150 mΩ zmin, then 100 mΩ is used.

zmax:

The maximum impedance value (top-most value on the chart). This value is always rounded up the next higher multiple of 10. So for example, if you give 800 kΩ as zmax, then 1 MΩ is used.

In addition, the following keyword arguments are optional.

axes:

Specifies which axes are desired, where the choices are f for frequency, z for impedance, c for capacitance, and l for inductance. axes is a string that contains any or all of the four characters, or not at all. If the characters are lower case, then only the major grid lines are drawn, and if given as upper case letters, both the major and minor grid lines are drawn. The visual clutter in the chart can be reduces by eliminating unneeded grid lines.

trace_width:

The width of a trace. The default is 0.025 inches.

trace_color:

The default color of the trace. You can use one of the named SVG colors, or you can use ‘rgb(R,G,B)’ where R, G, and B are integers between 0 and 255 that specify the intensity of red, blue, and green components of the color.

major_line_width:

The width of a major division line. The default is 0.01 inches.

minor_line_width:

The width of a minor division line. The default is 0.005 inches.

outline_line_width:

The width of grid outline. The default is 0.015 inches.

outline_line_color:

The color of the grid outline. The default is ‘black’.

fz_grid_color:

The color of the frequency and impedance grid lines. The default is ‘grey’.

cl_grid_color:

The color of the capacitance and inductance grid lines. The default is ‘grey’.

background:

The background color of the grid. The default is ‘white’.

minor_divs:

The minor divisions to include. The default is ‘123456789’. Other common values are ‘1’, ‘13’, ‘125’, and ‘12468’.

decade:

The size of one decade square. The default is 1 inch. With this value, a grid that is 6 decades wide and 4 decades high is 6” by 4”.

left_margin:

The size of the left margin. The default is 1 inch.

right_margin:

The size of the right margin. The default is 1 inch.

top_margin:

The size of the top margin. The default is 1 inch.

bottom_margin:

The size of the bottom margin. The default is 1 inch.

font_family:

The text font family. The default is “sans-serif”.

font_size:

The text font size. The default is 12.

text_color:

The text color size. The default is “black”.

text_offset:

The separation between the axis labels and the grid. The default is 0.15 inches.

pixels_per_unit:

This is a scaling factor that allows you specify your dimensions to what every units you wish. A value of 96, the default, means that you are specifying your units in inches. A value of 37.8 allows you specify values in centimeters. Etc.

In addition, many SVG parameters can be passed into RLC_Chart, in which case they are simple passed on to svgwrite.

Generally, RLC_Chart is the argument of a with statement. If you choose not to do this, then you must explicitly call the close method yourself. Other than close, RLC_Chart provides one other method: add_trace.

add_trace()

This method adds a trace to the graph. It may be called multiple times to add additional traces. There are two required arguments:

frequency:

An array of real values representing the frequency values of the points that when connected make up the trace.

impedance:

An array of real values representing the impedance values of the points that when connected make up the trace.

Each of these arrays can be in the form of a Python list or a numpy array, and they must be the same length.

It is also possible to specify additional keyword aruments, which are passed on to svgwrite and attached to the trace. This can be used to specify trace color and style. For example, specify stroke to specify the trace color.

Labeling

The chart object returned by RLC_Chart is a svgwrite Drawing object, and so you can call its methods to add SVG features to your chart. This can be used to add labels to your charts. Here is an example that demonstrates how to add labels:

from rlc_chart import RLC_Chart
from inform import fatal, os_error
from pathlib import Path
import csv

fmin = 100
fmax = 10e9
zmin = 0.01
zmax = 1e6

frequency = []
impedance = []
ESR = []
try:
    contents = Path('C0603C102K3GACTU_imp_esr.csv').read_text()
    data = csv.DictReader(contents.splitlines(), delimiter=',')
    for row in data:
        frequency.append(float(row['Frequency']))
        impedance.append(float(row['Impedance']))
        ESR.append(float(row['ESR']))

    with RLC_Chart('C0603C102K3GACTU.svg', fmin, fmax, zmin, zmax, axes='FZCL') as chart:
        chart.add_trace(frequency, impedance, stroke='red')
        chart.add_trace(frequency, ESR, stroke='blue')

        chart.add(chart.text(
            "1 nF",
            insert = (chart.to_x(150_000), chart.to_y(1_500)),
            font_size = 24,
            fill = 'black'
        ))
        chart.add(chart.text(
            "700 pH",
            insert = (chart.to_x(2_000_000_000), chart.to_y(10)),
            font_size = 24,
            fill = 'black',
            text_anchor = 'end',
        ))
        chart.add(chart.text(
            "20 mΩ",
            insert = (chart.to_x(175_000_000), chart.to_y(0.012)),
            font_size = 24,
            fill = 'black',
            text_anchor = 'middle',
        ))
        chart.add(chart.text(
            "C0603C102K3GACTU",
            insert = (chart.WIDTH/2, 36),
            font_size = 24,
            fill = 'black',
            text_anchor = 'middle',
        ))
except OSError as e:
    fatal(os_error(e))

This example demonstrates two different ways to specify the location of the label. The chart object provides the to_x and to_y methods that convert data values into coordinates within the grid. This is used to add labels on the traces. The chart object also provides the HEIGHT and WIDTH attributes. These can be used to compute coordinates within the entire canvas. This is used to add a title that is near the top.

figures/C0603C102K3GACTU.svg

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