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附录 C：运放设计公式速查

原始标题：Op Amp Equations Design Reference · 来源：https://www.analog.com/media/en/selection-guides/Equation_Pullout.pdf

说明：这是面向学习的中文详注 HTML，不是 ADI 官方中文译本。页面保留原文句子，并在每句下方给出中文译读和术语注释；涉及公式、参数和器件选择时，请回到 ADI 原文与对应数据手册复核。

本章中文详解重写讲义版

补充专题 C：运放设计公式速查

依据 ADI 原始资料 整理的中文学习笔记。

内容讲解

该一页 PDF 是 ADI 的运放公式速查表。使用时先确认电路处于线性负反馈，再区分信号增益与噪声增益；精密计算还要把输入失调、偏置电流、源阻抗和电阻噪声折算到同一参考端。速查表适合复核，不应替代对输入共模、输出摆幅、GBW 与稳定性的检查。

关键关系

  • 反相：$-R_f/R_g$；同相：$1+R_f/R_g$
  • 一阶带宽近似：$BW\approx GBW/NG$
  • 总噪声应按不相关分量的均方根合成

实际使用建议

  • 从最坏电源、温度、负载和器件容差出发，不只按典型值设计。
  • 对高阻、高速或大电流节点，原理图正确并不等于实物正确，布局和回流路径同样属于电路。
  • 任何超过电源轨、额定功耗或绝对最大值的工作方式，都应先设计限流、钳位或热保护。

配图

图 1：ADI 原教材图示

图 1：选自 ADI 原章节；请结合本章中文解释阅读。

来源与署名

  • 原始资料与图片：Analog Devices。
  • 供非商业教育学习使用，保留 Analog Devices, Inc. 署名。

原文逐句译读与注释按原站顺序

PDF 页面图与逐句译读原 PDF 已逐页渲染

这一章在 ADI 原站中以 PDF 形式提供。下面每个页面先给出 PDF 页面图，再给出抽取文本的中文译读和术语注释。由于 PDF 抽取文本可能存在换行或公式识别误差，设计计算请始终以页面图和原 PDF 为准。

PDF 第 1 页

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展开本页文本译读与注释
原句Op Amp Noise for Single-Pole System Closed-Loop Frequency Response for Voltage Feedback Amplifiers Resistor Johnson Noise Formula CLOSEDLOOP BW = fCL B A VN, R1 R1 R3 4kTR3 4kTR1 VN, R3 IN+ IN– VN 4kTR2 VN, R2 R2 NOISE GAIN = GAIN FROM “A” TO OUTPUT = NG = 1 + R2 R1 VOUT GAIN FROM “B” TO OUTPUT = – R2 R1 RTI NOISE = TOTAL BW /uni00D7.bold VN2 + 4kTR3 + 4kTR1 R2 R1 + R2 2 + IN+2 R32 + IN–2 R1 /uni00D7.bold R2 R1 + R2 2 + 4kTR2 R1 R1 + R2 2 RTO NOISE = NG /uni00D7.bold RTI NOISE RTI = REFER TO INPUT RTO = REFER TO OUTPUT BW = 1.57 fCL GAIN (dB) 6dB/OCTAVE ROLL-OFF LOOP GAIN, A/u1D6C3 A(S), OPEN-LOOP GAIN CLOSEDLOOP GAIN 1 /u1D6C3 NOISE GAIN, CLOSED-LOOP BANDWITH LOG FREQUENCY (HZ) RESISTANCE (/u1D6C0) 10,000 1000 10 1 0 10 1k 100k 10M100 10k 1M 100M 100en at 25°C nV Hz where: VR = resistor Johnson Noise spectral density k = Boltzmann’s constant (1.38 /uni00D7.bold 10–23 J/K) T = absolute temperature in Kelvin R = resistance in Ohms B = bandwidth in Hz = 4kTRBVR At 25°C, 4kT = 1.65 /uni00D7.bold 10–20 W/Hz, therefore, VR = 1.65 /uni00D7.bold 10–20RB Op Amp Noise for Single-Pole System Closed-Loop Frequency Response for Voltage Feedback Amplifiers Resistor Johnson Noise Formula CLOSEDLOOP BW = fCL B A VN, R1 R1 R3 4kTR3 4kTR1 VN, R3 IN+ IN– VN 4kTR2 VN, R2 R2 NOISE GAIN = GAIN FROM “A” TO OUTPUT = NG = 1 + R2 R1 VOUT GAIN FROM “B” TO OUTPUT = – R2 R1 RTI NOISE = TOTAL BW /uni00D7.bold VN2 + 4kTR3 + 4kTR1 R2 R1 + R2 2 + IN+2 R32 + IN–2 R1 /uni00D7.bold R2 R1 + R2 2 + 4kTR2 R1 R1 + R2 2 RTO NOISE = NG /uni00D7.bold RTI NOISE RTI = REFER TO INPUT RTO = REFER TO OUTPUT BW = 1.57 fCL GAIN (dB) 6dB/OCTAVE ROLL-OFF LOOP GAIN, A/u1D6C3 A(S), OPEN-LOOP GAIN CLOSEDLOOP GAIN 1 /u1D6C3 NOISE GAIN, CLOSED-LOOP BANDWITH LOG FREQUENCY (HZ) RESISTANCE (/u1D6C0) 10,000 1000 10 1 0 10 1k 100k 10M100 10k 1M 100M 100en at 25°C nV Hz where: VR = resistor Johnson Noise spectral density k = Boltzmann’s constant (1.38 /uni00D7.bold 10–23 J/K) T = absolute temperature in Kelvin R = resistance in Ohms B = bandwidth in Hz = 4kTRBVR At 25°C, 4kT = 1.65 /uni00D7.bold 10–20 W/Hz, therefore, VR = 1.65 /uni00D7.bold 10–20RB √P Decibel (dB) Formulas (Equal Impedances) db = 10 Log = 20 LogPOUT PIN VOUT VIN = 20 Log (Gain) IOUT IIN Transformers (Step-Up or Step-Down Ratios) Sinusoidal Voltages and Currents RMS = Root Mean Square = Effective VRMS = 0.707 VPEAK = VEFF VAVE = 0.637 VPEAK VEFF = 1.11 VAVE VPEAK = 1.57 VAVE VAVE = 0.9 VEFF Ohm’s Law (DC Circuits) Resistors in Series/Capacitors in Parallel RTOTAL = R1 /uni002B R2 /uni002B R3 /uni002B … / CTOTAL = C1 /uni002B C2 /uni002B C3 /uni002B … Resistors in Parallel/Capacitors in Series Two Resistors in Parallel Equal Resistors in Parallel == =NP NS EP ES IS IP ZP ZS 1 /uni002B 1 /uni002B 1 /uni002B …R1 R2 R3 1RTOTAL = 1 /uni002B 1 /uni002B 1 /uni002B …C1 C2 C3 1CTOTAL =/ R1/uni002BR2 R1 R2RTOTAL = Where R is the value of one of the equal resistors, and N is the number of equal resistors N RRTOTAL = VI IR √PR I P I2 P P V2 I V R P V PR V R V2 I2R B.W.
中文译读逐句译读：这句话围绕 运放、环路增益、噪声增益、阻抗、电阻、频率响应、带宽 展开；核心是在说明这些量/结构之间的定义、作用或约束关系。
补充注释运放：高增益差分放大器；分析时先确认是否处于负反馈线性区。；环路增益：开环增益与反馈因子的乘积，决定闭环精度和稳定裕量。；噪声增益：输入误差被放大到输出的倍数；稳定性分析经常看噪声增益而不是信号增益。；阻抗：交流中电压与电流的复数比，包含电阻和电抗。。
原句SR. (Tuned Circuit) Q = Q & Resonant Frequency Formulas Reactance Formulas R XL Figure of Merit of a CoilQ = SR =o rH z2π√LC 1 √LC .159 L = 4π2 SR2 C 1 C = 4π2 SR2 L 1 XC = XL = 2π fL 2π fC 1 Impedance Formulas (Series) Z = √R2 /uni002B XL2 (Series RL) Z = √R2 /uni002B XC2 (Series RC) Z = XL – XC (Series LC) Z = √R2 /uni002B (XL – XC)2 (Series RLC) Z = VA I Voltage and Impedance Formulas (Parallel) Z = RXL (RL) Z = VA √R2 /uni002B XL2 ILINE Z = RXC (RC) VA = VL = VC = VR √R2 /uni002B XC2 Z = XL XC (LC) VA = ILINEZ XL – XC Z = RX (RLC) √R2 /uni002B X2 PI VR √P Decibel (dB) Formulas (Equal Impedances) db = 10 Log = 20 LogPOUT PIN VOUT VIN = 20 Log (Gain) IOUT IIN Transformers (Step-Up or Step-Down Ratios) Sinusoidal Voltages and Currents RMS = Root Mean Square = Effective VRMS = 0.707 VPEAK = VEFF VAVE = 0.637 VPEAK VEFF = 1.11 VAVE VPEAK = 1.57 VAVE VAVE = 0.9 VEFF Ohm’s Law (DC Circuits) Resistors in Series/Capacitors in Parallel RTOTAL = R1 /uni002B R2 /uni002B R3 /uni002B … / CTOTAL = C1 /uni002B C2 /uni002B C3 /uni002B … Resistors in Parallel/Capacitors in Series Two Resistors in Parallel Equal Resistors in Parallel == =NP NS EP ES IS IP ZP ZS 1 /uni002B 1 /uni002B 1 /uni002B …R1 R2 R3 1RTOTAL = 1 /uni002B 1 /uni002B 1 /uni002B …C1 C2 C3 1CTOTAL =/ R1/uni002BR2 R1 R2RTOTAL = Where R is the value of one of the equal resistors, and N is the number of equal resistors N RRTOTAL = VI IR √PR I P I2 P P V2 I V R P V PR V R V2 I2R B.W.
中文译读逐句译读：这句话围绕 阻抗 展开；核心是在说明这些量/结构之间的定义、作用或约束关系。
补充注释阻抗：交流中电压与电流的复数比，包含电阻和电抗。。
原句SR. (Tuned Circuit) Q = Q & Resonant Frequency Formulas Reactance Formulas R XL Figure of Merit of a CoilQ = SR =o rH z2π√LC 1 √LC .159 L = 4π2 SR2 C 1 C = 4π2 SR2 L 1 XC = XL = 2π fL 2π fC 1 Impedance Formulas (Series) Z = √R2 /uni002B XL2 (Series RL) Z = √R2 /uni002B XC2 (Series RC) Z = XL – XC (Series LC) Z = √R2 /uni002B (XL – XC)2 (Series RLC) Z = VA I Voltage and Impedance Formulas (Parallel) Z = RXL (RL) Z = VA √R2 /uni002B XL2 ILINE Z = RXC (RC) VA = VL = VC = VR √R2 /uni002B XC2 Z = XL XC (LC) VA = ILINEZ XL – XC Z = RX (RLC) √R2 /uni002B X2 PI VR √P Decibel (dB) Formulas (Equal Impedances) db = 10 Log = 20 LogPOUT PIN VOUT VIN = 20 Log (Gain) IOUT IIN Transformers (Step-Up or Step-Down Ratios) Sinusoidal Voltages and Currents RMS = Root Mean Square = Effective VRMS = 0.707 VPEAK = VEFF VAVE = 0.637 VPEAK VEFF = 1.11 VAVE VPEAK = 1.57 VAVE VAVE = 0.9 VEFF Ohm’s Law (DC Circuits) Resistors in Series/Capacitors in Parallel RTOTAL = R1 /uni002B R2 /uni002B R3 /uni002B … / CTOTAL = C1 /uni002B C2 /uni002B C3 /uni002B … Resistors in Parallel/Capacitors in Series Two Resistors in Parallel Equal Resistors in Parallel == =NP NS EP ES IS IP ZP ZS 1 /uni002B 1 /uni002B 1 /uni002B …R1 R2 R3 1RTOTAL = 1 /uni002B 1 /uni002B 1 /uni002B …C1 C2 C3 1CTOTAL =/ R1/uni002BR2 R1 R2RTOTAL = Where R is the value of one of the equal resistors, and N is the number of equal resistors N RRTOTAL = VI IR √PR I P I2 P P V2 I V R P V PR V R V2 I2R B.W.
中文译读逐句译读：这句话围绕 阻抗 展开；核心是在说明这些量/结构之间的定义、作用或约束关系。
补充注释阻抗：交流中电压与电流的复数比，包含电阻和电抗。。
原句SR. (Tuned Circuit) Q = Q & Resonant Frequency Formulas Reactance Formulas R XL Figure of Merit of a CoilQ = SR =o rH z2π√LC 1 √LC .159 L = 4π2 SR2 C 1 C = 4π2 SR2 L 1 XC = XL = 2π fL 2π fC 1 Impedance Formulas (Series) Z = √R2 /uni002B XL2 (Series RL) Z = √R2 /uni002B XC2 (Series RC) Z = XL – XC (Series LC) Z = √R2 /uni002B (XL – XC)2 (Series RLC) Z = VA I Voltage and Impedance Formulas (Parallel) Z = RXL (RL) Z = VA √R2 /uni002B XL2 ILINE Z = RXC (RC) VA = VL = VC = VR √R2 /uni002B XC2 Z = XL XC (LC) VA = ILINEZ XL – XC Z = RX (RLC) √R2 /uni002B X2 PI VR √P Decibel (dB) Formulas (Equal Impedances) db = 10 Log = 20 LogPOUT PIN VOUT VIN = 20 Log (Gain) IOUT IIN Transformers (Step-Up or Step-Down Ratios) Sinusoidal Voltages and Currents RMS = Root Mean Square = Effective VRMS = 0.707 VPEAK = VEFF VAVE = 0.637 VPEAK VEFF = 1.11 VAVE VPEAK = 1.57 VAVE VAVE = 0.9 VEFF Ohm’s Law (DC Circuits) Resistors in Series/Capacitors in Parallel RTOTAL = R1 /uni002B R2 /uni002B R3 /uni002B … / CTOTAL = C1 /uni002B C2 /uni002B C3 /uni002B … Resistors in Parallel/Capacitors in Series Two Resistors in Parallel Equal Resistors in Parallel == =NP NS EP ES IS IP ZP ZS 1 /uni002B 1 /uni002B 1 /uni002B …R1 R2 R3 1RTOTAL = 1 /uni002B 1 /uni002B 1 /uni002B …C1 C2 C3 1CTOTAL =/ R1/uni002BR2 R1 R2RTOTAL = Where R is the value of one of the equal resistors, and N is the number of equal resistors N RRTOTAL = VI IR √PR I P I2 P P V2 I V R P V PR V R V2 I2R B.W.
中文译读逐句译读：这句话围绕 阻抗 展开；核心是在说明这些量/结构之间的定义、作用或约束关系。
补充注释阻抗：交流中电压与电流的复数比，包含电阻和电抗。。
原句SR. (Tuned Circuit) Q = Q & Resonant Frequency Formulas Reactance Formulas R XL Figure of Merit of a CoilQ = SR =o rH z2π√LC 1 √LC .159 L = 4π2 SR2 C 1 C = 4π2 SR2 L 1 XC = XL = 2π fL 2π fC 1 Impedance Formulas (Series) Z = √R2 /uni002B XL2 (Series RL) Z = √R2 /uni002B XC2 (Series RC) Z = XL – XC (Series LC) Z = √R2 /uni002B (XL – XC)2 (Series RLC) Z = VA I Voltage and Impedance Formulas (Parallel) Z = RXL (RL) Z = VA √R2 /uni002B XL2 ILINE Z = RXC (RC) VA = VL = VC = VR √R2 /uni002B XC2 Z = XL XC (LC) VA = ILINEZ XL – XC Z = RX (RLC) √R2 /uni002B X2 PI VR √P Decibel (dB) Formulas (Equal Impedances) db = 10 Log = 20 LogPOUT PIN VOUT VIN = 20 Log (Gain) IOUT IIN Transformers (Step-Up or Step-Down Ratios) Sinusoidal Voltages and Currents RMS = Root Mean Square = Effective VRMS = 0.707 VPEAK = VEFF VAVE = 0.637 VPEAK VEFF = 1.11 VAVE VPEAK = 1.57 VAVE VAVE = 0.9 VEFF Ohm’s Law (DC Circuits) Resistors in Series/Capacitors in Parallel RTOTAL = R1 /uni002B R2 /uni002B R3 /uni002B … / CTOTAL = C1 /uni002B C2 /uni002B C3 /uni002B … Resistors in Parallel/Capacitors in Series Two Resistors in Parallel Equal Resistors in Parallel == =NP NS EP ES IS IP ZP ZS 1 /uni002B 1 /uni002B 1 /uni002B …R1 R2 R3 1RTOTAL = 1 /uni002B 1 /uni002B 1 /uni002B …C1 C2 C3 1CTOTAL =/ R1/uni002BR2 R1 R2RTOTAL = Where R is the value of one of the equal resistors, and N is the number of equal resistors N RRTOTAL = VI IR √PR I P I2 P P V2 I V R P V PR V R V2 I2R B.W.
中文译读逐句译读：这句话围绕 阻抗 展开；核心是在说明这些量/结构之间的定义、作用或约束关系。
补充注释阻抗：交流中电压与电流的复数比，包含电阻和电抗。。
原句SR. (Tuned Circuit) Q = Q & Resonant Frequency Formulas Reactance Formulas R XL Figure of Merit of a CoilQ = SR =o rH z2π√LC 1 √LC .159 L = 4π2 SR2 C 1 C = 4π2 SR2 L 1 XC = XL = 2π fL 2π fC 1 Impedance Formulas (Series) Z = √R2 /uni002B XL2 (Series RL) Z = √R2 /uni002B XC2 (Series RC) Z = XL – XC (Series LC) Z = √R2 /uni002B (XL – XC)2 (Series RLC) Z = VA I Voltage and Impedance Formulas (Parallel) Z = RXL (RL) Z = VA √R2 /uni002B XL2 ILINE Z = RXC (RC) VA = VL = VC = VR √R2 /uni002B XC2 Z = XL XC (LC) VA = ILINEZ XL – XC Z = RX (RLC) √R2 /uni002B X2 PI VR √P Decibel (dB) Formulas (Equal Impedances) db = 10 Log = 20 LogPOUT PIN VOUT VIN = 20 Log (Gain) IOUT IIN Transformers (Step-Up or Step-Down Ratios) Sinusoidal Voltages and Currents RMS = Root Mean Square = Effective VRMS = 0.707 VPEAK = VEFF VAVE = 0.637 VPEAK VEFF = 1.11 VAVE VPEAK = 1.57 VAVE VAVE = 0.9 VEFF Ohm’s Law (DC Circuits) Resistors in Series/Capacitors in Parallel RTOTAL = R1 /uni002B R2 /uni002B R3 /uni002B … / CTOTAL = C1 /uni002B C2 /uni002B C3 /uni002B … Resistors in Parallel/Capacitors in Series Two Resistors in Parallel Equal Resistors in Parallel == =NP NS EP ES IS IP ZP ZS 1 /uni002B 1 /uni002B 1 /uni002B …R1 R2 R3 1RTOTAL = 1 /uni002B 1 /uni002B 1 /uni002B …C1 C2 C3 1CTOTAL =/ R1/uni002BR2 R1 R2RTOTAL = Where R is the value of one of the equal resistors, and N is the number of equal resistors N RRTOTAL = VI IR √PR I P I2 P P V2 I V R P V PR V R V2 I2R B.W.
中文译读逐句译读：这句话围绕 阻抗 展开；核心是在说明这些量/结构之间的定义、作用或约束关系。
补充注释阻抗：交流中电压与电流的复数比，包含电阻和电抗。。
原句SR. (Tuned Circuit) Q = Q & Resonant Frequency Formulas Reactance Formulas R XL Figure of Merit of a CoilQ = SR =o rH z2π√LC 1 √LC .159 L = 4π2 SR2 C 1 C = 4π2 SR2 L 1 XC = XL = 2π fL 2π fC 1 Impedance Formulas (Series) Z = √R2 /uni002B XL2 (Series RL) Z = √R2 /uni002B XC2 (Series RC) Z = XL – XC (Series LC) Z = √R2 /uni002B (XL – XC)2 (Series RLC) Z = VA I Voltage and Impedance Formulas (Parallel) Z = RXL (RL) Z = VA √R2 /uni002B XL2 ILINE Z = RXC (RC) VA = VL = VC = VR √R2 /uni002B XC2 Z = XL XC (LC) VA = ILINEZ XL – XC Z = RX (RLC) √R2 /uni002B X2 PI VR Op Amp Noise for Single-Pole System Closed-Loop Frequency Response for Voltage Feedback Amplifiers Resistor Johnson Noise Formula CLOSEDLOOP BW = fCL B A VN, R1 R1 R3 4kTR3 4kTR1 VN, R3 IN+ IN– VN 4kTR2 VN, R2 R2 NOISE GAIN = GAIN FROM “A” TO OUTPUT = NG = 1 + R2 R1 VOUT GAIN FROM “B” TO OUTPUT = – R2 R1 RTI NOISE = TOTAL BW /uni00D7.bold VN2 + 4kTR3 + 4kTR1 R2 R1 + R2 2 + IN+2 R32 + IN–2 R1 /uni00D7.bold R2 R1 + R2 2 + 4kTR2 R1 R1 + R2 2 RTO NOISE = NG /uni00D7.bold RTI NOISE RTI = REFER TO INPUT RTO = REFER TO OUTPUT BW = 1.57 fCL GAIN (dB) 6dB/OCTAVE ROLL-OFF LOOP GAIN, A/u1D6C3 A(S), OPEN-LOOP GAIN CLOSEDLOOP GAIN 1 /u1D6C3 NOISE GAIN, CLOSED-LOOP BANDWITH LOG FREQUENCY (HZ) RESISTANCE (/u1D6C0) 10,000 1000 10 1 0 10 1k 100k 10M100 10k 1M 100M 100en at 25°C nV Hz where: VR = resistor Johnson Noise spectral density k = Boltzmann’s constant (1.38 /uni00D7.bold 10–23 J/K) T = absolute temperature in Kelvin R = resistance in Ohms B = bandwidth in Hz = 4kTRBVR At 25°C, 4kT = 1.65 /uni00D7.bold 10–20 W/Hz, therefore, VR = 1.65 /uni00D7.bold 10–20RB Op Amp Noise for Single-Pole System Closed-Loop Frequency Response for Voltage Feedback Amplifiers Resistor Johnson Noise Formula CLOSEDLOOP BW = fCL B A VN, R1 R1 R3 4kTR3 4kTR1 VN, R3 IN+ IN– VN 4kTR2 VN, R2 R2 NOISE GAIN = GAIN FROM “A” TO OUTPUT = NG = 1 + R2 R1 VOUT GAIN FROM “B” TO OUTPUT = – R2 R1 RTI NOISE = TOTAL BW /uni00D7.bold VN2 + 4kTR3 + 4kTR1 R2 R1 + R2 2 + IN+2 R32 + IN–2 R1 /uni00D7.bold R2 R1 + R2 2 + 4kTR2 R1 R1 + R2 2 RTO NOISE = NG /uni00D7.bold RTI NOISE RTI = REFER TO INPUT RTO = REFER TO OUTPUT BW = 1.57 fCL GAIN (dB) 6dB/OCTAVE ROLL-OFF LOOP GAIN, A/u1D6C3 A(S), OPEN-LOOP GAIN CLOSEDLOOP GAIN 1 /u1D6C3 NOISE GAIN, CLOSED-LOOP BANDWITH LOG FREQUENCY (HZ) RESISTANCE (/u1D6C0) 10,000 1000 10 1 0 10 1k 100k 10M100 10k 1M 100M 100en at 25°C nV Hz where: VR = resistor Johnson Noise spectral density k = Boltzmann’s constant (1.38 /uni00D7.bold 10–23 J/K) T = absolute temperature in Kelvin R = resistance in Ohms B = bandwidth in Hz = 4kTRBVR At 25°C, 4kT = 1.65 /uni00D7.bold 10–20 W/Hz, therefore, VR = 1.65 /uni00D7.bold 10–20RB Op Amp Noise for Single-Pole System Closed-Loop Frequency Response for Voltage Feedback Amplifiers Resistor Johnson Noise Formula CLOSEDLOOP BW = fCL B A VN, R1 R1 R3 4kTR3 4kTR1 VN, R3 IN+ IN– VN 4kTR2 VN, R2 R2 NOISE GAIN = GAIN FROM “A” TO OUTPUT = NG = 1 + R2 R1 VOUT GAIN FROM “B” TO OUTPUT = – R2 R1 RTI NOISE = TOTAL BW /uni00D7.bold VN2 + 4kTR3 + 4kTR1 R2 R1 + R2 2 + IN+2 R32 + IN–2 R1 /uni00D7.bold R2 R1 + R2 2 + 4kTR2 R1 R1 + R2 2 RTO NOISE = NG /uni00D7.bold RTI NOISE RTI = REFER TO INPUT RTO = REFER TO OUTPUT BW = 1.57 fCL GAIN (dB) 6dB/OCTAVE ROLL-OFF LOOP GAIN, A/u1D6C3 A(S), OPEN-LOOP GAIN CLOSEDLOOP GAIN 1 /u1D6C3 NOISE GAIN, CLOSED-LOOP BANDWITH LOG FREQUENCY (HZ) RESISTANCE (/u1D6C0) 10,000 1000 10 1 0 10 1k 100k 10M100 10k 1M 100M 100en at 25°C nV Hz where: VR = resistor Johnson Noise spectral density k = Boltzmann’s constant (1.38 /uni00D7.bold 10–23 J/K) T = absolute temperature in Kelvin R = resistance in Ohms B = bandwidth in Hz = 4kTRBVR At 25°C, 4kT = 1.65 /uni00D7.bold 10–20 W/Hz, therefore, VR = 1.65 /uni00D7.bold 10–20RB Op Amp Noise for Single-Pole System Closed-Loop Frequency Response for Voltage Feedback Amplifiers Resistor Johnson Noise Formula CLOSEDLOOP BW = fCL B A VN, R1 R1 R3 4kTR3 4kTR1 VN, R3 IN+ IN– VN 4kTR2 VN, R2 R2 NOISE GAIN = GAIN FROM “A” TO OUTPUT = NG = 1 + R2 R1 VOUT GAIN FROM “B” TO OUTPUT = – R2 R1 RTI NOISE = TOTAL BW /uni00D7.bold VN2 + 4kTR3 + 4kTR1 R2 R1 + R2 2 + IN+2 R32 + IN–2 R1 /uni00D7.bold R2 R1 + R2 2 + 4kTR2 R1 R1 + R2 2 RTO NOISE = NG /uni00D7.bold RTI NOISE RTI = REFER TO INPUT RTO = REFER TO OUTPUT BW = 1.57 fCL GAIN (dB) 6dB/OCTAVE ROLL-OFF LOOP GAIN, A/u1D6C3 A(S), OPEN-LOOP GAIN CLOSEDLOOP GAIN 1 /u1D6C3 NOISE GAIN, CLOSED-LOOP BANDWITH LOG FREQUENCY (HZ) RESISTANCE (/u1D6C0) 10,000 1000 10 1 0 10 1k 100k 10M100 10k 1M 100M 100en at 25°C nV Hz where: VR = resistor Johnson Noise spectral density k = Boltzmann’s constant (1.38 /uni00D7.bold 10–23 J/K) T = absolute temperature in Kelvin R = resistance in Ohms B = bandwidth in Hz = 4kTRBVR At 25°C, 4kT = 1.65 /uni00D7.bold 10–20 W/Hz, therefore, VR = 1.65 /uni00D7.bold 10–20RB √P Decibel (dB) Formulas (Equal Impedances) db = 10 Log = 20 LogPOUT PIN VOUT VIN = 20 Log (Gain) IOUT IIN Transformers (Step-Up or Step-Down Ratios) Sinusoidal Voltages and Currents RMS = Root Mean Square = Effective VRMS = 0.707 VPEAK = VEFF VAVE = 0.637 VPEAK VEFF = 1.11 VAVE VPEAK = 1.57 VAVE VAVE = 0.9 VEFF Ohm’s Law (DC Circuits) Resistors in Series/Capacitors in Parallel RTOTAL = R1 /uni002B R2 /uni002B R3 /uni002B … / CTOTAL = C1 /uni002B C2 /uni002B C3 /uni002B … Resistors in Parallel/Capacitors in Series Two Resistors in Parallel Equal Resistors in Parallel == =NP NS EP ES IS IP ZP ZS 1 /uni002B 1 /uni002B 1 /uni002B …R1 R2 R3 1RTOTAL = 1 /uni002B 1 /uni002B 1 /uni002B …C1 C2 C3 1CTOTAL =/ R1/uni002BR2 R1 R2RTOTAL = Where R is the value of one of the equal resistors, and N is the number of equal resistors N RRTOTAL = VI IR √PR I P I2 P P V2 I V R P V PR V R V2 I2R B.W.
中文译读逐句译读：这句话围绕 运放、环路增益、噪声增益、阻抗、电阻、频率响应、带宽 展开；核心是在说明这些量/结构之间的定义、作用或约束关系。
补充注释运放：高增益差分放大器；分析时先确认是否处于负反馈线性区。；环路增益：开环增益与反馈因子的乘积，决定闭环精度和稳定裕量。；噪声增益：输入误差被放大到输出的倍数；稳定性分析经常看噪声增益而不是信号增益。；阻抗：交流中电压与电流的复数比，包含电阻和电抗。。
原句SR. (Tuned Circuit) Q = Q & Resonant Frequency Formulas Reactance Formulas R XL Figure of Merit of a CoilQ = SR =o rH z2π√LC 1 √LC .159 L = 4π2 SR2 C 1 C = 4π2 SR2 L 1 XC = XL = 2π fL 2π fC 1 Impedance Formulas (Series) Z = √R2 /uni002B XL2 (Series RL) Z = √R2 /uni002B XC2 (Series RC) Z = XL – XC (Series LC) Z = √R2 /uni002B (XL – XC)2 (Series RLC) Z = VA I Voltage and Impedance Formulas (Parallel) Z = RXL (RL) Z = VA √R2 /uni002B XL2 ILINE Z = RXC (RC) VA = VL = VC = VR √R2 /uni002B XC2 Z = XL XC (LC) VA = ILINEZ XL – XC Z = RX (RLC) √R2 /uni002B X2 PI VR √P Decibel (dB) Formulas (Equal Impedances) db = 10 Log = 20 LogPOUT PIN VOUT VIN = 20 Log (Gain) IOUT IIN Transformers (Step-Up or Step-Down Ratios) Sinusoidal Voltages and Currents RMS = Root Mean Square = Effective VRMS = 0.707 VPEAK = VEFF VAVE = 0.637 VPEAK VEFF = 1.11 VAVE VPEAK = 1.57 VAVE VAVE = 0.9 VEFF Ohm’s Law (DC Circuits) Resistors in Series/Capacitors in Parallel RTOTAL = R1 /uni002B R2 /uni002B R3 /uni002B … / CTOTAL = C1 /uni002B C2 /uni002B C3 /uni002B … Resistors in Parallel/Capacitors in Series Two Resistors in Parallel Equal Resistors in Parallel == =NP NS EP ES IS IP ZP ZS 1 /uni002B 1 /uni002B 1 /uni002B …R1 R2 R3 1RTOTAL = 1 /uni002B 1 /uni002B 1 /uni002B …C1 C2 C3 1CTOTAL =/ R1/uni002BR2 R1 R2RTOTAL = Where R is the value of one of the equal resistors, and N is the number of equal resistors N RRTOTAL = VI IR √PR I P I2 P P V2 I V R P V PR V R V2 I2R B.W.
中文译读逐句译读：这句话围绕 阻抗 展开；核心是在说明这些量/结构之间的定义、作用或约束关系。
补充注释阻抗：交流中电压与电流的复数比，包含电阻和电抗。。
原句SR. (Tuned Circuit) Q = Q & Resonant Frequency Formulas Reactance Formulas R XL Figure of Merit of a CoilQ = SR =o rH z2π√LC 1 √LC .159 L = 4π2 SR2 C 1 C = 4π2 SR2 L 1 XC = XL = 2π fL 2π fC 1 Impedance Formulas (Series) Z = √R2 /uni002B XL2 (Series RL) Z = √R2 /uni002B XC2 (Series RC) Z = XL – XC (Series LC) Z = √R2 /uni002B (XL – XC)2 (Series RLC) Z = VA I Voltage and Impedance Formulas (Parallel) Z = RXL (RL) Z = VA √R2 /uni002B XL2 ILINE Z = RXC (RC) VA = VL = VC = VR √R2 /uni002B XC2 Z = XL XC (LC) VA = ILINEZ XL – XC Z = RX (RLC) √R2 /uni002B X2 PI VR √P Decibel (dB) Formulas (Equal Impedances) db = 10 Log = 20 LogPOUT PIN VOUT VIN = 20 Log (Gain) IOUT IIN Transformers (Step-Up or Step-Down Ratios) Sinusoidal Voltages and Currents RMS = Root Mean Square = Effective VRMS = 0.707 VPEAK = VEFF VAVE = 0.637 VPEAK VEFF = 1.11 VAVE VPEAK = 1.57 VAVE VAVE = 0.9 VEFF Ohm’s Law (DC Circuits) Resistors in Series/Capacitors in Parallel RTOTAL = R1 /uni002B R2 /uni002B R3 /uni002B … / CTOTAL = C1 /uni002B C2 /uni002B C3 /uni002B … Resistors in Parallel/Capacitors in Series Two Resistors in Parallel Equal Resistors in Parallel == =NP NS EP ES IS IP ZP ZS 1 /uni002B 1 /uni002B 1 /uni002B …R1 R2 R3 1RTOTAL = 1 /uni002B 1 /uni002B 1 /uni002B …C1 C2 C3 1CTOTAL =/ R1/uni002BR2 R1 R2RTOTAL = Where R is the value of one of the equal resistors, and N is the number of equal resistors N RRTOTAL = VI IR √PR I P I2 P P V2 I V R P V PR V R V2 I2R B.W.
中文译读逐句译读：这句话围绕 阻抗 展开；核心是在说明这些量/结构之间的定义、作用或约束关系。
补充注释阻抗：交流中电压与电流的复数比，包含电阻和电抗。。
原句SR. (Tuned Circuit) Q = Q & Resonant Frequency Formulas Reactance Formulas R XL Figure of Merit of a CoilQ = SR =o rH z2π√LC 1 √LC .159 L = 4π2 SR2 C 1 C = 4π2 SR2 L 1 XC = XL = 2π fL 2π fC 1 Impedance Formulas (Series) Z = √R2 /uni002B XL2 (Series RL) Z = √R2 /uni002B XC2 (Series RC) Z = XL – XC (Series LC) Z = √R2 /uni002B (XL – XC)2 (Series RLC) Z = VA I Voltage and Impedance Formulas (Parallel) Z = RXL (RL) Z = VA √R2 /uni002B XL2 ILINE Z = RXC (RC) VA = VL = VC = VR √R2 /uni002B XC2 Z = XL XC (LC) VA = ILINEZ XL – XC Z = RX (RLC) √R2 /uni002B X2 PI VR √P Decibel (dB) Formulas (Equal Impedances) db = 10 Log = 20 LogPOUT PIN VOUT VIN = 20 Log (Gain) IOUT IIN Transformers (Step-Up or Step-Down Ratios) Sinusoidal Voltages and Currents RMS = Root Mean Square = Effective VRMS = 0.707 VPEAK = VEFF VAVE = 0.637 VPEAK VEFF = 1.11 VAVE VPEAK = 1.57 VAVE VAVE = 0.9 VEFF Ohm’s Law (DC Circuits) Resistors in Series/Capacitors in Parallel RTOTAL = R1 /uni002B R2 /uni002B R3 /uni002B … / CTOTAL = C1 /uni002B C2 /uni002B C3 /uni002B … Resistors in Parallel/Capacitors in Series Two Resistors in Parallel Equal Resistors in Parallel == =NP NS EP ES IS IP ZP ZS 1 /uni002B 1 /uni002B 1 /uni002B …R1 R2 R3 1RTOTAL = 1 /uni002B 1 /uni002B 1 /uni002B …C1 C2 C3 1CTOTAL =/ R1/uni002BR2 R1 R2RTOTAL = Where R is the value of one of the equal resistors, and N is the number of equal resistors N RRTOTAL = VI IR √PR I P I2 P P V2 I V R P V PR V R V2 I2R B.W.
中文译读逐句译读：这句话围绕 阻抗 展开；核心是在说明这些量/结构之间的定义、作用或约束关系。
补充注释阻抗：交流中电压与电流的复数比，包含电阻和电抗。。

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