EE 434 Lecture 19

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EE 434Lecture 19

• Model Extension
• Small signal model extension
• Small signal analysis

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Quiz 13
Assume the MOS transistor in this circuit was
designed in a 0.6u process with device parameters
µCOX100µA/V2 and VT1V. With the square-law
model of the device introduced in class, it can
be shown that the small-signal gain for this
circuit is
where gm is the transconductance gain of the
transistor. Assume a reverse-engineering team is
trying to determine what the dimensions are of
the device and can not open the package to see
the device. They did, however, measure the
small signal voltage gain and it was -4 and they
measured the quiescent VGS and it was 3V. What
is W/L for the transistor?
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And the number is .
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And the number is .
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Quiz 13
Assume the MOS transistor in this circuit was
designed in a 0.6u process with device parameters
µCOX100µA/V2 and VT1V. With the square-law
model of the device introduced in class, it can
be shown that the small-signal gain for this
circuit is
where gm is the transconductance gain of the
transistor. Assume a reverse-engineering team is
trying to determine what the dimensions are of
the device and can not open the package to see
the device. They did, however, measure the
small signal voltage gain and it was -4 and they
measured the quiescent VGS and it was 3V. What
is W/L for the transistor?
Solution
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Quiz 13
Assume the MOS transistor in this circuit was
designed in a 0.6u process with device parameters
µCOX100µA/V2 and VT1V. With the square-law
model of the device introduced in class, it can
be shown that the small-signal gain for this
circuit is
where gm is the transconductance gain of the
transistor. Assume a reverse-engineering team is
trying to determine what the dimensions are of
the device and can not open the package to see
the device. They did, however, measure the
small signal voltage gain and it was -4 and they
measured the quiescent VGS and it was 3V. What
is W/L for the transistor?
Solution
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Quiz 13
Assume the MOS transistor in this circuit was
designed in a 0.6u process with device parameters
µCOX100µA/V2 and VT1V. With the square-law
model of the device introduced in class, it can
be shown that the small-signal gain for this
circuit is
where gm is the transconductance gain of the
transistor. Assume a reverse-engineering team is
trying to determine what the dimensions are of
the device and can not open the package to see
the device. They did, however, measure the
small signal voltage gain and it was -4 and they
measured the quiescent VGS and it was 3V. What
is W/L for the transistor?
Solution
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Review from Last Time
Small signal model for MOS transistor was
developed
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Review from Last Time
Model Extension to Account for Slope of ID-VDS
Characteristics
Introduces a discontinuity between triode and
saturation regions Does not exist in real
devices Multiply by 1?VDS in triode
region as well in simulators
Issue of how gm varies with IDQ discussed and
apparent delima identified
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How does gm vary with IDQ?
Review from Last Time
Varies with the square root of IDQ
Varies linearly with IDQ
Doesnt vary with IDQ
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Graphical Interpretation of MOS Model
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Graphical Interpretation of MOS Model
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Further Model Extensions
Existing model does not depend upon the bulk
voltage !
Observe that changing the bulk voltage will
change the electric field in the channel region !
E
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Further Model Extensions
Existing model does not depend upon the bulk
voltage !
Observe that changing the bulk voltage will
change the electric field in the channel region !
E
Changing the bulk voltage will change the
thickness of the inversion layer
Changing the bulk voltage will change the
threshold voltage of the device
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Typical Effects of Bulk on Threshold Voltage for
n-channel Device
Bulk-Diffusion Generally Reverse Biased (VBSlt 0
or at least less than 0.3V) for n-channel
Shift in threshold voltage with bulk voltage can
be substantial Often VBS0
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Typical Effects of Bulk on Threshold Voltage for
p-channel Device
Bulk-Diffusion Generally Reverse Biased (VBS gt 0
or at least greater than -0.3V) for n-channel
Same functional form as for n-channel devices but
VT0 is now negative and the magnitude of VT still
increases with the magnitude of the reverse bias
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Model Extension Summary
Model Parameters µ,COX,VT0,f,?,?
Design Parameters W,L but only one degree
of freedom W/L
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Small-Signal Model Extension
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Small Signal Model Summary
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Small Signal Model Observation
Consider
3 alternate equivalent expressions for gm
If µCOX100µA/V2 , ?.01V-1, ? 0.4V0.5,
VEBQ1V, W/L1, VBSQ0V
In this example
This relationship is common
In many circuits, VBS0 as well
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Small Signal Model Summary
Large Signal Model
Small Signal Model
where
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How does gm vary with IDQ?
Varies with the square root of IDQ
Varies linearly with IDQ
Doesnt vary with IDQ
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How does gm vary with IDQ?
All of the above are true but with qualification
gm is a function of more than one variable (IDQ)
and how it varies depends upon how the remaining
variables are constrained
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Small Signal Model Summary
An equivalent circuit
This contains absolutely no more information than
the previous model
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Small Signal Model Summary
More convenient representation
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Small Signal Model Summary
Simplification that is often adequate
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Small Signal Model Summary
Even further simplification that is often adequate
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Small Signal Model Summary
Alternate equivalent representations for gm
from
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Small-Signal Circuit Analysis

• Obtain dc equivalent circuit by replacing all
  elements with large-signal (dc) equivalent
  circuits
• Obtain dc operating points (Q-point)
• Obtain ac equivalent circuit by replacing all
  elements with small-signal equivalent circuits
• Analyze linear small-signal equivalent circuit

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Dc and small-signal equivalent elements
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Dc and small-signal equivalent elements
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End of Lecture 19
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Small signal analysis example
uCOX100uA/V2 VT.75V ?.01V-1 VDD8V VSS
-1.25V W16u L1u R115K
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Small signal analysis example
Must solve 5 simultaneous equations to obtain VOUT
But one of these equations is nonlinear making
the solution very tedious
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Small signal analysis example
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Small signal analysis example
Q-point
Consider VIN very small
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Small signal analysis example
Consider VIN0,Vm,-Vm
Define VEBVGS-VT when VIN0 Thus VEB-VSS-VT
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Small signal analysis example
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Small signal analysis example
This is termed the quiescent output voltage
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Small signal analysis example
5V
Q-point
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Small signal analysis example
If VM0.1V
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Small signal analysis example
VIN-VM
3.68
5.0
6.08
VINVM
Note signal swing is not symmetric
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Small signal analysis example
Parametric expression for apparent gain
Note Apparent gain is independent of VM
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Small signal analysis example
Very simple expression for apparent gain
Derivation of apparent gain very tedious
Apparent gain gives minimal insight into design
strategies
Near the Q-point, all well-behaved circuits
operate linearly
Can this linear operation be exploited to
simplify the analysis?
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Small signal analysis example
Circuit Schematic
Linearized Small Signal Circuit
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Small signal analysis example
Linearized Small Signal Circuits
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Small signal analysis example
Linearized Small Signal Circuits

Still need IDQ and VEB
Small signal analysis much simpler (because
linear)
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Small signal analysis example
Linearized Small Signal Circuits
This is identical to the numerical value obtained
for the apparent gain !
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Small signal analysis example
How does small signal gain compare to apparent
gain for this circuit?
For this circuit the apparent gain and the actual
gain are identical
This is not true in general but they will be
close provided VM is reasonably small and they
become equal in the limit as VM approaches 0