Electronics Primer
• ohms law
• Kirchhoff's current node rule
• define resistor
• define capacitor
• high/low pass RC filters
• s = jw
j notation,
t ti
w=2
2pii f
• filter transfer functions
Amplifiers and Analog Signal Processing
• Most bioelectric signals are small
• voltages in micro-volts range
• currents in pA and nA range common
• Small signals require amplification and filtering
• op-amp, resistors and capacitors
• integrated circuit and surface-mount technology
• Most modern signal processing tasks (filtering) are performed
on a digital signal processor.
• little change in amplification/filtering requirements over last 40 years
• but new interest in putting DSP algorithms into analog circuits
• due to demand for low power portable/implantable instruments
ECE 445: Biomedical Instrumentation
Ch3 Amplifier Basics. p. 2
Ideal Op-Amp
• Operational amplifier (op-amp) is a high-DC-gain differential
amplifier
ideal op-amp
• Design circuits assuming op-amps are ideal
A
vo  0
• then verify/modify using simulations/prototyping
• Ideal op-amp model
Rd  
• “open loop” gain: A = 
• differential
diff
ti l input
i
t resistance:
i t
Rd = 
• output resistance: Ro = 0
Ro  0
• input current = 0
• output voltage:
• vo = 0 when v1-v2 = 0
ideal op-amp small signal model
ECE 445: Biomedical Instrumentation
Ch3 Amplifier Basics. p. 3
Op-Amp Properties
• Properties
• open-loop gain: ideally infinite: practical values 20k-200k
• high open-loop gain  virtual short between + and - inputs
•
•
•
•
input impedance: ideally infinite: CMOS opamps are close to ideal
output impedance: ideally zero: practical values 20-100
zero output offset: ideally zero: practical value <1mV
gain-bandwidth
i b d idth product
d t (GB):
(GB) practical
ti l values
l
~MHz
MH
• frequency where open-loop gain drops to 1 V/V
• Commercial opamps provide many different properties
•
•
•
•
•
•
low noise
low input current
low power
high bandwidth
low/high supply voltage
special purpose: comparator, instrumentation amplifier
ECE 445: Biomedical Instrumentation
Ch3 Amplifier Basics. p. 4
Basic Op-Amp Principles
typical op-amp schematic symbol
vo, v1, v2 referenced to ground
• Open loop gain: vo = A (v2-v1)
• since A is very large, v1-v2 must be very small
• When the op-amp output is in its linear range
• two input terminals are at (essentially) the same voltage
• i.e., “virtual ground” between op-amp inputs
• rely
l on this
thi for
f DC/bias
DC/bi calculations
l l ti
• Single vs. Dual Supply Voltage
• most modern ICs use single supply
• “ground”
“
d” in a d
duall supply
l becomes
b
VDD/2
/ in single
l supply
l
• mid way between VDD and Ground
ECE 445: Biomedical Instrumentation
Ch3 Amplifier Basics. p. 5
Basic Opamp Configuration
• Voltage Comparator
• digitize input
g DC gain
g
• assumes veryy high
• Vcc = supply voltage
Vref
• Negative Feedback
• output tied back into negative input
terminal
• generally avoid positive feedback
Vout = Vcc (sign(Vin-Vref))
• Voltage Follower
• buffer
• prevents input signal from being
loaded down by a low-resistance
load
Rin = 
ECE 445: Biomedical Instrumentation
Ch3 Amplifier Basics. p. 6
Inverting/Non-Inverting Configurations
• Inverting Amplifier (uses negative feedback)
A
vo  R f

vi
Ri
• Non-Inverting
N I
ti A
Amplifier
lifi (also
( l uses negative
ti feedback)
f db k)
A
R f Ri  R f
vo
 1

vi
Ri
Rf
ECE 445: Biomedical Instrumentation
Ch3 Amplifier Basics. p. 7
Transfer Function Derivation
• Ideal op-amp conditions (simplify derivation)
• virtual short at inputs (voltage at + same as at - )
• no current into input terminals
• Inverting amplifier gain transfer function
• write equations of operation from schematic using Ohms law
• V
Vx – Vin = R1 * i1
• Vout – Vx = R2 * i2
i2
• apply ideal op-amp conditions
• virtual short  Vx = 0
• no input current  i1 = i2 = i
• thus
• -Vin = R1 * i  i = -Vin/R1
• Vout = R2 * i  i = Vout/R2
• and setting i = i…
•  -Vin/R1 = Vout/R2  Vout= -Vin (R2/R1)
Vx
i1
More Opamp Configurations
• Summing Amp
• weighted sum of
p inputs
p
multiple
• inverting or non??
• Differential Amp
• match R1s and R2s
• inverting or non??
Single-Ended
l
d d Amplifier
l f Representation
signal
noise
V in
V out
gnd
gnd
Av 
Noise Amplification
Vout
Vin
• even smallll interference
f
at input gets amplified
l f d at output
ECE 445: Biomedical Instrumentation
Ch3 Amplifier Basics. p. 9
Differential vs. Common Mode Signal
• Define
• x+ = input at + terminal
• x- = input at – terminal
• c = common mode signal on both inputs
• Differential inputs
Vout  x   x 
d iinputt
• Add common mode
• c rejected by differential amplifier (not amplified)
• c must be small enough to keep op-amp biased in linear operation
x
x
Vout  ( x   c)  ( x   c)
x  x
c
2
ECE 445: Biomedical Instrumentation
Ch3 Amplifier Basics. p. 10
Noise in Differential Amplifiers
• Global interference (e.g., supply voltage variations)
• assumed to be located far away from amp. input terminals
• same interference on both the terminals
• appear as common mode disturbance.
• example: clock noise
• Differential amplifiers
• amplify only the difference
• reject the interference (common-mode)
Vin
Vin
+
-
-
+

Vout

Vout
g
gone
at
output
common-mode
input noise
ECE 445: Biomedical Instrumentation
Ch3 Amplifier Basics. p. 11
Desirable Properties of Amplifiers
• High differential gain, Av
Vin

Vout
+ - +
Vin

Vout


Vout
 Vout
Av 
Vin  Vin
• Low common mode gain, Acm
= high
hi h “common
“
mode
d rejection”
j ti ”
Common-mode signal

in
V
Vin
+ - +
Vin  Vin
2
ACM

Vout

Vout


Vout
 Vout

Vin  Vin
2
common mode rejection ratio:
ECE 445: Biomedical Instrumentation
CMRR 
Av
Acm
Ch3 Amplifier Basics. p. 12
3-Op-Amp Instrumentation Amplifier
• Differential amplifiers
• low common mode gain = Great!
• lower than ideal input resistance – Bad!
• 3-op-amp structure
• keeps
k
llow common mode
d gain
i
• provides very high input resistance
• why?
• call “instrumentation
instrumentation amp
amp”
• will discuss in detail later
total differential gain
2 R  R1  R4 
 
Gd  2
R1  R3 
A
2 R2  R1
R1
Acom  1
ECE 445: Biomedical Instrumentation
Ch3 Amplifier Basics. p. 13
Comparator
• Compare an input voltage vi to a reference voltage vref
• Output digital value (hi/low)
• llow if vi > vref why
h low
l
and
d nott hi?
• high if vi < vref
• Output voltage = supply voltage
• Op-amp comparator
• Add hysteresis to improve noise immunity
• hysteresis
y
= rising
g transition point
p
different that falling
g transition point
p
• R3 controls hysteresis
ECE 445: Biomedical Instrumentation
Ch3 Amplifier Basics. p. 14
Logarithmic Amplifiers
• Uses non-linear current-voltage relationship of BJT in feedback
path
 IC 
VBE  k log 
 IS 
• Useful for computing logarithms and anti-logs
• for compressing and multiplying/dividing signals
A 10
A=10
A=1
A 1
A=1
A=10
ECE 445: Biomedical Instrumentation
Ch3 Amplifier Basics. p. 15
Integrating/Differentiating Configurations
• Integrating Amp
t
1
v   i dt
Co
  2f
• Differentiating Amp
iC
dv
dt
ECE 445: Biomedical Instrumentation
Ch3 Amplifier Basics. p. 16
Converting Configuration
• Current-to-Voltage
• Voltage-to-Current
ECE 445: Biomedical Instrumentation
Ch3 Amplifier Basics. p. 17
Active Filters
• Passive low pass filter
If Z1 is a resistor (R) and Z2 is a capacitor (1/sC) then
• Active low pass filter
( Rf / jCf )
Vo ( j )
Z
[(1 / jCf )  Rf ]
 f 
Ri
Vi ( j )
Zi

Rf
R
1
 f
(1  jRf Cf ) Ri
Ri 1  s
-3dB
3dB frequency
0  1 R C
f
f
=2f
0
Rf
Vo ( j )
1

Vi ( j )
Ri 1  jR f C f
ECE 445: Biomedical Instrumentation
Ch3 Amplifier Basics. p. 18
Active Filters
• Active high pass filter
R f jRi Ci
Vo ( j )

Vi ( j )
Ri 1  jRi Ci
0  1 R C
i i
ECE 445: Biomedical Instrumentation
Ch3 Amplifier Basics. p. 19
Active Filters
Band Pass Filter
Rf
jR f Ci
Vo ( j )

Vi ( j )
Ri (1  jR f C f )(1  jRi Ci )
2-stage Band Pass Filter
High Q (narrow frequency) Band Pass Filter
ECE 445: Biomedical Instrumentation
Ch3 Amplifier Basics. p. 20
Non-ideal Characteristics
• Offset voltage
• output not zero when the inputs to the amplifiers are equal
• could be in order of millivolts
• cancel offset voltage by adding an external “nulling” potentiometer
• Temperature Drift
• offset voltage can drift by 0.1 microvolts over one degree variation
• Finite (lower than infinite) input impedance
• can cause errors at input
• High output impedance
• limits load driving capabilities
• Noise
• Thermal noise or high
high-frequency
frequency noise
• Flicker noise: low-frequency noise
ECE 445: Biomedical Instrumentation
Ch3 Amplifier Basics. p. 21