约翰逊噪声

JOHNSON NOISE

约翰逊噪声

约翰逊噪声也称为热噪声

关于电阻的非理想特性，最后一项内容是热噪声，也称为约翰逊噪声。其实这并不能称为完全意义上的非理想特性，它是电阻的固有性质，任何电阻器都不例外。

当温度在绝对零度以上，由于电荷载流子的热运动，所有电阻都有热噪声。热噪声的计算公式如下：

Vn= 4kTBR^0.5

其中k为波尔兹曼常数（1.38x10^23J/K），T为电阻的温度，B是带宽，R是电阻阻值。经验规则表明，1kohm电阻在室温下具有的噪声为4nV/Hz^1/2。

所有电阻器都有热噪声，由公式可知，可通过减小电阻、带宽或者温度的方法降低热噪声。由于噪声与绝对温度的平方根成正比，所以用降低温度的方法降低噪声通常没有明显效果。例如，将电阻的温度由室温（298K）降低到液态氮的温度（77K），热噪声仅下降50%。因此，如果希望用降低温度的方法降低热噪声，除非使用液态氦，否则效果不会很明显。

热噪声纯粹是电子热运动——电阻的体现。电抗器的热噪声等于其电抗中阻抗部分的热噪声，所以说理想电容器、理想电感器虽然有电抗，但是并没有热噪声。

电路中所有电阻产生的噪声及其带来的影响是总要考虑的问题。实际上，只有输入电路、反馈电路、高增益电路及前端电路的电阻才可能对总电路噪声有上述明显影响。

JOHNSON NOISE

A final "imperfection" of resistors is an inconvenience but cannot properly be regarded as an imperfection as it is a fundamental property of all resistors: thermal or Johnson noise.

At any temperature above absolute zero all resistors have noise due to thermal motion of their structure. This noise, which is described by

Vn= 4kTBR^0.5

(Where k is Boltzmann's constant: 1.38E- 23 J/K)

Johnson noise is present in ALL resistors and can only be reduced by reducing R, the resistance itself, B, the bandwidth of interest, or T, the temperature. Since the function involves a square root, the noise improvement for a drop in temperature from room temperature (298 oK) to liquid nitrogen (77 oK) is only of the order of 50%, so cooling a resistor, unless liquid helium is involved, is unlikely to be very profitable.

Johnson noise is purely an effect of resistance. The Johnson noise of complex impedances consists only of the Johnson noise of the resistive part of the impedance, so pure capacitance or inductance does not have Johnson noise, even though it has an impedance