Download Noise - MindMapped

𝑟𝑑 =
𝑘𝑇
𝑞𝐼𝐷𝐶
Noise current density, In
∴ 𝑉𝑛𝑜𝑖𝑠𝑒(𝑟𝑚𝑠)𝑠ℎ𝑜𝑡 = 𝐼𝑛𝑜𝑖𝑠𝑒(𝑟𝑚𝑠) 𝑟𝑑
Noise power density, Vn2
𝐼𝑛𝑜𝑖𝑠𝑒(𝑟𝑚𝑠) = √2𝑞𝐼𝐷𝐶 𝐵
= 𝐼𝑛 √𝐵
Also white noise
𝑉𝑛𝑜𝑖𝑠𝑒(𝑟𝑚𝑠)𝑡𝑜𝑡𝑎𝑙 = √𝑉𝑛𝑜𝑖𝑠𝑒(𝑟𝑚𝑠)1 2 + 𝑉𝑛𝑜𝑖𝑠𝑒(𝑟𝑚𝑠)2 2
𝑅𝐺 = [𝑅1 ∥ 𝑅2 ]
Where Vn is rms noise in
1Hz (noise density)
Shot noise
𝑉𝑛𝑜𝑖𝑠𝑒(𝑟𝑚𝑠) = √4𝑘𝑇𝐵𝑅
= 𝑉𝑛 √𝐵
No dependence on
Thermal/Johnson
frequency  white noise
RD
R1
Rsig
1
1
𝜔1 =
≅
𝐶1 (𝑅𝑠𝑖𝑔 + 𝑅𝐺 ) 𝐶1 𝑅𝐺
VS
1
𝐶2 (𝑅𝐿 + 𝑅𝑇𝐻 )
= [𝑟𝑜 ∥ 𝑅𝐷 ]
𝜔2 =
Vdd
𝑅𝑇𝐻
C2
Vout
C1
R2
RS
CS
RL
Burst (“popcorn”) noise
Flicker noise (1/f)
Also LF noise
𝑖(𝑟𝑚𝑠)𝑏𝑢𝑟𝑠𝑡 =
𝑟𝑑𝑠 =
1
𝑔𝑚
√
𝐾2
𝑖(𝑟𝑚𝑠)𝑓𝑙𝑖𝑐𝑘𝑒𝑟
rds2
𝐼𝑎
= √𝐾1 𝑏 √𝐵
𝑓
1 + 𝑔𝑚 𝑅𝑆
𝜔𝑆1
=
𝐶𝑆 𝑅𝑆
𝐶𝑆 𝑅𝑆
Combining
above graphs:
For ωS0<ω1
For ωS0>ω1
LF noise
1
Hence AV set by 𝐴𝑉 = −𝑔𝑚1 [𝑟𝑜1 ∥
]
𝑔𝑚2
transistor size
𝑔𝑚1
and is
=−
𝑔𝑚2
independent of
bias circuit
(𝑊/𝐿)1
=√
(𝑊/𝐿)2
Gate-drain connected load
i.e. diode connected
LF MOSFET
performance
dictated by C1,
C2 and CS
𝐼𝑐
√𝐵
𝑓 2
1+( )
𝑓𝑐
𝜔𝑆0 =
Emitter coupled transistors
responds only to different
signals VO2 VO2
Uses transistor in active
region as a load to maintain
gain and have low power
Common mode input, VCM = Vi1 = Vi2
Before:
𝐴𝐶𝑀1 ≅ −
After:
𝐴𝑉 = −𝑔𝑚1 [𝑟𝑜1 ∥ 𝑟𝑜2 ]
𝐼𝐶 = 𝐼𝑟𝑒𝑓 =
𝑅𝐶
2𝑅𝐸𝐸
REE is the current source
small signal resistance
Keep low
𝑉𝐶𝐶 − 𝑉𝐵𝐸
𝑅
Input common mode resistance,
𝑅𝑖𝑐𝑚 = 𝑟𝜋 + 2𝑅𝐸𝐸 (1 + 𝑔𝑚 𝑟𝜋 )
(Same applies to FETs)
If Io1 through Q1 has W/L, then
Io2 = 2Io1 for Q2 that has 2W/L
(half the current, half the
area)
Cascode 𝑅𝑜𝑢𝑡 ≅ (1 + 𝑔𝑚 𝑟𝑜2 )𝑟𝑜3
 massive CMRR
Differential mode
input, Vi1 = - Vi2
Currents can be set by adjusting W/L
ratio – can replace Rs with MOS Qs
MOS cascode current
sources increase Rout
Differential gain, Ad = 2Ad1
Transistor biased in active region
However, decreased Rout
 emitter degeneration
2. Wilson current mirror
𝐼𝑟𝑒𝑓
𝐼𝑜𝑢𝑡 ≅
2
1+
𝛽
ro effect decreased (Rout
increased)
Single ended differential gain, 𝐴𝑑1 =
−𝑔𝑚1 𝑅𝐶
BJT and FETs require large resistances
Solutions:
3. Widlar current source
Current mirror with RE on
transistor 2 emitter
Keep high
Figure of merit for op-amp, Common Mode
Rejection Ratio,
𝐴𝑑
𝐶𝑀𝑅𝑅 =
= 𝑔𝑚 𝑅𝐸𝐸 ≫ 10000(= 80𝑑𝐵)
𝐴𝐶𝑀
1. Current mirror
𝐼𝑜𝑢𝑡 =
𝐼𝑟𝑒𝑓
𝑉𝐶𝐸
(1 +
)
2
𝑉𝐴
1+
𝛽
Due to finite β
2
Input differential
resistance, 𝑅𝑖𝑑 =
2𝑟𝜋
2
𝐼𝑟𝑒𝑓 = 𝐼𝑜𝑢𝑡 (1 + )
𝛽
Due to finite ro
If β and ro = ∞  Iout = Iref