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6 Amplification Circuits
6.1 Requirements for Amplification
6.2 Structure of Amplifiers
6.3 Real Behaviour of Amplifiers
6.4.2 Zero Point Errors
6.4.3 Noise
Input Resistances, Output Resistance, Offset-Voltage,
Offset-Current, Bias-Current Drift, Transfer Behaviour, Output Voltage Swing,
Gain-Bandwidth-Product, Slew Rate , Common Mode Rejection
Difference Amplifier, Operation Amplifier
6.4 Correction of the Real Behavior
6.4.1 Frequency Behavior
P. 6-1
Prof. Dr.-Ing. O. Kanoun
Chair for Measurement and Sensor Technology
6.5 Instrumentation Amplifier
6.6 Applications of Inverting AmplifiersMultiplication, Division, Charge Amplifier,
Schmitt-Trigger, Control Circuits
6.7 Active Filters
defined transfer behaviour:
Linearity
Amplification independent on aging, fluctuations, environment influence and voltage supply
high input sensitivity
no influence on the measurand: High input resistance
for voltage amplifier very high
for current amplifier very low
stable output: Low output resistance
long life time
low noise
low energy consumption
6.1 Requirements to Amplification
P. 6-2
Prof. Dr.-Ing. O. Kanoun
Chair for Measurement and Sensor Technology
36.2 Structure of Amplifiers
Important:
Ouput circuit is galvanically independent
on the input circuit
positiver Eingangsruhestrom
Eingangswiderstand
negativer Eingangsruhestrom
Ue
Ua
Positive Input Bias Current
Output Resistance
Input ResistanceNegative Input Bias Current
Un
Ua
Ua
+ Uv
- Uv
Ud
Ua
+ Uv
- Uv
Saturation
Saturation
Equivalent Circuit and Transfer Characteristic
npd UUU
0V open loop voltage gain
Amplification
da UVU 0
CMCMda UVUVU 0
Total Amplification
with 740 1010 CMV
V
Real 104 < V0 < 107
Ideal
CMV common mode amplification
npCM UUU VUd 0
CMCMa UVU
Ideal 0
2
np
CM
UUUwith
(Differenzverstrkung)
(Gleichtaktverstrkung)
P. 6-4
Prof. Dr.-Ing. O. Kanoun
Chair for Measurement and Sensor Technology
6.2 Structure of Amplifiers
Principle of the Difference Amplifier
Ube1= Ube2 Ic1= Ic2 UA1= UA2
Ube1> Ube2 Ic1>> Ic2 UA1>> UA2
P. 6-5
Prof. Dr.-Ing. O. Kanoun
Chair for Measurement and Sensor Technology
6.2 Structure of Amplifiers
Simple Amplifier
Difference Amplifier Output stage
P. 6-6
Prof. Dr.-Ing. O. Kanoun
Chair for Measurement and Sensor Technology
6.2 Structure of Amplifiers
Integrated Standard Operation Amplifier xx741 (Principle)
Current Mirror
Difference Amplifier
Second Amplification Stage Output Stage
P. 6-7
Prof. Dr.-Ing. O. Kanoun
Chair for Measurement and Sensor Technology
6.2 Structure of Amplifiers
P. 6-8
Prof. Dr.-Ing. O. Kanoun
Chair for Measurement and Sensor Technology
6.2 Structure of Amplifiers
Integrated Standard Operation Amplifier xx741 (Principle)
Small Signal Equivalent Circuit of an Op-Amps(1)
Difference Input Resistance
Common Mode Input ResistancesInput Bias Currents
Offset Voltage
Output Resistances
P. 6-9
Prof. Dr.-Ing. O. Kanoun
Chair for Measurement and Sensor Technology
6.2 Structure of Amplifiers
uCM VCM
rCMrCM
P. 6-10
6.3 Real Behaviour of Amplifiers
Data Sheets
6.3 Real Behaviour of Amplifiers
Data Sheet OPA 365 [Texas Instruments]
Rail-To-Rail-inputs
Input voltages are amplified until the level of the supply voltage distortion-free
2.2V, 50MHz, Low-Noise, Single-Supply Rail-to-Rail
P. 6-11
Prof. Dr.-Ing. O. Kanoun
Chair for Measurement and Sensor Technology
uCM VCM
rCMrCM
)i(i
ur
NP
DE
2
1 ) (ideal 100T ... 1G ErDifferential Input Resistance
(Differenzeingangswiderstand)
) (ideal 1T ... 1M CMr)i(i
ur
NP
CMCM
2
1Common Mode Input Resistance
(Gleichtakteingangswiderstand)
const.uA
AA
D
i
ur
0) (ideal 100 ... 2Ar
Output Resistance
(Ausgangswiderstand )
6.3 Real Behaviour of Amplifiers
P. 6-12
Prof. Dr.-Ing. O. Kanoun
Chair for Measurement and Sensor Technology
uCM VCM
P. 6-13
Input Bias Current (Eingangsruhestrme):
(typ. 1 nA...500 nA)
IP = Ib+IO mit Ib Bias Current
IN = Ib- IO IO Offset Current (typ. 20 fA...20 nA) RCMP
+
-
Ri
kue
=
UO
=
In
Ip
ue
ua
RCMN
ud
(Bipolar)A 1 (FET);fA 50 bb II
6.3 Real Behaviour of Amplifiers
Common Mode Input Resistances RGlP RGlN(Gleichtakteingangswiderstnde)
Differential Input Voltage (Differenz-Eingangsspannung):
Ud (typ. 3V.... 30 V)
6.3 Real Behaviour of Amplifiers
Common Mode Input Voltage
(Gleichtakteingangsspannung):
UCM (typ. 13V... 16V )
Input voltage relative to ground
Output Voltage Swing (Ausgangsspannungshub):
UAmax (typ. 27 V.... 32 V)
Maximal value of the output voltage without
amplitude limitation
P. 6-14
Prof. Dr.-Ing. O. Kanoun
Chair for Measurement and Sensor Technology
Rail-to-Rail
output voltage swing next the voltage supply VCC
+VCC
-VCC
maximal output voltage
6.3 Real Behaviour of Amplifiers
Input-Offset Voltage U0 (Offset-Spannung):
(typ. 0,5 V... 5 mV)
Voltage between difference inputs, so that
the output voltage 0V is reached
VUUU da 0)( 0 RCMP
+
-
Ri
kue
=
UO
=
In
Ip
ue
ua
RCMN
ud
P. 6-15
Prof. Dr.-Ing. O. Kanoun
Chair for Measurement and Sensor Technology
Offset Voltage Drift (Offsetspannungsdrift):
(typ. 0,01 V/C ... 15 V/C)
tt
UU
U VV
OOO0
UUU
Input Current Drift (Eingangsstromdrift):
(typ. 10 fA/C ... 1 A/C)
..,
p,i
constUconstU
n
pN
i
6.3 Real Behaviour of Amplifiers
[OPA 365, TI]
Different behaviour compared to A 741 (see Page 13)
P. 6-16
Prof. Dr.-Ing. O. Kanoun
Chair for Measurement and Sensor Technology
6.3 Real Behaviour of Amplifiers
Transfer Function
Corresponds to the complex amplification
Hzf 101
MHzf 52 DecadedB /20
21
0
11)(
)()(
jj
V
U
UG
D
A
P. 6-17
Prof. Dr.-Ing. O. Kanoun
Chair for Measurement and Sensor Technology
agegea xkxkxxkx ''
'
'
'
'
1
1
1
1
kfrxk
x
kk
xkk
kx
e
g
e
g
e
g
a
Smaller amplification, but just dependent on kg if k is sufficently high
Selection of stabile circuit elements
independence on changes of amplifier properties
Band width (Frequenzbereich) becomes higher.
Input resistance of voltage Amplifiers and by Current Amplifiers
Output resistance by voltage output and and by current output
Advantages:
kxe xa
kgxg
-
6.3 Real Behaviour of Amplifiers
Feedback (Closed Loop)
P. 6-18
Prof. Dr.-Ing. O. Kanoun
Chair for Measurement and Sensor Technology
gkk
k'
'
1
gkk'1
'k
gg kkf '' 1
Prof. Dr.-Ing. O. Kanoun
Professur fr Mess- und Sensortechnik P. 6-19
Prof. Dr.-Ing. O. Kanoun
Chair for Measurement and Sensor Technology
6.3 Real Behaviour of Amplifiers
Feedback (Closed Loop)
Amplification
Amplification of the
system with feed
back
Amplification
Gain-Bandwidth-Product (Verstrkungs-Bandbreite-Produkt ): GBW
(typ. 0.8 MHz..3 MHz)
In the sector in which the amplification is sinking with 20 dB/Dekade, the product of
frequency and corresponding amplification is constant.
00GBW gfV
P. 6-20
Prof. Dr.-Ing. O. Kanoun
Chair for Measurement and Sensor Technology
6.3 Real Behaviour of Amplifiers
Slew Rate (Maximale Anstiegssteilheit):
SWR (typ. 0.5 V/s...50 V/s)
SWR is the maximum possible change of
the output voltage pro Time Unit
max
SWR
t
uA
P. 6-21
Prof. Dr.-Ing. O. Kanoun
Chair for Measurement and Sensor Technology
6.3 Real Behaviour of Amplifiers
dBV
VCMR
CM
12080lg20
Common Mode Rejection Ratio
(Gleichtaktunterdrckung ): CMRR
(typ. 80dB...120dB)
Proportion of the open voltage gain to
the common mode gain
Supply Voltage Rejection (Betriebsspannungsunterdrckung ): SVR
(typ. -60dB..-100dB)
Proportion of the offset voltage change related to the changes of the voltage supply
Signal-Noise-Ratio: SNR
P. 6-22
Prof. Dr.-Ing. O. Kanoun
Chair for Measurement and Sensor Technology
6.3 Real Behaviour of Amplifiers
Families of Op-Amps
P. 6-23
Prof. Dr.-Ing. O. Kanoun
Chair for Measurement and Sensor Technology
6.3 Real Behaviour of Amplifiers
Ideal Amplifier
is a useful Model for amplification circuits
any Ia, Ua are possible
very high difference amplification
Common mode amplification
low output resistance
no cut-off frequency
V
0aR
0GlV
Ie 0
High input resistance
eR
0eU
+
-
eU
aU
eI
P. 6-24
Prof. Dr.-Ing. O. Kanoun
Chair for Measurement and Sensor Technology
6.3 Real Behaviour of Amplifiers
Frequency Behaviour
Open Loop Amplification
e
a
U
Ulg20
gf
Tf
DecadedB /20
gf
fj
kk
1
'0'
6.4 Correction of the Real Behavior
P. 6-25
Prof. Dr.-Ing. O. Kanoun
Chair for Measurement and Sensor Technology
cut-off frequency
ideal behaviour
real behaviour
Smaller gain band width product Slew-Rate reduction
Frequency Behaviour
Correction
P. 6-26
Prof. Dr.-Ing. O. Kanoun
Chair for Measurement and Sensor Technology
Frequency Behaviour
6.4 Correction of the Real Behavior
P. 6-27
f1
|j| > 180 Oscillation
321
'0'
111f
fj
f
fj
f
fj
kk
Real amplifier
Many amplification stagesFrequency Behaviour
6.4 Correction of the Real Behavior
Closed loop
lower amplification more band width
Tg
gg
ffv
fvfv
100100
101011
For every amplification level, a different compensation is necessary
A transimpedance amplifier is a special amplifier with very high band width and
a variable amplification
P. 6-28
Prof. Dr.-Ing. O. Kanoun
Chair for Measurement and Sensor Technology
Frequency Behaviour
6.4 Correction of the Real Behavior
ReP
+
-
Ri
kue
=
UO
=
In
Ip
ue
ua
ReN
ud
How can we treat offset voltages and input bias currents?
Application of the superposition principle
Example: u/u amplifier
Zero Point Error
P. 6-29
Prof. Dr.-Ing. O. Kanoun
Chair for Measurement and Sensor Technology
6.4 Correction of the Real Behavior
Superposition Principle
The reaction on every source of errror is considererd alone:...... additionally available voltage sources are short-circuited
...... additionally available current sources are broken
The results are added to each other
+
-
Ri
kue
=
UO
=
In
Ip
ue
=Uq
Rq
R1
R2
IR
ug
ua
P. 6-30
Prof. Dr.-Ing. O. Kanoun
Chair for Measurement and Sensor Technology
Zero Point Error
6.4 Correction of the Real Behavior
+-
Ri
kue
=
UO
=
In
Ip
ue
=Uq
Rq
R1
R2
IR
ug
ua
Influence of Off-Set Voltage
OOa UR
RRUU
2
21)(0 gO UU
0,0 npq IIU
Input Mesh:
uk
P. 6-31
Prof. Dr.-Ing. O. Kanoun
Chair for Measurement and Sensor Technology
Zero Point Error
6.4 Correction of the Real Behavior
P. 6-32
Influence of Ip
pqpa IRR
RRIU
2
21)(
0,0,0 nOq IUU
Input Mesh: Ip flows over Rq
Influence of In
nna IRIU 1)(
0,0,0 pOq IUU
In flows to the node between R1 und R2 2RIIU Rng
Input Mesh: 0gU Rn II
+
-
Ri
kue
=
UO
=
In
Ip
ue
=Uq
Rq
R1
R2
IR
ug
ua
+
-
Ri
kue
=
UO
==
InIn
IpIp
ue
==Uq
Rq
R1
R2
IR
ug
ua
Influence of Input Bias Current
Zero Point Error
6.4 Correction of the Real Behavior
P. 6-33
npqOqnpOqa I
RR
RRIRUU
R
RRIIUUU
21
21
2
21),,,(
Superposition principle
+
-
Ri
kue
=
UO
=
In
Ip
ue
=Uq
Rq
R1
R2
IR
ug
ua
+
-
Ri
kue
=
UO
==
InIn
IpIp
ue
==Uq
Rq
R1
R2
IR
ug
ua
Compensation for Rq=R1R2
OqOqnpqOqa IRUUR
RRIIRUU
R
RRU
2
21
2
21
Zero Point Error
6.4 Correction of the Real Behavior
Noninverting Amplifier
qDn RR
eG
GTa U
R
RRU
P. 6-34
Prof. Dr.-Ing. O. Kanoun
Chair for Measurement and Sensor Technology
Zero Point Error
6.4 Correction of the Real Behavior
Input bias currents flowing through the resistances at the input are acting like an off-set voltage
If the resistances are equal to each other, no difference voltage is amplified
Rq
UE
Inverting Amplifier
Gq
qG
DpRR
RRR
ngpDp
q
Gnpa IRIR
R
RIIU
1),(
O
E
GOa U
R
RUU
1)(
The Offset voltage is not amplified!
nGna IRIU )(
DpR
Iq Rq
Ie
Ip over RDp has a similar influence to UO
Ognpa IRIIU ),(
P. 6-35
Prof. Dr.-Ing. O. Kanoun
Chair for Measurement and Sensor Technology
Zero Point Error
6.4 Correction of the Real Behavior
Reduction of the Signal-to-
Noise- Ratio
P. 6-36
Prof. Dr.-Ing. O. Kanoun
Chair for Measurement and Sensor Technology
Noise
6.4 Correction of the Real Behavior
... Is a precision amplifier
with difference input and
an output related to the ground
But a high input impedance is not easy to realise!
3
4
R
RV
3
43
21
2
R
RR
RR
RV
4
3
2
1
R
R
R
R
3
4
R
RV
ua
-
+
R3
R1
i1
u1
R4
R2u2
Subtraction
6.5 Instrumentation Amplifier (1)
P. 6-37
Prof. Dr.-Ing. O. Kanoun
Chair for Measurement and Sensor Technology
Impedance converter for amplification of difference voltages
121
2 UUR
RUa
Amplification changes only by changing two resistances!
For example for Bridges
6.5 Instrumentation Amplifier (2)
P. 6-38
Prof. Dr.-Ing. O. Kanoun
Chair for Measurement and Sensor Technology
Impedance Converter
121
221 UUR
RUa
2211'
1 URRIV R
1
211
R
UUIR
212
'
2 RIUV R
'
1
'
2 VVUa
211 2RRIU Ra
6.5 Instrumentation Amplifier (3)
P. 6-39
Prof. Dr.-Ing. O. Kanoun
Chair for Measurement and Sensor Technology
Multiplication
221221214
1uuuuuu
e. g. Thermal Transducer
u1u2
uaX k
21 uukua
6.6 Applications of Inverting Amplifier
P. 6-40
Prof. Dr.-Ing. O. Kanoun
Chair for Measurement and Sensor Technology
Division
-
+
Rg
R1
ig
i1
uau1
ug
X ku2
2uuku ag
2
1
12 u
u
Rk
R
uk
uu
gg
a
1
11
2
R
ui
R
uku
R
ui
g
a
g
g
g 11
uR
Ru
g
g
6.6 Applications of Inverting Amplifier
P. 6-41
Prof. Dr.-Ing. O. Kanoun
Chair for Measurement and Sensor Technology
Realisation of arithmetic operations by closed loop
(Generalization)
ea iku'
-
+
ei
gi
au
Gk
aGg uki
I U
'k
eg ii
aGg uki
e
G
ea ik
iku1'
Gkk
1'
The amplification in the forward direction should be always the
inverse operation to the element in the feedback
Forward Amplification Feedback Amplification
divide Multiply
square root square
integrate differenciate
logarithmize exponentiate
6.6 Applications of Inverting Amplifier
P. 6-42
43
Charge Amplifier for Piezoelectric Sensors
6.6 Applications of Inverting Amplifier
Prof. Dr.-Ing. O. Kanoun
Chair for Measurement and Sensor Technology
Electric polarized Crystals,
e.g. SiO2 (Quarz
F Force
Q Charge
k Transfer Faktor
++++- - - -
FkQ
ApF
[N]
[As]
F
F0
t
Uq
Uq0
ttq = RqCq
~1 sOutput voltage should be integrated!
Charge Amplifier
dt
tduC
dt
tdQti A
)()()(
Problem: Input bias currents will be also integrated!
)(1
)( tQC
tu A
d ttitQ )()(Charge
P. 6-44
Prof. Dr.-Ing. O. Kanoun
Chair for Measurement and Sensor Technology
6.6 Applications of Inverting Amplifier
Regulator Circuits (1)
P-Regulator Simple Amplifier
I-Regulator Integration
PI-Regulator
-
+
Reie
uaue
Rg Cg
dtuCR
uR
Ru e
ge
e
e
g
a 1
P. 6-45
Prof. Dr.-Ing. O. Kanoun
Chair for Measurement and Sensor Technology
6.6 Applications of Inverting Amplifier
Regulator Circuits (2)
PID- Regulator
-
+
Reie
uaue
Rg
Ce
dtuCRdt
duCRu
C
C
R
Ru e
ge
eege
g
e
e
g
a
1
Cg
P. 6-46
Prof. Dr.-Ing. O. Kanoun
Chair for Measurement and Sensor Technology
6.6 Applications of Inverting Amplifier
47
0
0
)(
)(
))((
))((
)(
)())(()(
dtetx
dtetx
tX
tX
pX
pXtgpG
pt
e
pt
a
e
a
e
a
)()()( pXpGpX ea
)()()( tgtXtX ea
Transfer Function
)(tg : pulse response
)(th : Step response )()( tht
tg
Time Domain
Frequency Domain
Frequency Response (Fourier-Transformed)
))(()()( tgFourierdtetgjF tj
dtep
pG
jp
pGth
j
j
tp
)(
2
1)()( 1
6.6 Applications of Inverting Amplifier
48
F(P) 1/F(P)xe(t) xa(t) xe(t)= xa(t) * g(t)
sensor dynamic
correction
)(*)()()(0
tgtxdtxtx a
t
ae tt
)(/1)( 1 PFLtg
aaae xxx
ktx
2
00
121)(
Transfer Function:
: Attenuation ratio
0: Angular frequency
of non attenuated oszillation
System of Second Order
System of First Order
aae xxk
tx t1
)(
t: Time constant
Realisation of Defined Transfer Functions (1)
6.6 Applications of Inverting Amplifier
Example: Dynamic Correction of Linear Systems
49
Realisation of Defined Transfer Functions (1)
-
+
ie
ue ua
Ze
Zgvirtual ground
Short Circuit Kernel Impedance Short Circuit Kernel Impedance
Zk
I2
U1
Short Circuit Kernel Impedance
e
e
g
a uZ
Zu
6.6 Applications of Inverting Amplifier
50
Realisation of Defined Transfer Functions (2)
Short Circuit Kernel ImpedanceCircuit
s=p
6.6 Applications of Inverting Amplifier
51
52
Realisation of Defined Transfer Functions (3)
PID-Regulator
Low pass filter
CRp
CR
2
1 1
11
tCR
eR
RU 2
1
1
2 1
p
CRp
CRp
CR
112222
11
t
CRCRt
CRCRCRU
22112211
12
1)(
11
Transfer Function
Transfer Function
Transfer Function
Transfer Function
6.6 Applications of Inverting Amplifier
53
Realisation of Defined Transfer Functions (3)
6.6 Applications of Inverting Amplifier
54
Low pass
High pass
Band pass
Notch
6.7 Active Filters
Pass Band
Attenuation Band
Filter: Circuit with a frequency dependent frequency response
Passive Filter: R, L, C - Filter
Active Filter: Op-Amps, No Inductivities
sperr
55
Ripple in the pass band
Ripple in the attenuation band
Properties of real filters
Cut-off frequency: decay of the modulus by )3(2
1dB
6.7 Active Filters
n
i
i
i pc
ApG
1
0
1
)(
Transfer Function of a Filter of order n
ic real Filter-Coefficientsn Order of the filter
R
CUe Ua RCp
pG
1
1)(
One negative Pol
n negative pols
Low pass- Filter 1st order
P. 6-56
Prof. Dr.-Ing. O. Kanoun
Chair for Measurement and Sensor Technology
6.7 Active Filters
57
Low pass filter High pass filter
Active filter
6.7 Active Filters
58
Gau (1): flat amplitude characteristic
Bessel (2): Optimal Transfer of square pulses for f < fggroup delay time indipendent on , low ripple.
Butterworth (3): Amplitude characteristic optimized for f < fg, constant.
Tschebyscheff (4): Filter with riple e = 0,5 dB
gr
g
gr tT
2
ttgr
Group delay time
Normed group delay time
Properties of different filter types
6.7 Active Filters
59
Amplitude characteristic of active Filter of 4th Order
6.7 Active Filters
1 RC with critical damping
2 Bessel
3 Butterworth
4 Tschebyscheff with 3 dB ripples
4. Ordnung
10. Ordnung
Butterworth
maximal constant frequency response
P. 6-60
Prof. Dr.-Ing. O. Kanoun
Chair for Measurement and Sensor Technology
6.7 Active Filters
Bessel
Group delay time independent on frequency
in the pass Band
P. 6-61
Prof. Dr.-Ing. O. Kanoun
Chair for Measurement and Sensor Technology
6.7 Active Filters
1 RC with critical damping
2 Bessel
3 Butterworth
4 Tschebyscheff with 3 dB ripples
62
Active Filter 2nd Order
2
21
0
1)(
SaSa
ASG
gg
jpS
Multiple feedback
2
3221
2
1
32321
12
1
)(
SRRCCSR
RRRRC
RRSG
gg
1
20
R
RA Comparison of Coefficients
1
323211
R
RRRRCa g
3221
2
2 RRCCa g
6.7 Active Filters
63
1
20
R
RA
1
323211
R
RRRRCa g
3221
2
2 RRCCa g
0
21
A
RR
21
0221
2
2
2
121
24
14
CCf
AaCCCaCaR
g
221
22
23
4 RCCf
aR
g
2
1
02
1
2 14
a
Aa
C
C
Capacitance values are given
2
21
0
1)(
SaSa
ASG
6.7 Active Filters
Active Filter 2nd Order
64
Low pass
Z1 = R1Z2 = open
Z3 = 1/s C1Z4 = R2Z5 = 1/s C2
High pass
Z1 = 1/s C1Z2 = open
Z3 = R1Z4 = 1/s C2Z5 = R2
Band pass
Z1 = R1Z2 = open
Z3 = 1/s C1Z4 = 1/s C2Z5 = R3 // C3
6.7 Active Filters
Sallen-Key-Filter
- For analoge filters 2nd Order
- Low pass filter, high pass filter and band pass filter are possible with the same
structure
- Notch und Cauer-Filter are not possible
Low pass High pass Band pass
General
6.7 Active Filters
Amplification is hold on a
specific value2
21
0
1)(
SaSa
ASG
0A
212111 1 CRRRCA g
3221
2
2 RRCCa g
Positive Feed Back Low Pass Amplifier 2nd Order
Transfer function
P. 6-66
Prof. Dr.-Ing. O. Kanoun
Chair for Measurement and Sensor Technology
6.7 Active Filters
67
0A
11 RCa g
22 RCa g
Fr R1=R2=R3=R und C1=C2=C
Critic
Damping
Bessel-
Filter
Butterworth-
Filter
Tschebyscheff-Filter
with 1 dB ripple
1,0 1,268 1,856 1,955
Special case:
defines the filter typ
)1(3 R
6.7 Active Filters
Positive Feed Back Low Pass Amplifier 2nd Order
Positive Feedback High Pass Filter
P. 6-68
Prof. Dr.-Ing. O. Kanoun
Chair for Measurement and Sensor Technology
6.7 Active Filters
69
Band Pass Filter with a Simple Positive Feed Back
Resonance frequency
(Extreme low damping)
Performance of rejection
RCfr
2
1
kf
fQ r
3
1
Amplification at frk
kAr
3
6.7 Active Filters
70
Aktives Doppel-T-Sperrfilter, Notch-Filter
Resonance frequency
(unfinite barrier effect)
Performance of rejection
RCfr
2
1
)2(2
1
kf
fQ r
Amplification kA 0
6.7 Active Filters