关键词: noise factor, noise figure, noise-figure analysis, receivers, cascaded, Friis equation, direct conversion, zero-IF, low-IF, Y-factor, noise temperature, SSB, DSB, mixer as DUT, mixer noise figure, noise folding, Boltzmann constant

 设计指南5594

# 现代无线电接收机的系统噪声系数分析

 Charles Razzell, 执行总监

#### 混频器噪声的概念模型

 NA = NSGS + NIGI + NIF (式. 1)

#### 噪声系数定义

 F = (SNRIN)/(SNROUT) (式. 2)

 NF = 10log10(F) (式. 3)

 (式. 4)

### 单边带噪声因子

(两端口变送器的)噪声因子。标准噪声温度(290K)时，在规定输入频率下，1)输出端口上对应输出频率下单位带宽总噪声功率与2)其中由输入端点在输入频率下产生的部分之比。

 (式. 5)

 (式. 6)

 (式. 7)

 (式. 8)

 (式. 9)

### 双边带噪声系数

 (式. 10)

 FDSB = 1 + (NA/(2kT0GS)) (式. 11)

 FSSB = 2 + NA/(kT0GS) (式. 12)

### 基线案例：线性电路模块的级联

 NOUT = kT0G1G2G3 + NA1 G2G3 + NA2G3 + NA3 (式. 13)

 NOT = kT0G1G2G3 (式. 14)

 (式. 15)

 (式. 16)

 (式. 17)

### 外差式转换级

 表1. 仿真的级联性能* 器件 CF (MHz) CNP (dBm) Gain (dB) CG (dB) CNF (dB) CWSource_1 2000 -113.975 0 0 0 BPF_Butter_1 2000 -113.975 -7.12E-04 -7.12E-04 6.95E-04 BasicMixer_1 2 -97.965 10 9.999 6.011
*滤波器无镜像抑制。

 表2. 仿真的级联性能* 器件 CF (MHz) CNP (dBm) Gain (dB) CG (dB) CNF (dB) CWSource_1 2000 -113.975 0 0 0 BPF_Butter_1 2000 -113.975 -7.12E-04 -7.12E-04 6.95E-04 BasicMixer_1 250 -99.218 10 9.999 4.758
*滤波器具有显著的镜像抑制。

 (式. 18)

 NA = 2kT0GS(10(3/10) - 1) (式. 19)

 NOUT = 2kT0GS(10(3/10) - 1) + kT0GS (式. 20)

 (式. 21)

 NF = 10log10(2(10(3/10) - 1) + 1) = 4.757dB (式. 22)

 FSSBe = 2(FDSB – 1) + 1 + α (式. 23)

### 外差式接收机

 表3. 系统中外差式混频器的仿真级联性能 器件 CF (MHz) CNP (dBm) Gain (dB) SNF (dB) CG (dB) CNF (dB) CWSource_1 2000 -113.975 0 0 0 0 Lin_1 2000 -100.975 10 3 10 3 BPF_Butter_1 2000 -100.976 -7.12E-04 7.12E-04 9.999 3 BasicMixer_1 250 -90.563 10 3 19.999 3.413 Lin_2 250 -61.695 25 25 44.999 7.281

### 零中频接收机

More detailed image
(PDF, 291kB)

 表4. ZIF接收机配置* 器件 CF (MHz) CP (dBm) CNP (dBm) Gain (dB) SNF (dB) CG (dB) CNF (dB) MultiSource_1 950 -79.999 -116.194 0 0 0 0 FE_BPF 950 -80.009 -116.194 -9.99E-03 1.00E-02 -9.99E-03 9.99E-03 Lin_1 950 -70.008 -103.194 10 3 9.99 3.01 Split2_1 950 -73.018 -105.992 -3.01 3.01 6.98 3.222 BasicMixer_1 0 -67.039 -99.425 5.979 4 12.959 3.81 LPF1 0 -67.04 -99.425 -8.23E-04 1.00E-02 12.958 3.81 Lin_2 0 -57.036 -83.078 9.995 25 22.953 10.163 LPF2 0 -57.038 -83.08 -1.90E-03 1.00E-02 22.951 10.163
*表格中列出的项目有通道频率(CF)、通道功率(CP)、级增益(GAIN)、级噪声系数(SNF)、级联增益(CGAIN)和级联噪声系数(CNF)。

 表5. 弗林斯级联公式计算结果 器件 F (dB) Gain (dB) CG (dB) CNF (dB) BPF滤波器 0.01 -0.01 -0.01 0.01 LNA 3 10 9.99 3.01 分配器 3.01 -3.01 6.98 3.22 混频器 4 5.979 12.96 3.81 LPF1 0.01 -0.01 12.95 3.81 VGA 25 9.995 22.94 12.65 LPF2 0.01 -0.01 22.93 12.65

 NOUT = 2kT0G1G2G3 + 2NA1G2G3 + NA2G3 + NA3 (式. 24)

 NOT = 2kT0G1G2G3 (式. 25)

 (式. 26)

 F1 = 1 + NA1/(kT0G1), F2DSB = 1 + NA2/(2kT0G2), and F3 = 1 + NA3/(kT0G3) (式. 27)

 FDSB = F1 + (F2DSB - 1)/G1 + (F3 - 1)/(2G1G2) (式. 28)

 表6. DSB级联公式的结果 Parts F (dB) Gain (dB) CG (dB) CNF (dB) BPF滤波器 0.01 -0.01 -0.01 0.01 LNA 3 10 9.99 3.01 分配器 3.01 -3.01 6.98 3.22 混频器 4 5.979 12.96 3.81 LPF1 0.01 -0.01 12.95 3.81 VGA 25 9.995 22.94 10.17 LPF2 0.01 -0.01 22.93 10.17

 表7. LIF接收机仿真结果 Parts CF (MHz) CP (dBm) CNP (dBm) Gain (dB) SNF (dB) CG (dB) CNF (dB) MultiSource_1 950.3 -79.999 -116.194 0 0 0 0 FE_BPF 950.3 -80.009 -116.194 -9.99E-03 1.00E-02 -9.99E-03 9.99E-03 Lin_1 950.3 -70.008 -103.194 10 3 9.99 3.01 Split2_1 950.3 -73.018 -105.992 -3.01 3.01 6.98 3.222 BasicMixer_1 0.3 -67.067 -96.335 5.938 4 12.918 6.94 LPF1 0.3 -68.467 -96.458 -1.64E-03 1.00E-02 12.916 6.819 Lin_2 0.3 -58.832 -80.068 9.969 25 22.885 13.241 LPF2 0.3 -58.483 -80.072 -4.68E-03 1.00E-02 22.88 13.241

 NOT = kT0G1G2G3 (式. 29)

 (式. 30)

 (式. 31)

 (式. 32)

(PDF，291kB)

 表8. LIF接收机镜像抑制仿真结果 Parts CF (MHz) CP (dBm) CNP (dBm) Gain (dB) SNF (dB) CG (dB) CNF (dB) MultiSource_1 950.3 -79.995 -116.194 0 0 0 0 FE_BPF 950.3 -80.005 -116.194 -9.99E-03 1.00E-02 -9.99E-03 9.99E-03 Lin_1 950.3 -70.004 -103.194 10 3 9.99 3.01 Split2_1 950.3 -73.014 -105.992 -3.01 3.01 6.98 3.222 BasicMixer_1 0.3 -67.053 -96.441 5.958 4 12.938 6.815 LPF1 0.3 -67.055 -96.443 -1.64E-03 1.00E-02 12.936 6.815 Lin_2 0.3 -57.047 -80.09 9.991 25 22.927 13.177 LPF2 0.3 -57.051 -80.094 -3.82E-03 1.00E-02 22.923 13.177 Split290_2 0.3 -54.062 -80.145 3.001 3.02 25.923 10.125

 表9. 推导公式汇总 结果 应用 级联噪声因子公式 三个增益模块 任意 外差式混频器 SSB，理想镜像滤波器 复合下变频器 ZIF 复合下变频器 LIF，无镜像抑制 复合下变频器 LIF，镜像抑制合成

#### 参考文献

1. For more information on Agilent’s mixer thermal noise model, see http://edocs.soco.agilent.com/display/genesys2010/MIXER_BASIC.
2. “IRE Standards on Electron Tubes: Definitions of Terms, 1957,” Proceedings of the IRE, vol. 45, pp. 983–1010, July 1957; http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4056638&isnumber=4056624.
3. Maas, S., Microwave Mixers, Artech House Microwave Library, Artech House, 1993.
4. “Telecommunications: Glossary of Telecommunication Terms,” Federal Standard 1037C, June 1991; www.its.bldrdoc.gov/fs-1037/fs-1037c.htm.
5. “Noise Figure Measurement Accuracy—The Y-Factor Method,” Agilent Technologies, Application Note 57–2, 2010; http://cp.literature.agilent.com/litweb/pdf/5952-3706E.pdf.

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 APP 5594: Apr 16, 2014 设计指南5594, AN5594, AN 5594, APP5594, Appnote5594, Appnote 5594