Plotting sectionwise defined function with python/matplotlib

Question

I'm new to Python and Scipy. Currently I am trying to plot a p-type transistor transfer curve in matplotlib. It is sectionwise defined and I am struggeling to find a good way to get the resulting curve. What I have so far is:

import matplotlib.pyplot as plt
import numpy as np
from scipy.constants import epsilon_0

V_GS = np.linspace(-15, 10, 100) # V
V_th = 1.9 # V
V_DS = -10 # V
mu_p = 0.1e-4 # m²/Vs
epsilon_r = 7.1
W = 200e-6 # m
L = 10e-6 # m
d = 70e-9 # m
C_G = epsilon_0*epsilon_r/d
beta = -mu_p*C_G*W/L

Ids_cutoff = np.empty(100); Ids_cutoff.fill(-1e-12)
Ids_lin = beta*((V_GS-V_th)*V_DS-V_DS**2/2)
Ids_sat = beta*1/2*(V_GS-V_th)**2

plt.plot(V_GS, Ids_lin, label='lin')
plt.plot(V_GS, Ids_sat, label='sat')
plt.plot(V_GS, Ids_cutoff, label='cutoff')

plt.xlabel('V_GS [V]')
plt.ylabel('I [A]')
plt.legend(loc=0)

plt.show()

This gives me the three curves over the complete V_GS range. Now I would like to define

Ids = Ids_cutoff for V_GS >= V_th
Ids = Ids_lin for V_GS < V_th; V_DS >= V_GS - V_th
Ids = Ids_sat for V_GS < V_th; V_DS < V_GS - V_th

I found an example for np.vectorize() but somehow I am struggeling to understand how to work with these arrays. I could create a for loop that goes through all the values but I am pretty sure that there are more effective ways to do this.

Besides deriving a list of values for Ids and plotting it vs V_GS is there also a possibility to just sectionswise plot the three equations with matplotlib as one curve?

Answer 1

Do you want to fill the array Vds according to your selectors?

Vds = np.zeros_like(V_GS)  # for the same shape
Vds[V_GS >= V_th] = Ids_cutoff
Vds[(V_GS < V_th) & (V_DS >= V_GS - V_th)] = Ids_lin
Vds[(V_GS < V_th) & (V_DS < V_GS - V_th)] = Ids_sat

By plotting sectionwise, you mean leaving out a certain range? You can use np.nan for that:

plt.plot([0,1,2,3,np.nan,10,11], np.arange(7))

results in:

As Not a Number is not plottable, no line will be drawn.

Answer 2

After having read more into the details of numpy I finally figured out a way to do this:

Ids_cutoff = -1e-12 # instead of creating an array as posted above
# create masks for range of validity for linear and saturation region
is_lin = np.zeros_like(V_GS, dtype=np.bool_)
is_lin[(V_GS < V_th) & (V_DS >= V_GS - V_th)] = 'TRUE'
is_sat = np.zeros_like(V_GS, dtype=np.bool_)
is_sat[(V_GS < V_th) & (V_DS < V_GS - V_th)] = 'TRUE'

# create final array and fill with off-current
Ids = np.zeros_like(V_GS); Ids.fill(Ids_cutoff)
# replace by values for linear and saturation region where valid
Ids = np.where(is_lin, Ids_lin, Ids)
Ids = np.where(is_sat, Ids_sat, Ids)
plt.plot(V_GS, Ids, '*', label='final')