Receiver Noise and sensitivity

1.1 Receiver Noise

在频率低于30MHz的时候，大气与环境的噪声占主导。因此从第一级放大器出来的noise相对显得并不是很重要。但是当频率达到VHF和UHF级别的时候，第一级放大器和接收机前端的任意滤波器就成为了接收机的噪声主要来源。如果我们考虑一个理想的“无噪声”接收机，那么它的sensitivity就完全由理论上的noise-floor决定。这可以由公式Pn= kTB (k为Boltzmann常数，T为Kelvin为单位的温度，B为系统bandwidth)，在标准环境温度17°C时，这个值通常是-174dBm每1Hz带宽。

                                Absolute noise floor at 17°C=-174dBm/Hz

从上面的公式，可以看到任何接收机系统的noise floor是由最终信号带宽决定的（i.e.解调器处的系统带宽）。当然在任何实际接收机中，接收机本身也会带来噪声，称作noise figure，这个noise figure必须被直接加到上面的影响里。

这里有必要详细说明下noise figure:

这是一个和天线直接相连的放大器的例子，假设天线与放大器都是Perfectly matched。测量带宽是25MHz，所以在-174dBm上加上74。在放大器输入端的噪声用kTB计算是-100dBm，这时的信号强度是-60dBm。因此输入端的C/N比为40dB。如果放大器是理想的那么它会将噪声与信号同时放大相同倍数，从而在输出端会有相同的C/N。而在实际中的放大器会加上一些自己的增益，在这个例子里，放大器的增益为20dB所以想好从-60dBm升到-40dBm。但是噪声却升高了30dB而不是20dB。所以C/N会跌到30dB因为放大器加上了10dB自身的噪声增益。

Noise Figure 被定义为：

                Noise Figure(NF) = 10log[输入端S/N比 /输出端S/N比]

对于一个完整的接收机系统，定义成下面这样更有用：

Noise Figure (NF) = （actual S/N dB at the output – S/N dB for a noise-free receiver）

如果我们考虑到实际上3dB的noise figure等于30%的最大视线范围的loss时，我们就会认识到保持noise figure到一个足够小的值是多么重要。

接收机的综合性能通常用最小接收信号（Mds）来定义，如：

Mds = -174 + NF + 10 (log BW), where BW is system bandwidth in Hz.

所以，对于一个给定的接收机如何去计算它的Mds呢？如下面的例子：

已知一个接收机的系统带宽为200kHz并且noise figure为5dB，那么：

        Mds=-174 + 5 + 10（log of 200000）=-174 + 5 +53 = -116dBm

注：这并不就等于接收机的灵敏度。在任何实际的系统里，解调的实现需要一个最小signal/noise比，也就是说信号比噪声要大多少才能被解调。在一个模拟系统中，S/N通常用SINAD（signal/noise and Distortion）表示典型值为12dB，而在数字系统内通常定义为carrier/noise ratio(C/N)其典型值为9dB。

在上面的例子里，如果它是一个数字接收机那么它的sensitivity为：

                                Receive sensitivity = -116 + 9 = -107dBm.

 

 

原文：

1.1. Receiver Noise

At frequencies below 30MHz, noise is predominantly atmospheric and environmental. The noise contribution from the first amplifier stage is therefore relatively unimportant. As the frequency reaches the VHF and UHF bands however, the first amplifier and any preceding filters become the dominant noise source in the receiver chain. If we consider an ideal ‘noise-free’ receiver, then the absolute sensitivity is limited by the theoretical noise-floor. This is determined by the expression P n  = kTB (where k is Boltzmann’s constant, T is temperature in degrees Kelvin and B is the system bandwidth) and, at a normal ambient temperature of 17°C, approximates to -174dBm in a 1Hz bandwidth.

Absolute noise floor at 17°C = -174dBm/Hz

From the above expression, it may be seen that the absolute noise floor of any receiver system is defined by the final signal bandwidth (i.e. system bandwidth at the demodulator). Also, in any practical receiver, the receiver itself will add to the noise and its Noise Figure must be added directly to the above figure. Noise Figure is defined as:

Noise Figure (NF) = 10 x log [S/N ratio at the input / S/N ratio at the output].

For a complete receiver system, this is more usefully defined as:

Noise Figure (NF) = (actual S/N dB at the output - S/N dB for a noise-free receiver).   [Equ. 1]

If we consider the fact that a 3dB noise figure equates to a 30% loss in maximum line-of-sight range, it may readily be seen that it is very important to keep the receiver noise figure to an absolute mini-mum.

The overall performance of a receiver system is usually defined by its minimum detectable signal, or‘Mds’ and is this is given by the following expression:

Mds = -174 + NF + 10 (log BW), where BW is system bandwidth in Hz.                   [Equ. 2]

Hence, to calculate the Mds for a given receiver, see the following example:

A receiver has a system bandwidth of 200kHz and a noise figure of 5dB. From equation 2 above:

Mds = -174 + 5 + 10 (log of 200,000) =  -174 + 5 + 53 = -116dBm.

Note that this is not the same as the receiver sensitivity. In any practical system, the demodulator requires a minimum signal/noise ratio. In an analogue system, this signal/noise is generally expressed as SINAD (Signal/Noise and Distortion) and is typically about 12dB, but for digital systems it is more usually defined as carrier/noise ratio (C/N) and is typically about 9dB.

In the above example, the sensitivity of a practical (digital) receiver is therefore given by:

Receiver sensitivity = -116 + 9 = -107dBm.