3-1

EE105Microelectronic Devices and Circuits

Prof. Ming C. Wu

wu@eecs.berkeley.edu

511 Sutardja Dai Hall (SDH)

3-2

Ideal Op Amp

Op-Ampwith dc bias

• Infinite open-loop gain, ! = ∞• Infinite input impedance

– No current goes in

• Zero output impedance

• %& = %' with feedback circuit

• Infinite bandwidth

• Infinite common-mode rejection

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3-3

Inverting Amplifier

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3-4

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3-5

Non-Inverting Amplifier

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3-6

Non-Inverting Amplifier:Input and Output Resistances

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3-7

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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3-8

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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3-9

Transfer Function

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

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3-10

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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3-11

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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3-12

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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3-13

Gain-Bandwidth Trade-off

3-14

Frequency Response of Open-Loop Op Amp

A( jω) = A0

1+ jω /ωb

A0 : dc gainωb : 3dB frequencyωt = A0ωb : unity-gain bandwidth(or "gain-bandwidth product")

For high frequency, ω >>ωb

A( jω) = ωt

jω

Single pole response with a dominant pole at ωb

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3-15

Bandwidth Extension with Feedback

• Overall transfer function with feedback:

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3-16

Bandwidth Extension and Gain Reduction

• Bandwidth increase:

!" = (1 + '())+,• Gain reduces:

- = '(1 + '()

• Gain-Bandwidth Product remains constant:

-×!" = '(+,

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3-17

Gain – Bandwidth Trade-off

3-18

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

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3-19

Voltage Gain of Inverting Amplifier with Finite Open-Loop Gain

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3-20

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:

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R2

R1

"

#$

%

&'

1

1+ (1+ R2 / R1)A

2. Substitute A with A( jω) = A0

1+ jω /ωb

3. Simplify the expression

G(ω) = −R2

R1

"

#$

%

&'

1

1+ (1+ R2 / R1)1+ jω /ωb

A0

= −R2

R1

"

#$

%

&'

1

1+ (1+ R2 / R1)A0

+jωA0ωb

1+ R2 / R1

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3-21

Frequency Response of Closed-Loop Inverting Amplifier Example

G(ω) ≈ −R2

R1

#

$%

&

'(

1

1+ jωω3dB

where ω3dB =A0ωb

1+ R2 / R1

Note: (1) 3-dB frequency is higher than open-loop bandwidth, ωb (2) Gain-bandwidth product remains unchanged:

G×BW =R2

R1

A0ωb

1+ R2 / R1

≈R2

R1

A0ωb

R2 / R1

= A0ωb =ωt

Same unity-gain frequency: ftR2R1

f3dB ≈A0

R2 / R1fb

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