Download Lecture32

EEL5225: Principles of MEMS Transducers (Fall 2003)
Instructor: Dr. Hui-Kai Xie
Introduction to Interface Electronics
z Lumped
Circuit Elements
z General Amplifiers
z Operational Amplifiers
Reading: Senturia, Chapter 14, p.353-395
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EEL5225: Principles of MEMS Transducers (Fall 2003)
Lecture 32 by
1
H.K. Xie 11/21/2003
Lumped Circuit Elements
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Linear 1-port (2-terminal) passive devices
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Resistor: energy dissipation
Capacitor: energy storage
Inductor: energy storage
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EEL5225: Principles of MEMS Transducers (Fall 2003)
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Lumped Circuit Elements
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Non-linear 1-port (2-terminal) passive devices
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P/N junction diode
Nonlinear I-V characteristic
 qvkTD

iD = I S  e − 1


Note: Diode voltage, vD = VD + vd
 qVkTD

DC : I D = I S  e − 1


 qI
Small − signal : i d =  D
 kT
1

=
v
 d r vd

d
Ref. Sedra and Smith, Microelectronic Circuits, p. 132.
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P/N Diode
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Low-frequency
large-signal
equivalent circuit
≈ 0.7V (silicon diode at
room temp.)
High-frequency
small-signal
equivalent circuit
Ref. Sedra and Smith, Microelectronic Circuits, p. 170.
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Zener Diode
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Exploits very sharp current-voltage characteristic at
reverse breakdown for voltage regulation
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Ref. Sedra and Smith, Microelectronic Circuits, p. 172.
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EEL5225: Principles of MEMS Transducers (Fall 2003)
Diode Circuits
AC-to-DC converter
Ref. Sedra and Smith, Microelectronic Circuits, p. 176,184.
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Active Devices
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Sources
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Energy supplied into system from external source
(sometimes not shown)
z Independent voltage source
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with series source resistance
i
v
v
i
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Independent current source
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with shunt source resistance
EEL5225: Principles of MEMS Transducers (Fall 2003)
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Active Devices
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Sources
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Dependent sources
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Dependent voltage source
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Dependent current source
EEL5225: Principles of MEMS Transducers (Fall 2003)
Ref. Van Valkenbur, Network Analysis, p. 38.
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Active Devices -- BJT & MOSFET
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Cross-section
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N/P/N Bipolar Junction
Transistor (BJT)
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n-channel Metal Oxide
Semiconductor Field
Effect Transistor
(n-channel MOSFET)
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EEL5225: Principles of MEMS Transducers (Fall 2003)
Ref. Sedra and Smith, Microelectronic
Circuits, p. 231, 355.
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Active Devices -- BJT & MOSFET
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Common-emitter configuration
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iC vs. vCE DC characteristics
with base-emitter voltage (or
base current) as parameter
Other configurations are
common-base and commoncollector
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Common-source configuration
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iD vs. vDS DC characteristics with
gate-to-source voltage as
parameter
Other configurations are commongate and common-drain
Ref. Sedra and Smith, Microelectronic Circuits, p. 240, 367.
EEL5225: Principles of MEMS Transducers (Fall 2003)
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Active Devices -- BJT & MOSFET
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BJT High-Frequency Small-signal Equivalent Circuit
MOSFET High-Frequency Small-signal Equivalent Circuit
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Ref. Sedra and Smith, Microelectronic Circuits, p. 470, 445.
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EEL5225: Principles of MEMS Transducers (Fall 2003)
General Amplifiers
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Signal Amplification
Voltage gain, A V ≡
vO
vI
( 20 log A
dB )
( 20 log A
dB )
V
Current gain, A I ≡
iO
iI
Power gain, A P ≡
PL vO iO
=
PI
vI iI
I
(10 log AP
dB )
Note: We will discuss the frequency response later.
Ref. Sedra and Smith, Microelectronic Circuits, p. 11.
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General Amplifiers
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Amplifier Saturation
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hard limit at power supply limits
Jargon: “rail” = power supply
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rail-to-rail
Amplifier Nonlinearity
AV =
dvO
dvI
At operating point (known also as Quiescent point)
vO (t ) = VO + vo (t )
vI (t ) = VI + vi (t )
Ref. Sedra and Smith, Microelectronic Circuits, p. 16.
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General Amplifiers
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Voltage Amplifier Equivalent Circuit
Ri ≡ input resistance
RO ≡ output resistance
AV 0 ≡ open circuit voltage gain
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Voltage amplifier with signal source and load connected
vO = ( AV 0 vi )
vi = vS
RL
RL + RO
Ri
Ri + RS
Overall gain:
vO
Ri
RL
= AV 0
vS
Ri + RS RL + RO
Ref. Sedra and Smith, Microelectronic Circuits, p. 16.
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General Amplifiers
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Frequency Response of Amplifiers
For a linear circuit, for a sinusoidal input,
vi (t ) = Vi sin ω t , the output is sinusoidal
with the same frequency:
vo (t ) = Vo sin(ω t + φ )
Amplifier transfer function, T(ω ):
T(ω ) =
Vo
Vi
function of ω
∠T(ω )= φ function of ω
Analyze amplifier circuit in the complex
frequency variable (s- or Laplace-domain).
Ref. Sedra and Smith, Microelectronic Circuits, p. 20, 21.
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General Amplifiers
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Frequency Response of Amplifiers
Capacitively coupled ac-amplifier
Tuned or bandpass amplifier
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Direct-coupled dc-amplifier
Ref. Sedra and Smith, Microelectronic Circuits, p. 26..
EEL5225: Principles of MEMS Transducers (Fall 2003)
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Single Time-Constant Networks
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Review of Single Time-Constant Networks
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circuits that can be reduced to one reactive
component (capacitance or inductance) and one
resistive component
Low Pass Filter
High Pass Filter
Ref. Sedra and Smith, Microelectronic Circuits, p. 22.
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Single Time-Constant Networks
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Low Pass Filter
Replacing the circuit elements with their impedances,
1
R → R and C →
sC
V (s)
1
1
T (s) = o
=
=
s
Vi ( s ) 1 + sRC
1+
ω0
where ω 0 =
T ( jω ) =
1
τ
=
1
. Replacing s with jω ,
RC
1
ω 
1+  
 ω0 
2
Vi ( s )
1
sC
Vo ( s)
ω 
∠T ( jω ) = − tan −1  
 ω0 
Ref. Sedra and Smith, Microelectronic Circuits, p. 22.
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Single Time-Constant Networks
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Magnitude and Phase Response of Low Pass STC Network
ω = ω0 =
1
RC
Ref. Sedra and Smith, Microelectronic Circuits, p. 32.
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Single Time-Constant Networks
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High Pass Filter
Replacing the circuit elements with their impedances,
1
sC
V (s)
sRC
s
T (s) = o
=
=
Vi ( s ) sRC + 1 s + ω 0
R → R and C →
where ω 0 =
T ( jω ) =
1
τ
=
1
. Replacing s with jω ,
RC
1
sC
1
ω 
1+  0 
ω 
2
Vi ( s )
ω 
∠T ( jω ) = tan −1  0 
ω 
Vo ( s)
Ref. Sedra and Smith, Microelectronic Circuits, p. 22.
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Single Time-Constant Networks
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Magnitude and Phase Response of High Pass STC Network
ω = ω0 =
1
RC
Ref. Sedra and Smith, Microelectronic Circuits, p. 33.
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Single Time-Constant Networks
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Amplifier Frequency Response
A V0Vi
Find the amplifier voltage transfer function, DC gain, and high frequency roll-off.
Ref. Sedra and Smith, Microelectronic Circuits, p. 33.
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Single Time-Constant Networks
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Direct-coupled amplifier with input capacitance
Vo ( s ) =
RL
AV 0Vi ( s ) and Vi ( s ) =
RL + Ro
Ri //
1
sCi
1
+ RS
Ri //
sCi
Vs ( s )



Vo ( s ) 
1
1 
1
A V0Vi


= AV 0
T (s) =


Ro
Rs   1 + sCi ( RS // Ri ) 
Vi ( s ) 
+
+
1
1

RL
Ri 

This voltage transfer function has the same form as the low pass STC network.



1
1 

DC gain: T(s) s →0 =  AV 0
Ro
Rs 

+
+
1
1

RL
Ri 

1
1
High frequency rolloff: ω 0 = =
τ Ci ( RS // Ri )
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Ref. Sedra and Smith, Microelectronic Circuits, p. 22.
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Single Time-Constant Networks
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Direct-coupled Amplifier with Input Capacitance
Example: Rs = 20k Ω, Ri = 100k Ω, Ci = 60 pF
A V0 = 144
V
, Ro = 200Ω, RL = 1k Ω
V
A V0Vi
DC gain:


1
1
K =  A V0
Ro
Rs

+
+
1
1

RL
Ri



V
 = 100
V



High frequency rolloff:
ω0 =
1
τ
=
1
Ci ( RS // Ri )
= 159kHz
Ref. Sedra and Smith, Microelectronic Circuits, p. 33.
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Single Time-Constant Networks
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Capacitively-coupled Voltage Amplifier
Example: Capacitively coupled ideal voltage amplifier
T (s) =
Vo ( s )
= AV 0
Vi ( s )
s
s+
1
RC
High frequency gain:
K = AV 0 = 100
Low frequency rolloff:
1
1
ω0 = =
= 15.9 Hz
τ RC
Ref. Sedra and Smith, Microelectronic Circuits, p. 33.
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Application: Piezoresistive Microphone
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Capacitively coupled amplifier used to reject DC offset
Vs+
Hybrid Package
Microphone
R0
Lid
Capacitor
Microphone
Resistor
R0
Diff. Amp.
C R
Vb
G
R0
R0
OUT
C R
Amplifier
GND
Silicon
Substrate
Vs-
Package
Body
Ref. Arnold, MEMS-based Directional Acoustic
Array, M.S. Thesis 2001.
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Operational Amplifiers
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Operational Amplifiers
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Basic building block for analog
signal processing circuits
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z
z
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First integrated circuit operational
amplifier, µ709, made by Fairchild
Semiconductor in 1960s followed
by the µ741.
Consists of active transistors,
resistors, and limited number of
capacitors
Approximated by single-pole
frequency response
Power supply
Inverting input
Three stages
¦
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§
¨
Output
Differential amplifier stage
Amplifies difference between
two inputs
High-gain amplifier stage
Output amplifier stage
Non-inverting input
Power supply
Ref. Senturia, Microsystem Design, p. 382.
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Operational Amplifiers
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u741 Opamp
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Operational Amplifiers
Wide variety of
operational amplifiers:
•High power
•Low power
•Precision
•Low noise
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Operational Amplifiers
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Operational Amplifiers
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Operational Amplifiers
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General input signals
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z
Differential signal from transducer
Common mode signal
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For example, 60 Hz
electromagnetic interference
appearing on both inputs
vd
+ vcm
2
v
v− = − d + vcm
2
vd
v+ =
z
Differential gain
v
vo
Ad = o =
vd ( v+ − v− )
z
Common-mode gain
Acm =
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vo
vo
=
vcm ( v+ + v− ) / 2
Common Mode Rejection Ratio (CMRR)
CMRR =
Ad
A
or 20 log d
Acm
Acm
Actual opamps, CMRR range from
1000 to 100,000 (60dB to 100dB)
EEL5225: Principles of MEMS Transducers (Fall 2003)
Ref. Senturia, Microsystem Design, p. 382.
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Operational Amplifiers
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Voltage Follower
z Output follows input
z Vo=Vi
z
z
z
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Serves as buffer
Very high input
impedance
Low output
impedance
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Operational Amplifiers
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Non-inverting Amplifier
Short op-amp analysis method:
Assume that the input current is zero (infinite input impedance) and ε =0 (v+ ≈ v− ).
Using this method, we can analyze the transfer function for the non-inverting
amplifier:
vo
R
= 1+ 1
R2
vs
If R 2 = ∞,
vo
=1
vs
[Unity-gain buffer or voltage follower.]
Ref. Senturia, Microsystem Design, p. 387.
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Operational Amplifiers
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Inverting Amplifier
Open-loop gain is A.
Equating currents:
Vs − ε ε + Aε
=
R1
R2




Vo
R2 
1
 → − R2
Closed-loop gain:
=−
Vs
R1 
R1
R2  
1
1 +  1 +


A
R1  

∵ ε → 0 when A → ∞.
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Ref. Senturia, Microsystem Design, p. 385.
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Operational Amplifiers
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Inverting Amplifier
What is the frequency response of this configuration?
Replace A with the STC single-pole response, A( s ) =
A0
s
1+
s0
.
Substituting the single-pole response for A gives:




Vo
A0 s0
R2 
 with a DC gain of R 2
=−

R1
Vs
R1 

R2 
+
s
s
 A0 s0 +  1 +

(
)

0
R



1 

R2 
+
+
A
1
 0
 s0
R1 
and 3dB frequency determined by the pole at s0 = − 
.
R2
1+
R1
ω0
A0ω 0
Note that the gain-bandwith product is preserved: A0 s0 .
Ref. Senturia, Microsystem Design, p. 387.
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Operational Amplifiers
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Transimpedance Amplifier
Since the input current is negligible,
vo = − R1 I s
The transimpedance amplifier (voltage at output proportional
to current at input) is used as a current-to-voltage converter.
Ref. Senturia, Microsystem Design, p. 389.
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Operational Amplifiers
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Integrator
Since the input current is negligible and the voltage at v− is approximately
the same as v+ at ground,
vs − 0
dv
= ic = C c
R1
dt
vc =
1
Vs (t )dt
R1C ∫
Note that the output voltage, vo = −vc .
Therefore,
vo = −
1
Vs (t )dt
∫
R1C
[Output is integral of input!]
Note: The integrator circuit is extremely sensitive to parasitic DC leakage currents.
Ref. Senturia, Microsystem Design, p. 389.
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Operational Amplifiers
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Differentiator
Similarly, we find that for the differentiator circuit,
vo = − R1C
dvs
dt
[Output is derivative of input!]
Note: The output of the differentiator is limited by how fast the output of the
change in output voltage
.
time
Typical slew rates are on the order of 1V/µ sec.
op-amp can change, defined by the slew rate=
Ref. Senturia, Microsystem Design, p. 390.
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