以阻值R=120Ω、灵敏度Sg=2的电阻丝应变片与阻值为120Ω的固定电阻组成电桥,供桥电压为3V,并假定负载电阻为无穷大,当应变片的应变为2με和2000με时,分别求出单臂、双臂电桥的输出电压,并比较两种情况下的电桥灵敏度
时间: 2023-12-06 13:43:01 浏览: 68
根据电桥原理,当电桥平衡时,电桥两侧的电势差为0,即:
R1/R2 = R3/R4
其中,R1和R2为电桥两侧的电阻,R3和R4为电桥对角线上的电阻。
假设电桥中的电阻为阻值为R的电阻丝应变片和一个阻值为120Ω的固定电阻,单臂电桥输出电压为:
U1 = 3 * R / (R + 120)
当应变片的应变为2με时,电阻丝的阻值变化为:
ΔR = R * Sg * ε = 120 * 2 * 10^-6 = 0.24Ω
此时,电桥的不平衡电压为:
U2 = 3 * ΔR / (R + 120)
双臂电桥输出电压为:
U3 = 3 * ΔR / R
当应变片的应变为2000με时,电阻丝的阻值变化为:
ΔR = R * Sg * ε = 120 * 2000 * 10^-6 = 0.24 * 10^3Ω
此时,电桥的不平衡电压为:
U4 = 3 * ΔR / (R + 120)
电桥的灵敏度为输出电压对应变的变化量的比值,即:
S = ΔU / Δε
单臂电桥的灵敏度为:
S1 = U2 / (Sg * ε) = 3 * ΔR / (R * Sg * ε) = 1/500
双臂电桥的灵敏度为:
S2 = U4 / (Sg * ε) = 3 * ΔR / (R * Sg * ε) = 1/500
可以发现,单臂电桥和双臂电桥的输出电压和灵敏度是相同的。但是,单臂电桥的不平衡电压随着电桥电压的变化而变化,而双臂电桥的不平衡电压不受电桥电压变化的影响。因此,双臂电桥比单臂电桥更适用于精密测量。
相关问题
4.采用阻值为12052 的应变片与阻值为1200的固定电阻组成电桥电路,应变片灵敏度K=2,桥路供电电压为8V,当应变片产生1x10-6ε应变时,试求惠斯通电桥、半桥以及全桥工作时的输出电压。
根据电桥电路的原理,当电桥平衡时,输出电压为0。当电桥不平衡时,输出电压为:
Vout = Vin * (R2/R1) * (1/(1+K*ε))
其中,Vin为桥路供电电压,R1和R2为固定电阻的阻值,K为应变片的灵敏度,ε为应变片的应变值。
对于采用阻值为12052的应变片与阻值为1200的固定电阻组成的电桥电路,应变片灵敏度K=2,桥路供电电压为8V,当应变片产生1x10-6ε应变时,可以计算出:
- 惠斯通电桥工作时的输出电压为:Vout = 0
- 半桥工作时的输出电压为:Vout = Vin * (R2/R1) * (1/(1+K*ε)) = 8 * (1200/12052) * (1/(1+2*1x10-6)) ≈ 0.0006V
- 全桥工作时的输出电压为:Vout = Vin * (R2/R1) * (2Kε/(1+2Kε)) = 8 * (1200/12052) * (2*2*1x10-6/(1+2*2*1x10-6)) ≈ 0.0012V
因此,当应变片产生1x10-6ε应变时,半桥和全桥工作时的输出电压分别为0.0006V和0.0012V。
E96 贴片电阻丝印与阻值对照表
以下是E96贴片电阻丝印与阻值对照表(单位:Ω):
<table>
<tr>
<td>丝印</td>
<td>阻值</td>
<td>丝印</td>
<td>阻值</td>
<td>丝印</td>
<td>阻值</td>
</tr>
<tr>
<td>01C</td>
<td>100</td>
<td>18C</td>
<td>18.2</td>
<td>35C</td>
<td>35.7</td>
</tr>
<tr>
<td>02C</td>
<td>102</td>
<td>19C</td>
<td>18.7</td>
<td>36C</td>
<td>36.5</td>
</tr>
<tr>
<td>03C</td>
<td>105</td>
<td>20C</td>
<td>19.1</td>
<td>37C</td>
<td>37.4</td>
</tr>
<tr>
<td>04C</td>
<td>107</td>
<td>21C</td>
<td>19.6</td>
<td>38C</td>
<td>38.3</td>
</tr>
<tr>
<td>05C</td>
<td>110</td>
<td>22C</td>
<td>20.0</td>
<td>39C</td>
<td>39.2</td>
</tr>
<tr>
<td>06C</td>
<td>113</td>
<td>23C</td>
<td>20.5</td>
<td>40C</td>
<td>40.2</td>
</tr>
<tr>
<td>07C</td>
<td>115</td>
<td>24C</td>
<td>21.0</td>
<td>41C</td>
<td>41.2</td>
</tr>
<tr>
<td>08C</td>
<td>118</td>
<td>25C</td>
<td>21.5</td>
<td>42C</td>
<td>42.2</td>
</tr>
<tr>
<td>09C</td>
<td>121</td>
<td>26C</td>
<td>22.1</td>
<td>43C</td>
<td>43.2</td>
</tr>
<tr>
<td>10C</td>
<td>124</td>
<td>27C</td>
<td>22.6</td>
<td>44C</td>
<td>44.2</td>
</tr>
<tr>
<td>11C</td>
<td>127</td>
<td>28C</td>
<td>23.2</td>
<td>45C</td>
<td>45.3</td>
</tr>
<tr>
<td>12C</td>
<td>130</td>
<td>29C</td>
<td>23.7</td>
<td>46C</td>
<td>46.4</td>
</tr>
<tr>
<td>13C</td>
<td>133</td>
<td>30C</td>
<td>24.3</td>
<td>47C</td>
<td>47.5</td>
</tr>
<tr>
<td>15C</td>
<td>137</td>
<td>31C</td>
<td>24.9</td>
<td>48C</td>
<td>48.7</td>
</tr>
<tr>
<td>16C</td>
<td>140</td>
<td>32C</td>
<td>25.5</td>
<td>49C</td>
<td>49.9</td>
</tr>
<tr>
<td>18C</td>
<td>143</td>
<td>33C</td>
<td>26.1</td>
<td>51C</td>
<td>51.1</td>
</tr>
<tr>
<td>20C</td>
<td>147</td>
<td>34C</td>
<td>26.7</td>
<td>52C</td>
<td>52.3</td>
</tr>
<tr>
<td>22C</td>
<td>150</td>
<td>35C</td>
<td>27.4</td>
<td>53C</td>
<td>53.6</td>
</tr>
<tr>
<td>24C</td>
<td>154</td>
<td>36C</td>
<td>28.0</td>
<td>54C</td>
<td>54.9</td>
</tr>
<tr>
<td>27C</td>
<td>158</td>
<td>37C</td>
<td>28.7</td>
<td>56C</td>
<td>56.2</td>
</tr>
<tr>
<td>30C</td>
<td>162</td>
<td>38C</td>
<td>29.4</td>
<td>57C</td>
<td>57.6</td>
</tr>
<tr>
<td>33C</td>
<td>169</td>
<td>39C</td>
<td>30.1</td>
<td>59C</td>
<td>59.0</td>
</tr>
<tr>
<td>36C</td>
<td>174</td>
<td>40C</td>
<td>30.9</td>
<td>60C</td>
<td>60.4</td>
</tr>
<tr>
<td>39C</td>
<td>178</td>
<td>41C</td>
<td>31.6</td>
<td>61C</td>
<td>61.9</td>
</tr>
<tr>
<td>43C</td>
<td>182</td>
<td>42C</td>
<td>32.4</td>
<td>63C</td>
<td>63.4</td>
</tr>
<tr>
<td>47C</td>
<td>187</td>
<td>43C</td>
<td>33.2</td>
<td>64C</td>
<td>64.9</td>
</tr>
<tr>
<td>51C</td>
<td>191</td>
<td>44C</td>
<td>34.0</td>
<td>66C</td>
<td>66.5</td>
</tr>
<tr>
<td>56C</td>
<td>196</td>
<td>45C</td>
<td>34.8</td>
<td>68C</td>
<td>68.1</td>
</tr>
<tr>
<td>62C</td>
<td>200</td>
<td>46C</td>
<td>35.7</td>
<td>69C</td>
<td>69.8</td>
</tr>
<tr>
<td>68C</td>
<td>205</td>
<td>47C</td>
<td>36.5</td>
<td>71C</td>
<td>71.5</td>
</tr>
<tr>
<td>75C</td>
<td>210</td>
<td>48C</td>
<td>37.4</td>
<td>73C</td>
<td>73.2</td>
</tr>
<tr>
<td>82C</td>
<td>215</td>
<td>49C</td>
<td>38.3</td>
<td>75C</td>
<td>75.0</td>
</tr>
<tr>
<td>91C</td>
<td>221</td>
<td>51C</td>
<td>39.2</td>
<td>76C</td>
<td>76.8</td>
</tr>
<tr>
<td>100C</td>
<td>226</td>
<td>52C</td>
<td>40.2</td>
<td>78C</td>
<td>78.7</td>
</tr>
<tr>
<td>110C</td>
<td>232</td>
<td>53C</td>
<td>41.2</td>
<td>80C</td>
<td>80.6</td>
</tr>
<tr>
<td>120C</td>
<td>237</td>
<td>54C</td>
<td>42.2</td>
<td>82C</td>
<td>82.5</td>
</tr>
<tr>
<td>130C</td>
<td>243</td>
<td>56C</td>
<td>43.2</td>
<td>84C</td>
<td>84.5</td>
</tr>
<tr>
<td>150C</td>
<td>249</td>
<td>57C</td>
<td>44.2</td>
<td>86C</td>
<td>86.6</td>
</tr>
<tr>
<td>160C</td>
<td>255</td>
<td>59C</td>
<td>45.3</td>
<td>88C</td>
<td>88.7</td>
</tr>
<tr>
<td>180C</td>
<td>261</td>
<td>60C</td>
<td>46.4</td>
<td>90C</td>
<td>90.9</td>
</tr>
<tr>
<td>200C</td>
<td>267</td>
<td>61C</td>
<td>47.5</td>
<td>93C</td>
<td>93.1</td>
</tr>
<tr>
<td>220C</td>
<td>274</td>
<td>63C</td>
<td>49.9</td>
<td>95C</td>
<td>95.3</td>
</tr>
<tr>
<td>240C</td>
<td>280</td>
<td>64C</td>
<td>51.1</td>
<td>97C</td>
<td>97.6</td>
</tr>
<tr>
<td>270C</td>
<td>287</td>
<td>66C</td>
<td>53.6</td>
<td>100C</td>
<td>100</td>
</tr>
</table>