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Unformatted text preview: nd T = 300 K, vo = (64 µV) Noise 11-10 Analog ICs; Jieh-Tsorng Wu Shot Noise
q = 1.6 × 10−19 C kT /q = UT i2 f =0∼∞ (Electronic Charge)
◦ ≈ 26 mV at T =300 K • Shot noise is also a white noise.
• The shot noise from a diode with 50 µA bias current is the same as the thermal noise
from a 1 kΩ resistor at room temperature.
Noise 11-11 Analog ICs; Jieh-Tsorng Wu Flicker Noise (1/f Noise)
• Flicker noise, which is always associated with a ﬂow of direct current, displays a
spectral density of the form
a ≈ 0.5 ∼ 2 b≈1 f =0∼∞ K1 = a constant for a particular device • The ﬂicker noise’s power spectral density is frequency dependent, and its amplitude
distribution is non-Gaussian.
• Flicker noise is caused mainly by traps associated with contamination and crystal
defects. The constant K1 can varies widely even for devices from the same wafer. Noise 11-12 Analog ICs; Jieh-Tsorng Wu BJT Noise Model
B rb 2
vb Cµ B 2
ib v1 rc C Ccs
rπ Cπ g m v1 2
ic ro E
vb ∆f = 4kT rb 2
ic ∆f = 2qIC 2
ib ∆f a = 2qIB + K1 IB
f • All noise sources are independent of each other.
• The thermal noise of rc is neglected.
• Avalanche noise is found to be negligible if VCE is kept at least 5 V below BVCE O .
• Cµ can be neglected in noise calculation.
Noise 11-13 Analog ICs; Jieh-Tsorng Wu FET Noise Model
ig v1 D Cgs g m v1 2
id ro S
ig ∆f = 2qIG + 16
id ∆f a = 4kT (γgd 0) + K1 ID
f • Since the channel material is resistive, it exhibits thermal noise. γ is a constant, gd 0
is the channel conductance at VDS = 0.
γ≈ Noise 2
3 gd 0 ≈ gm 11-14 Analog ICs; Jieh-Tsorng Wu FET Noise Model
• For short-channel device (L < 1 µm), the thermal noise is 2 to 5 times larger than
2 2 • The gate-current noise, (16/15)kT ω Cgs , is usually insigniﬁcant at low frequencies.
Its correlation with the thermal noise is 0.39.
• IG is the gate leakage current.
• Cgd can be neglected in noise calculation.
• The 1/f noise in the surface devices, such as MESFETs and MOSFETs, is usually
larger than that of BJTs.
• pMOSTs have less 1/f noise than nMOSTs, since holes are less likely to be trapped. Noise 11-15 Analog ICs; Jieh-Tsorng Wu Equivalent Input Noise Generators
Noisy RS Noiseless ii2 RS Network Network • The noise in network is lumped and represented by a noise voltage generator vi2 and
a noise current generator ii2. This representation is valid for any source impedance, if
correlation between the noise generators is considered.
• And the total input equivalent noise can be found by
vi N = vs + vi + ii RS Noise and 11-16 2
vi2 = vs + vi2 + ii2RS
N Analog ICs; Jieh-Tsorng Wu Equivalent Input Noise Generators
• In most practical circuits, the correlation between vi and ii is small and may be
neglected. If either vi2 or ii2 dominates, the correlation may be neglected in any case.
• The value of vi2 can be found by shorting the input ports and equating the output noise
in each case.
• The value of ii2 can be found by opening the input ports and equating the output noise
in each case. Noise 11-17 Analog ICs; Jieh-Tsorng Wu Noise Factor and Input Noise Generators
Noiseless RS ii2 Network 2
vs is the thermal noise of RS , i.e.,
vs = 4kT RS ∆f Assume no correlation between vi2 and ii2, we have
Na vi + ii RS
vs Noise 11-18 Analog ICs; Jieh-Tsorng Wu Noise Factor and Input Noise Generators
Thus, the noise factor for the two-port network is F= SNRin
4kT RS ∆f 4kT ∆f
(G · Si )/[G · (Ni + Na)]
Si /Ni • For small RS , vi2 dominates, whereas for large RS , ii2 dominates.
• There exits an optimal RS for minimum F : 2
RS,opt = vi2 and ii2 Fopt = 1 + ii2RS
2kT ∆f This is one reason for the widespread use of transformers at the input of low-noise
tuned ampliﬁers. Noise 11-19 Analog ICs; Jieh-Tsorng Wu Noise Generators of a BJT Common-Emitter Stage
ib vi2 v1 ∆f Noise Cπ v1 rπ Cπ g m v1 2
ic io rb ii2 2
vb rπ = 4kT rb 2
ib ∆f g m v1 a = 2qIB + K1 11-20 io IB 2
ic f ∆f = 2qIC Analog ICs; Jieh-Tsorng Wu Noise Voltage Generator of a BJT Common-Emitter Stage
By shorting the input ports, we obtain
io = gmvb + ic = gmvi
Since rb is small, ib is neglected. We have ic
vi = vb +
∆f = 4kT rb +
Req Noise 2qIC
gm = 4kT 2
vi2 = vb + rb + IC /UT
= 4kT rb +
2gm = 4kT Req 1
= Equivalent Input Noise Resistance = rb +
2gm 11-21 Analog ICs; Jieh-Tsorng Wu Noise Current Generator of a BJT Common-Emitter Stage
By opening the input ports, we obtain io = β (j ω)ib + ic = β (j ω)ii ⇒ ii = ib + ic 2
ii2 = ib + β (j ω) 2
ic |β (j ω)|2 Thus
∆f a = 2q IB + K1 IB
f + IC
|β (j ω)|2 K1
2q = 2qIeq a Ieq = Equivalent Input Shot Noise Current = IB + K1
β (j ω) = βo
1 + jω β Noise = βo
1+ j ff βo
T 11-22 = IB
f + IC
|β (j ω)|2 βo
1 + βo Cπ + Cµ
gm j ω Analog ICs; Jieh-Tsorng Wu BJT Equivalent Input Shot Noise Spectral Density log ii2
∆f f2 1/f log f
fb fa At high frequencies
|β (j ω)|2 = IC 1+ 2
βo 2 Let Noise IB = IC fb fT2 ⇒ 11-23 fb = fT ≈ IC f2
βF Analog ICs; Jieh-Tsorng Wu Total Equivalent Noise Voltage of a BJT Common-Emitter Stage
The total equivalent noise voltage with a source resistance RS can be found as
∆f = 2
vs ∆f + vi2
∆f + ii2
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