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FOAE-2 ACDCAnalysis.py
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FOAE-2 ACDCAnalysis.py
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from manim import *
from circuits import *
from math import exp, log
class BjtMosCharacteristics(Scene):
def construct(self):
mos_axis = Axes(
x_range=[-1, 5, 1],
y_range=[-0.001, 0.010, 0.002],
x_length=7,
y_length=6,
x_axis_config={
"include_tip": False
},
y_axis_config={
"include_tip": False
}
).add_coordinates()
x_label = MathTex("V_{DS}", color=YELLOW).scale(0.75).next_to(mos_axis.x_axis.get_right(), direction=DR)
y_label = MathTex("I_D", color=RED).scale(0.75).next_to(mos_axis.y_axis.get_top(), direction=UL)
axis_labels = VGroup(x_label, y_label)
self.vgs = 2
self.kn = 0.0043
self.vt = 0.5
def mos_op_func(vds):
if self.vgs < self.vt:
return 0
elif (self.vgs - self.vt) >= vds:
return self.kn * ((self.vgs - self.vt) * vds - vds**2 / 2)
else:
return self.kn * (self.vgs - self.vt)**2 / 2
def mos_op_locus(vds):
return self.kn * vds**2 / 2
idvds = VGroup()
for vgs in np.arange(0, 3, 0.5):
self.vgs = vgs
idvds.add(mos_axis.plot(mos_op_func, x_range=[0, 5], color=RED))
if self.vgs > 0.5:
idvds[-1].add(MathTex("V_{GS} =", str(self.vgs)).scale(0.65).next_to(idvds[-1].points[-1]))
idvds_locus = mos_axis.plot(mos_op_locus, x_range=[0, self.vgs - self.vt + 0.3], color=BLUE, stroke_width=2)
locus_label_pt = idvds_locus.points[-8]
measure_lines = VGroup(
DoubleArrow(np.array([mos_axis.y_axis.get_center()[0] + 0.25, locus_label_pt[1], 0]), locus_label_pt + RIGHT * 0.2).stretch(0.7, 1),
DoubleArrow(locus_label_pt + LEFT * 0.2, np.array([mos_axis.x_axis.get_right()[0], locus_label_pt[1], 0])).stretch(0.7, 1)
)
text = VGroup(
MathTex("V_{DS}<V_{GS}-V_{th}").next_to(measure_lines[0], direction=UP, buff=0.5).shift(LEFT),
MathTex("V_{DS}>V_{GS}-V_{th}").next_to(measure_lines[1], direction=UP, buff=0.5).shift(RIGHT),
).scale(0.6)
def mos_ip_func(vgs):
if vgs < self.vt:
return 0
else:
return self.kn * (vgs - self.vt)**2 / 2
mos_ip_axis = Axes(
x_range=[-0.5, 3, 0.5],
y_range=[-0.001, 0.010, 0.002],
x_length=7,
y_length=6,
x_axis_config={
"include_tip": False
},
y_axis_config={
"include_tip": False
}
).add_coordinates()
ip_axis_labels = mos_ip_axis.get_axis_labels(x_label=MathTex("V_{GS}", color=GREEN).scale(0.75), y_label=MathTex("I_D", color=RED).scale(0.75))
idvgs = mos_ip_axis.plot(mos_ip_func, x_range=[0, 2.75], color=RED)
vt_text = MathTex("V_t").next_to(mos_ip_axis.c2p(self.vt, 0), direction=UP)
# ip_condition = MathTex("V_{DS} \\geq V_{GS}-V_{th} ").scale(0.75).next_to(ip_axis.get_bottom(), direction=LEFT, buff=0)
mos_eqn = VGroup(
# MathTex("I_D", " = \\dfrac{\\mu C_{ox} W}{L}"),
MathTex("i_D", " = k_n"),
MathTex("(", "v_{GS}", "-V_{th})^2 \\over 2") # s, substrings_to_isolate="V_{GS}"),
).arrange_submobjects(buff=0.1)
mos_eqn.scale(0.8).next_to(idvgs.points[-20], direction=LEFT, buff=0.5)
mos_eqn[0].set_color_by_tex("i_D", RED)
mos_eqn[1].set_color_by_tex("v_{GS}", GREEN)
idvgs_grp = VGroup(mos_ip_axis, idvgs, ip_axis_labels, vt_text, mos_eqn)
idvds_grp = VGroup(mos_axis, axis_labels, idvds, idvds_locus, measure_lines, text)
def bjt_ip_func(vbe):
return 10**-12 * exp(vbe / 0.025)
bjt_axis = Axes(
x_range=[-0.1, 0.8, 0.1],
y_range=[-0.001, 0.010, 0.002],
x_length=7,
y_length=6,
x_axis_config={
"include_tip": False
},
y_axis_config={
"include_tip": False
}
).add_coordinates()
bjt_ip_axis_labels = bjt_axis.get_axis_labels(x_label=MathTex("V_{BE}", color=GREEN).scale(0.75), y_label=MathTex("I_C", color=RED).scale(0.75))
icvbe = bjt_axis.plot(bjt_ip_func, x_range=[0, 0.575, 0.001], color=RED)
bjt_eqn = MathTex("i_C", "= I_s \\, e^{(", "v_{BE}", "/V_t)}").next_to(icvbe).shift(LEFT * 4.25 + UP * 1.5)
bjt_eqn.set_color_by_tex("i_C", RED)
bjt_eqn.set_color_by_tex("v_{BE}", GREEN)
icvbe_grp = VGroup(bjt_axis, bjt_ip_axis_labels, icvbe, bjt_eqn)
bjt = BJT().shift(4 * LEFT + 1.5 * DOWN).add_labels()
mos = MOSFET().shift(3.5 * RIGHT + 1.5 * DOWN).add_labels()
bjt_text = Text("BJT").next_to(bjt, direction=UP, buff=0.6).scale(0.7)
mos_text = Text("MOSFET").next_to(mos, direction=UP, buff=1).scale(0.7)
bjt.add(bjt_text)
mos.add(mos_text)
self.play(Create(bjt), Create(mos))
transconamp = VGroup(
Tex(r"Voltage", r"\, Controlled", r"\, Current", r"\, Source"),
Tex(r"Transconductance Amplifier"),
).arrange_submobjects(direction=DOWN).scale(1.25).to_edge(UP)
self.play(
AnimationGroup(*[GrowFromCenter(t) for t in transconamp[0]], lag_ratio=0.5)
)
self.play(Write(transconamp[1]))
self.wait()
self.play(bjt.animate.to_edge(UP), FadeOut(mos, transconamp)) # .shift(LEFT * 0.25 + UP), FadeOut(mos, bjt_text))
mos.to_edge(UP).align_to(bjt, direction=LEFT).shift(LEFT)
bjt_active_region = VGroup(
Text("Active Region"),
Line(LEFT, RIGHT).scale(2.5),
Text("B-E Junction: FB"),
Text("B-C Junction: RB")
).scale(0.75).arrange_submobjects(direction=DOWN).next_to(bjt, direction=DOWN, buff=1).shift(LEFT * 0.25)
for t in bjt_active_region:
self.play(Write(t))
bjtamp = BJTAmp().shift(2 * RIGHT)
# bjt_eqn..next_to(bjtamp[0:9], direction=UL),
self.play(
TransformFromCopy(bjt[0:-1], bjtamp[0:9])
)
transconamp[1].to_edge(UP)
transconamp.remove(transconamp[0])
vcc = bjtamp.elements[-2]
temp_short = Line(bjtamp.collector(), vcc.get_bottom())
vcc.add(MathTex("V_{CC}").scale(0.75).next_to(vcc, direction=UR, buff=0))
ic, vbe = MathTex("i_c", color=RED), MathTex("v_{BE}", color=GREEN).scale(0.75)
ic_arrow = Arrow(UP, DOWN).scale(0.75).next_to(temp_short, buff=0.5)
ic.next_to(ic_arrow)
ic.add(ic_arrow)
vbe.next_to(bjtamp.elements[1][0], direction=DL, buff=0.1)
temp_bjt_amp = VGroup(bjtamp.elements[0:4:3], bjtamp.elements[-1], bjtamp[-1], temp_short)
self.play(
*[Create(m)
for m in temp_bjt_amp
],
)
self.play(Write(vbe))
self.play(Write(ic))
self.wait()
self.play(Wiggle(vbe))
self.play(Wiggle(ic))
self.wait()
self.play(FadeOut(temp_bjt_amp, bjtamp[:9], vbe, ic))
self.wait()
self.play(Create(icvbe_grp.to_edge(RIGHT, buff=0.1)[:-1]))
self.play(Write(icvbe_grp[-1]))
self.wait()
self.play(FadeOut(bjt_active_region, icvbe_grp[:-1], bjt, bjt_eqn))
self.wait()
# #########
mos_active_region = VGroup(
Text("Active Region").scale(0.75),
Line(LEFT, RIGHT).scale(2),
MathTex("V_{GS} > V_{th} "),
MathTex("V_{DS} \\geq V_{GS}-V_{th} "),
).arrange_submobjects(direction=DOWN, buff=0.25).next_to(mos, direction=DOWN, buff=.5).shift(LEFT * 0.25)
self.play(FadeIn(mos))
self.play(Write(mos_active_region[0:-1]))
# idvds_grp.to_edge(RIGHT)
# self.play(FadeIn(idvds_grp[:-2]))
self.play(Write(mos_active_region[-1]))
# self.play(FadeIn(idvds_grp[-2:]))
idvgs_grp.to_edge(RIGHT)
self.play(
# FadeOut(idvds_grp),
Create(idvgs_grp[:-1])
)
self.play(Write(idvgs_grp[:-1]))
self.wait()
bjt.move_to(LEFT * 3.5)
bjt_eqn.next_to(bjt, direction=DOWN, buff=0.5)
self.play(
FadeOut(idvgs_grp[:-1], mos_active_region),
*[FadeIn(m) for m in [bjt, bjt_eqn]],
mos.animate.move_to(RIGHT * 3.5),
mos_eqn.animate.next_to(RIGHT * 3.5, direction=DOWN, buff=2)
)
self.wait()
# #############################
voltageamp = Tex(r"Voltage Amplifier").scale(1.25).to_corner(UL)
self.play(Write(transconamp))
self.play(FadeOut(mos, mos_eqn))
for m in [bjtamp, vbe, ic, temp_short]:
m.shift(LEFT)
self.play(
bjt_eqn.animate.next_to(voltageamp, direction=DOWN, buff=0.75),
FadeOut(bjt[-1]),
ReplacementTransform(bjt[0:-1], bjtamp[0:9])
)
self.play(
*[Create(m)
for m in [bjtamp.elements[0:4:3], bjtamp.elements[-1], bjtamp[-1], temp_short]
],
transconamp.animate.to_corner(UL)
)
rc = bjtamp.elements[2]
self.play(Write(vbe))
self.play(Write(ic))
self.play(ReplacementTransform(transconamp, voltageamp))
rc_text = MathTex("R_C").scale(0.75).next_to(rc, direction=LEFT)
self.play(ReplacementTransform(temp_short, rc), FadeIn(rc_text))
self.wait()
icrc = MathTex("i_C\\,R_C", color=BLUE).scale(0.75).next_to(rc)
plusmin = VGroup(MathTex("+"), MathTex("-")).arrange_submobjects(DOWN, buff=1).move_to(icrc).shift(UP * 0.1)
self.play(ReplacementTransform(ic[0], icrc), FadeOut(ic_arrow), FadeIn(plusmin))
self.play(FadeOut(bjtamp.elements[1][-3:]))
self.wait()
vce_term = Line(bjtamp.collector(), bjtamp.collector() + 2 * RIGHT)
op_node = vce_term.points[-1]
vce_term.add(Dot(op_node))
vce_gnd = Ground().next_to(vce_term.points[-1], direction=DOWN).align_to(bjtamp.elements[-1], direction=UP)
vce_gnd.add(Dot(vce_gnd.get_top()))
vce_text = MathTex("v_C", " = V_{CC} -").scale(0.75).set_color_by_tex("v_C", YELLOW)
vo_text = MathTex("v_C", " = V_{CC} -", "i_C R_C").set_color_by_tex("v_C", YELLOW).set_color_by_tex("i_C R_C", BLUE).next_to(bjt_eqn, direction=DOWN)
self.play(
plusmin[0].animate.next_to(op_node, direction=DOWN, buff=0.5),
plusmin[-1].animate.next_to(vce_gnd, direction=UP, buff=0.5),
)
vce_text.move_to(plusmin).shift(LEFT * 0.5)
self.play(
*[FadeIn(m) for m in [vce_term, vce_gnd, vce_text]]
)
self.play(icrc.animate.next_to(vce_text, buff=0.1))
self.play(TransformFromCopy(vce_text, vo_text))
self.wait()
class SS1(MovingCameraScene):
def construct(self):
title = MathTex("v_C", " = V_{CC} - R_C \\,\\, I_s \\, e^{(", "v_{BE}", "/V_t)}").to_corner(UR).scale(0.9)
title.set_color_by_tex("v_C", YELLOW)
title.set_color_by_tex("v_{BE}", GREEN)
self.play(FadeIn(title))
temp_axis = Axes(
x_range=[-0.1, 1, 0.25],
y_range=[-2, 11, 2],
x_length=10,
# y_length=14,
x_axis_config={
"include_tip": False
},
y_axis_config={
"include_tip": False
}
).add_coordinates().to_edge(LEFT)
temp_axis_labels = temp_axis.get_axis_labels(x_label=MathTex("v_{BE}", color=GREEN), y_label=MathTex("v_C", color=YELLOW))
temp_axis.add(temp_axis_labels)
self.Rc = 1e3
def diode_func(x):
vce = 10 - self.Rc * 1e-12 * exp(x / 0.025)
if vce > 0:
return vce
elif vce <= 0:
return 0
x_lim = 0.025 * log(10 / (1e-12 * self.Rc))
diode_eqn_temp = temp_axis.plot(diode_func, x_range=[0, x_lim, 0.001], color=BLUE)
self.play(Create(temp_axis))
self.play(Create(diode_eqn_temp))
marker_pts = [temp_axis.i2gp(0.5, diode_eqn_temp), temp_axis.i2gp(x_lim, diode_eqn_temp)]
marker_dots = VGroup(*[
Dot(pt, color=BLUE)
for pt in marker_pts
])
marker_lines = VGroup(*[
DashedLine(ORIGIN, UP * 5.5).next_to(pt, direction=UP, buff=0)
for pt in [temp_axis.c2p(0.5, 0), temp_axis.c2p(x_lim, 0)]
])
marker_text = VGroup(Text("A").scale(0.75).next_to(marker_dots[0], direction=UR, buff=0.1), Text("B").scale(0.75).next_to(marker_dots[1], direction=UR))
markers = VGroup(marker_dots, marker_lines, marker_text)
regions = VGroup(*[Tex(t) for t in ["Cutoff", "Active", "Saturation"]])
regions[0].next_to(marker_lines[0], direction=LEFT, buff=1)
regions[1].rotate(PI / 2).next_to(marker_lines[0], buff=0.1).add_background_rectangle()
regions[2].next_to(marker_lines[1], buff=1)
self.play(FadeIn(marker_dots), FadeIn(marker_text))
self.play(
*[Create(m) for m in marker_lines]
)
for m in regions:
self.play(FadeIn(m))
axis = Axes(
x_range=[0.35, 0.65, 0.05],
y_range=[-0.25, 11, 1],
x_length=10,
y_length=7,
x_axis_config={
"include_tip": False,
},
y_axis_config={
"include_tip": False
}
).add_coordinates()
axis_labels = axis.get_axis_labels(x_label=MathTex("v_{BE}", color=GREEN), y_label=MathTex("v_C", color=YELLOW))
axis.add(axis_labels)
diode_eqn = axis.plot(diode_func, x_range=[0.35, x_lim, 0.0001], color=BLUE)
self.play(
ReplacementTransform(temp_axis, axis),
ReplacementTransform(diode_eqn_temp, diode_eqn),
FadeOut(regions, marker_lines),
marker_dots[0].animate.move_to(axis.i2gp(0.5, diode_eqn)),
marker_dots[1].animate.move_to(axis.i2gp(x_lim, diode_eqn)),
marker_text[0].animate.next_to(axis.i2gp(0.5, diode_eqn), direction=UR),
marker_text[1].animate.next_to(axis.i2gp(x_lim, diode_eqn), direction=UR),
)
self.wait()
self.q_point = 0.55 # 0.56
small_sig_amp = 0.02
q_point_in_graph = axis.i2gp(self.q_point, diode_eqn)
q_point_dot = Dot(q_point_in_graph, color=ORANGE)
dot = q_point_dot.copy() # .set_color(YELLOW)
upper_dummy_dot = Dot(axis.i2gp(self.q_point + small_sig_amp, diode_eqn)).scale(0.001)
lower_dummy_dot = Dot(axis.i2gp(self.q_point - small_sig_amp, diode_eqn)).scale(0.001)
dots = VGroup(q_point_dot, upper_dummy_dot, lower_dummy_dot)
self.t, self.x, self.f = 0, 0, 2
temp_amp = 0.0075
def q_point_updater(q_point, dt):
self.t += dt
self.x = self.q_point + temp_amp * np.sin(self.t)
q_point.move_to(axis.i2gp(self.x, diode_eqn))
def upper_dummy_updater(q_point, dt):
x = self.q_point + small_sig_amp + temp_amp * np.sin(self.t)
upper_dummy_dot.move_to(axis.i2gp(x, diode_eqn))
def lower_dummy_updater(q_point, dt):
x = self.q_point - small_sig_amp + temp_amp * np.sin(self.t)
lower_dummy_dot.move_to(axis.i2gp(x, diode_eqn))
def lim_line_updater(line):
new_line = axis.get_lines_to_point(q_point_dot.get_center())
line.become(new_line)
x_lim_nos = [self.q_point, self.q_point + small_sig_amp, self.q_point - small_sig_amp]
up_lim_line = axis.get_lines_to_point(upper_dummy_dot.get_center()).add_updater(lambda x: x.become(axis.get_lines_to_point(upper_dummy_dot.get_center())))
low_lim_line = axis.get_lines_to_point(lower_dummy_dot.get_center()).add_updater(lambda x: x.become(axis.get_lines_to_point(lower_dummy_dot.get_center())))
q_point_lim_line = axis.get_lines_to_point(q_point_dot.get_center()).add_updater(lambda x: x.become(axis.get_lines_to_point(q_point_dot.get_center())))
lim_lines = VGroup(up_lim_line, low_lim_line, q_point_lim_line)
temp_grp = VGroup(*[*dots, *lim_lines])
self.play(*[Create(mobj) for mobj in temp_grp])
def get_horizontally_moving_tracing(dot, color, stroke_width=3, rate=0.25):
path = VMobject()
path.set_stroke(color, stroke_width)
path.start_new_path(np.array([axis.c2p(self.q_point - small_sig_amp, 0)[0], dot.get_center()[1], 0]))
path.Vector = Vector
def update_path(p, dt):
p.shift(rate * dt * 3 * (LEFT))
p.add_smooth_curve_to(np.array([axis.c2p(self.q_point - small_sig_amp, 0)[0], dot.get_center()[1], 0]))
path.add_updater(update_path)
return path
def get_vertically_moving_tracing(dot, color, stroke_width=3, rate=0.25):
path = VMobject()
path.set_stroke(color, stroke_width)
path.start_new_path(np.array([dot.get_center()[0], axis.i2gp(self.q_point + small_sig_amp, diode_eqn)[1], 0]))
# path.start_new_path(dot.get_center())
path.Vector = Vector
def update_path(p, dt):
p.shift(rate * dt * 3 * DOWN)
p.add_smooth_curve_to(np.array([dot.get_center()[0], axis.i2gp(self.q_point + small_sig_amp, diode_eqn)[1], 0]))
path.add_updater(update_path)
return path
x_mark, y_mark = Dot(color=GREEN), Dot(color=YELLOW)
def x_mark_updater(x_mark):
x_mark.move_to(ip_path.points[-1])
def y_mark_updater(y_mark):
y_mark.move_to(op_path.points[-1])
ip_path = get_vertically_moving_tracing(dot, GREEN)
op_path = get_horizontally_moving_tracing(dot, YELLOW)
x_mark.add_updater(x_mark_updater)
y_mark.add_updater(y_mark_updater)
def dot_updater(dot, dt):
self.t += 5 * dt
self.x = self.q_point + small_sig_amp * np.sin(self.t)
# y = diode_func(x)
dot.move_to(axis.i2gp(self.x, diode_eqn))
dot.add_updater(dot_updater)
self.play(GrowFromCenter(dot), FadeOut(q_point_dot))
self.add(dot, op_path, ip_path, x_mark, y_mark)
self.wait(20)
class SS_linear(MovingCameraScene):
def construct(self):
# title = MathTex("v_C", " = V_{CC} - R_C \\,\\, I_s \\, e^{(", "v_{BE}", "/V_t)}").to_corner(UR).scale(0.9)
# title.set_color_by_tex("v_C", YELLOW)
# title.set_color_by_tex("v_{BE}", GREEN)
# self.play(FadeIn(title))
# temp_axis = Axes(
# x_range=[-0.1, 1, 0.25],
# y_range=[-2, 11, 2],
# x_length=10,
# # y_length=14,
# x_axis_config={
# "include_tip": False
# },
# y_axis_config={
# "include_tip": False
# }
# ).add_coordinates().to_edge(LEFT)
# temp_axis_labels = temp_axis.get_axis_labels(x_label=MathTex("v_{BE}", color=GREEN), y_label=MathTex("v_C", color=YELLOW))
# temp_axis.add(temp_axis_labels)
self.Rc = 1e3
def diode_func(x):
vce = 10 - self.Rc * 1e-12 * exp(x / 0.025)
if vce > 0:
return vce
elif vce <= 0:
return 0
def line_func(x):
x_lim = 0.025 * log(10 / (1e-12 * self.Rc))
y1 = diode_func(0.5)
y2 = diode_func(x_lim)
line = y1 + (y2 - y1) * (x - 0.5) / (x_lim - 0.5) # * + (1 - x) * diode_func(x_lim)
return line
# if vce > 0:
# return vce
# elif vce <= 0:
# return 0
x_lim = 0.025 * log(10 / (1e-12 * self.Rc))
# diode_eqn_temp = temp_axis.plot(diode_func, x_range=[0, x_lim, 0.001], color=BLUE)
# self.play(Create(temp_axis))
# self.play(Create(diode_eqn_temp))
# self.play(FadeIn(marker_dots), FadeIn(marker_text))
# self.play(
# *[Create(m) for m in marker_lines]
# )
# for m in regions:
# self.play(FadeIn(m))
axis = Axes(
x_range=[0.35, 0.65, 0.05],
y_range=[-0.25, 11, 1],
x_length=10,
y_length=7,
x_axis_config={
"include_tip": False,
},
y_axis_config={
"include_tip": False
}
).add_coordinates()
axis_labels = axis.get_axis_labels(x_label=MathTex("v_{BE}", color=GREEN), y_label=MathTex("v_C", color=YELLOW))
axis.add(axis_labels)
diode_eqn = axis.plot(diode_func, x_range=[0.35, x_lim, 0.0001], color=BLUE)
line = axis.plot(line_func, x_range=[0.5, x_lim, 0.0001], color=BLUE)
self.add(axis)
self.add(line)
marker_pts = [axis.i2gp(0.5, diode_eqn), axis.i2gp(x_lim, diode_eqn)]
marker_dots = VGroup(*[
Dot(pt, color=BLUE)
for pt in marker_pts
])
marker_text = VGroup(Text("A").scale(0.75).next_to(marker_dots[0], direction=UR, buff=0.1), Text("B").scale(0.75).next_to(marker_dots[1], direction=UR))
markers = VGroup(marker_dots, marker_text)
# marker_dots[0].move_to(axis.i2gp(0.5, diode_eqn)),
# marker_dots[1].move_to(axis.i2gp(x_lim, diode_eqn)),
marker_text[0].next_to(axis.i2gp(0.5, diode_eqn), direction=UR),
marker_text[1].next_to(axis.i2gp(x_lim, diode_eqn), direction=UR),
self.add(markers)
self.q_point = 0.55 # 0.56
small_sig_amp = 0.02
q_point_in_graph = axis.i2gp(self.q_point, line)
q_point_dot = Dot(q_point_in_graph, color=ORANGE)
dot = q_point_dot.copy() # .set_color(YELLOW)
upper_dummy_dot = Dot(axis.i2gp(self.q_point + small_sig_amp, line)).scale(0.001)
lower_dummy_dot = Dot(axis.i2gp(self.q_point - small_sig_amp, line)).scale(0.001)
dots = VGroup(q_point_dot, upper_dummy_dot, lower_dummy_dot)
self.t, self.x, self.f = 0, 0, 2
temp_amp = 0.0075
def q_point_updater(q_point, dt):
self.t += dt
self.x = self.q_point + temp_amp * np.sin(self.t)
q_point.move_to(axis.i2gp(self.x, line))
def upper_dummy_updater(q_point, dt):
x = self.q_point + small_sig_amp + temp_amp * np.sin(self.t)
upper_dummy_dot.move_to(axis.i2gp(x, line))
def lower_dummy_updater(q_point, dt):
x = self.q_point - small_sig_amp + temp_amp * np.sin(self.t)
lower_dummy_dot.move_to(axis.i2gp(x, line))
def lim_line_updater(line):
new_line = axis.get_lines_to_point(q_point_dot.get_center())
line.become(new_line)
x_lim_nos = [self.q_point, self.q_point + small_sig_amp, self.q_point - small_sig_amp]
up_lim_line = axis.get_lines_to_point(upper_dummy_dot.get_center()).add_updater(lambda x: x.become(axis.get_lines_to_point(upper_dummy_dot.get_center())))
low_lim_line = axis.get_lines_to_point(lower_dummy_dot.get_center()).add_updater(lambda x: x.become(axis.get_lines_to_point(lower_dummy_dot.get_center())))
q_point_lim_line = axis.get_lines_to_point(q_point_dot.get_center()).add_updater(lambda x: x.become(axis.get_lines_to_point(q_point_dot.get_center())))
lim_lines = VGroup(up_lim_line, low_lim_line, q_point_lim_line)
temp_grp = VGroup(*[*dots, *lim_lines])
self.play(*[Create(mobj) for mobj in temp_grp])
def get_horizontally_moving_tracing(dot, color, stroke_width=3, rate=0.25):
path = VMobject()
path.set_stroke(color, stroke_width)
path.start_new_path(np.array([axis.c2p(self.q_point - small_sig_amp, 0)[0], dot.get_center()[1], 0]))
path.Vector = Vector
def update_path(p, dt):
p.shift(rate * dt * 3 * (LEFT))
p.add_smooth_curve_to(np.array([axis.c2p(self.q_point - small_sig_amp, 0)[0], dot.get_center()[1], 0]))
path.add_updater(update_path)
return path
def get_vertically_moving_tracing(dot, color, stroke_width=3, rate=0.25):
path = VMobject()
path.set_stroke(color, stroke_width)
path.start_new_path(np.array([dot.get_center()[0], axis.i2gp(self.q_point + small_sig_amp, line)[1], 0]))
# path.start_new_path(dot.get_center())
path.Vector = Vector
def update_path(p, dt):
p.shift(rate * dt * 3 * DOWN)
p.add_smooth_curve_to(np.array([dot.get_center()[0], axis.i2gp(self.q_point + small_sig_amp, line)[1], 0]))
path.add_updater(update_path)
return path
x_mark, y_mark = Dot(color=GREEN), Dot(color=YELLOW)
def x_mark_updater(x_mark):
x_mark.move_to(ip_path.points[-1])
def y_mark_updater(y_mark):
y_mark.move_to(op_path.points[-1])
ip_path = get_vertically_moving_tracing(dot, GREEN)
op_path = get_horizontally_moving_tracing(dot, YELLOW)
x_mark.add_updater(x_mark_updater)
y_mark.add_updater(y_mark_updater)
def dot_updater(dot, dt):
self.t += 5 * dt
self.x = self.q_point + small_sig_amp * np.sin(self.t)
# y = diode_func(x)
dot.move_to(axis.i2gp(self.x, line))
dot.add_updater(dot_updater)
self.play(GrowFromCenter(dot), FadeOut(q_point_dot))
self.add(dot, op_path, ip_path, x_mark, y_mark)
self.wait(15)
class SS2(MovingCameraScene):
def construct(self):
title = MathTex("v_C", " = V_{CC} - R_C \\,\\, I_s \\, e^{(", "v_{BE}", "/V_t)}").to_corner(UR).scale(0.9)
title.set_color_by_tex("v_C", YELLOW)
title.set_color_by_tex("v_{BE}", GREEN)
self.play(FadeIn(title))
temp_axis = Axes(
x_range=[-0.1, 1, 0.25],
y_range=[-2, 11, 2],
x_length=10,
# y_length=14,
x_axis_config={
"include_tip": False
},
y_axis_config={
"include_tip": False
}
).add_coordinates().to_edge(LEFT)
temp_axis_labels = temp_axis.get_axis_labels(x_label=MathTex("v_{BE}", color=GREEN), y_label=MathTex("v_C", color=YELLOW))
temp_axis.add(temp_axis_labels)
self.Rc = 1e3
def diode_func(x):
vce = 10 - self.Rc * 1e-12 * exp(x / 0.025)
# vds =
if vce > 0:
return vce
# elif vce <= 0.3 and vce >= 0:
# return 1e-10 * vce
elif vce <= 0:
return 0
x_lim = 0.025 * log(10 / (1e-12 * self.Rc))
diode_eqn_temp = temp_axis.plot(diode_func, x_range=[0, x_lim, 0.001], color=BLUE)
self.play(Create(temp_axis))
self.play(Create(diode_eqn_temp))
marker_pts = [temp_axis.i2gp(0.5, diode_eqn_temp), temp_axis.i2gp(x_lim, diode_eqn_temp)]
marker_dots = VGroup(*[
Dot(pt, color=BLUE)
for pt in marker_pts
])
marker_lines = VGroup(*[
DashedLine(ORIGIN, UP * 5.5).next_to(pt, direction=UP, buff=0)
for pt in [temp_axis.c2p(0.5, 0), temp_axis.c2p(x_lim, 0)]
])
marker_text = VGroup(Text("A").scale(0.75).next_to(marker_dots[0], direction=UR, buff=0.1), Text("B").scale(0.75).next_to(marker_dots[1], direction=UR))
markers = VGroup(marker_dots, marker_lines, marker_text)
regions = VGroup(*[Tex(t) for t in ["Cutoff", "Active", "Saturation"]])
regions[0].next_to(marker_lines[0], direction=LEFT, buff=1)
regions[1].rotate(PI / 2).next_to(marker_lines[0], buff=0.1).add_background_rectangle()
regions[2].next_to(marker_lines[1], buff=1)
self.play(FadeIn(marker_dots), FadeIn(marker_text))
self.play(
*[Create(m) for m in marker_lines]
)
for m in regions:
self.play(FadeIn(m))
axis = Axes(
x_range=[0.35, 0.65, 0.05],
# x_range=[0, 0.8, 0.1],
y_range=[-0.25, 11, 1],
x_length=10,
y_length=7,
x_axis_config={
"include_tip": False,
},
y_axis_config={
"include_tip": False
}
).add_coordinates()
axis_labels = axis.get_axis_labels(x_label=MathTex("v_{BE}", color=GREEN), y_label=MathTex("v_C", color=YELLOW))
axis.add(axis_labels)
diode_eqn = axis.plot(diode_func, x_range=[0.35, x_lim, 0.0001], color=BLUE)
self.play(
ReplacementTransform(temp_axis, axis),
ReplacementTransform(diode_eqn_temp, diode_eqn),
FadeOut(regions, marker_lines),
marker_dots[0].animate.move_to(axis.i2gp(0.5, diode_eqn)),
marker_dots[1].animate.move_to(axis.i2gp(x_lim, diode_eqn)),
marker_text[0].animate.next_to(axis.i2gp(0.5, diode_eqn), direction=UR),
marker_text[1].animate.next_to(axis.i2gp(x_lim, diode_eqn), direction=UR),
# ReplacementTransform(temp_axis_labels, axis_labels),
# self.camera.frame.animate.shift(DOWN * 4) # .scale(2),
)
self.wait()
self.q_point = 0.56
small_sig_amp = 0.002
q_point_in_graph = axis.i2gp(self.q_point, diode_eqn)
q_point_dot = Dot(q_point_in_graph, color=ORANGE)
# self.play(
# self.camera.frame.animate.move_to(q_point_in_graph + LEFT),
# axis.x_axis.animate.move_to(np.array([axis.x_axis.get_center()[0], q_point_dot.get_center()[1] - 3, 0]))
# ) # .scale(2)
# self.add(axis1, diode_eqn_1)
# self.play(Transform(axis1, axis2), Transform(diode_eqn_1, diode_eqn_2))
# self.wait()
dot = q_point_dot.copy() # .set_color(YELLOW)
upper_dummy_dot = Dot(axis.i2gp(self.q_point + small_sig_amp, diode_eqn)).scale(0.001)
lower_dummy_dot = Dot(axis.i2gp(self.q_point - small_sig_amp, diode_eqn)).scale(0.001)
dots = VGroup(q_point_dot, upper_dummy_dot, lower_dummy_dot)
self.t, self.x, self.f = 0, 0, 2
# rd = 0.025 / diode_func(self.q_point)
# print(rd)
# self.op_amp = (diode_func(self.q_point + small_sig_amp) - diode_func(self.q_point - small_sig_amp)) / 2
temp_amp = 0.0075
def q_point_updater(q_point, dt):
self.t += dt
self.x = self.q_point + temp_amp * np.sin(self.t)
# y = diode_func(x)
q_point.move_to(axis.i2gp(self.x, diode_eqn))
# self.camera.frame.move_to(q_point.get_center() + LEFT)
# axis.x_axis.move_to(np.array([axis.x_axis.get_center()[0], q_point_dot.get_center()[1] - 3, 0]))
def upper_dummy_updater(q_point, dt):
x = self.q_point + small_sig_amp + temp_amp * np.sin(self.t)
upper_dummy_dot.move_to(axis.i2gp(x, diode_eqn))
def lower_dummy_updater(q_point, dt):
x = self.q_point - small_sig_amp + temp_amp * np.sin(self.t)
lower_dummy_dot.move_to(axis.i2gp(x, diode_eqn))
def lim_line_updater(line):
new_line = axis.get_lines_to_point(q_point_dot.get_center())
line.become(new_line)
x_lim_nos = [self.q_point, self.q_point + small_sig_amp, self.q_point - small_sig_amp]
up_lim_line = axis.get_lines_to_point(upper_dummy_dot.get_center()).add_updater(lambda x: x.become(axis.get_lines_to_point(upper_dummy_dot.get_center())))
low_lim_line = axis.get_lines_to_point(lower_dummy_dot.get_center()).add_updater(lambda x: x.become(axis.get_lines_to_point(lower_dummy_dot.get_center())))
q_point_lim_line = axis.get_lines_to_point(q_point_dot.get_center()).add_updater(lambda x: x.become(axis.get_lines_to_point(q_point_dot.get_center())))
lim_lines = VGroup(up_lim_line, low_lim_line, q_point_lim_line)
tgt_line = Line(LEFT, RIGHT, color=ORANGE, stroke_width=3).put_start_and_end_on(upper_dummy_dot.get_center(), lower_dummy_dot.get_center() + DOWN * 0.000000001)
def tgt_line_updater(tgt):
tgt.move_to(q_point_dot)
x = axis.p2c(q_point_dot.get_center())[0]
y0 = axis.i2gp(x, diode_eqn)
y1 = axis.i2gp(x + 1e-12, diode_eqn)
tgt.put_start_and_end_on(
axis.i2gp(x, diode_eqn),
axis.i2gp(x + 1e-12, diode_eqn)
)
tgt_line.scale(2e10)
# tgt.slope = (y1[1] - y0[1]) / 1e-12
tgt.slope = (diode_func(x + 1e-12) - diode_func(x)) / 1e-12
# tgt.slope = 1
slope_text = MathTex("\\dfrac{\\Delta v_c}{\\Delta v_{be}} = ")
slope_val = DecimalNumber(0).add_updater(lambda x: x.set_value(tgt_line.slope))
slope_mobj = VGroup(slope_text, slope_val).arrange_submobjects(direction=RIGHT).next_to(q_point_dot, buff=1)
self.play(Write(slope_text))
temp_grp = VGroup(*[*dots, *lim_lines, tgt_line, slope_val])
self.play(*[Create(mobj) for mobj in temp_grp[:-1]])
q_point_dot.add_updater(q_point_updater)
upper_dummy_dot.add_updater(upper_dummy_updater)
lower_dummy_dot.add_updater(lower_dummy_updater)
tgt_line.add_updater(tgt_line_updater)
self.add(*temp_grp)
self.wait(2 * PI)
for mobj in [*dots, *lim_lines]:
mobj.clear_updaters()
self.wait()
def get_horizontally_moving_tracing(dot, color, stroke_width=3, rate=0.25):
path = VMobject()
path.set_stroke(color, stroke_width)
path.start_new_path(np.array([axis.c2p(self.q_point - small_sig_amp, 0)[0], dot.get_center()[1], 0]))
path.Vector = Vector
def update_path(p, dt):
p.shift(rate * dt * 3 * (LEFT))
p.add_smooth_curve_to(np.array([axis.c2p(self.q_point - small_sig_amp, 0)[0], dot.get_center()[1], 0]))
path.add_updater(update_path)
return path
def get_vertically_moving_tracing(dot, color, stroke_width=3, rate=0.25):
path = VMobject()
path.set_stroke(color, stroke_width)
path.start_new_path(np.array([dot.get_center()[0], axis.i2gp(self.q_point + small_sig_amp, diode_eqn)[1], 0]))
# path.start_new_path(dot.get_center())
path.Vector = Vector
def update_path(p, dt):
p.shift(rate * dt * 3 * DOWN)
# p.add_smooth_curve_to(np.array([dot.get_center()[0], self.q_point - 0.005, 0]))
p.add_smooth_curve_to(np.array([dot.get_center()[0], axis.i2gp(self.q_point + small_sig_amp, diode_eqn)[1], 0]))
path.add_updater(update_path)
return path
x_mark, y_mark = Dot(color=GREEN), Dot(color=YELLOW)
def x_mark_updater(x_mark):
x_mark.move_to(ip_path.points[-1])
def y_mark_updater(y_mark):
y_mark.move_to(op_path.points[-1])
ip_path = get_vertically_moving_tracing(dot, GREEN)
op_path = get_horizontally_moving_tracing(dot, YELLOW)
x_mark.add_updater(x_mark_updater)
y_mark.add_updater(y_mark_updater)
def dot_updater(dot, dt):
self.t += 5 * dt
self.x = self.q_point + small_sig_amp * np.sin(self.t)
# y = diode_func(x)
dot.move_to(axis.i2gp(self.x, diode_eqn))
# op_path = axis.plot(lambda x: self.op_amp * np.sin(self.f * self.q_point * 2 * PI * x / self.q_point) + diode_func(self.q_point), x_range=[0, 1])
# op_path = axis.plot(, x_range=[0,1])
# def op_path_updater(op_path):
# op_path.become(
# axis.plot(lambda x: self.op_amp * np.sin(self.f * self.q_point * 2 * PI * x / self.q_point) + diode_func(self.q_point), x_range=[0, self.x])
# )
dot.add_updater(dot_updater)
# op_path.add_updater(op_path_updater)
self.play(GrowFromCenter(dot), FadeOut(q_point_dot))
self.add(dot, op_path, ip_path, x_mark, y_mark)
self.wait(20)
class SSExpln(Scene):
def construct(self):
ip = MathTex("v_{BE}(t)", "=", " V_{BE}", " +", " v_{be}(t)")
for i, c in zip(ip[::2], [GREEN, GREEN_A, GREEN_B]):
i.set_color(c)
op1 = VGroup(
MathTex("= I_s \\,e^{v_{BE}/V_t}"),
MathTex("= I_s \\,e^{(V_{BE}+v_{be})/V_t}"),
MathTex("= I_s \\quad e^{V_{BE}/V_t}", "\\, e^{v_{be}/V_t}"),
MathTex("= I_C\\, e^{v_{be}/V_t}"),
MathTex("= I_C \\, \\bigg( 1 + \\dfrac{v_{be}}{V_t} \\bigg)"),
).arrange_submobjects(direction=DOWN)
for o in op1[1:]:
o.align_to(op1[0].get_left(), direction=LEFT)
for o in op1[:-1]:
if o is not op1[2]:
o[0][4:].scale(0.75).next_to(o[0][3], direction=UR, buff=0)
else:
o[0][4:12].scale(0.75).next_to(o[0][3], direction=UR, buff=0)
o[1][1:].scale(0.75).next_to(o[1][0], direction=UR, buff=0)
op1.shift(LEFT * 3 + UP * 0.3)
IC_box = SurroundingRectangle(op1[2][0][1:12])
ic = MathTex("i_C ")
ic.next_to(op1[0], direction=LEFT)
op2 = VGroup(
MathTex("= I_C \\, \\bigg( 1 + \\dfrac{v_{be}}{V_t} \\bigg)"),
MathTex("= I_C + I_C\\dfrac{v_{be}}{V_t}"),
MathTex("= I_C + ", "\\dfrac{I_C}{V_t}", "\\,v_{be}"),
MathTex("= I_C + ", "g_m", "\\,v_{be}").set_color_by_tex("g_m", YELLOW)
).arrange_submobjects(direction=DOWN)
op2[0].next_to(ic)
# gm = MathTex("gm = \\dfrac{I_C}{V_t}", color=YELLOW).move_to(op1[0])
for o in op2[1:]:
o.align_to(op1[0].get_left(), direction=LEFT)
taylor = MathTex("e^{v_{be}/V_t} = 1 + \\dfrac{(v_{be}/V_t)}{1!}", " + \\dfrac{(v_{be}/V_t)^2}{2!} + \\dfrac{(v_{be}/V_t)^3}{3!} + .\\,.\\,.\\,")
taylor.next_to(op1[-2], direction=DOWN).align_to(op1[-2].get_left(), direction=LEFT).shift(LEFT * 0.2)
ss_condition = MathTex("v_{be}<<V_t")
vbe_axis = Axes(
x_range=[-0.1, 2, 0.5],
# x_range=[0, 0.8, 0.1],
y_range=[-0.1, 1, 0.25],
x_length=5,
y_length=3,
x_axis_config={
"include_tip": False,
},
y_axis_config={
"include_tip": False
}
).to_corner(UR)
vbe_axis_labels = vbe_axis.get_axis_labels(x_label=MathTex("t", color=WHITE), y_label=MathTex("v_{BE}", color=GREEN))
vbe_axis.add(vbe_axis_labels)
x_lim = 1.5
vbe_plot = vbe_axis.plot(lambda vbe: 0.1 * np.sin(15 * vbe), x_range=[0, x_lim], color=GREEN_B)
vBE_plot = vbe_axis.plot(lambda vbe: 0.1 * np.sin(15 * vbe) + 0.56, x_range=[0, x_lim], color=GREEN)
VBE_plot = DashedLine(stroke_width=1, color=GREEN_A).set_width(0.75 * vbe_axis.x_axis.get_width())\
.move_to(vbe_axis.c2p(2.1 / 2, 0)).align_to(vbe_axis.c2p(0, 0.56), direction=LEFT)
vbe = VGroup(
MathTex("V_{BE}", color=GREEN_A).scale(0.7).next_to(vbe_axis.c2p(0, 0.56), direction=LEFT),
MathTex("v_{be}(t)", color=GREEN_B).next_to(vbe_plot.get_right(), direction=UR),
MathTex("v_{BE}(t)", color=GREEN).scale(0.7).next_to(vBE_plot.get_right())
)
ip.next_to(vbe_axis, direction=LEFT, buff=2)
self.play(Create(vbe_axis))
self.play(
VBE_plot.animate.move_to(vbe_axis.c2p(2.1 / 2, 1.1 / 2)).align_to(vbe_axis.c2p(0, 0.56), direction=LEFT),
Write(vbe[0]), Write(ip[2])
)
self.wait()
self.play(Create(vbe_plot), Write(vbe[1]), Write(ip[-1]))
self.wait()
self.play(ReplacementTransform(vbe_plot, vBE_plot), ReplacementTransform(vbe[1], vbe[-1]), Write(ip[0:2]), Write(ip[3]))
self.wait()
self.play(ip.animate.to_corner(UL))
self.wait()
self.play(Write(ic))
for i in range(len(op1[:-2])):
if i == 0:
self.play(Write(op1[i]))
else:
self.play(TransformFromCopy(op1[i - 1], op1[i]))
self.play(Create(IC_box))
line3 = op1[3][0]
self.play(Write(line3[0]), TransformFromCopy(op1[2][0][1:12], line3[1:3]), FadeOut(IC_box))
self.wait()
self.play(TransformFromCopy(op1[2][1], line3[3:]))
self.wait()
ss_condition.next_to(taylor, direction=DOWN)
self.play(Write(taylor))
self.wait()
self.play(Write(ss_condition))
self.wait()
self.play(FadeOut(taylor[1]))
self.wait()
self.play(TransformFromCopy(VGroup(taylor[0], op1[-2]), op1[-1]), FadeOut(taylor[0], ss_condition))
self.play(FadeOut(op1[:-1]), op1[-1].animate.move_to(op2[0]))