ee105 microelectronic devices and...
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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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3-4
Inverting Amplifier:Input and Output ResistancesRI
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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
OTABuffer if
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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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3-14
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:
!" = $ %& !' − )!" ; $ %& = $"1 + % &&-j
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3-16
Bandwidth Extension and Gain Reduction
• Bandwidth increase:
!" = (1 + '())+,• Gain reduces:
- = '(1 + '()
• Gain-Bandwidth Product remains constant:
-×!" = '(+,
extension
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
" = $%1 + $%(
= $%1 + $%
≈ 1
*+ = (1 + $%()./ = (1 + $%)./ ≈ $%./
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3-19
Voltage Gain of Inverting Amplifier with Finite Open-Loop Gain
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3-20
Frequency Response of Closed-Loop Op Amp
Steps to find frequency response of closed-loop amplifiers:1. Find the transfer function with finite open-loop gain. For example, for inverting amplifier:
G =vovI= −
R2
R1
"
#$
%
&'
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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