Analog Integrated Circuits (Jieh Tsorng Wu)

There exits an optimal rs for minimum f 2 rsopt vi2

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Unformatted text preview: nd T = 300 K, vo = (64 µV) Noise 11-10 Analog ICs; Jieh-Tsorng Wu Shot Noise ID rd i2 = 2qID ∆f kT rd = qID 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 i2 Ia = K1 ∆f fb 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 2 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 Cgd G 2 ig v1 D Cgs g m v1 2 id ro S 2 ig ∆f = 2qIG + 16 2 kT ω2Cgs 15 2 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 4kT (2/3)gm. 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 vi2 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 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 2 vs vi2 Noiseless RS ii2 Network 2 vs is the thermal noise of RS , i.e., 2 vs = 4kT RS ∆f Assume no correlation between vi2 and ii2, we have 2 22 Na vi + ii RS = Ni 2 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 SNRout vi2 ii2RS Na + = =1+ =1+ Ni 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 rb 2 vb 2 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 2 Since rb is small, ib is neglected. We have ic vi = vb + gm vi2 ∆f = 4kT rb + Req Noise 2qIC 2 gm = 4kT 2 vi2 = vb + rb + IC /UT 2 2gm 2 ic 2 gm 1 = 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 ii2 ∆f a = 2q IB + K1 IB f + IC |β (j ω)|2 K1 K1 = 2q = 2qIeq a Ieq = Equivalent Input Shot Noise Current = IB + K1 β (j ω) = βo ω 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 IC |β (j ω)|2 = IC 1+ 2 βo f2 fT2 2 βo 2 Let Noise IB = IC fb fT2 ⇒ 11-23 fb = fT ≈ IC f2 fT2 fT IB = IC 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 vi2 N ∆f = 2 vs ∆f + vi2 ∆f + ii2 ∆...
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This note was uploaded on 03/26/2013 for the course EE 260 taught by Professor Choma during the Winter '09 term at USC.

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