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2026-04-27 14:51:49 +08:00
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<clipPath id="p25cefb3eec">
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</clipPath>
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After

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experiment1/print_image_code/fig1.py
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import os
os.environ.setdefault("MPLCONFIGDIR", "/tmp/matplotlib")
import schemdraw
import schemdraw.elements as elm
from schemdraw.segments import SegmentText
FONT_NAME = "LXGW WenKai"
OUTPUT_FILE = "terminal_voltage_diagram.svg"
def add_text(
drawing,
position,
text,
*,
rotation=0,
align=("center", "center"),
fontsize=18,
):
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)
with schemdraw.Drawing(show=False) as d:
d.config(
unit=1.0,
fontsize=18,
font=FONT_NAME,
lw=2.0,
margin=0.18,
bgcolor="white",
)
# ===== 几何参数 =====
left_x = 1.5
top_y = 6.3
bottom_y = 2.1
node_x = 6.1
term_x = 8.45
# 电池位置
battery_x = left_x
battery_bottom_y = 3.55
battery_len = 1.55
# 电阻尺寸控制
top_res_start_x = 3.0
top_res_len = 2.2
vertical_res_len = 2.25
# 关键点
top_node = (node_x, top_y)
bottom_node = (node_x, bottom_y)
a_pos = (term_x, top_y)
b_pos = (term_x, bottom_y)
top_battery_end_y = battery_bottom_y + battery_len
# ===== 左支路 + 电池 =====
# 下导线到电池
d.add(
elm.Line()
.at((battery_x, bottom_y))
.up(battery_bottom_y - bottom_y)
.hold()
)
# 电池
d.add(
elm.BatteryCell()
.at((battery_x, battery_bottom_y))
.up(battery_len)
.hold()
)
# 电池上端到顶端导线
d.add(
elm.Line()
.at((battery_x, top_battery_end_y))
.up(top_y - top_battery_end_y)
.hold()
)
# ===== 上支路 =====
d.add(elm.Line().at((battery_x, top_y)).right(top_res_start_x - battery_x).hold())
d.add(elm.ResistorIEC().at((top_res_start_x, top_y)).right(top_res_len).hold())
d.add(
elm.Line()
.at((top_res_start_x + top_res_len, top_y))
.right(node_x - (top_res_start_x + top_res_len))
.hold()
)
# 上节点
d.add(elm.Dot(radius=0.085).at(top_node).hold())
# a 端
d.add(elm.Line().at(top_node).right(term_x - node_x).hold())
d.add(elm.Dot(open=True, radius=0.105).at(a_pos).hold())
# ===== 中间竖支路 =====
d.add(elm.ResistorIEC().at(top_node).down(vertical_res_len).hold())
d.add(
elm.Line()
.at((node_x, top_y - vertical_res_len))
.down((top_y - vertical_res_len) - bottom_y)
.hold()
)
# 下节点
d.add(elm.Dot(radius=0.085).at(bottom_node).hold())
# b 端
d.add(elm.Line().at(bottom_node).right(term_x - node_x).hold())
d.add(elm.Dot(open=True, radius=0.105).at(b_pos).hold())
# ===== 下支路闭合 =====
d.add(elm.Line().at((battery_x, bottom_y)).right(node_x - battery_x).hold())
# ===== 文本标注 =====
# 9V：竖排，放在电池右侧偏中间，更贴近教材风格
add_text(
d,
(battery_x + 0.92, battery_bottom_y + battery_len / 2),
"10V",
rotation=0,
fontsize=16,
)
# 1kΩ：水平，置于上方电阻正下方
add_text(
d,
(top_res_start_x + top_res_len / 2, top_y - 0.72),
"1kΩ",
rotation=0,
fontsize=16,
)
# 2kΩ：竖排，置于竖直电阻左侧，方向要注意
add_text(
d,
(node_x - 0.82, top_y - vertical_res_len / 2),
"2kΩ",
rotation=0,
fontsize=16,
)
# a / b 端标注
add_text(
d,
(a_pos[0] + 0.42, a_pos[1] - 0.02),
"a",
fontsize=19,
)
add_text(
d,
(b_pos[0] + 0.42, b_pos[1] - 0.02),
"b",
fontsize=19,
)
d.save(OUTPUT_FILE, transparent=False)
experiment1/print_image_code/print.py
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import os
os.environ.setdefault("MPLCONFIGDIR", "/tmp/matplotlib")
import schemdraw
import schemdraw.elements as elm
from schemdraw.segments import SegmentText, SegmentCircle
FONT_NAME = "LXGW WenKai"
BG_COLOR = "white"
# 这里改成你自己的输出目录
OUTDIR = os.path.abspath(os.path.join(os.path.dirname(__file__), "..", "image"))
os.makedirs(OUTDIR, exist_ok=True)
def make_drawing():
d = schemdraw.Drawing(show=False)
d.config(
unit=1.0,
fontsize=16,
font=FONT_NAME,
lw=2.2,
margin=0.18,
bgcolor=BG_COLOR,
)
return d
def add_text(
drawing,
position,
content,
*,
rotation=0,
align=("center", "center"),
fontsize=16,
):
element = elm.Element().at(position).anchor("center").hold()
element.anchors["center"] = (0, 0)
element.segments.append(
SegmentText(
(0, 0),
content,
rotation=rotation,
align=align,
fontsize=fontsize,
font=FONT_NAME,
)
)
drawing.add(element)
def add_dot(drawing, position, *, open_dot=False, radius=0.085):
drawing.add(elm.Dot(open=open_dot, radius=radius).at(position).hold())
def wire(drawing, start, end):
drawing.add(elm.Line().at(start).to(end).hold())
def save_drawing(drawing, filename):
drawing.save(os.path.join(OUTDIR, filename), transparent=False)
# -------------------------
# 图 (a)
# -------------------------
def make_circuit_a():
d = make_drawing()
x_left = 0.9
x_meter = 3.0
x_node = 5.7
x_res_top = 7.2
x_right = 10.1
y_top = 4.2
y_bottom = 1.0
y_mid = 2.55
# 左侧电池
batt = d.add(elm.BatteryCell().at((x_left, y_bottom)).up(2.1).hold())
wire(d, batt.end, (x_left, y_top))
wire(d, batt.start, (x_left, y_bottom))
# 上边：A表 + 节点 + 1k
wire(d, (x_left, y_top), (x_meter, y_top))
am = d.add(elm.MeterA().at((x_meter, y_top)).right().hold())
wire(d, am.end, (x_node, y_top))
add_dot(d, (x_node, y_top))
wire(d, (x_node, y_top), (x_res_top, y_top))
r1 = d.add(elm.ResistorIEC().at((x_res_top, y_top)).right(1.5).hold())
wire(d, r1.end, (x_right, y_top))
# 右侧竖直 2k 电阻
r2 = d.add(elm.ResistorIEC().at((x_right, y_top)).down(1.9).hold())
wire(d, r2.end, (x_right, y_bottom))
# 中间 V 表支路
wire(d, (x_node, y_top), (x_node, 3.45))
vm = d.add(elm.MeterV().at((x_node, 3.45)).down().hold())
wire(d, vm.end, (x_node, y_bottom))
add_dot(d, (x_node, y_bottom))
# 底边闭合
wire(d, (x_left, y_bottom), (x_node, y_bottom))
wire(d, (x_node, y_bottom), (x_right, y_bottom))
# 文字
add_text(d, (8.0, 4.75), "1kΩ", fontsize=16)
add_text(d, (10.75, 2.45), "2kΩ", fontsize=16)
add_text(d, (5.4, 0.25), "(a)", fontsize=18)
save_drawing(d, "circuit_a.svg")
# -------------------------
# 图 (b)
# -------------------------
def make_circuit_b():
d = make_drawing()
x_left = 0.9
x_node = 3.4
x_meter = 5.0
x_res_top = 7.2
x_right = 10.1
y_top = 4.2
y_bottom = 1.0
# 左侧电池
batt = d.add(elm.BatteryCell().at((x_left, y_bottom)).up(2.1).hold())
wire(d, batt.end, (x_left, y_top))
wire(d, batt.start, (x_left, y_bottom))
# 上边左节点
wire(d, (x_left, y_top), (x_node, y_top))
add_dot(d, (x_node, y_top))
# 中间 V 表
wire(d, (x_node, y_top), (x_node, 3.45))
vm = d.add(elm.MeterV().at((x_node, 3.45)).down().hold())
wire(d, vm.end, (x_node, y_bottom))
add_dot(d, (x_node, y_bottom))
# 上边右支路：A + 1k
wire(d, (x_node, y_top), (x_meter, y_top))
am = d.add(elm.MeterA().at((x_meter, y_top)).right().hold())
wire(d, am.end, (x_res_top, y_top))
r1 = d.add(elm.ResistorIEC().at((x_res_top, y_top)).right(1.5).hold())
wire(d, r1.end, (x_right, y_top))
# 右侧竖直 2k
r2 = d.add(elm.ResistorIEC().at((x_right, y_top)).down(1.9).hold())
wire(d, r2.end, (x_right, y_bottom))
# 下边闭合
wire(d, (x_left, y_bottom), (x_node, y_bottom))
wire(d, (x_node, y_bottom), (x_right, y_bottom))
# 文字
add_text(d, (8.0, 4.75), "1kΩ", fontsize=16)
add_text(d, (9.1, 3.0), "2kΩ", fontsize=16)
add_text(d, (5.6, 0.25), "(b)", fontsize=18)
save_drawing(d, "circuit_b.svg")
# -------------------------
# 图 (c)
# -------------------------
def make_circuit_c():
d = make_drawing()
x_left = 1.2
x_v = 3.2
x_node = 6.0
x_right = 8.8
y_top = 4.2
y_bottom = 1.0
# 左侧电压源
# 左侧理想电压源：圆圈 + 竖线
source_center_y = 2.45
source_radius = 0.55
# 上下导线
wire(d, (x_left, y_top), (x_left, source_center_y + source_radius))
wire(d, (x_left, source_center_y - source_radius), (x_left, y_bottom))
# 圆圈
src = elm.Element().at((x_left, source_center_y)).anchor("center").hold()
src.anchors["center"] = (0, 0)
src.segments.append(SegmentCircle((0, 0), radius=source_radius))
d.add(src)
# 圆圈中间竖线
wire(d, (x_left, source_center_y - 0.5), (x_left, source_center_y + 0.5))
# 顶部 V 表
wire(d, (x_left, y_top), (x_v, y_top))
vm = d.add(elm.MeterV().at((x_v, y_top)).right().hold())
wire(d, vm.end, (x_node, y_top))
add_dot(d, (x_node, y_top))
# 右侧电阻支路
wire(d, (x_node, y_top), (x_right, y_top))
r = d.add(elm.ResistorIEC().at((x_right, y_top)).down(1.9).hold())
wire(d, r.end, (x_right, y_bottom))
# 中间开关支路
wire(d, (x_node, y_top), (x_node, 3.2))
add_dot(d, (x_node, 3.2), open_dot=True, radius=0.11)
add_dot(d, (x_node, 2.1), open_dot=True, radius=0.11)
d.add(elm.Line().at((x_node - 0.05, 2.18)).to((x_node + 0.35, 2.95)).hold())
wire(d, (x_node, 2.1), (x_node, y_bottom))
add_dot(d, (x_node, y_bottom))
# 下边闭合
wire(d, (x_left, y_bottom), (x_node, y_bottom))
wire(d, (x_node, y_bottom), (x_right, y_bottom))
# 文字
add_text(d, (0.25, 2.25), "Uₛ", fontsize=18)
add_text(d, (6.65, 2.6), "K", fontsize=18)
add_text(d, (9.5, 2.55), "R", fontsize=18)
save_drawing(d, "circuit_c.svg")
# -------------------------
# 图 (d)
# -------------------------
def make_circuit_d():
d = make_drawing()
x_left = 1.0
x_mid = 4.2
x_right = 7.2
y_top = 6.5
y_bottom = 0.7
# 外框
wire(d, (x_left, y_top), (x_mid, y_top))
add_dot(d, (x_mid, y_top))
wire(d, (x_mid, y_top), (x_right, y_top))
wire(d, (x_left, y_bottom), (x_mid, y_bottom))
add_dot(d, (x_mid, y_bottom))
wire(d, (x_mid, y_bottom), (x_right, y_bottom))
# 左支路：电流源
# 左支路：理想电流源（圆圈 + 竖线）
source_center_y = 4.2
source_radius = 0.55
wire(d, (x_left, y_top), (x_left, source_center_y + source_radius))
wire(d, (x_left, source_center_y - source_radius), (x_left, y_bottom))
# 圆圈
src = elm.Element().at((x_left, source_center_y)).anchor("center").hold()
src.anchors["center"] = (0, 0)
src.segments.append(SegmentCircle((0, 0), radius=source_radius))
d.add(src)
# 圆圈中间竖线
wire(d, (x_left, source_center_y - 0.5), (x_left, source_center_y + 0.5))
# 标注
add_text(d, (x_left + 0.7, source_center_y - 0.6), "Iₛ", fontsize=18)
# 右支路：A 表
wire(d, (x_right, y_top), (x_right, 5.0))
am = d.add(elm.MeterA().at((x_right, 5.0)).down().hold())
wire(d, am.end, (x_right, y_bottom))
# 中间支路：开关 + 可变电阻
wire(d, (x_mid, y_top), (x_mid, 5.2))
add_dot(d, (x_mid, 5.2), open_dot=True, radius=0.11)
add_dot(d, (x_mid, 4.25), open_dot=True, radius=0.11)
d.add(elm.Line().at((x_mid - 0.05, 4.35)).to((x_mid + 0.4, 5.0)).hold())
wire(d, (x_mid, 4.25), (x_mid, 3.6))
r = d.add(elm.ResistorIEC().at((x_mid, 3.6)).down(1.5).hold())
wire(d, r.end, (x_mid, y_bottom))
# 文字
add_text(d, (4.85, 4.85), "K", fontsize=18)
add_text(d, (4.8, 2.05), "R", fontsize=18)
save_drawing(d, "circuit_d.svg")
def main():
make_circuit_a()
make_circuit_b()
make_circuit_c()
make_circuit_d()
print("Created: circuit_a.svg, circuit_b.svg, circuit_c.svg, circuit_d.svg")
if __name__ == "__main__":
main()
experiment1/report.pdf
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experiment1/report.typ
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#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: 0.8em,
)
#set heading(numbering: none)
#let line(len: 5em) = box(
width: len,
inset: 0pt,
)[#h(len)]
#let field(label, len: 7em) = [
#label：#underline[#box(width: len)[]]
]
#let photo-box(title, height: 6cm) = 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 small-gap = v(0.45em)
#let mid-gap = v(0.8em)
#let big-gap = v(1.2em)
#show heading.where(level: 1): it => {
big-gap
block(width: 100%)[
#text(16pt, weight: "bold")[#it.body]
]
v(0.5em)
}
#show heading.where(level: 2): it => {
v(0.9em)
block(width: 100%)[
#text(14pt, weight: "bold")[#it.body]
]
v(0.35em)
}
#show heading.where(level: 3): it => {
v(0.6em)
block(width: 100%)[
#text(12pt, weight: "bold")[#it.body]
]
v(0.2em)
}
#show math.equation: set text(size: 12pt)
#let note-box(body) = block(
width: 100%,
inset: 9pt,
radius: 4pt,
stroke: 0.6pt + rgb("#999"),
fill: rgb("#fcfcfc"),
)[#body]
#let report-table(..args) = table(
stroke: 0.7pt + black,
inset: 6pt,
align: center + horizon,
..args,
)
#align(center)[
#text(size: 20pt, weight: "bold")[实验报告]
]
= 实验一：采用不同电表测量同一电压
== （一）实验原理
实际测量中，电压表或万用表并联接入被测支路。由于仪表内阻不是无穷大，接入后会改变原电路参数，因此不同仪表测得的电压值会略有差异。仪表的准确度等级、量程和内阻大小都会影响测量结果。
本实验通过分别使用C65-V型直流电压表、MF47型万用表和UT52型数字万用表测量同一电压，比较其测量结果并分析误差来源。
== （二）实验方案和具体步骤
1. 连接实验电路，调节电源。
2. 检查电路连接无误后接通电源。
3. 分别使用C65-V型直流电压表、MF47型万用表和UT52型数字万用表测量a、b两端电压。
4. 记录各仪表的准确度等级、所选量程和内阻。
5. 将各仪表测得的$U_"ab"$记录于数据表中。
6. 计算相对误差。
== （三）实验电路连接及实测数据
#figure(
image("image/terminal_voltage_diagram.svg", width: 55%),
caption: [端电压测量图],
)
#grid(
columns: (1fr, 1fr),
gutter: 1em,
figure(
image("image/87d91b822e6565f30ddd47f6f19c4d3f.jpg", width: 90%),
caption: [测量实物图],
),
figure(
image("image/47862a98ad85295a46ef3f86169e6772.jpg", width: 90%),
caption: [测量实物图],
),
)
== （四）实验数据或结果
#figure(
caption: [不同仪表测量电压数据比较],
placement: none,
report-table(
columns: (1.8fr, 1.2fr, 1.2fr, 1.4fr, 1.4fr, 1.2fr, 1.4fr),
[仪表名称],
[准确度等级],
[量程 / V],
[内阻 / Ω],
[实测值 / V],
[$U_"ab"$理论值 / V],
[相对误差 / %],
[C65-V型直流电压表],
[0.5],
[12],
[120k],
[6.39],
[6.68],
[-4.43],
[MF47型万用表],
[2.5],
[10],
[200k],
[6.9],
[6.68],
[3.29],
[UT52型数字万用表],
[0.5],
[20],
[10M],
[6.66],
[6.68],
[-0.30],
),
)
#small-gap
按照图示电路连接，电源电压为10.02V，电路由1kΩ和2kΩ电阻构成分压网络，被测量为 a、b 两端电压$U_"ab"$。
在理想情况下，根据分压原理可得：
$
U_"ab" = 10.02 times 2 / (1 + 2) = 6.68"V"
$
相对误差计算公式为：
$
gamma = (A_x- A_0) / A_0 times 100%
$
其中，$U$为实测值，$U_0$为理论值。
== （五）分析和结论
分析：三种仪表测量同一电压时，读数基本接近，但仍有一定差异。其中UT52型数字万用表的测量值最接近理论值。其原因主要与仪表的准确度等级、量程和内阻有关。准确度越高，测量结果越准确；量程选择越合适，读数误差越小。电压表内阻越大，对原电路影响越小，测得结果越接近真实值。
结论：实验表明，不同仪表测量同一电压时会产生一定差异。选用准确度高、内阻大、量程合适的仪表，可以减小测量误差，提高测量结果的准确性。
#pagebreak()
= 实验二：测量电路的功率
== （一）实验原理
由于电流表与电压表都具有内阻，不同测量接法会引入不同系统误差，因此两种接法下测得功率会存在差异。
== （二）实验方案和具体步骤
1. 按图4 （a）连接电路。
2. 接通电源，读取并记录电压表和电流表的示值。
3. 按图5 （b）重新连接电路。
4. 再次读取并记录电压表和电流表的示值。
5. 利用测得数据计算电路功率。
6. 将实测功率与理论功率进行比较，并分析误差原因。
== （三）实验电路连接及实测数据
#grid(
columns: (2fr, 2fr),
gutter: 2em,
figure(
image("image/circuit_a.svg", width: 118.5%),
caption: [电路图（a）],
),
figure(
image("image/circuit_b.svg", width: 110%),
caption: [电路图（b）],
),
)
#grid(
columns: (2fr, 2fr),
gutter: 1em,
figure(
image("image/2279c7165d6594290b17dffb33f5a361.jpg", width: 90%),
caption: [测量实物图（a）],
),
figure(
image("image/3674dc017e2f1b40809317414f516c64.jpg", width: 90%),
caption: [测量实物图（a）],
),
figure(
image("image/6c91e279c55eed5092813572ce7b1705.jpg", width: 90%),
caption: [测量实物图（b）],
),
figure(
image("image/61f4ef8495d7f52ce1b4d6cc9316e93c.jpg", width: 90%),
caption: [测量实物图（b）],
),
)
== （四）实验数据或结果
功率计算公式为：
$
P = U I
$
按图所示的两种接法连接电路，通过测量电压和电流，可以计算负载功率或电路功率。已知电源电压为10.02V，电路中电阻分别为1kΩ和2kΩ，则总电阻为：
$
R = 1"kΩ" + 2"kΩ" = 3"kΩ"
$
理论总电流为：
$
I = (10.02"V") / (3"kΩ") = 3.34"mA"
$
负载理论功率为：
$
P = U I = 10.02"V" times 3.34"mA" = 33.47"mW"
$
相对误差计算公式为：
$
gamma = (P - P_0) / P_0 times 100%
$
其中，$P$为实测功率，$P_0$为理论功率。
#figure(
caption: [不同测量电功率的电路数据比较],
placement: none,
report-table(
columns: (1.6fr, 1.6fr, 1.6fr, 1.6fr, 1.5fr, 1.5fr),
[接法],
[电压表示值 / V],
[电流表示值 / mA],
[计算功率 / mW],
[理论功率 / mW],
[相对误差 / %],
[图 3.4（a）],
[10.01],
[4.31],
[43.14],
[33.47],
[28.90],
[图 3.4（b）],
[9.12],
[3.25],
[29.64],
[33.47],
[-11.44],
),
)
#small-gap
== （五）分析和结论
分析：两种接法下测得的功率值存在一定差异，但总体接近理论值。造成差异的主要原因是电流表和电压表都具有一定内阻，接入电路后会改变原有工作状态。若电流表接入位置不同，其内阻引起的影响不同；电压表并联位置不同，其分流作用也不同，因此会影响电压和电流的测量结果。
结论：
实验表明，不同接法会对功率测量结果产生影响。选择合适的测量方法和仪表，可减小误差，提高功率测量的准确性。
#pagebreak()
= 实验三：测量万用表电压挡和直流电流 5mA 挡的内阻
== （一）实验原理
电压表和电流表都不是理想仪表，其内部存在一定内阻。利用分压法和分流法可以测量万用表不同挡位的内阻。
=== 1. 电压挡内阻测量原理
设电压表内阻为$R_v$，已知标准电阻为$R$。开关闭合时电压表示数为$U_1$，开关断开后电压表示数为$U_2$，并有$U_s = U_1$。
根据分压原理：
$
U_2 = R_v / (R + R_v) times U_s
$
又因为 $U_s = U_1$，所以有：
$
U_2 = R_v / (R + R_v) times U_1
$
整理可得电压挡内阻：
$
R_v = U_2 / (U_1 - U_2) times R
$
=== 2. 直流 5mA 挡内阻测量原理
分流法测量电流表内阻的电路如图 3.2 所示。设电流表内阻为$R_a$，开关闭合时电流表的读数为$I_2$，开关打开后电流表的读数为$I_1$。根据分流原理，有
$
I_2 = R / (R + R_a) I_s
$
又因为
$
I_s = I_1
$
故可得电流表内阻为
$
R_a = (I_1 - I_2) / I_2 R
$
== （二）实验方案和具体步骤
=== 1. 测量电压挡内阻
1. 按照分压法连接实验电路，选用MF47型万用表直流10V电压挡。
2. 闭合开关，记录电压表示数$U_1$。
3. 断开开关后，记录电压表示数$U_2$。
4. 记录标准电阻$R$的阻值。
5. 代入公式计算电压挡内阻$R_v$。
=== 2. 测量直流 5mA 挡内阻
1. 按照分流法连接实验电路，将MF4 型万用表置于直流5mA挡。
2. 先断开开关，测得电流表读数为$I_1$
3. 再闭合开关，测得电流表读数为$I_2$。
4. 记录并联支路中标准电阻 $R$ 的阻值。
5. 代入公式计算
== （三）实验电路连接及实测数据
#v(0.2em)
#grid(
columns: 2fr,
gutter: 1em,
figure(
image("image/circuit_c.svg", width: 70%),
caption: [分压法测电压表内阻],
),
figure(
image("image/circuit_d.svg", height: 25%),
caption: [分流法测电流表内阻],
),
)
== （四）实验数据或结果
=== 1. 电压挡内阻测量数据表
#report-table(
columns: (1.6fr, 1.4fr, 1.4fr, 1.8fr, 1.8fr),
[电压挡量程],
[U₁ / V],
[U₂ / V],
[标准电阻 R / Ω],
[计算所得 Rᵥ / Ω],
[10V],
[10.02],
[5.09],
[200k],
[207k],
)
#mid-gap
=== 2. 直流 5mA 挡内阻测量数据表
#report-table(
columns: (1.6fr, 1.5fr, 1.5fr, 1.8fr, 1.8fr),
[电流挡量程],
[$I_1$ / mA],
[$I_2$ / mA],
[标准电阻 R / Ω],
[计算所得 Rₐ / Ω],
[5mA],
[4.00],
[2.74],
[100],
[45.99],
)
#small-gap
电压挡内阻计算公式为：
$
R_v = U_2 / (U_1 - U_2) times R
$
电流挡内阻计算公式为：
$
R_a = (I_1 - I_2) / I_2 R
$
== （五）分析和结论
分析：实验中采用分压法和分流法分别测量电压挡与电流挡的内阻，测得结果与仪表标称值基本接近，但仍存在一定差异。造成误差的主要原因是标准电阻本身具有一定误差，接入电路后会影响实际分压或分流情况；同时，仪表读数过程中存在估读误差，也会使测量结果产生偏差。
结论：实验表明，分压法和分流法都能够较好地测量仪表内阻，所得结果与理论值基本一致，说明实验方法正确可行。
#pagebreak()
= 思考题及实验心得
== （一）思考题
=== 1. 电容值、电感值测量有哪些方法？
电容值的测量方法主要有：利用电容挡或数字万用表直接测量、电桥法测量、交流参数法测量，以及通过测量充放电时间常数间接计算。
电感值的测量方法主要有：利用电感挡直接测量、电桥法测量、交流阻抗法测量，以及根据线圈在交流电路中的电压、电流和频率关系进行计算。不同方法适用于不同精度要求和不同元件范围，其中电桥法精度较高，数字仪表法操作较方便。
=== 2. 是不是仪表准确度等级越高，测量结果越精确？
仪表准确度等级越高，通常说明其基本误差越小，测量结果更接近真实值，但这并不意味着实际测量结果一定更精确。测量结果还受到量程选择、读数方式、仪表内阻、被测电路状态、环境条件以及操作方法等因素影响。如果量程选择不合适，或接线、读数存在误差，即使使用高准确度仪表，也可能得不到理想结果。因此，仪表准确度等级高只是提高测量精度的重要条件之一，而不是唯一条件。
=== 3. 三用表为什么测量电阻时读数是从右至左且刻度为不均匀设置？
三用表测量电阻时内部带有电池，实质上是通过被测电阻大小来决定表头电流大小。被测电阻越小，电流越大，指针偏转越大；被测电阻越大，电流越小，指针偏转越小。因此零欧姆对应满偏，位于刻度右端，而无穷大电阻对应电流接近零，位于刻度左端，所以电阻刻度是从右向左读数。又由于电流与电阻之间不是线性关系，而是反比关系，因此电阻刻度不能均匀分布，只能采用不均匀刻度。
== （二）实验心得
通过本次实验，我进一步掌握了电压、电流、电阻及功率等基本电参量的测量方法，熟悉了电工仪器的使用。本次实验不仅巩固了理论知识，也提高了我的动手能力和分析问题的能力。
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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
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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
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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
+84
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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
+87
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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
+136
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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
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#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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experiment3/main.typ
+329
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@@ -0,0 +1,329 @@
#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: 0.8em,
)
#set heading(numbering: none)
#let line(len: 5em) = box(
width: len,
inset: 0pt,
)[#h(len)]
#let field(label, len: 7em) = [
#label：#underline[#box(width: len)[]]
]
#let image-slot(title, height: 6cm) = 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 fig(title, height: 6cm, caption: none) = figure(
image-slot(title, height: height),
caption: caption,
)
#let fig-image(path, height: 6cm, caption: none) = figure(
image(path, width: 100%, height: height, fit: "contain"),
caption: caption,
)
#let fig-two(left-title, right-title, height: 6cm, caption: none) = figure(
grid(
columns: 2,
gutter: 0.8cm,
image-slot(left-title, height: height),
image-slot(right-title, height: height),
),
caption: caption,
)
#let fig-two-images(left-path, right-path, height: 6cm, caption: none) = figure(
grid(
columns: 2,
gutter: 0.8cm,
image(left-path, width: 100%, height: height, fit: "contain"),
image(right-path, width: 100%, height: height, fit: "contain"),
),
caption: caption,
)
#let small-gap = v(0.45em)
#let mid-gap = v(0.8em)
#let big-gap = v(1.2em)
#show heading.where(level: 1): it => {
big-gap
block(width: 100%)[
#text(16pt, weight: "bold")[#it.body]
]
v(0.5em)
}
#show heading.where(level: 2): it => {
v(0.9em)
block(width: 100%)[
#text(14pt, weight: "bold")[#it.body]
]
v(0.35em)
}
#show heading.where(level: 3): it => {
v(0.6em)
block(width: 100%)[
#text(12pt, weight: "bold")[#it.body]
]
v(0.2em)
}
#show math.equation: set text(size: 12pt)
#let note-box(body) = block(
width: 100%,
inset: 9pt,
radius: 4pt,
stroke: 0.6pt + rgb("#999"),
fill: rgb("#fcfcfc"),
)[#body]
#let report-table(..args) = table(
stroke: 0.7pt + black,
inset: 6pt,
align: center + horizon,
..args,
)
#align(center)[
#text(size: 20pt, weight: "bold")[实验报告一：一阶 RC 电路充放电过程的观察]
]
= 1. 实验原理
一阶 RC 电路，在电容没有初始储能的条件下，由外加激励所引起的响应就是电路的零状态响应。此时电容两端电压的变化规律为
$
u_C(t)=U_s (1-e^(-t/tau)),quad t >= 0
$
其中 $tau=R C$ 为一阶 RC 电路的时间常数。零状态响应实际上就是电容的充电过程，当 $t=tau$ 时，$u_C(t)=0.632U_s$。
在没有外加激励时，由动态元件的初始储能所引起的响应就是一阶电路的零输入响应。零输入响应时，电容两端电压的变化规律为
$
u_C(t)=U_s e^(-t/tau),quad t >= 0
$
当 $t=tau$ 时，$u_C(t)=0.368U_s$。时间常数 $tau$ 是衡量一阶电路特性的一个重要参数，可以通过示波器直接进行测量，即找出 $0.632U_s$ 和 $0.368U_s$，对应的时间轴坐标就是时间常数 $tau$。
在动态电路的过渡过程中，用普通示波器观察过渡过程和测量有关参数，必须使这种单次变化的过程重复出现。因此，在观察一阶电路的过渡过程时，总是利用方波输出作为零状态响应的正阶跃激励信号，利用方波输出作为零输入响应的负阶跃激励信号。只要选择方波的周期远大于电路的时间常数，那么这样反复的阶跃信号激励下，它的响应就和直流电接通与断开的过渡过程基本相同。
= 2. 实验方案与具体步骤
实验采用信号源输出方波作为激励信号，通过示波器同时观察输入方波信号与电容两端电压信号，分析一阶 RC 电路的充电与放电过程，并测量时间常数 $tau$。
具体步骤如下：
+ 按实验电路图连接一阶 RC 电路，取 $R = 10 "kΩ"$，$C = 0.01 "μF"$。
+ 将信号源设置为方波输出，幅值约为 $U_(p-p) = 2 "V"$，频率为 $f = 1 "kHz"$。
+ 将示波器 CH1 接输入信号 $u_i$，CH2 接电容两端电压 $u_C$。
+ 调节示波器时基和幅值档位，使输入方波和电容电压波形稳定显示。
+ 观察电容充电过程中的零状态响应曲线，并测量 $u_C=0.632U_s$ 对应的时间。
+ 观察电容放电过程中的零输入响应曲线，并测量 $u_C=0.368U_s$ 对应的时间。
+ 将理论时间常数与实测时间常数进行比较，计算相对误差。
= 3. 实验电路连接与实测数据
== 3.1 实验电路连接
实验电路由信号源、电阻 $R$、电容 $C$ 和示波器组成。输入端接方波信号 $u_i$，输出端取电容两端 电压 $u_C$。示波器 CH1 观察输入方波，CH2 观察电容电压。
#v(.5em)
#fig-image(
"image/581da739f44c3ba158e78250bb1de788.jpg",
height: 7cm,
caption: [一阶 RC 充放电实验装置],
)
== 3.2 实验参数与实测数据
#v(.6em)
#report-table(
columns: (1fr, 1fr, 1fr, 1fr),
table.header([测量项目], [理论判据], [实测时间], [相对误差]),
[零状态响应], [$u_C = 0.632 U_s$], [$96 "μs"$], [$4%$],
[零输入响应], [$u_C = 0.368 U_s$], [$96 "μs"$], [$4%$],
)
#v(.5em)
#fig-image(
"image/a16d35732bc3dd501151661168f397af.jpg",
height: 7cm,
caption: [示波器测得的一阶 RC 电路充放电波形],
)
= 4. 实验数据与结果
理论时间常数为
$
tau = R C = 10 "kΩ" times 0.01 "μF" = 100 "μs"
$
理论上，零状态响应在 $t = tau$ 时满足 $u_C = 0.632 U_s$，零输入响应在 $t = tau$ 时满足 $u_C = 0.368 U_s$，对应曲线如图所示。
#fig-two-images(
"image/1e87032c-d14a-4581-a2c7-cb159c164570.png",
"image/dae073f3-6846-4e8f-8cfe-7ae58b01f88f.png",
height: 5.7cm,
caption: [零状态响应与零输入响应曲线],
)
根据示波器截图中的光标读数，时间差约为 $Delta X = 96 "μs"$。据此估计，零状态响应对应的实测时间常数约为 $tau_1 = 96 "μs"$，零输入响应对应的实测时间常数约为 $tau_2 = 96 "μs"$。
相对误差计算公式为
$
delta = abs((tau_"测"-tau_"理")/tau_"理") times 100%
$
#report-table(
columns: (1fr, 1fr),
table.header([项目], [测量结果]),
[充电过程], [$tau_1 = 96 "μs"$],
[放电过程], [$tau_2 = 96 "μs"$],
)
= 5. 分析和结论
通过实验可以观察到，一阶 RC 电路在方波激励下，电容两端电压呈指数规律变化。方波上升沿相当于对电路施加正阶跃激励，电容进入充电过程，表现为零状态响应；方波下降沿相当于负阶跃激励，电容进入放电过程，表现为零输入响应。
从示波器截图读取的结果看，实测时间常数约为 $96 "μs"$，与理论值 $tau = 100 "μs"$ 相比误差约为 $4%$，说明实验测量结果与理论分析基本一致。剩余误差可能来自元件参数偏差、信号源内阻、示波器光标读数位置以及人工读数误差等因素。
#pagebreak()
#align(center)[
#text(size: 20pt, weight: "bold")[实验报告二：RC 微分电路与积分电路]
]
= 1. 实验原理
积分电路与微分电路是有着广泛应用的两种电路，它们不仅可以实现基本的积分运算和微分运算，还可以实现波形的变换。
当输入为周期性脉冲信号（方波）时，输出信号 $u_o$ 为输入信号 $u_i$ 的积分，因此称该电路为积分电路。该电路中，时间常数 $tau = R C$ 应远大于输入信号的周期，通常满足
$
tau = R C >> T / 2
$
当输入为周期性脉冲信号（方波）时，输出信号 $u_o$ 为输入信号 $u_i$ 的微分，因此称该电路为微分电路。该电路中，时间常数 $tau = R C$ 应远小于输入信号的周期，通常满足
$
tau = R C << T / 2
$
利用示波器观察微分电路和积分电路的输入、输出波形，可以分析电路参数 $R$、$C$ 和输入信号频率对输出波形的影响。
= 2. 实验方案与具体步骤
实验采用 RC 积分电路和 RC 微分电路分别对方波信号进行波形变换，观察输出波形与理论规律是否一致。
具体步骤如下：
+ 连接 RC 积分电路，使输出端取电容两端电压 $u_o$。
+ 设置函数信号发生器输出方波信号，幅值约为 $2 "V"$，频率初设为 $1 "kHz"$。
+ 用示波器 CH1 观察输入信号 $u_i$，CH2 观察输出信号 $u_o$。
+ 调节 $R$ 或 $C$ 的值，使电路时间常数满足 $R C >> T / 2$，观察积分输出波形。
+ 连接 RC 微分电路，使输出端取电阻两端电压 $u_o$。
+ 调节 $R$ 或 $C$ 的值，使电路时间常数满足 $R C << T / 2$，观察微分输出波形。
+ 改变输入方波频率，比较不同频率下积分和微分波形的变化。
+ 记录输入、输出波形及主要测量数据。
= 3. 实验电路连接与实测数据
== 3.1 RC 积分电路
#fig-image(
"image/68462c92-fc5f-46ae-8b32-b1805dc3ba34.png",
height: 6cm,
caption: [RC 积分电路连接图],
)
积分电路中，电阻 $R$ 与电容 $C$ 串联，输出端取电容两端电压。当电路时间常数 $R C$ 远大于输入信号半周期时，电容充放电较慢，输出波形接近三角波。
#fig-image(
"image/bf720993e76031df1172e7ac9c12e8cc.jpg",
height: 7cm,
caption: [积分电路输入 $u_i$ 与输出 $u_o$ 波形],
)
== 3.2 RC 微分电路
#fig-image(
"image/0b9c1205-2ec9-4d35-95f1-39549d3f1fd3.png",
height: 6.2cm,
caption: [RC 微分电路连接图],
)
微分电路中，电容 $C$ 与电阻 $R$ 串联，输出端取电阻两端电压。当电路时间常数 $R C$ 远小于输入信号半周期时，在方波跳变沿处输出尖脉冲波形。
#v(.6em)
#fig-image(
"image/3fbe65eda59e0cbac57b8f5d6275974d.jpg",
height: 7cm,
caption: [微分电路输入 $u_i$ 与输出 $u_o$ 波形],
)
= 4. 实验数据与结果
== 4.1 积分电路结果
当 $R C > T / 2$ 时，实验观察到积分电路的输出波形由方波变为近似三角波。由示波器截图可见，输入信号频率约为 $1 "kHz"$，即半周期约为 $0.5 "ms"$；输出波形在每个半周期内近似线性升降，基本符合积分电路特性。
#fig-image(
"image/2d05e1fa-1c52-4a19-866a-6e500d5fde0f.png",
height: 7cm,
caption: [积分电路形],
)
== 4.2 微分电路结果
当 $R C << T / 2$ 时，实验观察到微分电路在输入方波的上升沿输出正尖脉冲，在下降沿输出负尖脉冲。其余时间输出电压迅速衰减接近零，说明电路对输入信号的突变部分敏感。
#fig-image(
"image/61b03717-5ce4-4260-a7bb-2fd6f5787cfa.png",
height: 5.5cm,
caption: [微分电路理论输出波形],
)
= 5. 分析和结论
RC 积分电路和微分电路本质上都是由一阶 RC 暂态过程形成的波形变换电路。积分电路要求时间常数远大于输入信号半周期，使电容电压变化缓慢，输出波形表现为对输入方波的积分效果；微分电路要求时间常数远小于输入信号半周期，使输出只在输入信号突变瞬间产生明显变化，表现为尖脉冲波形。
实验结果表明，改变 $R$、$C$ 或输入频率都会改变 $R C$ 与 $T / 2$ 的相对关系，从而影响输出波形。本实验中积分电路取 $R = 10 "kΩ"$、$C = 0.1 "μF"$，故 $R C = 1 "ms"$，大于输入信号半周期 $0.5 "ms"$，输出波形接近三角波，表现出较明显的积分特性；微分电路取 $R = 1 "kΩ"$、$C = 0.01 "μF"$，故 $R C = 10 "μs"$，远小于输入信号半周期，输出波形为正、负尖脉冲。实验误差主要来源于元件参数误差、示波器读数误差、信号源输出内阻以及导线连接接触不良等因素。
experiment3/亓涵玉202502320021.pdf
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