Analog Integrated Circuits

1
Analog Integrated Circuits Frequency Response
of Amplifiers Tai-Cheng Lee Electrical
Engineering/GIEE, NTU
2
Miller Effect
Millers Theorem
Miller Theorem only holds if we know a priori
that the circuit can be converted. The following
example is invalid for Millers theorem.
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Association of Poles with Nodes
Cascade amplifier
Each node has a time constant tj, thus the
transfer function can be represented as
,where tj is the product of the capacitance and
resistance seen at node j to ground.
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Common-Source (Emitter) Stage (I)
Common-source stage Based on Miller Effect
Thus, we can write the transfer function as

• Two primary errors
• Zeros are not taken into account.
• The gain gmRD would change with frequency.

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Common-Source (Emitter) Stage (II)
High-frequency small-signal model
Thus, we can write down KCL at X and Vout.
This circuit has a zero at sgm/CGD and two
poles. For small CL (load capacitance), we can
assume the pole at node X is dominant and make
an approximation. If the denominator is written
as.
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Common-Source (Emitter) Stage (II)
This output pole approach is valid if CGS
dominates the response. The transfer function
also exhibits a zero at sgm/CGD ? It yields a
serious problem when it is used in negative
feedback configuration.
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Common-Source (Emitter) Stage (III)
In high-speed applications, the input impedance
of the common- source stage is also important.
First-order approximation
At high frequencies, the effect of the output
node must be taken into account (if CGS is
negligible)
At low frequencies ? At high frequencies ?
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Source Follower (I)
Source follower with output load CL.
Not much intuition here, but for small CL, the
followers usually have a wide band. If two
poles are far apart, the dominant pole is
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Source Follower (II)
Input impedance
At low frequencies ? At high frequencies ?
Output impedance
How does this impedance vary with frequency?
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Source Follower (III)
Can we represent Zout with a passive R-L network?
Since Zout is first order, it can have only one
inductor and no other stage element. Considering
the cases at f0 and f8 , we arrive at this
equivalent circuit
The inductive behavior resulting from finite
source impedance may cause significant ringing or
even oscillation in the presence of heavy load
capacitance. Example Source follower as a
output buffer
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Common-Gate Stage
Common-base stage The input and output poles are
isolated from Each others. ? No Miller effect.
Input pole ? Output pole ?
Therefore, it has a wideband operation. But low
input impedance. Also, requires a low dc input
level.
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Cascode Stage (I)
Miller effect is much less significant, why?
Also a pole at node X, usually quite far.
Another pole at node Y, usually quite far.
Thus, contains a pole at and
falls at frequencies higher than this value.
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Cascode Stage (II)
If RD is replaced by a ideal current source
How does Miller effect affect the frequency
response of such circuit?
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Common-Mode AC Response
What happens to Av,CM at high frequency? Whats
the trade-off between CMRR and headroom?
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Differential Pair with Active Load

• For differential signals
• Two poles
• Miller effect at input
• Load cap at output

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Differential Pair with Current Mirror Load (I)

• Three poles
• Miller effect at input
• Load cap at output
• Time constant at node E

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Differential Pair with Current Mirror Load (II)
The appearance of the zero can be understood by
noting that the circuit consists of a slow path
in parallel with a fast path.