SOR
312 lines
13 KiB
Python
312 lines
13 KiB
Python
import math
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from decimal import Decimal
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from utils import (
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scientific_round,
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calculate_stats,
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input_decimal,
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input_int
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)
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"""
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Wheatstone Bridge Resistance Measurement Calculator
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电桥法测量电阻计算器
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参考了表面张力系数计算器的高精度与不确定度修约逻辑。
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公式说明:
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1. 惠斯通电桥平衡条件 (Bridge Balance Equation):
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当检流计示数为零时，电桥平衡：
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Rx / R0 = R1 / R2
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即:
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Rx = R0 * (R1 / R2) （也写作 Rx = R0 * C，C = R1/R2 为比例臂比值）
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其中:
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Rx : 待测电阻
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R0 : 比较臂标准电阻（电桥读数）
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R1/R2 : 比例臂之比，取 1:1, 1:10, 10:1
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2. 灵敏度公式 (Bridge Sensitivity):
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S = Δn / (ΔR0 / R0)
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其中:
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S : 电桥灵敏度（格/相对变化量）
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Δn : 检流计偏转格数（通常取 5 小格）
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ΔR0 : 使检流计偏转 Δn 格时 R0 的改变量
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ΔR0 = |R0' - R0|，R0' 为偏转 5 格时的读数
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R0 : 平衡时的标准电阻读数
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也可写为:
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S = Δn * R0 / ΔR0
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3. 不确定度传递公式 (Uncertainty Propagation):
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Rx = R0 * C (C 为比例臂比值)
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(a) R0 的不确定度:
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u(R0) = sqrt( u_A(R0)^2 + u_B(R0)^2 )
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其中:
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u_A(R0) = s(R0) / sqrt(n) (A 类不确定度, s 为标准偏差)
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u_B(R0) = Δ_inst / sqrt(3) (B 类不确定度, Δ_inst 为仪器误差限)
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(b) 仪器误差限 Δ_inst 的确定 (与灵敏度有关):
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Δ_inst = R0 / S
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即由灵敏度决定的电桥最小可分辨电阻变化量
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(c) 比例臂 C 视为精确值（标准电阻箱），则:
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u(Rx) = C * u(R0)
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(d) 相对不确定度:
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u_r(Rx) = u(Rx) / Rx = u(R0) / R0
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(e) 修约规则:
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不确定度保留一位有效数字，四舍六入五凑偶
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Rx 末位与不确定度对齐
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"""
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def measure_one_ratio(ratio_label, C_value, R_nominal, n_measurements):
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"""
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对单一比例臂进行测量与分析
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参数:
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ratio_label: 比例臂标签，如 "1:1"
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C_value: 比例臂比值 C = R1/R2
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R_nominal: 标定电阻标称值 (Ω)
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n_measurements: 测量次数
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"""
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C = Decimal(str(C_value))
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print(f"\n{'─'*50}")
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print(f" 比例臂 Rx:R0 = {ratio_label}，比例因子 C = {C_value}")
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print(f" 标定电阻标称值: {R_nominal} Ω")
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print(f"{'─'*50}")
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# --- 输入平衡时的 R0 读数 ---
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print(f"\n请输入 {n_measurements} 次平衡时的 R0 读数 (Ω):")
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R0_data = []
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for i in range(n_measurements):
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while True:
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try:
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val = input(f" 第 {i+1} 次 R0 = ").strip()
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if not val: continue
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R0_data.append(Decimal(val))
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break
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except Exception:
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print(" 输入无效，请输入数字。")
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# --- 输入偏差 5 小格时的 R0' ---
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print(f"\n请输入偏转 5 小格时的 R0' 读数 (Ω):")
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R0_prime = input_decimal(" R0'")
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delta_n = Decimal("5") # 检流计偏转格数
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# --- 计算 R0 的平均值 ---
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R0_mean = sum(R0_data) / Decimal(len(R0_data))
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# --- 计算灵敏度 ---
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# S = Δn * R0 / |R0' - R0|
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delta_R0 = abs(R0_prime - R0_mean)
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if delta_R0 == 0:
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print(" ⚠ 警告: R0' = R0，无法计算灵敏度，请检查数据！")
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S = Decimal("Infinity")
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delta_inst = Decimal("0")
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else:
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S = delta_n * R0_mean / delta_R0
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# 仪器误差限 (由灵敏度决定)
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# Δ_inst = R0 / S = |R0' - R0| / Δn = ΔR0 / 5
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delta_inst = R0_mean / S
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# --- 不确定度分析 ---
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R0_mean_final, u_R0, u_a_R0, u_b_R0, _ = calculate_stats(R0_data, str(delta_inst))
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# Rx = C * R0
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Rx_mean = C * R0_mean_final
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u_Rx = C * u_R0
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# 相对不确定度
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if Rx_mean != 0:
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u_r_Rx = u_Rx / Rx_mean
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else:
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u_r_Rx = Decimal("0")
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# --- 修约 ---
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Rx_final, u_Rx_final = scientific_round(Rx_mean, u_Rx)
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# --- 输出结果 ---
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print(f"\n{'═'*50}")
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print(f" 结果 (比例臂 {ratio_label}, 标定 {R_nominal} Ω)")
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print(f"{'═'*50}")
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# 打印 R0 测量数据表
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print(f"\n R0 测量数据:")
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for i, val in enumerate(R0_data):
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print(f" 第 {i+1} 次: {val} Ω")
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print(f"\n R0 平均值 = {R0_mean_final:.4f} Ω")
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print(f" R0' = {R0_prime} Ω")
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print(f" ΔR0 = |R0'-R0| = {delta_R0:.4f} Ω")
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print(f" 偏转格数 Δn = {delta_n} 格")
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print(f"{'─'*50}")
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print(f" 灵敏度 S = Δn·R0/ΔR0 = {S:.2f}")
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print(f" 仪器误差限 Δ_inst = R0/S = {delta_inst:.4f} Ω")
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print(f"{'─'*50}")
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print(f" u_A(R0) = {u_a_R0:.6f} Ω")
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print(f" u_B(R0) = {u_b_R0:.6f} Ω")
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print(f" u(R0) = {u_R0:.6f} Ω")
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print(f"{'─'*50}")
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print(f" Rx = C × R0 = {C} × {R0_mean_final:.4f} = {Rx_mean:.4f} Ω")
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print(f" u(Rx) = C × u(R0) = {u_Rx:.6f} Ω")
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print(f" 相对不确定度 u_r = {u_r_Rx*100:.2f}%")
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print(f"{'─'*50}")
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print(f" ★ 最终结果: Rx = {Rx_final} ± {u_Rx_final} Ω")
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print(f"{'═'*50}")
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return {
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"ratio_label": ratio_label,
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"C": C,
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"R_nominal": R_nominal,
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"R0_data": R0_data,
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"R0_mean": R0_mean_final,
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"R0_prime": R0_prime,
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"delta_R0": delta_R0,
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"S": S,
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"delta_inst": delta_inst,
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"u_a_R0": u_a_R0,
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"u_b_R0": u_b_R0,
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"u_R0": u_R0,
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"Rx_mean": Rx_mean,
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"u_Rx": u_Rx,
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"u_r_Rx": u_r_Rx,
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"Rx_final": Rx_final,
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"u_Rx_final": u_Rx_final
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}
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def main():
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print("════════════════════════════════════════════════")
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print(" 电桥法测量电阻计算器 (Wheatstone Bridge)")
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print("════════════════════════════════════════════════")
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print()
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print("实验原理:")
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print(" 惠斯通电桥平衡条件: Rx = R0 × C (C = R1/R2)")
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print(" 灵敏度: S = Δn × R0 / ΔR0")
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print(" 不确定度: u(Rx) = C × u(R0), u(R0) = √(u_A² + u_B²)")
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print()
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# --- 1. 基本参数 ---
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n_meas = input_int("每组测量次数 n", default=5)
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# --- 2. 定义测量方案 ---
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# 标定电阻: 10kΩ 和 2kΩ
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# 比例臂: 1:1, 1:10, 10:1
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# 注意: 2kΩ 不会有 1:10 的比例臂 (因为 R0 = Rx/(C) 会超出电阻箱量程)
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calibration_plan = [
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# (标定电阻标称值, 比例臂标签, C 值)
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# ---- 10kΩ 标定 ----
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("10000", "1:1", 1),
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("10000", "10:1", 10),
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# ---- 2kΩ 标定 ----
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("2000", "1:1", 1),
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("2000", "10:1", 10),
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# ---- 200Ω 标定 ----
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("200", "1:1", 1),
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("200", "1:10", 0.1),
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("200", "10:1", 10),
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]
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print(f"\n{'━'*55}")
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print(" 测量方案如下:")
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print(f"{'━'*55}")
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print(f" {'序号':<6}{'标定电阻':>10}{'比例臂 Rx:R0':>14}{'C = R1/R2':>12}")
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print(f" {'─'*46}")
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for idx, (R_nom, ratio, C_val) in enumerate(calibration_plan, 1):
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print(f" {idx:<6}{R_nom + ' Ω':>10}{ratio:>14}{C_val:>12}")
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print(f"{'━'*55}")
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print()
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print(" 注: 2kΩ 标定不进行 1:10 比例臂测量")
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print(" (R0 = 2000/0.1 = 20000 Ω，超出电阻箱量程)")
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print()
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# --- 3. 逐项测量 ---
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all_results = []
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for idx, (R_nom, ratio_label, C_val) in enumerate(calibration_plan, 1):
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print(f"\n{'▓'*55}")
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print(f" 第 {idx} 组: 标定 {R_nom} Ω，比例臂 Rx:R0 = {ratio_label}")
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print(f"{'▓'*55}")
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result = measure_one_ratio(ratio_label, C_val, R_nom, n_meas)
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all_results.append(result)
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if idx < len(calibration_plan):
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input("\n按回车继续下一组测量...")
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# --- 4. 汇总表 ---
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print("\n")
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print("╔══════════════════════════════════════════════════════════════════════════════╗")
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print("║ 测 量 结 果 汇 总 表 ║")
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print("╠══════════════════════════════════════════════════════════════════════════════╣")
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header = (f" {'标定':>6} {'比例臂':>8} {'R0均值(Ω)':>12} "
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f"{'S(灵敏度)':>10} {'Δ_inst(Ω)':>10} "
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f"{'Rx(Ω)':>12} {'u(Rx)(Ω)':>10} {'u_r(%)':>8}")
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print(header)
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print(f" {'─'*74}")
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for res in all_results:
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S_str = f"{res['S']:.1f}" if res['S'] != Decimal("Infinity") else "∞"
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line = (f" {res['R_nominal']:>6} {res['ratio_label']:>8} "
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f"{res['R0_mean']:>12.4f} {S_str:>10} "
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f"{res['delta_inst']:>10.4f} "
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f"{res['Rx_mean']:>12.4f} {res['u_Rx']:>10.6f} "
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f"{res['u_r_Rx']*100:>7.2f}%")
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print(line)
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print("╚══════════════════════════════════════════════════════════════════════════════╝")
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# --- 5. 灵敏度分析总结 ---
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print("\n")
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print("┌──────────────────────────────────────────────┐")
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print("│ 灵 敏 度 分 析 总 结 │")
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print("├──────────────────────────────────────────────┤")
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for res in all_results:
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S_str = f"{res['S']:.2f}" if res['S'] != Decimal("Infinity") else "∞"
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print(f"│ 标定 {res['R_nominal']:>5}Ω 比例臂 {res['ratio_label']:>4} "
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f"S = {S_str:>8} │")
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print("├──────────────────────────────────────────────┤")
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# 找灵敏度最大和最小
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finite_results = [r for r in all_results if r['S'] != Decimal("Infinity")]
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if finite_results:
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best = max(finite_results, key=lambda r: r['S'])
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worst = min(finite_results, key=lambda r: r['S'])
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print(f"│ 最高灵敏度: 标定{best['R_nominal']:>5}Ω 比例臂{best['ratio_label']:>4} │")
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print(f"│ S = {best['S']:.2f} │")
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print(f"│ 最低灵敏度: 标定{worst['R_nominal']:>5}Ω 比例臂{worst['ratio_label']:>4} │")
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print(f"│ S = {worst['S']:.2f} │")
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print("├──────────────────────────────────────────────┤")
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print("│ 分析: │")
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print("│ · 灵敏度 S 越大，测量精度越高 │")
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print("│ · S = Δn·R0/ΔR0 │")
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print("│ · 比例臂比值影响灵敏度 │")
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print("│ · 合理选择比例臂可优化测量精度 │")
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print("└──────────────────────────────────────────────┘")
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# --- 6. 最终修约结果汇总 ---
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print("\n")
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print("╔═══════════════════════════════════════════════════╗")
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print("║ 最 终 结 果 (修约后) ║")
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print("╠═══════════════════════════════════════════════════╣")
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for res in all_results:
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print(f"║ 标定 {res['R_nominal']:>5}Ω 比例臂 {res['ratio_label']:>4}: ║")
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print(f"║ Rx = {res['Rx_final']} ± {res['u_Rx_final']} Ω ║")
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print(f"║ (相对不确定度 {res['u_r_Rx']*100:.2f}%) ║")
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print(f"╟───────────────────────────────────────────────────╢")
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print("╚═══════════════════════════════════════════════════╝")
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if __name__ == "__main__":
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main()
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