Analog Integrated Circuits (Jieh Tsorng Wu)

Cascode current sources for better current matching

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Unformatted text preview: M2 V M6 M1 IO2 Let M3=M4, then M5 IIN = IO = I 1 W W 2 Vov 1 = k 2 L1 L √ 2( α − 1)2 1 ∆V = I= α R k (W/L)1 R 2 1 I= k 2 Voltage and Current References · ∆V Vov 1 = √ α−1 √ √ 2( α − 1) 2 α − 1 2I ∆V ·√ = = = √ Vov 1 R R α∆V α (Vov 1 − ∆V )2 2 gm1 9-14 √ α ⇒ Analog ICs; Jieh-Tsorng Wu Self-Biasing MOST VBE and UT Referenced Current Source VBE Reference VDD M4 M3 IIN M6 IIN V M2 R Q1 Voltage and Current References R V ∆V = VBE 1 ∆V = UT ln 9-15 M6 IO M1 M2 Q1 M4 M3 IO M1 UT Reference VDD Q2 IS 2 (W/L)3 · IS 1 (W/L)4 Analog ICs; Jieh-Tsorng Wu Band-Gap References IC VBE VO = VBE + K UT PTAT Generator K · UT ◦ ◦ • UT = kT /q = 26 mV at T = 300 K. ∂UT /∂T = k/q = 0.087 mV/ C. ◦ ◦ • VBE = 600 mV at T = 300 K. ∂VBE /∂T ≈ −2 mV/ C. ◦ • Want K = 23 so that ∂Vo/∂T = 0 at 300 K and VO ≈ 1.2 V. Voltage and Current References 9-16 Analog ICs; Jieh-Tsorng Wu Band-Gap References For a BJT biased in the forward-active region, we have VBE = VG 0 VG 0 k m T0 JC JC0 T0 JC T T 1− + VBE 0 + mUT ln + UT ln T0 T0 T JC0 kT q ◦ Bandgap voltage of Si extrapolated to 0 K (≈ 1.206 V) Boltzmann’s constant Constant (≈ 2.3) Reference temperature Collector current density (= IC /AE ) Collector current density at T0 Let VO = VBE + K UT We have UT = and JC JC0 = T T0 α T0 T + K · UT VO = VG 0 + (VBE 0 − VG 0) + (m − α )UT ln T0 T Voltage and Current References 9-17 Analog ICs; Jieh-Tsorng Wu Band-Gap References Then ∂VO T0 1 k k = (VBE 0 − VG 0) + (m − α ) −1 +K · ln q q ∂T T0 T Set ∂VO /∂T = 0 at T = T0, we obtain K= 1 · VG 0 + (m − α )UT 0 − VBE 0 UT 0 VO = VG 0 + UT (m − α ) 1 + ln UT 0 = T0 ∂ VO T ∂T • At T = T0, VO = VG 0 + UT 0(m − α ) = ∂VO ∂T kT0 q T0 k (m − α ) ln q T =0 ◦ • If T0 = 300 K and α = 1, then, K= 1.24 − VBE 0 0.0258 Voltage and Current References and 9-18 VO = 1.24 V at T = T0 Analog ICs; Jieh-Tsorng Wu Kujik Band-Gap References VCC I1 R1 I2 ∆VBE Q1 R2 I1 Q2 Q1 VEE I1 R2 = I2 R1 VR 2 R2 = ∆VBE R3 VO = |VBE 1 | + VR 2 Voltage and Current References I2 ∆VBE VO R3 R1 R2 VO R3 Q2 VEE ∆VBE I1 IS 2 = UT ln · I2 IS 1 R2 IS 2 = UT ln · R1 IS 1 R2 R2 R2 IS 2 = |VBE 1 | + ∆VBE = |VBE 1 | + UT × ln · R3 R3 R1 IS 1 9-19 Analog ICs; Jieh-Tsorng Wu Kujik Band-Gap References • Both IC1 and IC2 are proportional to T . • In n-well CMOS technologies, use vertical pnp BJTs with with collectors tied to VSS . • Reference: Kujik, JSSC 6/73, pp. 222–226. Let VOS be the opamp’s input offset voltage. I1 R1 I2 R2 VR 3 = |VBE 1 | − |VBE 2 | + VOS = ∆VBE + VOS VOS VR 2 R2 R2 = V= (∆VBE + VOS ) R3 R 3 R3 VO = |VBE 1 | + VOS + VR 2 VO R3 Q1 = |VBE 1 | + Q2 VEE Voltage and Current References R2 R2 VOS ∆VBE + 1 + R3 R3 • The ratio R2/R3 is typically 5 ∼ 10. 9-20 Analog ICs; Jieh-Tsorng Wu Ahuja Band-gap Reference VDD M1 M2 M3 M4 M5 M6 M12 M7 M8 M9 M10 M11 Cc R2 R3 VO Q6 Q1 V BE Q2 Q5 Q3 Q4 VSS Voltage and Current References 9-21 Analog ICs; Jieh-Tsorng Wu Ahuja Band-gap Reference VO = 3|VBE | + 3 R2 R2 VOS ∆VBE + 1 + R3 R3 • Increase number of VBE to suppress the contribution from VOS . • Opamp doesn’t need to drive resistive load. • Cc provides a feedforward path for negative feedback to ensure stability. • Cascode current sources for better current matching. • M12 is added for auto start-up to avoid the zero-current state. • Reference: Ahuja, JSSC 12/84, pp. 892–899. Voltage and Current References 9-22 Analog ICs; Jieh-Tsorng Wu Brokaw Band-Gap References VCC R1 I1 VCC I2 Q3 R2 Q4 1 I1 V o1 Q1 R11 VEE Q1 Q2 ∆VBE R3 V o2 Rx VEE Q2 I2 ∆VBE R3 R12 VEE R4 R4 VEE βF → ∞ ⇒ Voltage and Current References VEE I1 R2 = I2 R1 I2 = ∆VBE R3 9-23 ∆VBE = UT ln I1 IS 2 · I2 IS 1 Analog ICs; Jieh-Tsorng Wu Brokaw Band-Gap References The output voltages are VO2 = = VO1 ∆VBE VBE 1 + (I1 + I2)R4 = VBE 1 + R3 R4 R2 R2 IS 2 VBE 1 + UT × + 1 ln · R3 R1 R1 IS 1 R11 = 1+ R12 I1 + 1 R4 I2 R4 I1 I1 IS 2 VBE 1 + UT + 1 ln · R3 I2 I2 IS 1 • Both I1 and I2 are proportional to T . R • The resistor Rx = R3 R11 4 currents going through R11. R12 is added to cancel the effects of the finite base • Reference: Brokaw, JSSC 12/74, pp. 388–393. Voltage and Current References 9-24 Analog ICs; Jieh-Tsorng Wu Widlar Band-Gap Reference VCC βF → ∞ I3 I3 I1 = IS 1 IS 3 VBE 1 = VBE 3 Q4 I2 R2 I1 R1 Vo I1 R2 = I2 R1 ∆VBE I1 IS 2 R2 IS 2 = UT ln = UT ln I2 IS 1 R1 IS 1 VEE Q3 Q2 ∆VBE Q1 VO = VBE 1 + R3 R2 ∆VBE R3 R2 R2 IS 2 = VBE 1 + UT × ln · R3 R1 IS 1 VEE • Both I1 and I2 are proportional to T . I3 can be mirrored from a separate PTAT source. • In the simplest form, I3 can be implemented with a resistor. Voltage and Current References 9-25 Analog ICs; Jieh-Tsorng Wu Song Band-Gap Reference VDD M3 M5 M4 M6 M8 M6 M9 Io V M10 o M11 M1 M2 V Ry = y R R R Q1 x Q3 Q2 VSS Voltage and Current References 9-26 Analog ICs; Jieh-Tsorng Wu Song Band-Gap Reference Let Q2=Q3, IS 2/IS 1 = n, and M3=M4=M5, then ∆V = UT ln(n) The output voltage, VO, and current, IO, are thus VO = VBE 3 + UT · y ln(n) and IO = VO Rx • A PTAT current from M8 develops a UT -dependent voltage across resistor Ry . A proper choice of the ratio y can give a band-gap voltage at VO . • All currents are proportional to T . • If desired, a temperature-independent output current can be realized by choosing y to give an appropriate TC to VO to cancel the TC of...
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