Unit 1 Feedback Amplifiers
Transcript of Unit 1 Feedback Amplifiers
Feedback: Is the process where by a portion of the output is returned to the input to form a part of the system excitation.
Introduction to feedback amplifier
Open-Loop Amplifier Closed loop Amplifier
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Why feedback?
• Positive Feedback (oscillators)
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• Negative Feedback (Amplifiers)
•The feedback improve the frequency response and make the amplifier more stable
•The feedback improve the sensitivity of the amplifier•The feedback decrease the nonlinear distortion.•The feedback decrease the noise effect on the amplifier
Types
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Block diagram of amplifier with feedback
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General Feedback Structure
Open loop gain & closed loop gain are )(- + fsi XXX
fisf XX
XXXA
00
iXXA 0
sf X
XA 0
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Dividing the numerator and denominator by
5
ifi
if XXX
XXA/)(
/0
iff XX
AA/1
i
o
o
ff
XX
XX
AA
1
AAA f
1
iX
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Gain De-sensitivity • Feedback can be used to desensitize the closed-loop gain to variations in the
basic amplifiler. • Assume is constant. Take differentials of the closed loop gain equation
gives,
• Divided by Av, the close loop gain sensitivity is equal to,
• This result shows the effects of variations in A on ACL is mitigated by the feedback amount.
• (1+A) is also called the desensitivity amount.
22 )1(or
)1(1
1 AdAdA
AdAdA
AAA CL
CLCL
Differential respected with A
AdA
AAA
AdA
AdA
CL
CL
1
1)1()1( 2
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Bandwidth improvement
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AAAf
1
fhigh
fhighfhigh
flow
flowflow
mid
midfmid
AA
A
AA
A
AAA
1
1
1
We can write
-----1
---2
---3
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Lower cutoff frequency
ffjA
ALmid
low
1
1
ffj
AAL
midlow
1
Substituting the value of in equation 2 lowA
ffj
A
ffj
A
A
L
mid
L
mid
flow
1(1
1
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ffjA
AAL
mid
midflow
)1(
fAfj
AA
A
mid
L
mid
mid
flow
)1(1
1
fAfj
AA
mid
L
fmidflow
)1(1
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ff
j
AA
Lf
fmidflow
1
Lower cutoff frequency is given by
)1( mid
LLf A
ff
Upper cutoff frequency
H
mid
high
ffj
AA
1
1
H
midhigh
ffj
AA1
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Substituting the value of in equation 3 highA
H
mid
H
mid
fhigh
ffj
A
ffj
A
A
1(1
1
Dividing numerator and denominator by
Hmid
mid
mid
fhigh
fAfj
AA
A
)1(1
1
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Hmid
fmidfhigh
fAfj
AA
)1(1
Hf
fmidfhigh
ffj
AA
1
where upper cutoff frequency with feedback is given as
HmidHf fAf )1(
)1()1(
mid
LHmidf A
ffABW
Bandwidth = Upper cutoff frequency – lower cutoff frequency
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Effect of negative feedback on gain and bandwidth
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Basic Feedback Topologies
Depending on the input signal (voltage or current) to be amplified and form of the output (voltage or current), amplifiers can be classified into four categories. Depending on the amplifier category, one of four types of feedback structures should be used.
(Type of Feedback) (Type of Sensing)• Series (Voltage) Shunt (Voltage)• Series (Voltage) Series (Current)• Shunt (Current) Shunt (Voltage)• Shunt (Current) Series (Current)
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Figure 8.4 The four basic feedback topologies: (a) voltage-mixing voltage-sampling (series–shunt) topology; (b) current-mixing current-sampling (shunt–series) topology; (c) voltage-mixing current-sampling (series–series) topology; (d) current-mixing voltage-sampling (shunt–shunt) topology.www.Vidyarthiplus.com
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The series–shunt feedback amplifier: (a) ideal structure and (b) equivalent circuit.
Series–shunt feedback amplifier
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• Voltage amplifier voltage-controlled voltage source
• Requires high input impedance, low output impedance
• Voltage-voltage feedback
io VAV
of VV
oo
fis VA
VVVV
)1(1
get weAnd,
AVVA
AVV
is
so
Voltage Gain Calculation:
i
o
VVA
A
AVVA
s
of 1
Gain) Voltage Loop (Close
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Input Resistance (Series-Shunt)
Input Resistance:
i
i
s
i
s
RVV
IVR if
i
iii
i
si V
AVVRIVRR
if
)1(if ARR i
)1( AVV s
i
)()(1)()( ssAsZsZ iif
In general input impedance can be written as
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Output Resistance (Series-Shunt)
Measuring the output resistance of the feedback amplifier
IVR t
of
0RAVVI it
tofi VVVV
0RAVVI tt
ARRof
1
0
)()(1)()( 0
0 ssAsZsZ f
To find output resistance Rof , put Vs = 0 and apply test voltage at output
Since Vs =0,
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Derivation of the A circuit and b circuit for the series–shunt feedback amplifier. (a) Block diagram of a practical series–shunt feedback amplifier. (b) The circuit in (a) with the feedback network represented by its h parameters.
Practical series–shunt feedback amplifier.
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(Continued) (c) The circuit in (b) with h21 neglected.
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iVVA 0
021
2110 //)(
//)(rRRR
RRRVVL
L
)//( 211 RRRR
VRVids
iid
series–shunt feedback amplifier.
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)//(//)(//)(
21021
21
RRRRVR
rRRRRRRA
ids
iid
L
L
21
1
0 RRR
VV f
AA
VVA
sf
1
0
)1( ARR iif
series–shunt feedback amplifier.
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21 // RRRRR idsi
sifin RRR
ARRof
1
0
)//(// 2100 RRRrR L
Loutof RRR //
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The series–series feedback amplifier: (a) ideal structure and (b) equivalent circuit.
series–series feedback amplifier
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of IV
i
o
VIA
A
AVIA
s
of 1
Gain) Voltage Loop (Close
Transconductance gain
)1(if ARR i
tof I
VR
Measuring the output resistance of the feedback amplifierTo find output resistance Rof , put Vs = 0 and apply test voltage at output
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Measuring the output resistance Rof of the series–series feedback amplifier.
tofi IIVV
00 )()( RIAIRAVIV ttit
)1(0 ARRof
Since Vs =0,
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Series series Circuits
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)]//([)//(
211
211
FEEe
c
i
c
RRRrrR
VV
))]}//(()[1//({ 123221
2FEEefecm
c
c RRRrhRgVV
Series series Circuits
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)]//([1
1233
3
2 FEEeb
e
c
o
RRRrVI
VI
i
o
VIA
112
2E
FEE
E
o
f RRRR
RIV
A
AVIA
s
of 1
Gain) Voltage Loop (Close
Series series Circuits
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3303
cfs
c
s
cc
s
o RAV
RIV
RIVV
)1(if ARR i
))]//(()[1( 211i EFEefe RRRrhR
1)]//([ 2
312
fet
ceEFEo h
RrRRRR
)1(0 ARRof
)//)(1( 3030 rRrgrR ofmout
Voltage gain is
Measuring the output resistance of the feedback amplifier To find output resistance Rof , put Vs = 0 and apply test voltage at output
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Ideal structure for the shunt–shunt feedback amplifier.
s
of I
VA
A
AA f 1
Gain) Voltage Loop (Close
)1(if ARR i
)1(0
ARRof
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Block diagram for a practical shunt–shunt feedback amplifier.
sRR
R11
1
if
in
Lof RR
R11
1out
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Finding the A circuit and b for the current-mixing voltage-sampling (shunt–shunt) feedback amplifier
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)////( rRRIV fsi
)//(0 cfm RRVgV
)////)(//(0rRRRRg
VVA fscfm
i
)////( rRRR fsi
)//( cfo RRR
shunt–shunt) feedback amplifier
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fo
f
RVI 1
A
AIVA
s
of 1
Gain) Voltage Loop (Close )1(if ARR i
)1(0
ARRof
shunt–shunt) feedback amplifier
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Ideal structure for the shunt–series feedback amplifier.
s
of I
IA
A
AIIA
s
of 1
Gain) Voltage Loop (Close
)1(if ARR i
)1(0 ARRof
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Block diagram for a practical shunt–series feedback amplifier.
sRR
R11
1
if
in
Lof RRR out
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Finding the A circuit and b for the current-mixing current-sampling (shunt–series) feedback amplifier .
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121 ////)//( rRRRRIV BfEsi
)]//)(1(//[// 2211112 fEcomb RRrRrVgV
)//( 22
2
fEe
bo RRr
VI
shunt–series) feedback amplifier .
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Voltage gain is
i
o
IIA
12 ////)//( rRRRRR BfEsi
1//)//( 11
22
oc
efEirRrRRR
fE
E
o
f
RRR
II
2
2
)1(if ARR i
sRR
R11
1
if
in
shunt–series) feedback amplifier .
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shunt–series) feedback amplifier .
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AA
IIA
s
of
1
s
o
Lc
c
s
c
Lc
c
s
out
in
out
II
RRR
II
RRR
II
II
2
2
2
2
)1(0 ARRof
)]//(1[ 222out ofmo RrgrR
shunt–series) feedback amplifier .
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The Stability Problem
• Closed-loop transfer function is similar to the one of the middle band gain.
• The condition for negative feedback to oscillate
• Any right-half-plane poles results in instability. Amplifier with a single-pole is unconditionally stable. Amplifier with two-pole is also unconditionally stable. Amplifier with more than two poles has the possibility to be
unstable.• Stability study using bode plot
1)()()( jjAjL
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The Definitions of the Gain and Phase margins
Gain margin represents the amount by which the loop gain can be increased while stability is maintained.
Unstable and oscillatory
Stable and non-oscillatory
Only when the phase margin exceed 45º or gain margin exceed 6dB, can the amplifier be stable.
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Stability analysis using Bode plot of |A|.
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Stability Analysis Using Bode Plot of |A|
• Gain margin and phase margin• The horizontal line of inverse of feedback factor in dB.• A rule of thumb:
The closed-loop amplifier will be stable if the 20log(1/β) line intersects the 20log|A| curve at a point on the –20dB/decade segment.
• The general rule states:At the intersection of 20log[1/ | β (jω)| ] and 20log |A(jω)| the difference of slopes should not exceed 20dB/decade.
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Frequency Compensation
• The purpose is to modifying the open-loop transfer function of an amplifier having three or more poles so that the closed-loop amplifier is stable for any desired value of closed-loop gain.
• Theory of frequency compensation is the enlarge the –20dB/decade line.
• ImplementationCapacitance Cc addedMiller compensation and pole splitting
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Frequency Compensation
Two cascaded gain stages of a multistage amplifier.
Equivalent circuit for the interface between the two stages in (a).
Same circuit as in (b) but with a compensating capacitor CC added. www.Vidyarthiplus.com
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Frequency compensation for = 102. The response labeled A is obtained by introducing an additional pole at fD. The A response is obtained by moving the original low-frequency pole to f D.
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Frequency Compensation
A gain stage in a multistage amplifier with a compensating capacitor connected in the feedback path
An equivalent circuit.
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