低噪声电路设计

Time vs frequency domain - 3
• Phase difference between two signals can be clearly seen in time domain. • However, in frequency domain, they are almost identical. • Power spectrum does not convey the phase information.
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I n,rms
1 T 2 in (t )dt T 0
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T – Time during which the noise is observed
Noise presentation in frequency-domain
Mean squared value (total noise power):
Noise summation
Vno t Vn1 t Vn 2 t
Vn1(t ) Vn0(t )
2 Vno ,rms
(Vn1 and Vn2 are not correlated)
Vn2(t )
1 T 2 V ( t ) V ( t ) dt n 1 n 2 0 T 2 T 2 2 Vn1,rms Vn 2,rms Vn1 (t ) Vn 2 (t )dt T 0 Vn21,rms Vn22,rms
Signal-to-noise ratio (SNR) Noise figure (NF)
Signal-to-niose ratio (SNR):
P SNR ( dB ) 10 log s Pn
Vn,rms 0.5 10
60 20
0.5mV
Performance evaluation
Input referred noise (equivalent input noise)
RS
In1 Vs Vin Zin In2 Vn
1
v0 Av vin
Vn
2
V0
v0 Zin Av Av ,ov vs Rs Zin
Low-Noise Circuit Design
Xu Yong Ping
Dept of Electrical & Computer Engineering National University of Singapore
Outline
1. 2. 3. 4. Basics of noise analysis Noise sources and models Noise analysis Noise reduction techniques
•
It is quite different result if the signal is observed in the frequency-domain through Fourier Transformation (FFT). Its spectral contents are clearly seen.
V2nw
V2nw
V
2 no ,rms
2 2 Vnw Vnw f 0 df 2 2 0 1 f f0

f0
f
fe
f
Equivalent noise bandwidth:
f eq
f0 2
q
Equivalent noise bandwidth (cont’d)
For second-order lowpass system:
2 Vn2,rms vn (n)f n 1
Noise power
Resolution BW
Noise power

Noise spectrum
f
1 2 3 4 5 6
n
Equivalent noise bandwidth
White noise Vni(f )
H(s)
Vno ( f ) H ( j 2f ) V ( f )
t
Average noise power:
Pn ,av lim
1 T T

T
0
2 vn (t )dt
Pn ,av lim
1 T T

T
0
2 in (t )dt
rms noise voltage or current: Vn,rms
1 T 2 vn (t )dt T 0
20log(103 ) 20log(0.2236) 60 13.01 46.99dBm
0dBm
V 20log s ,rms 16.99dB 0.2236
Vs,rms (max) 10
16.99 20
0.2236 0.0316 V
* dBm value depends on the load resistance
Vno ,rms Vn2 Vn22 ,rms 1,rms
In0(t)
Similarly,
In1(t) In2(t)
2 2 2 I no I I , rms n1, rms n 2, rms
I no ,rms I n21,rms I n22 ,rms
Noise measures
Noisy circuit
Noisy circuit
vn0 Av,ov vni
2 Z in 2 2 2 2 vni v v i R Z 1 n ,th n ,rms n ,rms s in Rs Z in
2
2
v Av vni1 A v
2 no 2 v
2 n ,th
2 ni

2
ቤተ መጻሕፍቲ ባይዱ

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V2nw
Filtered out
f0
f
White noise
V2nw
f 0dB
Single-pole transfer function
H ( j 2f )
1 f 2 1 f 0
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f0
f
The total output noise power is
Noise presentation in time-domain
(Referring to random noise)
Vn2,rm s Pn Vn2,rm s 1
2 2 Pn I n , rms 1 I n, rms
noise
Normalized noise power:
– dBc
• Measured with reference to the power of carrier, which is 0dBc
Examples
dBm:
Find the rms voltage of a 0-dBm signal referenced to a 50- resistor. What is the level in dBm of a noise with 1 mV (rms) ? If the maximum SNR is 30 dBm, what is the maximum signal strength in Vrms? Solution: 0 dBm corresponds to
Vn,th – Thermal noise from the signal source
Noisy circuit
Input referred noise
RS Vn,t
h
Vn,rms In,rms Vni
1
RS
Zin
Noiseless circuit
Vno
Vni
Vni1
Zi
n
Noiseless circuit
Maximum signal strength in dBm
Vrms R P 50 1mW 0.2236 V
dBm corresponds to a noise of 1mV(rms):
Ps,max 30 (46.99) 16.99dBm
Maximum signal strength in Vrms
20log1 106 20log2 120 6 126dBv
dBc:
If a carrier signal is 0.5V rms and the noise is -60dBc, what is the rms noise level? Solution:
Vn ,rms 20log 60dB 0 . 5
V
2 n ,rms
0 V ( f )df
2 n

2 2 In I , rm s 0 n ( f )df

V2n,rms(f ) and I2n,rms (f ) are the power spectral density (V2/Hz or A2/Hz)
Understand noise spectrum:
v
2 n ,rms
2 2 in R Z Av2in R Z ,rms s in s Z in
2 vno 2 2 2 2 2 2 2 v 2 vn ,th vn ,rms in ,rms Rs 4kTRs f vn ,rms in ,rms Rs Av ,ov 2 ni
Input referred noise
Noise equivalent circuit:
RS Vn,t
h
Vn,rms
In,rms
RS Noiseless circuit
Outpu t
Vs
Inpu t
Vni
Vs
Input
Zi
n
Noiseless circuit
Outpu Vno t
Noisy circuit
Examples (cont’d)
dBv:
What is the noise level in dBv if the measured noise is 1mV rms and 0dBv is corresponding to a 2-V rms signal? 0dB Solution: The noise level is
Noise definition
• Any unwanted signals or interferences to the desired signal can be considered as noise. • Examples
– Random interferences (thermal noise) – Toned interference (50/60Hz from main, dc offset) – Spectral interference (flicker noise, aliasing) – Mixed interference (inter-modulation)
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f eq 1.05 f0
Time vs frequency domain - 1
V
P
f f3 f0 0 f1 f2 t
Time vs frequency domain - 2
• None of the signals cannot be identified except for a slight DC offset.
• Noise power is often measured with different references
– dBm
• Noise power of 1mW -> 0dBm
– dBv
• Measured with reference to a given voltage level which is defined as 0dBv
H ( j 2f )
1 f 4 1 f 0
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feq 1.11 f0
For third-order lowpass system:
H ( j 2f )
1 f 6 1 f 0
1. Basics of Noise Analysis
Outline



Noise definition Noise presentation in time domain Noise presentation in frequency domain Noise measures Performance evaluation