Jupyter Notebook - Electronics Demos¶
This notebook demonstrates several packages that can be used to support the creation of assets relating to electronics.
In [24]:
%matplotlib inline
Drawing Electrical Circuit Diagrams / Schematics¶
One way of using the notebooks is an an envionment to support the creation of schematic diagrams.
schemdraw¶
The schemdraw package can be used to write descriptions of electrical circuit diagrams.
Examples: https://cdelker.bitbucket.io/SchemDraw/SchemDraw.html
We can parameterise values to allow us to refer to diagrams in text using similar values.
In [2]:
import SchemDraw as schem
import SchemDraw.elements as e
In [55]:
#Would be nice if we could find a way of handling units better?
#Maybe a package that gets this from value and chooses unit modifier appropriately?
R=100 * 10**3
V=10
C=0.1 * 10**-6
V_str='{V}V'.format(V=V)
R_str='{R}K$\Omega$'.format(R=R/10**3)
C_str='{C}$\mu$F'.format(C=C/10**-6)
d = schem.Drawing()
V1 = d.add(e.SOURCE_V, label=V_str)
d.add(e.RES, d='right', label=R_str)
d.add(e.CAP, d='down', botlabel=C_str)
d.add(e.LINE, to=V1.start);
The following circuit shows a {{print(V_str)}} source connected in series to a {{R_str}} resistor and a {{print(C_str)}} capacitor.
{{d.draw()}}
Double click on the cell to see how the components are embedded.
We can also update diagrams dynamically:
In [3]:
from ipywidgets import interact
import ipywidgets
import matplotlib.pyplot as plt
@interact(V=ipywidgets.IntSlider(min=0,max=15,step=1,value=5),
R=ipywidgets.IntSlider(min=100,max=1500,step=100,value=100),
C=ipywidgets.IntSlider(min=0,max=15,step=1,value=1))
def schem_demo(V, R, C, xkcdmode=False):
if xkcdmode: plt.xkcd()
d = schem.Drawing()
V1 = d.add(e.SOURCE_V, label='{}V'.format(V))
d.add(e.LINE, d='right', l=d.unit*.75)
S1 = d.add(e.SWITCH_SPDT2_CLOSE, d='up', anchor='b', rgtlabel='$t=0$')
d.add(e.LINE, d='right', xy=S1.c, l=d.unit*.75)
d.add(e.RES, d='down', label='${}\Omega$'.format(R), botlabel=['+','$v_o$','-'])
d.add(e.LINE, to=V1.start)
d.add(e.CAP, xy=S1.a, d='down', toy=V1.start, label='{}$\mu$F'.format(C))
d.add(e.DOT)
d.draw(showplot=False)
circuitikz¶
Draw circuits using circuitikz.
In [4]:
%load_ext tikz_magic
In [5]:
%%tikz -p circuitikz,gnuplottex -s 0.3
%Example circuit from: https://tex.stackexchange.com/a/379915
[every pin/.append style={align=left, text=blue}]
\draw
(0, 0) node[op amp] (opamp) {}
(opamp.-) to[short,-o] (-2, 0.5)
(opamp.-) to[short,*-] ++(0,1.5) coordinate (leftC)
to[C] (leftC -| opamp.out)
to[short,-*] (opamp.out)
to[short,-o] ++ (0.5,0)
(leftC) to[short,*-] ++ (0,1) coordinate (leftR)
to[R] (leftR -| opamp.out)
to[short,-*] (leftC -| opamp.out)
(opamp.+) -- ++ (0,-0.5) node[ground] {};
Out[5]:
In [6]:
cct=r'''
\draw
(0, 0) node[op amp] (opamp) {}
(opamp.-) to[short,-o] (-2, 0.5)
(opamp.-) to[short,*-] ++(0,1.5) coordinate (leftC)
to[C] (leftC -| opamp.out)
to[short,-*] (opamp.out)
to[short,-o] ++ (0.5,0)
(leftC) to[short,*-] ++ (0,1) coordinate (leftR)
to[R] (leftR -| opamp.out)
to[short,-*] (leftC -| opamp.out)
(opamp.+) -- ++ (0,-0.5) node[ground] {};'''
%tikz -p circuitikz -s 0.3 --var cct
Out[6]:
In [7]:
!kpsewhich bodegraph.sty
/usr/share/texlive/texmf-dist/tex/latex/bodegraph/bodegraph.sty
In [61]:
!kpsewhich circuitikz.sty
/usr/share/texlive/texmf-dist/tex/latex/circuitikz/circuitikz.sty
Simulating Circuits¶
As well as drawing circuits, there several different approaches to simulating circuit behaviour.
Circuit Analysis - lcapy¶
lcapy is a linear circuit analysis package.
In [2]:
%%capture
#It seems as if lcapy, as of 7/9/18 doesn't work with current symp 1.2+
!pip install --upgrade sympy==1.1
In [3]:
from lcapy import Circuit, j, omega
cct = Circuit()
cct.add("""
Vi 1 0_1 step 20; down
C 1 2; right, size=1.5
R 2 0; down
W 0_1 0; right
W 0 0_2; right, size=0.5
P1 2_2 0_2; down
W 2 2_2;right, size=0.5""")
cct.draw()
In [4]:
H = (cct.R.V('s') / cct.Vi.V('s')).simplify()
H
Out[4]:
$\frac{C R s}{C R s + 1}$
In [5]:
!jupyter nbextension enable --py widgetsnbextension
Enabling notebook extension jupyter-js-widgets/extension...
- Validating: OK
In [8]:
from ipywidgets import interact
@interact(R=(1,10,1))
def response(R=1):
cct = Circuit()
cct.add('V 0_1 0 step 10;down')
cct.add('L 0_1 0_2 1e-3;right')
cct.add('C 0_2 1 1e-4;right')
cct.add('R 1 0_4 {R};down'.format(R=R))
cct.add('W 0_4 0; left')
import numpy as np
t = np.linspace(0, 0.01, 1000)
vr = cct.R.v.evaluate(t)
from matplotlib.pyplot import figure, savefig
fig = figure()
ax = fig.add_subplot(111, title='Resistor voltage (R={}$\Omega$)'.format(R))
ax.plot(t, vr, linewidth=2)
ax.set_xlabel('Time (s)')
ax.set_ylabel('Resistor voltage (V)')
ax.grid(True)
cct.draw()
A Jupyter Widget
In [9]:
#Example from http://lcapy.elec.canterbury.ac.nz/schematics.html#introduction
sch='''
Vi 1 0_1 {sin(t)}; down
R1 1 2 22e3; right, size=1.5
R2 2 0 1e3; down
P1 2_2 0_2; down, v=V_{o}
W 2 2_2; right, size=1.5
W 0_1 0; right
W 0 0_2; right
'''
fn="voltageDivider.sch"
with open(fn, "w") as text_file:
text_file.write(sch)
cct = Circuit(fn)
cct.draw(style='american') #american, british, european
#I wonder if we could blend the styles to make an OU style?
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%matplotlib inline
In [11]:
#How do I analyse the circuit with the ac voltage source?
import numpy as np
t = np.linspace(0, 5, 1000)
vr = cct.R2.v.evaluate(t)
from matplotlib.pyplot import figure, savefig
fig = figure()
ax = fig.add_subplot(111, title='Resistor R2 voltage')
ax.plot(t, vr, linewidth=2)
ax.plot(t, cct.Vi.v.evaluate(t), linewidth=2, color='red')
ax.plot(t, cct.R1.v.evaluate(t), linewidth=2, color='green')
ax.set_xlabel('Time (s)')
ax.set_ylabel('Resistor voltage (V)');
In [12]:
?cct.R2.v
In [13]:
from lcapy import Circuit
cct = Circuit()
cct.add("""
W _0 _1; right
W _1 _2; up,size=0.4
R _2 _3 1e6; right
L _3 _4 2e-3;right
W _4 _5; down,size=0.4
W _5 _6; right
W _5 _7; down,size=0.4
C _7 _8 3e-6; left
W _8 _1; up,size=0.4
""")
cct.draw(style='british')
In [14]:
#alternative way of drawing circuits
from lcapy import R, C, L
cct2= (R(1e6) + L(2e-3)) | C(3e-6)
#For some reason, the style= argument is not respected
cct2.draw()
In [15]:
print(cct2.netlist())
W 1 2; right=0.5 W 2 4; up=0.4 W 3 5; up=0.4 R 4 6 1000000.0; right W 6 7; right=0.5 L 7 5 0.002; right W 2 8; down=0.4 W 3 9; down=0.4 C 8 9 3e-06; right W 3 0; right=0.5
In [16]:
from lcapy import *
from numpy import linspace
n = Vstep(20) + R(5) + C(10)
vf = linspace(0, 4, 400)
Isc = n.Isc.frequency_response().evaluate(vf)
In [17]:
from numpy import logspace, linspace
from lcapy import Vstep, R, C, L
n = Vstep(20) + R(5) + C(10)
n.draw()
vf = linspace(0, 1, 4000)
n.Isc.frequency_response().plot(vf, log_scale=True);
In [18]:
from ipywidgets import interact
@interact(R1=(0.1, 10),L1=(0.01, 1),C1=(0.01,0.5))
def damping(R1=0.1,L1=0.2,C1=0.4):
underDampedRLC = Vstep(10) + R(R1) + L(L1)+ C(C1)
underDampedRLC.draw();
t = linspace(0, 10, 1000)
underDampedRLC.Isc.transient_response().plot(t);
A Jupyter Widget
In [19]:
R_1 =R('R_1')
Rtot = R_1 | R('R_2')
Rtot
Out[19]:
$\mathrm{R}(R_1) | \mathrm{R}(R_2)$
In [20]:
from IPython.display import display, Latex
parallelR = R('R_1') | R('R_2')
parallelR.draw()
parallelR.simplify().R
Out[20]:
$\frac{R_{1} R_{2}}{R_{1} + R_{2}}$
In [21]:
parallelC = C('C_1') | C('C_2')
parallelC.draw()
parallelC.simplify().C
Out[21]:
$C_{1} + C_{2}$
In [22]:
from lcapy import Vac, t, s, pi
#Representation of AC voltage source in time domain
#Vac(amplitude, phase)
Vac(20, pi/2).Voc(t)
Out[22]:
$20 \sin{\left (\omega t \right )}$
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#Representation of AC voltage source in s domain
Vac(20).Voc(s)
Out[23]:
$\frac{20 s}{\omega^{2} + s^{2}}$
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display( Latex('The overall resistance value simplifies to'+parallelR.simplify().R._repr_latex_()))
The overall resistance value simplifies to$\frac{R_{1} R_{2}}{R_{1} + R_{2}}$
In [25]:
#Transfer function
cct = Circuit()
cct.add('V1 1 0 {1}')
cct.add('R1 1 2')
cct.add('C1 2 0 C1 0')
print(cct[0].V.s)
print(cct[1].V.s)
print(cct[2].V.s)
0 1/s 1/(C_1*R_1*(s**2 + s/(C_1*R_1)))
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#pole-zero plot
from lcapy import s, j, Hs
from matplotlib.pyplot import savefig, show
H = Hs((s - 2) * (s + 3) / (s * (s - 2 * j) * (s + 2 * j)))
H.plot();
In [27]:
print( str(H) )
H
(s - 2)*(s + 3)/(s*(s - 2*j)*(s + 2*j))
Out[27]:
$\frac{\left(s - 2\right) \left(s + 3\right)}{s \left(s - 2 j\right) \left(s + 2 j\right)}$
In [28]:
#bode - just does the amplitude response?
from lcapy import s, j, pi, f, Hs
from numpy import logspace
import matplotlib.pyplot as plt
H = Hs((s - 2) * (s + 3) / (s * (s - 2 * j) * (s + 2 * j)))
A = H(j * 2 * pi * f)
fv = logspace(-1, 4, 400)
A.plot(fv, log_scale=True)
A.phase_degrees.plot(fv,log_scale=True);
control¶
Pyhton control systems library.
Can be used for a wide range of control applications and chart generation.
In [1]:
%matplotlib inline
In [2]:
import control
#State space system definition
sys=control.ss("1. -2; 3. -4", "5.; 7", "6. 8", "9.")
#It would be nice if we could print the sys diagram as LaTeX styled matrices?
sys
Out[2]:
A = [[ 1. -2.] [ 3. -4.]] B = [[5.] [7.]] C = [[6. 8.]] D = [[9.]]
In [17]:
sys.A
Out[17]:
matrix([[ 1., -2.],
[ 3., -4.]])
In [25]:
#https://stackoverflow.com/a/17131750/454773
#Note that https://pypi.org/project/PyLaTeX/ may also be generally handy???
import numpy as np
def bmatrix(a):
"""Returns a LaTeX bmatrix
:a: numpy array
:returns: LaTeX bmatrix as a string
"""
if len(a.shape) > 2:
raise ValueError('bmatrix can at most display two dimensions')
lines = str(a).replace('[', '').replace(']', '').splitlines()
rv = [r'\begin{bmatrix}']
rv += [' ' + ' & '.join(l.split()) + r'\\' for l in lines]
rv += [r'\end{bmatrix}']
return '\n'.join(rv)
from IPython.display import display,Latex
display(Latex(bmatrix(sys.A)))
display(Latex(bmatrix(sys.B)))
display(Latex(bmatrix(sys.C)))
display(Latex(bmatrix(sys.D)))
\begin{bmatrix}
1. & -2.\\
3. & -4.\\
\end{bmatrix}
\begin{bmatrix}
5.\\
7.\\
\end{bmatrix}
\begin{bmatrix}
6. & 8.\\
\end{bmatrix}
\begin{bmatrix}
9.\\
\end{bmatrix}
In the control diagrams below, **kwargs can be passed in to style the matplotlib figure further. It would be handy if could get access the the figure object too? The plotting routines themselves are in control/freqplot.py.
Nyquist diagrams¶
In [10]:
real, imag, freq = control.nyquist_plot(sys, omega=None, Plot=True, color='b', labelFreq=0)
Bode plots¶
In [8]:
#sys = ss("1. -2; 3. -4", "5.; 7", "6. 8", "9.")
mag, phase, omega = control.bode(sys)
Circuit Sandbox¶
The Circuit Sandbox is a simple, standalone Javascript circuit simulator that we can embed in a notebook or run in its own browser tab.
The Circuit Sandbox can save and load simple netlists (I don't know if these can then be used by other packages?)
In [63]:
from IPython.display import IFrame
IFrame('js/circuit-sandbox-master/index-mobile.html', width=1000,height=600)
Out[63]:
Digital Circuit Simulator¶
simcirjs [docs) is a syandalone Javascript digital circuit simulator that we can embed in a notebook or run in its own browser tab.
In [64]:
#!ls js/simcirjs-master/
from IPython.display import IFrame
IFrame('js/simcirjs-master/blank.html', width=600,height=300)
Out[64]:
ahkab¶
ahkab is an open-source SPICE-like interactive circuit simulator.
Unfortunately, it doesn't render the schematic diagram from the circuit description. It would be useful if we ahkab could work with something like schemdraw to support such a dual behaviour from the same circuit descrpition.
The examples below are based on the original documentation.
In [65]:
import ahkab
In [66]:
cct = ahkab.Circuit('Simple Example Circuit')
cct.add_resistor('R1', 'n1', cct.gnd, value=5)
cct.add_vsource('V1', 'n2', 'n1', dc_value=8)
cct.add_resistor('R2', 'n2', cct.gnd, value=2)
cct.add_vsource('V2', 'n3', 'n2', dc_value=4)
cct.add_resistor('R3', 'n3', cct.gnd, value=4)
cct.add_resistor('R4', 'n3', 'n4', value=1)
cct.add_vsource('V3', 'n4', cct.gnd, dc_value=10)
cct.add_resistor('R5', 'n2', 'n4', value=4)
opa = ahkab.new_op()
r = ahkab.run(cct, opa)['op']
print(r)
OP simulation results for 'Simple Example Circuit'. Run on 2017-12-08 22:28:25, data file /tmp/tmp_k1yz97v.op. Variable Units Value Error % ---------- ------- --------- ------------ --- VN1 V -3.86364 3.86358e-12 0 VN2 V 4.13636 -4.13591e-12 0 VN3 V 8.13636 -8.13602e-12 0 VN4 V 10 -1.00027e-11 0 I(V1) A -0.772727 0 0 I(V2) A -0.170455 0 0 I(V3) A -3.32955 0 0
Boolean Algebra - PyEDA¶
PyEDA is a Python package for exploring Boolean algebra.
In [67]:
from pyeda.inter import *
A = exprvar('A')
B = exprvar('B')
C = exprvar('C')
In [68]:
A & B
Out[68]:
And(A, B)
In [69]:
A & ~B
Out[69]:
And(A, ~B)
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(A | B) & C
Out[70]:
And(Or(A, B), C)
In [71]:
A ^ B
Out[71]:
Xor(A, B)
In [72]:
expr2truthtable(A & ~B)
Out[72]:
B A 0 0 : 0 0 1 : 1 1 0 : 0 1 1 : 0
In [73]:
expr2truthtable( Or(And(A, B), And(A, C)) )
Out[73]:
C B A 0 0 0 : 0 0 0 1 : 0 0 1 0 : 0 0 1 1 : 1 1 0 0 : 0 1 0 1 : 1 1 1 0 : 0 1 1 1 : 1
In [74]:
expr2truthtable( And('X', 'Y') )
Out[74]:
Y X 0 0 : 0 0 1 : 0 1 0 : 0 1 1 : 1
In [75]:
tt = truthtable(reversed([A,B,C]), "00010111")
tt
Out[75]:
A B C 0 0 0 : 0 0 0 1 : 0 0 1 0 : 0 0 1 1 : 1 1 0 0 : 0 1 0 1 : 1 1 1 0 : 1 1 1 1 : 1
In [76]:
truthtable2expr( tt )
Out[76]:
Or(And(~A, B, C), And(A, ~B, C), And(A, B, ~C), And(A, B, C))
In [ ]: