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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 LNA Example
Let's design a LNA using Infineon's BFU520 transistor. First we need to import scikit-rf and a bunch of other utilities
Step1:  Let's plot the smith chart for it
Step2:  Now let's calculate the source and load stability curves.
I'm slightly misusing the Network type to plot the curves; normally the curves you pass in to Network should be a function of frequency, but it also works to draw these circles as long as you don't try to use any other functions on them
Step3:  So we can see that we need to avoid inductive loads near short circuit in the input matching network and high impedance inductive loads on the output.
Let's draw some constant noise circles. First we grab the noise parameters for our target frequency from the network model
Step4:  So we can see from the chart that just leaving the input at 50 ohms gets us under 0.1 dB of extra noise, which seems pretty good. I'm actually not sure that these actually correspond to the noise figure level increments I have listed up there, but the circles should at least correspond to increasing noise figures
So let's leave the input at 50 ohms and figure out how to match the output network to maximize gain and stability. Let's see what matching the load impedance with an unmatched input gives us
Step5:  This looks like it may be kind of close to the load instability circles, so it might make sense to pick a load point with less gain for more stability, or to pick a different source impedance with more noise.
But for now let's just build a matching network for this and see how it performs
Step6:  Let's calculate what the component values are
Step7:  The capacitance is kind of low but the inductance seems reasonable. Let's test it out
Step8:  That looks pretty reasonable; let's take a look at the S21 to see what we got
Step9:  So about 18 dB gain; let's see what our noise figure is
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Python Code:
import numpy as np
import matplotlib.pyplot as plt
plt.rcParams['figure.figsize'] = [10, 10]
import skrf as rf
from skrf.media import DistributedCircuit
f = rf.Frequency(0.4, 2, 101)
tem = DistributedCircuit(f, z0=50)
# import the scattering parameters/noise data for the transistor
bjt = rf.Network('BFU520_05V0_010mA_NF_SP.s2p').interpolate(f)
print(bjt)
Explanation: LNA Example
Let's design a LNA using Infineon's BFU520 transistor. First we need to import scikit-rf and a bunch of other utilities:
End of explanation
bjt.plot_s_smith(lw=2)
Explanation: Let's plot the smith chart for it:
End of explanation
sqabs = lambda x: np.square(np.absolute(x))
delta = bjt.s11.s*bjt.s22.s - bjt.s12.s*bjt.s21.s
rl = np.absolute((bjt.s12.s * bjt.s21.s)/(sqabs(bjt.s22.s) - sqabs(delta)))
cl = np.conj(bjt.s22.s - delta*np.conj(bjt.s11.s))/(sqabs(bjt.s22.s) - sqabs(delta))
rs = np.absolute((bjt.s12.s * bjt.s21.s)/(sqabs(bjt.s11.s) - sqabs(delta)))
cs = np.conj(bjt.s11.s - delta*np.conj(bjt.s22.s))/(sqabs(bjt.s11.s) - sqabs(delta))
def calc_circle(c, r):
    theta = np.linspace(0, 2*np.pi, 1000)
    return c + r*np.exp(1.0j*theta)
for i, f in enumerate(bjt.f):
    # decimate it a little
    if i % 100 != 0:
        continue
    n = rf.Network(name=str(f/1.e+9), s=calc_circle(cs[i][0, 0], rs[i][0, 0]))
    n.plot_s_smith()
for i, f in enumerate(bjt.f):
    # decimate it a little
    if i % 100 != 0:
        continue
    n = rf.Network(name=str(f/1.e+9), s=calc_circle(cl[i][0, 0], rl[i][0, 0]))
    n.plot_s_smith()
Explanation: Now let's calculate the source and load stability curves.
I'm slightly misusing the Network type to plot the curves; normally the curves you pass in to Network should be a function of frequency, but it also works to draw these circles as long as you don't try to use any other functions on them
End of explanation
idx_915mhz = rf.util.find_nearest_index(bjt.f, 915.e+6)
# we need the normalized equivalent noise and optimum source coefficient to calculate the constant noise circles
rn = bjt.rn[idx_915mhz]/50
gamma_opt = bjt.g_opt[idx_915mhz]
fmin = bjt.nfmin[idx_915mhz]
for nf_added in [0, 0.1, 0.2, 0.5]:
    nf = 10**(nf_added/10) * fmin
    
    N = (nf - fmin)*abs(1+gamma_opt)**2/(4*rn)
    c_n = gamma_opt/(1+N)
    r_n = 1/(1-N)*np.sqrt(N**2 + N*(1-abs(gamma_opt)**2))
    
    n = rf.Network(name=str(nf_added), s=calc_circle(c_n, r_n))
    n.plot_s_smith()
print("the optimum source reflection coefficient is ", gamma_opt)
Explanation: So we can see that we need to avoid inductive loads near short circuit in the input matching network and high impedance inductive loads on the output.
Let's draw some constant noise circles. First we grab the noise parameters for our target frequency from the network model:
End of explanation
gamma_s = 0.0
gamma_l = np.conj(bjt.s22.s - bjt.s21.s*gamma_s*bjt.s12.s/(1-bjt.s11.s*gamma_s))
gamma_l = gamma_l[idx_915mhz, 0, 0]
is_gamma_l_stable = np.absolute(gamma_l - cl[idx_915mhz]) > rl[idx_915mhz]
gamma_l, is_gamma_l_stable
Explanation: So we can see from the chart that just leaving the input at 50 ohms gets us under 0.1 dB of extra noise, which seems pretty good. I'm actually not sure that these actually correspond to the noise figure level increments I have listed up there, but the circles should at least correspond to increasing noise figures
So let's leave the input at 50 ohms and figure out how to match the output network to maximize gain and stability. Let's see what matching the load impedance with an unmatched input gives us:
End of explanation
def calc_matching_network_vals(z1, z2):
    flipped = np.real(z1) < np.real(z2)
    if flipped:
        z2, z1 = z1, z2
        
    # cancel out the imaginary parts of both input and output impedances    
    z1_par = 0.0
    if abs(np.imag(z1)) > 1e-6:
        # parallel something to cancel out the imaginary part of
        # z1's impedance
        z1_par = 1/(-1j*np.imag(1/z1))
        z1 = 1/(1./z1 + 1/z1_par)
    z2_ser = 0.0
    if abs(np.imag(z2)) > 1e-6:
        z2_ser = -1j*np.imag(z2)
        z2 = z2 + z2_ser
        
    Q = np.sqrt((np.real(z1) - np.real(z2))/np.real(z2))
    x1 = -1.j * np.real(z1)/Q
    x2 = 1.j * np.real(z2)*Q
    
    x1_tot = 1/(1/z1_par + 1/x1)
    x2_tot = z2_ser + x2
    if flipped:
        return x2_tot, x1_tot
    else:
        return x1_tot, x2_tot
z_l = rf.s2z(np.array([[[gamma_l]]]))[0,0,0]
# note that we're matching against the conjugate;
# this is because we want to see z_l from the BJT side
# if we plugged in z the matching network would make
# the 50 ohms look like np.conj(z) to match against it, so
# we use np.conj(z_l) so that it'll look like z_l from the BJT's side
z_par, z_ser = calc_matching_network_vals(np.conj(z_l), 50)
z_l, z_par, z_ser
Explanation: This looks like it may be kind of close to the load instability circles, so it might make sense to pick a load point with less gain for more stability, or to pick a different source impedance with more noise.
But for now let's just build a matching network for this and see how it performs:
End of explanation
c_par = np.real(1/(2j*np.pi*915e+6*z_par))
l_ser = np.real(z_ser/(2j*np.pi*915e+6))
print(c_par, l_ser)
Explanation: Let's calculate what the component values are:
End of explanation
output_network = tem.shunt_capacitor(c_par) ** tem.inductor(l_ser)
amplifier = bjt ** output_network
amplifier.plot_s_smith()
Explanation: The capacitance is kind of low but the inductance seems reasonable. Let's test it out:
End of explanation
amplifier.s21.plot_s_db()
Explanation: That looks pretty reasonable; let's take a look at the S21 to see what we got:
End of explanation
10*np.log10(amplifier.nf(50.)[idx_915mhz])
Explanation: So about 18 dB gain; let's see what our noise figure is:
End of explanation
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