EE105 – Fall 2015 Microelectronic Devices and Circuits Prof. Ming C. Wu [email protected] 511 Sutardja Dai Hall (SDH) 3-1 Ideal Op Amp • Infinite open-loop gain, � = ∞ • Infinite input impedance – No current goes in • Zero output impedance • �& = �' with feedback circuit • Infinite bandwidth Op-Amp • Infinite common-mode with dc bias rejection 3-2 1 Inverting Amplifier 3-3 Inverting Amplifier: Input and Output Resistances 3-4 2 Non-Inverting Amplifier 3-5 Non-Inverting Amplifier: Input and Output Resistances 3-6 3 Practical Op-Amps • Linear Imperfections: – Finite open-loop gain (�� < ∞ ) – Finite input resistance (�� < ∞ ) – Non-zero output resistance (�� > � ) – Finite bandwidth / Gain-BW Trade-off • Other (non-linear) imperfections: – Slew rate limitations – Finite swing – Offset voltage – Input bias and offset currents – Noise and distortion 3-7 Simple Model of Amplifier • Input and output capacitances are added • Any amplifier has input capacitance due to transistors and packaging / board parasitics • Output capacitance is usually dominated by load – Driving cables or a board trace 3-8 4 Transfer Function • Using the concept of impedance, it’s easy to derive the transfer function 3-9 Operational Transconductance Amp • Also known as an “OTA” – If we “chop off” the output stage of an op-amp, we get an OTA • An OTA is essentially a Gm amplifier. It has a current output, so if we want to drive a load resistor, we need an output stage (buffer) • Many op-amps are internally constructed from an OTA + buffer 3-10 5 Op-Amp Model • The model closely resembles the insides of an op-amp • The input OTA stage drives a high Z node to generate a very large voltage gain • The output buffer then can drive a low impedance load and preserve the high voltage gain 3-11 Op-Amp Gain / Bandwidth • The dominant frequency response of the op-amp is due to the time constant formed at the high-Z node � = �/�1 1 �345 = �6 = �1�1 • An interesting observation is that the gain-bandwidth product depends on Gm and Cx only 1 �/ �×�345 = �/�1 = �1�1 �1 3-12 6 Gain-Bandwidth Trade-off 3-13 Frequency Response of Open-Loop Op Amp A A( jω) = 0 1+ jω /ωb A0 : dc gain ωb : 3dB frequency ωt = A0ωb : unity-gain bandwidth (or "gain-bandwidth product") For high frequency, ω >> ωb ω A( jω) = t jω Single pole response with a dominant pole at ωb 3-14 7 Bandwidth Extension with Feedback • Overall transfer function with feedback: �; �; = � �� �> − ��; ; � �� = � 1 + � �6 3-15 Bandwidth Extension and Gain Reduction • Bandwidth increase: �� = (1 + �;�)�6 • Gain reduces: � � = ; 1 + �;� • Gain-Bandwidth Product remains constant: �×�� = �;�6 3-16 8 Gain – Bandwidth Trade-off 3-17 Unity Gain Feedback Amplifier • An amplifier that has a feedback factor � = 1, such as a unity gain buffer, has the full GBW product frequency range � � � = ; = ; ≈ 1 1 + �;� 1 + �; �� = (1 + �;�)�6 = (1 + �;)�6 ≈ �;�6 3-18 9 Voltage Gain of Inverting Amplifier with Finite Open-Loop Gain 3-19 Frequency Response of Closed- Loop Op Amp Steps to find frequency response of closed-loop amplifiers: 1. Find the transfer function with finite open-loop gain. For example, for inverting amplifier: v " R % 1 G = o = $− 2 ' v R (1+ R2 / R1) I # 1 &1+ A A 2. Substitute A with A( jω) = 0 1+ jω /ωb 3. Simplify the expression " R % 1 G(ω) = − 2 $ ' 1 j / # R1 & + ω ωb 1+ (1+ R2 / R1) A0 " R % 1 = $− 2 ' R (1+ R2 / R1) jω # 1 &1+ + A " A ω % 0 $ 0 b ' #1+ R2 / R1 & 3-20 10 Frequency Response of Closed-Loop Inverting Amplifier Example # R & 1 A ω G(ω) ≈ %− 2 ( where ω = 0 b R jω 3dB 1 R / R $ 1 '1+ + 2 1 ω3dB Note: (1) 3-dB frequency is higher than open-loop bandwidth, ωb (2) Gain-bandwidth product remains unchanged: R2 A0ωb R2 A0ωb G × BW = ≈ = A0ωb = ωt R1 1+ R2 / R1 R1 R2 / R1 R2 R1 Same unity-gain frequency: ft A0 f3dB ≈ fb R2 / R1 3-21 11.