Operational amplifiers junyoung song

Operational Amplifiers Junyoung Song

Operational Amplifiers Junyoung Song Topics Ideal OP-AMP Various Configurations DC Imperfections Finite Open-Loop Gain & Bandwidth Large-signal Operation of OP-AMP Electronic Circuits Electronic Circuits Terminals Ideal OP-AMP OP-AMP with DC Power Supplies Electronic Circuits Function Purpose of OP-AMP ▪ Designed to sense the difference between the voltage signals applied at its two input terminals ▪ A: Differential gain (Open-loop gain) ▪ Common-mode rejection Electronic Circuits Characteristics of Ideal OP-AMP Infinite input impedance Zero output impedance Zero common-mode gain ▪ Infinite common-mode rejection Infinite open-loop gain A ▪ OP-AMP is not used alone Infinite bandwidth Electronic Circuits Differential & Common-mode Signals Differential input ▪ 𝒗𝑰𝒅 = 𝒗𝟐 − 𝒗𝟏 Common-mode input signal ▪ 𝒗𝑰𝒄𝒎 = 𝟏 𝟐 𝒗𝟏 + 𝒗𝟐 Each inputs 𝒗𝑰𝒅 𝟐 𝒗𝑰𝒅 𝒗𝑰𝒄𝒎 + 𝟐 ▪ 𝒗𝟏 = 𝒗𝑰𝒄𝒎 − ▪ 𝒗𝟐 = Electronic Circuits Electronic Circuits Inverting Configuration Circuit Virtual Ground Negative feedback Closed-loop Gain (G) ▪𝑮≡ 𝒗𝑶 𝒗𝑰 =? (Next page) Electronic Circuits With Circuit Model Virtual Ground 𝟎 − 𝒗𝑰 𝟎 − 𝒗𝑶 + =𝟎 𝑹𝟏 𝑹𝟐 𝑹𝟐 𝑮≡− 𝑹𝟏 Input Resistance 𝒗𝑰 𝒗𝑰 𝑹𝒊 ≡ = = 𝑹𝟏 𝒊𝟏 𝒗𝑰 − 𝟎 𝑹𝟏 Electronic Circuits 10 Offset Voltage Definition ▪ Input voltage which makes output to be “0” ▪ Caused by the mismatch of the OP-AMP Circuit Model Electronic Circuits 35 Analysis with offset voltage Case) Noninverting Operation 𝑽𝑶𝑺 𝑽𝑶𝑺 − 𝟎 𝑽𝑶𝑺 − 𝑽𝑶 + =𝟎 𝑹𝟏 𝑹𝟐 𝑽𝑶 = 𝑽𝑶𝑺 Electronic Circuits 𝑹𝟐 𝟏+ 𝑹𝟏 36 AC-coupling Configuration Capacitively Coupled Inverting Amplifier ▪ Widely used when we need to block the input DC voltage Electronic Circuits 37 Input Bias and Offset Currents Model (For OP-AMP based on BJT) 𝑰𝑶𝑺 = 𝑰𝑩𝟏 − 𝑰𝑩𝟐 Usage 𝑰𝑩𝟏 + 𝑰𝑩𝟐 𝑰𝑩 = 𝟐 𝑽𝑶 = 𝑰𝑩𝟏 𝑹𝟐 ≈ 𝑰𝑩 𝑹𝟐 Electronic Circuits 38 Effect of VOS and IOS with Inverting Integrator Analysis (VOS) ▪ With nodal analysis • 𝑉𝑂𝑆 −0 𝑅 • 𝑣𝑂 = + 𝑉𝑂𝑆 −𝑣𝑂 𝑠𝐶 1+𝑠𝐶𝑅 𝑉𝑂𝑆 𝑠𝐶𝑅 Analysis (IOS) • =0 = 𝑉𝑂𝑆 −𝐼𝐵2 𝑅−0 −𝐼𝐵2 𝑅−𝑣𝑂 + 𝑅 • 𝑣𝑂 = −𝐼𝐵2 − 𝑠𝐶 + 𝐼𝐵1 11 (𝐼 𝐶 𝑠 𝐵1 1 + 𝑅𝐶 𝑠 Integration→ Increasing over time 𝑹𝑭 can solve it!! =0 − 𝐼𝐵2 ) Same issue Electronic Circuits 39 Electronic Circuits 40 Typical Frequency Response of OP-AMP Bandwidth Unity-gain bandwidth Electronic Circuits 41 Freq Response of Closed-loop Amplifiers Case) Inverting Amplifier ▪ 𝑽𝒐 𝑽𝒊 = 𝑹 − 𝟐 𝑹𝟏 𝑹 𝟏+𝑹𝟐 𝟏+ 𝑨 𝟏 ▪𝑨 𝒔 = 𝑽𝒐 (𝒔) → 𝑽𝒊 (𝒔) = (Previously derived equation) 𝑨𝟎 𝒔 𝝎𝒃 𝟏+ (One-pole model) 𝑹 − 𝟐 𝑹𝟏 𝑹 𝟏 𝟏+𝑨 𝟏+𝑹𝟐 𝟏 𝟎 →𝝎𝟑𝒅𝑩 = 𝝎𝒕 𝑹 𝟏+𝑹𝟐 𝟏 𝒔 + 𝝎𝒕 𝑹 𝟏+ 𝟐 𝑹𝟏 ≈ 𝑹 − 𝟐 𝑹𝟏 𝒔 𝟏+ 𝝎𝒕 𝑹 𝟏+ 𝟐 𝑹𝟏 (Reduced by DC gain) Electronic Circuits 𝑨𝟎 ≫ 𝟏 𝑹𝟐 + 𝑹𝟏 Gain-bandwidth Product 42 Gain-bandwidth Product Electronic Circuits 43 Electronic Circuits 44 Characteristics of OP-AMP Output Voltage Saturation ▪ Limit of output voltage ▪ Can cause clipping Output Current Limits ▪ Practical OP-AMP has a current limit Electronic Circuits 45 Electronic Circuits 46 Ex 2.7 (Solution) a 𝑽𝒑 = 𝟏𝑽, 𝑹𝑳 = 𝟏𝒌𝛀 c 𝑹𝑳 = 𝟏𝒌𝛀, Max 𝑽𝒑 ? ▪ 𝑨𝒗 = 𝟏𝟎 [𝑽/𝑽] ▪ Because of supply, 𝑽𝒑,𝒎𝒂𝒙 = 𝟏 𝟑𝑽 ▪ 𝒗𝑶,𝒑𝒆𝒂𝒌 = 𝟏𝟎𝑽 ▪ 𝒊𝑳,𝒑𝒆𝒂𝒌 = 𝟏𝟎𝒎𝑨, 𝒊𝑭,𝒑𝒆𝒂𝒌 = 𝟏𝒎𝑨 →𝒊𝑶,𝒑𝒆𝒂𝒌 = 𝟏𝟏𝒎𝑨 b 𝑽𝒑 = 𝟏 𝟓𝑽, 𝑹𝑳 = 𝟏𝒌𝛀 ▪ 𝒗𝑶,𝒑𝒆𝒂𝒌 = 𝟏𝟑𝑽 (Clipping by supply) d 𝑽𝒑 = 𝟏𝑽, Lowest 𝑹𝑳 ? ▪ 𝒊𝑶,𝒎𝒂𝒙 = 𝟐𝟎𝒎𝑨 = ▪ 𝑹𝑳,𝒎𝒊𝒏 = 𝟓𝟐𝟔𝛀 𝟏𝟎𝑽 𝑹𝑳,𝒎𝒊𝒏 + 𝟏𝟎 𝟗𝒌𝛀+𝟏𝒌𝛀 ▪ 𝒊𝑳,𝒑𝒆𝒂𝒌 = 𝟏𝟑𝒎𝑨, 𝒊𝑭,𝒑𝒆𝒂𝒌 = 𝟏 𝟑𝒎𝑨 →𝒊𝑶,𝒑𝒆𝒂𝒌 = 𝟏𝟒 𝟑𝒎𝑨 Electronic Circuits 47 Slew-rate Definition ▪ Maximum rate of change ▪ 𝑺𝑹 = 𝒅𝒗𝑶 ቚ 𝒗𝒕 𝒎𝒂𝒙 Electronic Circuits 48