Analog Integrated Circuits (Jieh Tsorng Wu)

For high frequency circuits cgs 1rs 2 f 1 rs 2cgs

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Unformatted text preview: f 2 RS 1 2 + RS · 2q = 4kT RS + rb + 2gm a IB + K1 = 4kT = Noise 2 2qRS 2UT 2 RS 1 RS + rb + + 2gm 11-24 f + a 2 RS 1 + RS + rb + 2gm 2UT IB IB + K1 IB f IB + K1 + a IB f IC |β (j ω)|2 IC |β (j ω)|2 + IC |β (j ω)|2 Analog ICs; Jieh-Tsorng Wu Noise Generators of a FET Common-Source Stage 2 ig v1 Cgs g m v1 ro g m v1 io 2 id ro vi2 ii2 v1 Cgs 2 ig 16 2 = 2qIG + kT ω2Cgs 15 ∆f Noise 11-25 2 id ∆f io a = 4kT (γgd 0) + K1 ID f Analog ICs; Jieh-Tsorng Wu Noise Voltage Generator of a FET Common-Source Stage By shorting the input ports, we obtain io = id = gmvi vi2 ∆f = 4kT γ gd 0 2 gm ⇒ vi2 = a + K1 ID 2 gm f = 4kT Req Req = Equivalent Input Noise Resistance = γ gd 0 2 gm 2 id 2 gm K1 K1 = 4kT a a ID ID 21 + K1 + K1 ≈ 2 2 3 gm gm f gm f • For MOST, its voltage generator for flicker noise is approximately independent of bias current and voltage and is inversely proportional to the gate-oxide capacitance, i.e., vi2 ∆f Noise ≈ 4kT Kf 1 21 + · 3 gm W LCox f 11-26 Kf ∼ 3 × 10−24 V2-F Analog ICs; Jieh-Tsorng Wu MOST Equivalent Input Noise Voltage Spectral Density log vi2 ∆f 1/f log f fa • At frequencies above the flicker noise region, the Req of a FET is significantly higher than that of a BJT at a comparable bias current. • For a MOST, it is not uncommon for the fa to extend well into the MHz region. Noise 11-27 Analog ICs; Jieh-Tsorng Wu Noise Current Generator of a FET Common-Source Stage By opening the input ports, we obtain gm gm + id = ii io = ig j ωCgs j ωCgs ⇒ 2 ii2 2 ω Cgs 16 22 = 2qIG + kT ω Cgs + 2 15 ∆f gm Req = γ gd 0 2 gm ii = ig + j ωCgs 4kT γgd 0 + K1 a a ID f 2 gm 2 id 2 = 2qIG + ω2Cgs (4kT Req ) a K1 ID 21 4 4 ≈ + ·+ + ·+ 2 2 15 3 gm gm f 15 4kT gm f K1 ID gm 2 ii2 = ig + id 2 ω2Cgs • When the source impedance is large, ii2 dominates. Since Ig is very small, FETs have noise performance much superior to that of BJTs. However, for low source impedances where vi2 dominates, BJTs often have noise performance superior to that of FETs. Noise 11-28 Analog ICs; Jieh-Tsorng Wu Noise Factor of a BJT Common-Emitter Stage Neglecting flicker noise, vi2 ii2 1 = 4kT rb + 2gm ∆f ∆f = 2q IB + IC |β (j ω)|2 = 2q IC βF + IC |β (j ω)|2 The noise factor is F =1+ vi2 4kT RS ∆f + ii2 1 4kT R ∆f S gm gm 1 1 r+ + RS =1+ + RS b 2gm 2βF 2|β (j ω)|2 gm gm 1 1 rb + + RS =1+ + 2 2gm RS 2βF 2βo Noise 11-29 2 1 + βo ω ωT 2 Analog ICs; Jieh-Tsorng Wu Noise Factor of a BJT Common-Emitter Stage For high-frequency circuits, if ω/ωT 1/βo and ω/ωT 1/βF , gm 1 1 ω + RS · · · rb + F ≈1+ ωT 2gm 2 RS 2 • For fixed RS and ωT , gm,opt 1 ωT = · RS ω Fopt rb ω =1+ + Rs ωT • For fixed gm and ωT , RS,opt = Noise 2rb 1 ωT + · gm g 2 ω m Fopt = 1 + 11-30 ω 2rbgm + 1 · ωT Analog ICs; Jieh-Tsorng Wu Noise Factor of a BJT Common-Emitter Stage For low-frequency circuits, if ω/ωT 1/βo and ω/ωT ≈ gm 1 1 + RS · · 1+ · rb + 2gm 2 RS ≈ F 1+ 1/βF , 1 1 + 2 βF βo gm 1 1 1 + RS · · · rb + 2gm 2 βF RS • For fixed RS and βF , 1 = · RS βF Fopt = 1 + 2rb 1 + · 2 gm gm βF Fopt = 1 + gm,opt rb Rs + 1 βF • For fixed gm and βF , RS,opt = Noise 11-31 2rbgm + 1 · 1 βF Analog ICs; Jieh-Tsorng Wu Noise Factor of an FET Common-Source Stage Neglecting flicker noise, IG , and gate-current noise, vi2 ∆f = 4kT γgd 0 · 1 ii2 2 gm ∆f =ω 2 2 Cgs · 4kT γgd 0 · 1 2 gm The noise factor is F = = Noise 1+ vi2 4kT RS ∆f + ii2 1 4kT R ∆f S γgd 0 1 γgd 0 22 · + RS · ω Cgs · 1+ 2 2 RS gm gm 11-32 Analog ICs; Jieh-Tsorng Wu Noise Factor of an FET Common-Source Stage For low-frequency circuits, ωCgs 1/RS , 1 γgd 0 F ≈1+ · 2 RS gm • For fixed RS , gm,opt → ∞ and Fopt → 1 • For fixed gm, RS,opt → ∞ and Fopt → 1 • For RS of the order of MΩ or higher, the FET usually has significantly lower noise figure than a BJT. For high-frequency circuits, ωCgs 1/RS , 2 F ≈ 1 + RS · ω2Cgs · Noise γgd 0 2 gm ω ≈ 1 + RS · γgd 0 · ωT 11-33 2 Analog ICs; Jieh-Tsorng Wu Noise Performance of Other Configurations vi2 Common−Base Stage ii2 vi2 ii2 Emitter Follower vi2 vi2 ii2 Noise ii2 zL 11-34 zL Analog ICs; Jieh-Tsorng Wu Noise Performance of Other Configurations • The equivalent input noise generators of a common-base stage or emitter follower are the same as those of a common-emitter stage. • For the common-base configuration, since its current gain ≈ 1, any noise current at the output is referred directly back to the input without reduction. • For the emitter follower, since its voltage gain ≈ 1, any noise voltage at the output, including noise due to zL, is transformed unchanged to the input. • In most low-noise designs, common-emitter connection is used for the input stage. Noise 11-35 Analog ICs; Jieh-Tsorng Wu Emitter-Coupled Pair Noise Performance VCC VCC RL RL vi2 1 RL vi2 2 vo Q1 vi2 1 Q2 ii2 1 vi2 2 vo Q1 Q2 ii2 1 ii2 2 RE E IE E RL ii2 2 RE E IE E VEE VEE • If the circuit is b...
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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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