共模电压和差模电压

共模电压(common mode voltage):在每一导体和所规定的参照点之间(往往是大地或机架)出现的相量电压的平均值。或者说同时加在电压表两测量端和规定公共端之间的那部分输入电压。
差模电压(differential mode voltage):一对导线上电压的差值;
共模、差模正是“输入信号”整体的属性,差分输入可以表示为 vi = (vi+ , vi-); 也可以表示为vi = (vic, vid)c 表示共模,d 表示差模。两种描述是 完全等价的。只不过换了一个认识角度,就像几何学里的坐标变换,同一个点在不同坐标系中的坐标值不同,但始终是同一个点。

Signal-Mode Definitions
Electrical signals carried on cables can be described as normal mode, differential mode, or common mode.
  • A normal-mode signal is any type (other than common mode) that appears between a pair of wires, or on a single wire referenced to (or returned through) the earth, chassis, or shield. Normal-mode signals are read between two wires in a balanced or unbalanced transmission path. (For a balanced 2-wire path, one wire is driven positive while the other is driven negative by an equal amount, both with respect to a static or no-signal condition in which both lines assume the same voltage level relative to circuit common.)
  • A differential-mode signal appears differentially on a pair of wires in an ungrounded cable configuration.
  • A common-mode signal appears equally (with respect to local circuit common) on both lines of a 2-wire cable not connected to earth, shield, or local common. Usually, but not always, this is an unwanted signal that should be rejected by the receiving circuit. Common-mode voltage (VCM) is expressed mathematically as the average of the two signal voltages with respect to local ground or common:  Vcm = (Va+Vb)/2

Figure shows a 3V differential-mode signal riding on a 2.5V common-mode signal. The DC offset is typical of differential-mode data transmitters operating from a single supply. The common-mode voltage can be AC, DC, or a combination of AC and DC. (Figure represents the simplest case, a DC common-mode voltage with no AC component.)  

   

### 运算放大器输入端共模电压电压概念 #### 共模电压定义 对于运算放大器而言,当两个输入端之间的压很小的情况下,任意一个输入端的电压几乎等于这两个输入端电压的平均值。这种情况下测量到的电压称为共输入电压[^1]。 #### 电压定义 电压指的是运放两输入端之间存在的电位异。这是运放用来执行信号处理的主要参数之一,即实际被放大的部分就是这个分量[^2]。 ### 计算方法 #### 共模电压计算公式 假设正相输入端(IN+) 反相输入端(IN-) 的电压分别为 \( V_{in+} \) \( V_{in-} \),则共模电压 \( V_{CM} \) 可以通过下面的公式来表示: \[ V_{CM} = \frac{V_{in+} + V_{in-}}{2} \] 此表达式表明了如何基于两端口网络理论中的节点分析法求得共成分。 #### 电压计算公式 而电压 \( V_{DM} \) 则由下述关系给出: \[ V_{DM} = V_{in+} - V_{in-} \] 这代表了理想状态下运放所感知并加以放大的那部分信号变化。 ```python def calculate_common_mode_voltage(V_in_plus, V_in_minus): """Calculate common mode voltage.""" return (V_in_plus + V_in_minus) / 2 def calculate_differential_voltage(V_in_plus, V_in_minus): """Calculate differential voltage.""" return abs(V_in_plus - V_in_minus) # Example usage with given values from the reference material example_V_in_plus = 48 # Volts example_V_in_minus = 15 # Volts common_mode_volt_example = calculate_common_mode_voltage(example_V_in_plus, example_V_in_minus) differential_volt_example = calculate_differential_voltage(example_V_in_plus, example_V_in_minus) print(f"Common Mode Voltage: {common_mode_volt_example:.1f}V") print(f"Differential Voltage: {differential_volt_example:.0f}V") ```
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