Operational amplifiers junyoung song

Operational Amplifiers Junyoung Song

Operational Amplifiers Junyoung Song

Finite Open-Loop Gain & Bandwidth

Large-signal Operation of OP-AMP

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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

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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

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Effect of Finite Open-loop Gain

Model with Finite Open-loop Gain ( 𝒗𝟏 ≠ 𝒗𝟐)

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𝑨𝟎 = ∞Max 𝑹𝒊𝒏 = 𝟏𝑴

𝑹𝒊𝒏 = 𝟏𝑴

𝑮 = 𝟏𝟎𝟎

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Example 2.2

𝑨𝟎 = ∞Max 𝑹𝒊𝒏 = 𝟏𝑴

𝑹𝒊𝒏 = 𝟏𝑴

𝑮 = 𝟏𝟎𝟎

𝑹𝟏 ≪ 𝑨

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Voltage Follower

Unity-gain Buffer 𝑮 = 𝟏

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Difference Amplifier (1/3)

Circuit & Analysis

▪ With superposition analysis

• For differential gain

Gain through positive and

negative feedbacks should

be matched

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Difference Amplifier (2/3)

Circuit & Analysis

▪ For common-mode gain

▪ 𝒊𝟏 = 𝒗𝑰𝒄𝒎−

𝑹𝟒 𝑹𝟑+𝑹𝟒𝒗𝑰𝒄𝒎

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Difference Amplifier (3/3)

Circuit & Analysis

▪ Differential input resistance

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Instrumentation Amplifier (2/2)

Issues

▪ CMRR degradation

• Caused by the 1st stage

• Mismatching between A1 and A2

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Configuration

▪ Transient response 𝟎 ≤ 𝒕 ≤ 𝟏 𝒎𝒔

• 𝑣𝑂 𝑡 = −100(1 − 𝑒−0.01𝑡 )

At 𝒕 = 𝟏𝒎𝒔

▪ 𝒗𝑶 𝒕 = −𝟏𝟎𝟎 𝟏 − 𝒆−𝟎.𝟏 = −𝟗 𝟓

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Offset & Input Bias

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Offset Voltage

Definition

▪ Input voltage which makes output to be “0”

▪ Caused by the mismatch of the OP-AMP

Circuit Model

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Analysis with offset voltage

Case) Noninverting Operation

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AC-coupling Configuration

Capacitively Coupled Inverting Amplifier

▪ Widely used when we need to block the input DC voltage

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Input Bias and Offset Currents

Model (For OP-AMP based on BJT)

Usage

𝑰𝑶𝑺 = 𝑰𝑩𝟏 − 𝑰𝑩𝟐

𝑽𝑶 = 𝑰𝑩𝟏𝑹𝟐 ≈ 𝑰𝑩𝑹𝟐

𝑰𝑩 = 𝑰𝑩𝟏 + 𝑰𝟐 𝑩𝟐

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Typical Frequency Response of OP-AMP

Unity-gain bandwidthBandwidth

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Freq Response of Closed-loop Amplifiers

Case) Inverting Amplifier

▪ 𝑽𝒐

𝑽𝒊 = −

𝑹𝟐 𝑹𝟏

𝟏+𝟏+

𝑹𝟐 𝑹𝟏 𝑨

(Previously derived equation)

≈ 𝟏+−𝑹𝟐𝑹𝟏𝒔

𝝎𝒕 𝟏+ 𝑹𝟐 𝑹𝟏

𝑨𝟎 ≫ 𝟏 + 𝑹𝟐

𝑹𝟏

→𝝎𝟑𝒅𝑩 = 𝝎𝒕

𝟏+ 𝑹𝟐 𝑹𝟏

(Reduced by DC gain) Gain-bandwidth Product

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Gain-bandwidth Product

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Characteristics of OP-AMP

Output Voltage Saturation

▪ Limit of output voltage

▪ Can cause clipping

Output Current Limits

▪ Practical OP-AMP has a current limit

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