第四讲Noise 游飞博导，副教授 feiyou@uestc.edu.cn
第四讲 Noise 游飞 博导，副教授 feiyou@uestc.edu.cn
Noise as a random Process Figure 2.29.(a)Noise generated in a resistor,(b)effect of higher temperature. Ve R R 兽-wWw (a) b 1 Pn lim 2(0d. 0 Figure 2.30.Computation of noise power. n(t) n2(t) AYAAAba )))))))
Noise as a Random Process
Noise Spectrum Frequency-domain or statistical analysis is more interesting than time- domain for a random process Band-Pass Filter Power Meter Average Microphone 1 Hz Power Po x(t 10k方 10 kHz (a Band-Pass Filters Power 1 Hz Meters sx(f) 1 Hz x(t)o- 2 42 1 Hz (b) ))))
Noise Spectrum Frequency-domain or statistical analysis is more interesting than timedomain for a random process
Noise Spectrum Power conservation Equation 2.81 T 1 x20)d. Figure 2.32.Two-sided and one-sided spectra. [View full size image] Sx(n Sx(f) -f2-11051f2 0
Noise Spectrum Power conservation
Noise Spectrum Example 2.15. A resistor of value R1 generates a noise voltage whose one-sided PSD is given by Equation 2.82 S(f)=4kTR1. where k=1.38 x 10-23 J/K denotes the Boltzmann constant and Tthe absolute temperature. a.The area under S(f)appears to be infinite,an implausible result because the resistor noise arises from the finite ambient heat.In reality,Sv(f)begins to fall at f>1 THz,exhibiting a finite total energy,i.e.,thermal noise is not quite white. b.The dimension of Sv(f)is voltage squared per unit bandwidth(V2/Hz)rather than power per unit bandwidth (W/Hz).In fact,we may write the PSD as Equation 2.83 V牙=4kTR. V2 where n denotes the average power of Vn in 1 Hz. ))))
Noise Spectrum
Noise Spectrum c.For a 50-resistor at T=300 K, Equation 2.84 V=8.28×1019V2/Hz. Equation 2.85 V-0.91 nV/HZ. )
Noise Spectrum
Effect of Transfer Function on Noise Equation 2.86 S,(f月=Sr(H()2 Figure 2.33.Effect of low-pass filter on white noise. LPF
Effect of Transfer Function on Noise
Device Noise Thermal Noise of Resistors Figure 2.34.(a)Thevenin and (b)Norton models of resistor thermal noise. R 多R1 (a) (b) ))
Device Noise Thermal Noise of Resistors
Device Noise Thermal Noise of Resistors [View full size imagel Sv(n) 4kTR R,辛L自卡c,04虹⊙，辛L:复卡c1%) R (a) (b) (e) Equation 2.87 =22. ))))))
Device Noise Thermal Noise of Resistors
Device Noise Thermal Noise of Resistors If a resistor converts the ambient heat to a noise voltage or current,can we extract energy from the resistor? Figure 2.36.Transfer of noise from one resistor to another. oVout R2 suppose R2 is held at T=0 K. Equation2.88,2.89,2.90 P2= This quantity reaches a maximum if R2 R1: R2 Equation 2.91 R2 21 R1+R2 R2 PR2.max =kT. 4kT- RR2 R1+R2)P
Device Noise Thermal Noise of Resistors