EE105 – Fall 2015 Microelectronic Devices and Circuits Ideal Op

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EE105 – Fall 2015 Microelectronic Devices and Circuits

Prof. Ming C. Wu [email protected] 511 Sutardja Dai Hall (SDH)

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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

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1 Inverting Amplifier

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Inverting Amplifier: Input and Output Resistances

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2 Non-Inverting Amplifier

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Non-Inverting Amplifier: Input and Output Resistances

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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

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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

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4 Transfer Function

• Using the concept of impedance, it’s easy to derive the transfer function

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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

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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

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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 � = � = ��

• An interesting observation is that the gain-bandwidth

product depends on Gm and Cx only 1 � �×� = �� = ��

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6 Gain-Bandwidth Trade-off

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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

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7 Bandwidth Extension with Feedback • Overall transfer function with feedback:

� � = � �� − �� ; � �� = � 1 + � �

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Bandwidth Extension and Gain Reduction • Bandwidth increase:

�� = (1 + ��)� • Gain reduces: � � = 1 + �� • Gain-Bandwidth Product remains constant:

�×�� = ��

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8 Gain – Bandwidth Trade-off

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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 + ��)� = (1 + �)� ≈ ��

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9 Voltage Gain of Inverting Amplifier with Finite Open-Loop Gain

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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

R1 Same unity-gain frequency: ft

A0 f3dB ≈ fb R2 / R1 3-21