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Qihuanye
2026-04-27 14:51:49 +08:00
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experiment2/image/exp4/vi_characteristic_curve_exp4.svg
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experiment2/image/exp5/power_load_curve.svg
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experiment2/image_code/exp0_ro_measure_diagram.py
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import os
from pathlib import Path
import sys
os.environ.setdefault("MPLCONFIGDIR", "/tmp/matplotlib")
import matplotlib.pyplot as plt
FONT_NAME = "STIXGeneral"
BG_COLOR = "white"
LINE_COLOR = "#111111"
DEFAULT_OUTPUT = (
Path(__file__).resolve().parent.parent / "image" / "exp0" / "ro_measure_diagram.svg"
)
def draw_diagram(save_path=DEFAULT_OUTPUT):
save_path = Path(save_path)
save_path.parent.mkdir(parents=True, exist_ok=True)
plt.rcParams["font.family"] = FONT_NAME
plt.rcParams["axes.unicode_minus"] = False
fig, ax = plt.subplots(figsize=(5.2, 5.5), dpi=160)
fig.patch.set_facecolor(BG_COLOR)
ax.set_facecolor(BG_COLOR)
# 坐标范围
ax.set_xlim(-0.6, 9.8)
ax.set_ylim(-0.45, 9.85)
ax.axis("off")
# 关键点
origin = (0.0, 0.0)
u_oc = (0.0, 8.8)
i_sc = (8.3, 0.0)
a_pt = (2.6, 6.05)
b_pt = (5.5, 2.95)
# 坐标轴
ax.annotate(
"",
xy=(9.35, 0.0),
xytext=origin,
arrowprops=dict(arrowstyle="-|>", lw=1.9, color=LINE_COLOR),
)
ax.annotate(
"",
xy=(0.0, 9.65),
xytext=origin,
arrowprops=dict(arrowstyle="-|>", lw=1.9, color=LINE_COLOR),
)
# 主特性直线
ax.plot([u_oc[0], i_sc[0]], [u_oc[1], i_sc[1]], color=LINE_COLOR, lw=2.2)
# A/B 点
ax.text(a_pt[0] + 0.18, a_pt[1] + 0.22, "A", fontsize=14)
ax.text(b_pt[0] + 0.18, b_pt[1] - 0.1, "B", fontsize=14)
# ΔU / ΔI 虚线框
x_left = a_pt[0]
x_right = b_pt[0]
y_top = a_pt[1]
y_bottom = b_pt[1]
dash = (0, (6, 4))
ax.plot([x_left, x_left], [0, y_top], color=LINE_COLOR, lw=1.3, ls=dash)
ax.plot([x_right, x_right], [0, y_bottom], color=LINE_COLOR, lw=1.3, ls=dash)
ax.plot([0, x_left], [y_top, y_top], color=LINE_COLOR, lw=1.3, ls=dash)
ax.plot([0, x_right], [y_bottom, y_bottom], color=LINE_COLOR, lw=1.3, ls=dash)
# ΔU 竖向双箭头
x_du = 1.45
ax.annotate(
"",
xy=(x_du, y_top),
xytext=(x_du, y_bottom),
arrowprops=dict(arrowstyle="<|-|>", lw=1.4, color=LINE_COLOR),
)
ax.text(x_du - 0.55, (y_top + y_bottom) / 2 - 0.15, r"$\Delta U$", fontsize=14)
# ΔI 横向双箭头
y_di = 1.05
ax.annotate(
"",
xy=(x_right, y_di),
xytext=(x_left, y_di),
arrowprops=dict(arrowstyle="<|-|>", lw=1.4, color=LINE_COLOR),
)
ax.text((x_left + x_right) / 2 - 0.35, y_di - 0.72, r"$\Delta I$", fontsize=14)
# 角度 phi
ax.text(4.32, 2.3, r"$\varphi$", fontsize=16)
# 轴与截距标注
ax.text(9.05, -0.48, r"$I$", fontsize=18)
ax.text(0.25, 9.35, r"$U$", fontsize=18)
ax.text(-0.18, -0.35, "0", fontsize=13)
ax.text(0.22, 8.9, r"$U_{oc}$", fontsize=14)
ax.text(8.06, -0.62, r"$I_{sc}$", fontsize=14)
fig.tight_layout(pad=0.2)
fig.savefig(save_path, bbox_inches="tight")
plt.close(fig)
print(f"saved to: {save_path}")
if __name__ == "__main__":
output_path = sys.argv[1] if len(sys.argv) > 1 else DEFAULT_OUTPUT
draw_diagram(output_path)
experiment2/image_code/exp1_circuit.py
+121
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import os
from pathlib import Path
import sys
os.environ.setdefault("MPLCONFIGDIR", "/tmp/matplotlib")
import schemdraw
import schemdraw.elements as elm
from schemdraw.segments import SegmentText
FONT_NAME = "STIXGeneral"
BG_COLOR = "white"
DEFAULT_OUTPUT = Path(__file__).resolve().parent.parent / "image" / "target_circuit.svg"
def add_text(
drawing,
position,
text,
*,
fontsize=18,
rotation=0,
align=("center", "center"),
):
element = elm.Element().at(position).anchor("center").hold()
element.anchors["center"] = (0, 0)
element.segments.append(
SegmentText(
(0, 0),
text,
rotation=rotation,
align=align,
fontsize=fontsize,
font=FONT_NAME,
)
)
drawing.add(element)
def draw_circuit(save_path=DEFAULT_OUTPUT):
save_path = Path(save_path)
save_path.parent.mkdir(parents=True, exist_ok=True)
with schemdraw.Drawing(show=False) as d:
d.config(
unit=1.0,
fontsize=18,
font=FONT_NAME,
lw=2.2,
margin=0.2,
bgcolor=BG_COLOR,
)
# 关键节点，整体布局按参考图重排。
a_node = (1.4, 4.0)
top_node = (5.2, 6.6)
bottom_node = (5.2, 1.9)
right_node = (9.3, 4.0)
bottom_left = (1.4, 0.8)
top_term = (10.9, 4.0)
bottom_term = (10.9, 1.9)
source_start = (4.8, 0.8)
source_len = 1.6
source_end = (source_start[0] + source_len, source_start[1])
# 主电路元件
d.add(elm.ResistorIEC().at(a_node).to(top_node).hold())
d.add(elm.ResistorIEC().at(a_node).to(bottom_node).hold())
d.add(elm.ResistorIEC().at(top_node).to(right_node).hold())
d.add(elm.Source().at(bottom_node).up(top_node[1] - bottom_node[1]).hold())
d.add(elm.ResistorIEC().at(bottom_left).up(a_node[1] - bottom_left[1]).hold())
# 下方电压源支路
d.add(elm.Line().at(bottom_left).right(source_start[0] - bottom_left[0]).hold())
d.add(elm.Source().at(source_start).right(source_len).hold())
d.add(elm.Line().at(source_end).right(right_node[0] - source_end[0]).hold())
# 右侧导线与端子
d.add(elm.Line().at(right_node).right(top_term[0] - right_node[0]).hold())
d.add(elm.Line().at(right_node).down(right_node[1] - source_start[1]).hold())
d.add(elm.Line().at(bottom_node).right(bottom_term[0] - bottom_node[0]).hold())
# 电流源符号细节：空心圆、内部横线、外部向上箭头。
source_center_y = (top_node[1] + bottom_node[1]) / 2
d.add(elm.Line().at((4.74, source_center_y)).right(0.92).hold())
d.add(elm.Arrow().at((5.2, 4.9)).up(1.0).hold())
# 电压源符号细节：圆内水平线。
d.add(elm.Line().at(source_start).right(source_len).hold())
# 节点和开口端子
for point in [a_node, top_node, bottom_node, right_node]:
d.add(elm.Dot(radius=0.085).at(point).hold())
d.add(elm.Dot(open=True, radius=0.1).at(top_term).hold())
d.add(elm.Dot(open=True, radius=0.1).at(bottom_term).hold())
# 文本标注
add_text(d, (2.35, 5.18), r"$R_1$", fontsize=19)
add_text(d, (8.78, 5.12), r"$R_3$", fontsize=19)
add_text(d, (2.42, 2.62), r"$R_2$", fontsize=19)
add_text(d, (0.55, 1.28), r"$R_4$", fontsize=19)
add_text(d, (6.42, 4.82), r"$I_S$", fontsize=19)
add_text(d, (4.3, 0.36), "-", fontsize=21)
add_text(d, (6.98, 0.36), "+", fontsize=21)
add_text(d, (4.78, -0.05), r"$U_S$", fontsize=19)
d.save(str(save_path), transparent=False)
print(f"saved to: {save_path}")
if __name__ == "__main__":
output_path = sys.argv[1] if len(sys.argv) > 1 else DEFAULT_OUTPUT
draw_circuit(output_path)
experiment2/image_code/exp1_circuit_measure.py
+129
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import os
from pathlib import Path
import sys
os.environ.setdefault("MPLCONFIGDIR", "/tmp/matplotlib")
import schemdraw
import schemdraw.elements as elm
from schemdraw.segments import SegmentText
FONT_NAME = "STIXGeneral"
BG_COLOR = "white"
DEFAULT_OUTPUT = Path(__file__).resolve().parent.parent / "image" / "target_circuit_measure.svg"
def add_text(
drawing,
position,
text,
*,
fontsize=18,
rotation=0,
align=("center", "center"),
):
element = elm.Element().at(position).anchor("center").hold()
element.anchors["center"] = (0, 0)
element.segments.append(
SegmentText(
(0, 0),
text,
rotation=rotation,
align=align,
fontsize=fontsize,
font=FONT_NAME,
)
)
drawing.add(element)
def draw_circuit(save_path=DEFAULT_OUTPUT):
save_path = Path(save_path)
save_path.parent.mkdir(parents=True, exist_ok=True)
with schemdraw.Drawing(show=False) as d:
d.config(
unit=1.0,
fontsize=18,
font=FONT_NAME,
lw=2.2,
margin=0.2,
bgcolor=BG_COLOR,
)
# 左侧原电路
left_node = (1.4, 4.0)
top_node = (5.2, 6.6)
bottom_node = (5.2, 1.9)
right_node = (9.3, 4.0)
bottom_left = (1.4, 0.8)
source_start = (4.8, 0.8)
source_len = 1.6
source_end = (source_start[0] + source_len, source_start[1])
d.add(elm.ResistorIEC().at(left_node).to(top_node).hold())
d.add(elm.ResistorIEC().at(left_node).to(bottom_node).hold())
d.add(elm.ResistorIEC().at(top_node).to(right_node).hold())
d.add(elm.Source().at(bottom_node).up(top_node[1] - bottom_node[1]).hold())
d.add(elm.ResistorIEC().at(bottom_left).up(left_node[1] - bottom_left[1]).hold())
d.add(elm.Line().at(bottom_left).right(source_start[0] - bottom_left[0]).hold())
d.add(elm.Source().at(source_start).right(source_len).hold())
d.add(elm.Line().at(source_end).right(right_node[0] - source_end[0]).hold())
d.add(elm.Line().at(right_node).down(right_node[1] - source_start[1]).hold())
# 左侧源符号细节
source_center_y = (top_node[1] + bottom_node[1]) / 2
d.add(elm.Line().at((4.74, source_center_y)).right(0.92).hold())
d.add(elm.Arrow().at((5.2, 4.9)).up(1.0).hold())
d.add(elm.Line().at(source_start).right(source_len).hold())
# 右侧测量电路，尽量使用 schemdraw 自带电表与可变电阻元件。
meter_top = (10.75, 4.0)
meter_bottom_y = bottom_node[1]
b_node = (14.2, bottom_node[1])
a_left = (12.15, meter_top[1])
a_node = (14.2, meter_top[1])
load_x = 15.8
d.add(elm.Line().at(right_node).right(meter_top[0] - right_node[0]).hold())
d.add(elm.MeterV().at(meter_top).down(meter_top[1] - meter_bottom_y).hold())
d.add(elm.Line().at(bottom_node).right(b_node[0] - bottom_node[0]).hold())
d.add(elm.MeterA().at(meter_top).right(a_left[0] - meter_top[0]).hold())
d.add(elm.Line().at(a_left).right(a_node[0] - a_left[0]).hold())
d.add(elm.Dot(open=True, radius=0.1).at(a_node).hold())
d.add(elm.Dot(open=True, radius=0.1).at(b_node).hold())
d.add(elm.Line().at(a_node).right(load_x - a_node[0]).hold())
d.add(elm.Line().at(b_node).right(load_x - b_node[0]).hold())
d.add(elm.ResistorVarIEC().at((load_x, b_node[1])).up(a_node[1] - b_node[1]).hold())
# 关键节点
for point in [left_node, top_node, bottom_node, right_node, (right_node[0], bottom_node[1])]:
d.add(elm.Dot(radius=0.085).at(point).hold())
# 文本标注
add_text(d, (2.35, 5.18), r"$R_1$", fontsize=19)
add_text(d, (8.78, 5.12), r"$R_3$", fontsize=19)
add_text(d, (2.42, 2.62), r"$R_2$", fontsize=19)
add_text(d, (0.55, 1.28), r"$R_4$", fontsize=19)
add_text(d, (6.42, 4.82), r"$I_S$", fontsize=19)
add_text(d, (4.3, 0.36), "-", fontsize=21)
add_text(d, (6.98, 0.36), "+", fontsize=21)
add_text(d, (4.78, -0.05), r"$U_S$", fontsize=19)
add_text(d, (13.35, 1.35), "B", fontsize=16)
add_text(d, (16.55, 3.0), r"$R_L$", fontsize=19)
d.save(str(save_path), transparent=False)
print(f"saved to: {save_path}")
if __name__ == "__main__":
output_path = sys.argv[1] if len(sys.argv) > 1 else DEFAULT_OUTPUT
draw_circuit(output_path)
experiment2/image_code/exp2_vi_curve.py
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import os
from pathlib import Path
import sys
os.environ.setdefault("MPLCONFIGDIR", "/tmp/matplotlib")
import matplotlib.pyplot as plt
import numpy as np
from matplotlib.ticker import AutoMinorLocator
FONT_NAME = "LXGW WenKai"
BG_COLOR = "white"
GRID_MAJOR = "#111111"
GRID_MINOR = "#8a8a8a"
LINE_COLOR = "#111111"
POINT_COLOR = "#111111"
CURRENT_MA = np.array([11.20, 12.10, 13.00, 14.80, 16.36], dtype=float)
VOLTAGE_V = np.array([11.25, 10.75, 10.25, 9.25, 8.75], dtype=float)
DEFAULT_OUTPUT = (
Path(__file__).resolve().parent.parent / "image" / "exp2" / "vi_characteristic_curve.svg"
)
def draw_curve(save_path=DEFAULT_OUTPUT):
save_path = Path(save_path)
save_path.parent.mkdir(parents=True, exist_ok=True)
plt.rcParams["font.family"] = FONT_NAME
plt.rcParams["axes.unicode_minus"] = False
slope, intercept = np.polyfit(CURRENT_MA, VOLTAGE_V, 1)
fit_x = np.linspace(CURRENT_MA.min() - 0.4, CURRENT_MA.max() + 0.4, 200)
fit_y = slope * fit_x + intercept
fig, ax = plt.subplots(figsize=(8.2, 6.0), dpi=160)
fig.patch.set_facecolor(BG_COLOR)
ax.set_facecolor(BG_COLOR)
ax.plot(
fit_x,
fit_y,
color=LINE_COLOR,
linewidth=2.2,
zorder=2,
)
ax.scatter(
CURRENT_MA,
VOLTAGE_V,
s=60,
color=POINT_COLOR,
edgecolors="white",
linewidths=0.8,
zorder=3,
)
ax.set_xlabel("端口电流 I / mA", fontsize=13)
ax.set_ylabel("端口电压 U / V", fontsize=13)
ax.set_xlim(11.0, 16.5)
ax.set_ylim(8.5, 11.5)
ax.set_xticks(np.arange(11, 17, 1))
ax.set_yticks(np.arange(8.5, 11.6, 0.5))
ax.xaxis.set_minor_locator(AutoMinorLocator(2))
ax.yaxis.set_minor_locator(AutoMinorLocator(2))
ax.set_box_aspect(6 / 5)
ax.grid(True, which="major", color=GRID_MAJOR, linewidth=0.95, alpha=0.9)
ax.grid(True, which="minor", color=GRID_MINOR, linewidth=0.55, alpha=0.8)
for spine in ax.spines.values():
spine.set_linewidth(1.0)
spine.set_color("#111111")
fig.tight_layout()
fig.savefig(save_path, bbox_inches="tight")
plt.close(fig)
print(f"saved to: {save_path}")
if __name__ == "__main__":
output_path = sys.argv[1] if len(sys.argv) > 1 else DEFAULT_OUTPUT
draw_curve(output_path)
experiment2/image_code/exp2_vi_curve_table4.py
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import os
from pathlib import Path
import sys
os.environ.setdefault("MPLCONFIGDIR", "/tmp/matplotlib")
import matplotlib.pyplot as plt
import numpy as np
from matplotlib.ticker import AutoMinorLocator
FONT_NAME = "LXGW WenKai"
BG_COLOR = "white"
GRID_MAJOR = "#111111"
GRID_MINOR = "#8a8a8a"
LINE_COLOR = "#111111"
POINT_COLOR = "#111111"
CURRENT_MA = np.array([10.63, 11.54, 12.71, 13.62, 14.76], dtype=float)
VOLTAGE_V = np.array([10.82, 10.17, 9.57, 8.91, 8.21], dtype=float)
DEFAULT_OUTPUT = (
Path(__file__).resolve().parent.parent
/ "image"
/ "exp3"
/ "vi_characteristic_curve_table4.svg"
)
def draw_curve(save_path=DEFAULT_OUTPUT):
save_path = Path(save_path)
save_path.parent.mkdir(parents=True, exist_ok=True)
plt.rcParams["font.family"] = FONT_NAME
plt.rcParams["axes.unicode_minus"] = False
slope, intercept = np.polyfit(CURRENT_MA, VOLTAGE_V, 1)
fit_x = np.linspace(CURRENT_MA.min() - 0.4, CURRENT_MA.max() + 0.4, 200)
fit_y = slope * fit_x + intercept
fig, ax = plt.subplots(figsize=(8.2, 6.0), dpi=160)
fig.patch.set_facecolor(BG_COLOR)
ax.set_facecolor(BG_COLOR)
ax.plot(
fit_x,
fit_y,
color=LINE_COLOR,
linewidth=2.2,
zorder=2,
)
ax.scatter(
CURRENT_MA,
VOLTAGE_V,
s=60,
color=POINT_COLOR,
edgecolors="white",
linewidths=0.8,
zorder=3,
)
ax.set_xlabel("端口电流 I / mA", fontsize=13)
ax.set_ylabel("端口电压 U / V", fontsize=13)
ax.set_xlim(10.5, 14.9)
ax.set_ylim(8.0, 11.0)
ax.set_xticks(np.arange(11, 15, 1))
ax.set_yticks(np.arange(8.0, 11.1, 0.5))
ax.xaxis.set_minor_locator(AutoMinorLocator(2))
ax.yaxis.set_minor_locator(AutoMinorLocator(2))
ax.set_box_aspect(6 / 5)
ax.grid(True, which="major", color=GRID_MAJOR, linewidth=0.95, alpha=0.9)
ax.grid(True, which="minor", color=GRID_MINOR, linewidth=0.55, alpha=0.8)
for spine in ax.spines.values():
spine.set_linewidth(1.0)
spine.set_color("#111111")
fig.tight_layout()
fig.savefig(save_path, bbox_inches="tight")
plt.close(fig)
print(f"saved to: {save_path}")
if __name__ == "__main__":
output_path = sys.argv[1] if len(sys.argv) > 1 else DEFAULT_OUTPUT
draw_curve(output_path)
experiment2/image_code/exp3_thevenin_equiv.py
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import os
from pathlib import Path
import sys
os.environ.setdefault("MPLCONFIGDIR", "/tmp/matplotlib")
import schemdraw
import schemdraw.elements as elm
from schemdraw.segments import Segment, SegmentCircle, SegmentText
FONT_NAME = "STIXGeneral"
BG_COLOR = "white"
DEFAULT_OUTPUT = Path(__file__).resolve().parent.parent / "image" / "thevenin_equiv.svg"
def add_text(
drawing,
position,
text,
*,
fontsize=18,
rotation=0,
align=("center", "center"),
color="black",
):
element = elm.Element().at(position).anchor("center").hold()
element.anchors["center"] = (0, 0)
element.segments.append(
SegmentText(
(0, 0),
text,
rotation=rotation,
align=align,
fontsize=fontsize,
font=FONT_NAME,
color=color,
)
)
drawing.add(element)
def add_circle_symbol(
drawing,
center,
*,
radius=0.42,
text=None,
fontsize=16,
horizontal_line=False,
):
element = elm.Element().at(center).anchor("center").hold()
element.anchors["center"] = (0, 0)
element.segments.append(SegmentCircle((0, 0), radius))
if horizontal_line:
element.segments.append(Segment([(-radius, 0), (radius, 0)]))
if text:
element.segments.append(
SegmentText((0, 0), text, fontsize=fontsize, font=FONT_NAME)
)
drawing.add(element)
def draw_circuit(save_path=DEFAULT_OUTPUT):
save_path = Path(save_path)
save_path.parent.mkdir(parents=True, exist_ok=True)
with schemdraw.Drawing(show=False) as d:
d.config(
unit=1.0,
fontsize=18,
font=FONT_NAME,
lw=2.0,
margin=0.2,
bgcolor=BG_COLOR,
)
# 总线节点
top_y = 5.8
bottom_y = 1.4
left_bus_x = 3.0
meter_x = 6.45
ammeter_x = 8.05
load_x = 10.2
circle_r = 0.48
# 左侧戴维南等效支路
branch_x = 2.1
source_top_y = 4.95
source_bottom_y = 3.75
resistor_top_y = 3.05
resistor_bottom_y = 1.95
d.add(elm.Line().at((left_bus_x, top_y)).to((branch_x, top_y)).hold())
source_center_y = (source_top_y + source_bottom_y) / 2
d.add(elm.Line().at((branch_x, top_y)).down(top_y - (source_center_y + circle_r)).hold())
add_circle_symbol(d, (branch_x, source_center_y), radius=circle_r, horizontal_line=True)
d.add(elm.Line().at((branch_x, source_center_y - circle_r)).down((source_center_y - circle_r) - resistor_top_y).hold())
d.add(elm.ResistorIEC().at((branch_x, resistor_top_y)).to((branch_x, resistor_bottom_y)).hold())
d.add(elm.Line().at((branch_x, resistor_bottom_y)).down(resistor_bottom_y - bottom_y).hold())
d.add(elm.Line().at((branch_x, bottom_y)).to((left_bus_x, bottom_y)).hold())
# 中间电压表和右侧负载支路
d.add(elm.Line().at((left_bus_x, top_y)).right((ammeter_x - circle_r) - left_bus_x).hold())
d.add(elm.Line().at((left_bus_x, bottom_y)).right(load_x - left_bus_x).hold())
add_circle_symbol(d, (ammeter_x, top_y), radius=circle_r, text="A", fontsize=15)
d.add(elm.Line().at((ammeter_x + circle_r, top_y)).right(load_x - (ammeter_x + circle_r)).hold())
d.add(elm.Line().at((meter_x, top_y)).down(top_y - (3.6 + circle_r)).hold())
add_circle_symbol(d, (meter_x, 3.6), radius=circle_r, text="V", fontsize=15)
d.add(elm.Line().at((meter_x, 3.6 - circle_r)).down((3.6 - circle_r) - bottom_y).hold())
d.add(elm.ResistorVarIEC().at((load_x, bottom_y + 0.7)).up(2.0).hold())
# 右侧支路收口
d.add(elm.Line().at((load_x, top_y)).down(top_y - (bottom_y + 2.7)).hold())
d.add(elm.Line().at((load_x, bottom_y + 0.7)).down(0.7).hold())
# 关键节点
d.add(elm.Dot(radius=0.075).at((left_bus_x, top_y)).hold())
d.add(elm.Dot(radius=0.075).at((left_bus_x, bottom_y)).hold())
# 标注
add_text(d, (3.2, 4.32), r"$U_{oc}$", fontsize=21)
add_text(d, (3.0, 2.72), r"$R_0$", fontsize=21)
# 负载标注
add_text(d, (10.95, 3.02), r"$R_L$", fontsize=21)
d.save(str(save_path), transparent=False)
print(f"saved to: {save_path}")
if __name__ == "__main__":
output_path = sys.argv[1] if len(sys.argv) > 1 else DEFAULT_OUTPUT
draw_circuit(output_path)
experiment2/image_code/exp4_norton_equiv.py
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import os
from pathlib import Path
import sys
os.environ.setdefault("MPLCONFIGDIR", "/tmp/matplotlib")
import schemdraw
import schemdraw.elements as elm
from schemdraw.segments import Segment, SegmentCircle, SegmentText
FONT_NAME = "STIXGeneral"
BG_COLOR = "white"
DEFAULT_OUTPUT = (
Path(__file__).resolve().parent.parent / "image" / "exp4" / "norton_equiv.svg"
)
def add_text(
drawing,
position,
text,
*,
fontsize=18,
rotation=0,
align=("center", "center"),
color="black",
):
element = elm.Element().at(position).anchor("center").hold()
element.anchors["center"] = (0, 0)
element.segments.append(
SegmentText(
(0, 0),
text,
rotation=rotation,
align=align,
fontsize=fontsize,
font=FONT_NAME,
color=color,
)
)
drawing.add(element)
def add_circle_outline(drawing, center, *, radius=0.48, vertical_line=False):
element = elm.Element().at(center).anchor("center").hold()
element.anchors["center"] = (0, 0)
element.segments.append(SegmentCircle((0, 0), radius))
if vertical_line:
element.segments.append(Segment([(0, -radius), (0, radius)]))
drawing.add(element)
def draw_circuit(save_path=DEFAULT_OUTPUT):
save_path = Path(save_path)
save_path.parent.mkdir(parents=True, exist_ok=True)
with schemdraw.Drawing(show=False) as d:
d.config(
unit=1.0,
fontsize=18,
font=FONT_NAME,
lw=2.0,
margin=0.2,
bgcolor=BG_COLOR,
)
top_y = 5.8
bottom_y = 1.4
source_x = 2.0
resistor_x = 3.45
node_x = 4.35
meter_x = 6.15
ammeter_x = 7.95
load_x = 10.1
circle_r = 0.48
source_center_y = 3.6
resistor_top_y = 4.9
resistor_bottom_y = 2.3
# 诺顿等效支路：电流源与电阻并联
d.add(elm.Line().at((source_x, top_y)).to((node_x, top_y)).hold())
d.add(elm.Line().at((source_x, bottom_y)).to((node_x, bottom_y)).hold())
d.add(
elm.Line()
.at((source_x, top_y))
.down(top_y - (source_center_y + circle_r))
.hold()
)
add_circle_outline(
d,
(source_x, source_center_y),
radius=circle_r,
vertical_line=True,
)
d.add(
elm.Line()
.at((source_x, source_center_y - circle_r))
.down((source_center_y - circle_r) - bottom_y)
.hold()
)
d.add(elm.ResistorIEC().at((resistor_x, resistor_top_y)).to((resistor_x, resistor_bottom_y)).hold())
d.add(elm.Line().at((resistor_x, top_y)).down(top_y - resistor_top_y).hold())
d.add(elm.Line().at((resistor_x, resistor_bottom_y)).down(resistor_bottom_y - bottom_y).hold())
# 右侧测量与负载
d.add(elm.Line().at((node_x, top_y)).right((ammeter_x - circle_r) - node_x).hold())
d.add(elm.Line().at((node_x, bottom_y)).right(load_x - node_x).hold())
element_a = elm.Element().at((ammeter_x, top_y)).anchor("center").hold()
element_a.anchors["center"] = (0, 0)
element_a.segments.append(SegmentCircle((0, 0), circle_r))
element_a.segments.append(SegmentText((0, 0), "A", fontsize=15, font=FONT_NAME))
d.add(element_a)
d.add(elm.Line().at((ammeter_x + circle_r, top_y)).right(load_x - (ammeter_x + circle_r)).hold())
d.add(elm.Line().at((meter_x, top_y)).down(top_y - (3.6 + circle_r)).hold())
element_v = elm.Element().at((meter_x, 3.6)).anchor("center").hold()
element_v.anchors["center"] = (0, 0)
element_v.segments.append(SegmentCircle((0, 0), circle_r))
element_v.segments.append(SegmentText((0, 0), "V", fontsize=15, font=FONT_NAME))
d.add(element_v)
d.add(elm.Line().at((meter_x, 3.6 - circle_r)).down((3.6 - circle_r) - bottom_y).hold())
d.add(elm.ResistorVarIEC().at((load_x, bottom_y + 0.7)).up(2.0).hold())
d.add(elm.Line().at((load_x, top_y)).down(top_y - (bottom_y + 2.7)).hold())
d.add(elm.Line().at((load_x, bottom_y + 0.7)).down(0.7).hold())
# 节点
d.add(elm.Dot(radius=0.075).at((node_x, top_y)).hold())
d.add(elm.Dot(radius=0.075).at((node_x, bottom_y)).hold())
# 标注
add_text(d, (1.2, 3.42), r"$I_{sc}$", fontsize=21, align=("right", "center"))
add_text(d, (4.15, 3.55), r"$R_0$", fontsize=21)
add_text(d, (10.85, 3.02), r"$R_L$", fontsize=21)
d.save(str(save_path), transparent=False)
print(f"saved to: {save_path}")
if __name__ == "__main__":
output_path = sys.argv[1] if len(sys.argv) > 1 else DEFAULT_OUTPUT
draw_circuit(output_path)
experiment2/image_code/exp4_vi_curve.py
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import os
from pathlib import Path
import sys
os.environ.setdefault("MPLCONFIGDIR", "/tmp/matplotlib")
import matplotlib.pyplot as plt
import numpy as np
from matplotlib.ticker import AutoMinorLocator
FONT_NAME = "LXGW WenKai"
BG_COLOR = "white"
GRID_MAJOR = "#111111"
GRID_MINOR = "#8a8a8a"
LINE_COLOR = "#111111"
POINT_COLOR = "#111111"
CURRENT_MA = np.array([11.30, 12.71, 13.82, 15.47, 16.66], dtype=float)
VOLTAGE_V = np.array([11.39, 10.69, 9.97, 9.21, 8.58], dtype=float)
DEFAULT_OUTPUT = (
Path(__file__).resolve().parent.parent
/ "image"
/ "exp4"
/ "vi_characteristic_curve_exp4.svg"
)
def draw_curve(save_path=DEFAULT_OUTPUT):
save_path = Path(save_path)
save_path.parent.mkdir(parents=True, exist_ok=True)
plt.rcParams["font.family"] = FONT_NAME
plt.rcParams["axes.unicode_minus"] = False
slope, intercept = np.polyfit(CURRENT_MA, VOLTAGE_V, 1)
fit_x = np.linspace(CURRENT_MA.min() - 0.4, CURRENT_MA.max() + 0.4, 200)
fit_y = slope * fit_x + intercept
fig, ax = plt.subplots(figsize=(8.2, 6.0), dpi=160)
fig.patch.set_facecolor(BG_COLOR)
ax.set_facecolor(BG_COLOR)
ax.plot(
fit_x,
fit_y,
color=LINE_COLOR,
linewidth=2.2,
zorder=2,
)
ax.scatter(
CURRENT_MA,
VOLTAGE_V,
s=60,
color=POINT_COLOR,
edgecolors="white",
linewidths=0.8,
zorder=3,
)
ax.set_xlabel("端口电流 I / mA", fontsize=13)
ax.set_ylabel("端口电压 U / V", fontsize=13)
ax.set_xlim(11.0, 17.1)
ax.set_ylim(8.5, 11.5)
ax.set_xticks(np.arange(11, 18, 1))
ax.set_yticks(np.arange(8.5, 11.6, 0.5))
ax.xaxis.set_minor_locator(AutoMinorLocator(2))
ax.yaxis.set_minor_locator(AutoMinorLocator(2))
ax.set_box_aspect(6 / 5)
ax.grid(True, which="major", color=GRID_MAJOR, linewidth=0.95, alpha=0.9)
ax.grid(True, which="minor", color=GRID_MINOR, linewidth=0.55, alpha=0.8)
for spine in ax.spines.values():
spine.set_linewidth(1.0)
spine.set_color("#111111")
fig.tight_layout()
fig.savefig(save_path, bbox_inches="tight")
plt.close(fig)
print(f"saved to: {save_path}")
if __name__ == "__main__":
output_path = sys.argv[1] if len(sys.argv) > 1 else DEFAULT_OUTPUT
draw_curve(output_path)
experiment2/image_code/exp5_power_curve.py
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import os
from pathlib import Path
import sys
os.environ.setdefault("MPLCONFIGDIR", "/tmp/matplotlib")
import matplotlib.pyplot as plt
import numpy as np
from matplotlib.ticker import AutoMinorLocator
FONT_NAME = "LXGW WenKai"
BG_COLOR = "white"
GRID_MAJOR = "#111111"
GRID_MINOR = "#8a8a8a"
LINE_COLOR = "#111111"
POINT_COLOR = "#111111"
LOAD_RESISTANCE_OHM = np.array(
[888.43, 788.46, 625.00, 534.84, 468.16, 494.69, 439.93, 415.40],
dtype=float,
)
POWER_MW = np.array(
[130.07, 133.25, 136.90, 143.15, 142.23, 142.29, 142.22, 141.25],
dtype=float,
)
DEFAULT_OUTPUT = (
Path(__file__).resolve().parent.parent / "image" / "exp5" / "power_load_curve.svg"
)
def draw_curve(save_path=DEFAULT_OUTPUT):
save_path = Path(save_path)
save_path.parent.mkdir(parents=True, exist_ok=True)
plt.rcParams["font.family"] = FONT_NAME
plt.rcParams["axes.unicode_minus"] = False
order = np.argsort(LOAD_RESISTANCE_OHM)
x = LOAD_RESISTANCE_OHM[order]
y = POWER_MW[order]
fig, ax = plt.subplots(figsize=(8.2, 6.0), dpi=160)
fig.patch.set_facecolor(BG_COLOR)
ax.set_facecolor(BG_COLOR)
ax.plot(
x,
y,
color=LINE_COLOR,
linewidth=2.2,
zorder=2,
)
ax.scatter(
x,
y,
s=55,
color=POINT_COLOR,
edgecolors="white",
linewidths=0.8,
zorder=3,
)
ax.set_xlabel("负载电阻 R_L / Ω", fontsize=13)
ax.set_ylabel("负载功率 P / mW", fontsize=13)
ax.set_xlim(400, 900)
ax.set_ylim(129, 144)
ax.set_xticks(np.arange(400, 901, 100))
ax.set_yticks(np.arange(130, 145, 2))
ax.xaxis.set_minor_locator(AutoMinorLocator(2))
ax.yaxis.set_minor_locator(AutoMinorLocator(2))
ax.set_box_aspect(6 / 5)
ax.grid(True, which="major", color=GRID_MAJOR, linewidth=0.95, alpha=0.9)
ax.grid(True, which="minor", color=GRID_MINOR, linewidth=0.55, alpha=0.8)
for spine in ax.spines.values():
spine.set_linewidth(1.0)
spine.set_color("#111111")
fig.tight_layout()
fig.savefig(save_path, bbox_inches="tight")
plt.close(fig)
print(f"saved to: {save_path}")
if __name__ == "__main__":
output_path = sys.argv[1] if len(sys.argv) > 1 else DEFAULT_OUTPUT
draw_curve(output_path)
experiment2/main.typ
+696
View File
@@ -0,0 +1,696 @@
#set page(
paper: "a4",
margin: (
top: 2.3cm,
bottom: 2.3cm,
left: 2.5cm,
right: 2.5cm,
),
)
#set text(
font: "LXGW WenKai",
size: 13pt,
lang: "zh",
)
#set par(
first-line-indent: (amount: 2em, all: true),
justify: true,
leading: 0.85em,
)
#set heading(numbering: none)
#show math.equation: set text(size: 12pt)
#show figure.caption: set text(size: 11pt)
#let small-gap = v(0.45em)
#let mid-gap = v(0.75em)
#let big-gap = v(1.1em)
#show heading.where(level: 1): it => {
big-gap
block(width: 100%)[
#text(19pt, weight: "black")[#it.body]
]
v(0.38em)
}
#show heading.where(level: 2): it => {
v(0.8em)
block(width: 100%)[
#text(15.5pt, weight: "black")[#it.body]
]
v(0.22em)
}
#let note-box(body) = block(
width: 100%,
inset: 9pt,
radius: 4pt,
stroke: 0.6pt + rgb("#999"),
fill: rgb("#fcfcfc"),
)[#body]
#let img-box(title, height: 5.8cm) = block(
width: 100%,
height: height,
inset: 10pt,
stroke: 0.8pt + rgb("#888"),
radius: 4pt,
fill: rgb("#fafafa"),
)[
#align(center + horizon)[
#text(11pt, fill: rgb("#777"))[#title]
]
]
#let report-table(..args) = table(
stroke: 0.7pt + black,
inset: 6pt,
align: center + horizon,
..args,
)
#align(center)[
#text(size: 26pt, weight: "black")[实验报告]
]
#mid-gap
= 实验原理
== 1. 线性有源二端网络及其等效电路
线性有源二端网络是由线性元件和独立电源构成的，对外可以用其等效电路来等效代替。
线性有源二端网络在电路中能等效成的最简形式就是一个实际电压源模型或一个实际电流源模型，反映这种等效变换关系的就是戴维南定理和诺顿定理。
在戴维南等效电路中，电压源的电压就是有源二端网络的开路电压 $U_"oc"$，等效电阻 $R_0$ 等于有源二端网络中所有独立源均置零时的等效电阻。而在诺顿等效电路中，电流源的电流等于有源二端网络的端口短路电流 $I_"sc"$，其等效电阻 $R_0$ 定义则同戴维南定理一样。
因此，将线性有源二端网络进行等效变换的关键就是要求其等效电路参数：开路电压 $U_"oc"$、短路电流 $I_"sc"$ 和等效电阻 $R_0$。
== 2. 线性有源二端网络等效参数的测量方法
这三个等效电路参数的实验测量方法如下。
（1）直接法测开路电压 $U_"oc"$ 和短路电流 $I_"sc"$
将待测支路从有源二端网络断开，直接用电压表测量其两个端钮间的电压，此时电压表的读数即为 $U_"oc"$。同理，直接用电流表测量两个端钮间的电流，电流表的读数即为短路电流 $I_"sc"$。
（2）零示法测 $U_"oc"$
在测量具有高内阻的有源二端网络的开路电压 $U_"oc"$ 时，直接测量法会造成较大的误差。因此可以采用零示法进行测量。
零示法的基本原理是用一个低内阻的直流稳压电源与被测有源二端网络进行比较，当稳压电源的输出电压与有源二端网络的开路电压 $U_"oc"$ 相等时，电压表的读数将为“0”，此时将电路断开，测出稳压电源的输出电压，即为被测有源二端网络的开路电压 $U_"oc"$。
（3）等效电阻 $R_0$ 的测量
等效电阻的测量方法比较多，常用的有：
① 直接测量法
将有源二端网络内部所有的独立电源置零（电压源用短路代替，电流源用开路代替），然后直接用万用表欧姆挡测量端口的电阻，此时万用表的读数即为二端网络的等效电阻 $R_0$。
② 开路－短路法
对于端口允许直接短路的二端网络，分别测出二端网络的开路电压 $U_"oc"$ 和短路电流 $I_"sc"$，则其等效电阻可以表示为
$
R_0 = U_"oc" / I_"sc"
$
③ 半电压法
先测出二端网络的开路电压 $U_"oc"$，然后给二端网络接上一个可变电阻 $R_L$ 作为负载，调节可变电阻使其端电压等于被测网络开路电压的一半，此时负载电阻 $R_L$ 的大小就等于被测线性有源二端网络的等效电阻。
④ 伏安法
给二端网络接一个可变电阻 $R_L$ 作为负载，改变 $R_L$，分别测出负载两端的电压和流过负载的电流，然后作出线性有源二端网络的伏安特性曲线，如图1 所示，则该曲线的斜率即为等效电阻 $R_0$：
$
R_0 = tan phi = Delta U / Delta I = U_"oc" / I_"sc"
$
#v(0.2em)
#figure(
[
#move(dx: 2mm)[
#image("image/exp0/ro_measure_diagram.svg", height: 23%)
]
],
caption: [伏安法测 $R_0$],
)
== 3. 最大功率传输条件
在电子技术中，经常希望负载能够从线性有源二端网络得到最大功率。最大功率传输定理表明：当可变负载与线性有源二端网络的等效电阻相等（即 $R_0 = R_L$）时，负载上可获得最大功率，该最大功率的值为
$
P_"max" = U_"oc"^2 / (4 R_0)
$
此时称电路达到最大功率匹配。
#v(1.2em)
本次实验围绕上述原理展开，内容分为五个部分：先测定有源二端网络的等效参数，再绘制伏安特性曲线，随后分别验证戴维南等效电路与诺顿等效电路，最后验证最大功率传输定理。
#pagebreak()
= 实验一：等效参数测定
== （一）实验任务
本实验的任务是测定被测线性有源二端网络的开路电压 $U_"oc"$、短路电流 $I_"sc"$ 和等效电阻 $R_0$。
== （二）实验方案和具体步骤
1. 按设计好的有源二端网络连接电路。
2. 根据电路参数进行理论分析，先计算该网络的理论等效值。
3. 测量开路电压、短路电流。
4. 将网络内部独立源置零后，采用直接测量法读出等效电阻。
5. 将实验测量值与理论值进行对比，分析误差来源。
== （三）实验电路连接及实测数据
#v(1.2em)
#figure(
align(center)[#image("image/exp1/target_circuit.svg", height: 7.4cm)],
caption: [被测有源二端网络电路图],
)
#v(1.7em)
#figure(
caption: [等效参数测量值],
report-table(
columns: (1.5fr, 1.6fr, 1.6fr, 1.9fr),
[类别],
[$U_"oc"$ / V],
[$I_"sc"$ / mA],
[$R_0$ / Ω],
[测量值],
[16.98],
[33.3],
[519],
),
)
#figure(
[
#grid(
columns: (1fr, 1fr, 1fr),
gutter: 1em,
align(center)[#image("image/exp1/9d03b27592cef750db61dc54bb1a967c.jpg", height: 6cm)],
align(center)[#image("image/exp1/dac026261e99c0b8e5fad88b7bd8c08b.jpg", height: 6cm)],
align(center)[#image("image/exp1/740ac5828e6f3804c2a0d0a5b969d7d8.jpg", height: 6cm)],
)
#v(0.7em)
#grid(
columns: (1fr, 1fr),
gutter: 1em,
align(center)[#image("image/exp1/021d3dac0a0c629c642c5ec2c9863ed5.jpg", height: 6cm)],
align(center)[#image("image/exp1/d784fca2df13c59c83b9191327a0c82e.jpg", height: 6cm)],
)
],
caption: [实验电路与测量数据],
)
#v(0.2em)
== （四）实验数据处理或结果
根据所设计电路的元件参数，对原电路进行理论分析，可得该有源二端网络的理论等效参数近似为：
$
U_"oc, th" approx 17"V"
$
$
R_"0, th" approx 520"Ω"
$
因此理论短路电流为：
$
I_"sc, th" = U_"oc, th" / R_"0, th" = 17 / 520 approx 0.0327"A" approx 33"mA"
$
#figure(
caption: [等效参数理论值与测量值],
report-table(
columns: (1.5fr, 1.6fr, 1.6fr, 1.9fr),
[类别],
[$U_"oc"$ / V],
[$I_"sc"$ / mA],
[$R_0$ / Ω],
[理论值],
[17],
[33],
[520],
[测量值],
[16.98],
[33.3],
[519],
),
)
则该有源二端网络可等效为一个电压约为 $16.98"V"$、串联等效电阻约为 $519"Ω"$ 的戴维南电源；与之对应的诺顿等效电路则为电流约为 $33.3"mA"$、并联等效电阻约为 $519"Ω"$ 的电流源模型。
== （五）分析和结论
由实验结果可知，该有源二端网络的理论参数分别为 $U_"oc" = 17"V"$、$I_"sc" = 33"mA"$、$R_0 = 520"Ω"$，实测参数分别为 $U_"oc" = 16.98"V"$、$I_"sc" = 33.3"mA"$、$R_0 = 519"Ω"$。两组数据非常接近，说明实验测量结果与理论分析基本一致。
#pagebreak()
= 实验二：伏安特性曲线绘制
== （一）实验任务
通过改变负载阻值，测量电压与电流的对应关系，绘制有源二端网络的伏安特性曲线。
== （二）实验方案和具体步骤
1. 在被测有源二端网络输出端接入可调负载电阻 $R_L$。
2. 连接电压表和电流表，构成伏安法测量电路。
3. 调节负载电阻，记录多组电压 $U$ 与电流 $I$ 数据。
4. 以电流为横坐标、电压为纵坐标绘制伏安特性曲线。
== （三）实验电路连接及实测数据
#v(1em)
#figure(
align(center)[#image("image/exp2/target_circuit_measure.svg", height: 6.6cm)],
caption: [伏安法测量电路图],
)
#v(1em)
#figure(
[
#grid(
columns: (1fr, 1fr, 1fr),
gutter: 0.8em,
align(center)[#rotate(-90deg, reflow: true)[#image(
"image/exp2/3aabccc85f442f848d51fa73515ac138.jpg",
height: 5.2cm,
)]],
align(center)[#image("image/exp2/f373240e46deb6d8b14f84e40d4e97bf.jpg", height: 3.9cm)],
align(center)[#image("image/exp2/5f52978293280f05a449b6b0de96929f.jpg", height: 3.9cm)],
)
],
caption: [实验接线与仪表示数照片],
)
#v(0.7em)
#figure(
caption: [电压与电流测量数据],
report-table(
columns: (1fr, 1.7fr, 1.7fr),
[序号],
[电压 $U$ / V],
[电流 $I$ / mA],
[1],
[11.25],
[11.20],
[2],
[10.75],
[12.10],
[3],
[10.25],
[13.00],
[4],
[9.25],
[14.80],
[5],
[8.75],
[16.36],
),
)
#v(0.7em)
== （四）实验数据处理或结果
根据表中数据绘制 $U-I$ 关系曲线，如下图所示。
#figure(
[
#align(center)[
#move(dx: -6mm)[
#image("image/exp2/vi_characteristic_curve.svg", height: 49.65%)
]
]
],
caption: [伏安特性曲线],
)
== （五）分析和结论
由伏安特性曲线可见，测量点基本分布在一条下降直线附近，说明该有源二端网络在本实验测量范围内可近似看作线性有源二端网络。当负载电流增大时，端口电压逐渐减小。
#pagebreak()
= 实验三：戴维南等效电路验证
== （一）实验任务
验证戴维南等效电路。
== （二）实验方案和具体步骤
1. 根据实验一测得的 $U_"oc"$ 和 $R_0$ 搭建戴维南等效电路。
2. 分别连接原网络和戴维南等效电路。
3. 改变负载阻值，分别测量两种电路的端电压和负载电流。
4. 将测量数据整理成表格，并比较两种电路的输出结果。
5. 根据对比结果验证戴维南定理。
== （三）实验电路连接及实测数据
#v(0.3em)
#figure(
align(center)[#image("image/exp3/thevenin_equiv.svg", height: 6.6cm)],
caption: [戴维南等效电路图],
)
#v(1.7em)
#figure(
[
#grid(
columns: (1fr, 1fr, 1fr),
gutter: 0.8em,
align(center)[#image("image/exp3/88d53dc25f8008ae731c17e520cf716f.jpg", height: 3.9cm)],
align(center)[#rotate(-90deg, reflow: true)[#image(
"image/exp3/9423278937e795f55a60204335aead6d.jpg",
height: 5.2cm,
)]],
align(center)[#image("image/exp3/e2d8745fd73d6a57c7210d9083b671ab.jpg", height: 3.9cm)],
)
],
caption: [实验接线与仪表示数照片],
)
#v(0.7em)
#figure(
caption: [原网络与戴维南等效电路测量数据对比],
report-table(
columns: (1fr, 1.4fr, 1.4fr, 1.4fr, 1.4fr),
[序号],
[原网络电压 $U$ / V],
[原网络电流 $I$ / mA],
[戴维南电压 $U$ / V],
[戴维南电流 $I$ / mA],
[1],
[11.25],
[11.20],
[10.82],
[10.63],
[2],
[10.75],
[12.10],
[10.17],
[11.54],
[3],
[10.25],
[13.00],
[9.57],
[12.71],
[4],
[9.25],
[14.80],
[8.91],
[13.62],
[5],
[8.75],
[16.36],
[8.21],
[14.76],
),
)
#v(0.7em)
== （四）实验数据处理或结果
由表中数据和下图可以看出，原网络与戴维南等效电路的伏安特性曲线整体趋势基本一致。
#figure(
[
#grid(
columns: (1fr, 1fr),
gutter: 1em,
[
#align(center)[
#image("image/exp2/vi_characteristic_curve.svg", height: 8.8cm)
]
#align(center)[
（a）原网络伏安特性曲线
]
],
[
#align(center)[
#image("image/exp3/vi_characteristic_curve_table4.svg", height: 8.85cm)
]
#align(center)[
（b）戴维南等效电路伏安特性曲线
]
],
)
#v(0.7em)
],
caption: [原网络与戴维南等效电路伏安特性曲线对比],
)
== （五）分析和结论
由原网络与戴维南等效电路的对比结果可知，两者的伏安特性曲线形状基本一致，说明戴维南等效电路在外部负载看来能够较好地等效原网络。虽然对应测量值之间仍存在一定差异，但总体上保持相同变化规律。
#pagebreak()
= 实验四：诺顿等效电路验证
== （一）实验任务
验证诺顿等效电路。
== （二）实验方案和具体步骤
1. 根据实验一测得的 $I_"sc"$ 和 $R_0$ 搭建诺顿等效电路。
2. 分别连接原网络和诺顿等效电路。
3. 改变负载阻值，分别测量两种电路的端电压和负载电流。
4. 将测量数据整理成表格，并比较两种电路的输出结果。
5. 根据对比结果验证诺顿定理。
== （三）实验电路连接及实测数据
#v(0.3em)
#figure(
align(center)[#image("image/exp4/norton_equiv.svg", height: 6.6cm)],
caption: [诺顿等效电路图],
)
#v(1.7em)
#figure(
[
#grid(
columns: (1fr, 1fr, 1fr),
gutter: 0.8em,
align(center)[#image("image/exp4/64006530c818529e3a7eb2ff2c1ffc8a.jpg", height: 4.8cm)],
align(center)[#image("image/exp4/741dfec78e4643db3cc0a1bf3b357461.jpg", height: 4.8cm)],
align(center)[#image("image/exp4/fa26dcab4225002e5d142b84a58f3979.jpg", height: 4.8cm)],
)
],
caption: [实验接线与仪表示数照片],
)
#v(0.7em)
#figure(
caption: [原网络与诺顿等效电路测量数据对比],
report-table(
columns: (1fr, 1.4fr, 1.4fr, 1.4fr, 1.4fr),
[序号],
[原网络电压 $U$ / V],
[原网络电流 $I$ / mA],
[诺顿电压 $U$ / V],
[诺顿电流 $I$ / mA],
[1],
[11.25],
[11.20],
[11.39],
[11.30],
[2],
[10.75],
[12.10],
[10.69],
[12.71],
[3],
[10.25],
[13.00],
[9.97],
[13.82],
[4],
[9.25],
[14.80],
[9.21],
[15.47],
[5],
[8.75],
[16.36],
[8.58],
[16.66],
),
)
#v(0.7em)
== （四）实验数据处理或结果
由表中数据和下图可以看出，原网络与诺顿等效电路的伏安特性曲线同样基本一致。
#figure(
[
#grid(
columns: (1fr, 1fr),
gutter: 1em,
[
#align(center)[
#image("image/exp2/vi_characteristic_curve.svg", height: 8.8cm)
]
#align(center)[
（a）原网络伏安特性曲线
]
],
[
#align(center)[
#image("image/exp4/vi_characteristic_curve_exp4.svg", height: 8.85cm)
]
#align(center)[
（b）诺顿等效电路伏安特性曲线
]
],
)
#v(0.7em)
],
caption: [原网络与诺顿等效电路伏安特性曲线对比],
)
== （五）分析和结论
由原网络与诺顿等效电路的对比结果可见，两者在相同负载条件下测得的电压、电流数值比较接近，伏安特性曲线也基本重合，说明诺顿等效电路在端口外特性上与原网络具有较好的一致性。
#pagebreak()
= 实验五：最大功率传输定理验证
== （一）实验任务
本实验的任务是研究负载阻值变化时负载功率的变化规律，并验证当负载电阻与等效内阻匹配时，负载获得最大功率的结论。
== （二）实验方案和具体步骤
1. 在被测有源二端网络输出端接入可调负载电阻 $R_L$。
2. 改变负载阻值，分别测量负载两端电压与通过负载的电流。
3. 根据测得数据计算各组负载功率 $P = U I$。
4. 绘制负载功率随负载阻值变化的关系曲线。
5. 找出功率最大时对应的负载阻值，并与实验一得到的等效电阻 $R_0$ 进行比较。
== （三）实验电路连接及实测数据
#v(0.7em)
#figure(
caption: [负载功率测量数据],
report-table(
columns: (1.5fr, 1.3fr, 1.3fr, 1.3fr),
[负载电阻 $R_L$ / Ω],
[端电压 $U$ / V],
[端电流 $I$ / mA],
[负载功率 $P$ / mW],
[888.43],
[10.75],
[12.10],
[130.07],
[788.46],
[10.25],
[13.00],
[133.25],
[625.00],
[9.25],
[14.80],
[136.90],
[534.84],
[8.75],
[16.36],
[143.15],
[494.69],
[8.39],
[16.96],
[142.29],
[468.16],
[8.16],
[17.43],
[142.23],
[439.93],
[7.91],
[17.98],
[142.22],
[415.40],
[7.66],
[18.44],
[141.25],
),
)
== （四）实验数据处理或结果
根据表中数据计算各组负载功率，并绘制 $P-R_L$ 关系曲线，如下图所示。由图中可以看出，随着负载电阻逐渐减小，负载功率先增大，在接近最大值后又略有减小。
对测量数据进行比较可知，当负载电阻约为
$
R_L = 534.84"Ω"
$
时，负载功率达到最大，约为
$
P_"max" = 143.15"mW"
$
该结果与实验一测得的等效电阻 $R_0 = 519"Ω"$ 较为接近。
#figure(
image("image/exp5/power_load_curve.svg", height: 9.85cm),
caption: [负载功率曲线],
)
== （五）分析和结论
由实验结果可见，负载功率并不是随着负载电阻的变化单调增大或减小，而是在某一范围内取得最大值。本实验较好地验证了最大功率传输定理。
#pagebreak()
= 思考题
1. 对比理论计算与实验结果，分析产生误差的原因。
理论计算值是在理想条件下得到的，而实验结果会受到多种实际因素影响。此外，在作图或拟合过程中，若测量点数量有限，也会使结果与理论值之间产生一定差异。
2. 对于内部结构未知的实际电路，应采用什么方法测量其等效电阻？
对于内部结构未知的实际电路，一般不宜直接采用置零法测量等效电阻，因为无法确定其内部独立电源和元件结构。较合适的方法是采用开路-短路法、半电压法或伏安法等。
experiment2/亓涵玉202502320021.pdf
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