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Analog Circuits and Systems Prof. K Radhakrishna Rao Lecture 15: Amplifiers 1
Analog Circuits and Systems Prof. K Radhakrishna Rao
Lecture 15: Amplifiers
1
Review
Negative Feedback Systems were discussed Output variation follows the input variation if loop-gain is very large
compared to one. Voltage follower and current follower application as voltage/current
buffer and voltage/current regulator Phase follower and frequency follower application as FM detector
and FSK detector
2
Review (contd.,)
Lock range as the range over which loop gain is much greater than one.
Dynamic operation of feedback systems in terms of first order and second order systems
Gain bandwidth product as a measure of quality of the feedback system
Q=1 for high speed feedback systems
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Feedback amplifier design
Earlier lecture (Lecture 8) used nullator-norator (as an active device) in the synthesis of ideal amplifiers: ◦ Voltage Amplifiers ◦ Current Amplifiers ◦ Trans-conductance Amplifiers ◦ Trans-resistance Amplifiers
Feedback in systems has also been presented in the previous lecture (Lecture 14). It used ideal amplifiers (unilateral) and feedback which was also unilateral.
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Amplification
Signal sources cannot deliver directly required power to the load
Amplification is required to enhance the signal power Amplification is one of the major analog signal processing
function
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Types of Amplifiers
Based on the output power levels
Preamplifiers (tuned or wide band amplifiers)
Power amplifiers (tuned or wide band amplifiers)
Based on input and output variables Voltage Controlled Voltage Source
(VCVS) (Voltage Amplifiers) Voltage Controlled Current Source
(VCCS) (Trans-conductance Amplifiers) Current Controlled Voltage Source
(CCVS) (Trans-resistance Amplifiers) Current Controlled Current Source
(CCCS) (Current Amplifiers)
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Types of Amplifiers (contd.,)
Preamplifiers Signal levels are very low (pico/micro/milli volts and pico/micro/milli
amperes) Enhancing signal-to-noise ratio is the primary requirement Power Amplifiers Signal levels are high in terms of voltage and current Efficiency is the primary requirement
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Types of Amplifiers (contd.,)
Ideal Amplifiers have zero input power and deliver finite output power providing
infinite power gain have input power zero if the input current to the amplifier is zero
(Ii = 0) or the input voltage to the amplifier is zero (Vi = 0)
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Types of Amplifiers (contd.,)
Active devices for amplification Op amps MOSFETs (available as power devices and only in ICs) JFETs (require several discrete passive devices increasing the foot
print of the amplifier) BJTs (require several discrete passive devices increasing the foot
print of the amplifier)
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Types of Amplifiers (contd.,)
Op Amps Operational Voltage Amplifiers are available with a very wide range
of specifications Numbers of available operational trans-resistance, current
amplifiers and trans-conductance amplifiers are limited
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Major manufacturers of Op Amps
Texas Instruments National Semiconductors Analog Devices Linear Technologies Maxim Intersil Fairchild
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Non-idealities of Op Amps
Finite Gain, Finite Bandwidth, Finite Gain-Bandwidth product Offset voltages and currents Offset drifts Finite input impedance and output impedance Slew rate Current and voltage limitations Finite Common Mode Rejection Ratio (CMRR) Parameter dependence on temperature and supply voltage
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Some popular Op Amps Compensated Op amps include
741 Single bipolar Op Amp
747 Dual bipolar Op Amp
TL081 Single BIFET Op Amp
TL082 Dual BIFET Op Amp
TL084 Quad BIFET Op Amp
LF351 Single BIFET Op Amp
LF353 Dual Op Amp
741 Single bipolar Op Amp
Uncompensated Op Amps
LM748 Single bipolar Op Amp
THS4011 Single bipolar high
bandwidth Op Amp
THS4012 Dual bipolar high
bandwidth Op Amp
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Parameters of TL081
All the parameters are defined for +15V TL081
1. Total Supply Voltage 7 to 36 V
2. Gain-Bandwidth Product at 25OC 3 MHz
3. Slew Rate 13 V/msec
4. CMRR 70 dB
5. Input Offset Voltage 20mV (max)
6. Input Offset Voltage Temperature Coefficient 18mV/OC
7. Input Offset Current 2 nA (max)
8. Input Bias Current 10 nA (max)
9. Input Resistance 1012 W
10. Output Resistance 200 W 14
Feedback in two-port active networks
A general two-port network in Y-parameters
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i ia ra i
o fa oa o
I Y Y V=
I Y Y V⎡ ⎤ ⎡ ⎤ ⎡ ⎤⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦ ⎣ ⎦
Feedback in two-port active networks (contd.,)
If the two-port network is an active device, which is assumed to be unilateral the reverse transfer parameter Yra=0
Yia and Yoa are finite and small compared to Yfa
All the Y-parameters of the active device are sensitive to temperature, time and bias supply voltage and have poor manufacturing tolerances
Using a suitable passive two-port work with the active device it is possible to make resultant system close to the ideal amplifier
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Feedback in two-port active networks (contd.,)
We choose the passive two-port network with Y-matrix
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ip rp
rp op
fa rp
Y Y
Y Y
Y Y
⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦
?andwith
Feedback in two-port active networks (contd.,)
The passive two-port network is connected to the active device in shunt at both the input and output
Admittances are added at the input and output
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ia ip ia ip ra rp i ia ipi
ooa op fa fp oa op o oa op
ra rp rp fa fp fa
I I Y Y Y Y V (V V )III I Y Y Y Y V (V V )
whereY Y Y andY Y Y
+ + + =⎡ ⎤ ⎡ ⎤ ⎡ ⎤⎡ ⎤= =⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎢ ⎥+ + + =⎣ ⎦⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦ ⎣ ⎦+ = + ≈
Feedback in two-port active networks (contd.,)
When admittances increase at the input the resultant input impedance is decreasing leading to the system becoming near ideal current controlled (CC)
When admittances increase at thee output the resultant controlled source becomes a near ideal voltage source (VS)
The resultant ideal CCVS should have an impedance matrix
with Z independent of parameters of the active device
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0 0Z 0⎡ ⎤⎢ ⎥⎣ ⎦
Feedback in two-port active networks (contd.,)
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( )( )
( )( )
( )
oa op L rp1ia ip S rp
fa oa op L ia ip Sfa
ia ip S oa op L fa rp
fa rpfa rp
ia ip S oa op L
fa rp
ia ip S
Y +Y Y -YY +Y Y Y
Y Y +Y Y Y +Y Y-Y
where thedetrminant Y +Y Y Y +Y Y Y Y
Y YIf 1thenΔ= -Y Y
Y +Y +Y Y +Y +Y
Y Ywhere
Y +Y +Y
−+⎡ ⎤
⎢ ⎥+⎡ ⎤ Δ Δ⎢ ⎥=⎢ ⎥+ +⎢ ⎥⎢ ⎥⎣ ⎦ ⎢ ⎥⎣ Δ Δ ⎦
Δ= + + −
⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦
?
( )oa op Lis the loop gain
Y +Y +Y
If negative then, negative feedback, otherwise it is positive feedback.
⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦
Z-Matrix – CCVS
The use of feedback passive network around an active device made the input-output relationship independent of parameters of the active device as well as source and load admittances
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( )
( )
oa op L rp
fa rp fa rpfa
ia ip Sfa rp
fa rp fa rp
Y +Y Y Y0 0Y Y Y Y1 asY is large0Y +Y YY Y
Y Y Y Y
⎡ ⎤+⎢ ⎥ ⎡ ⎤−⎢ ⎥ ⎢ ⎥≈⎢ ⎥ ⎢ ⎥+⎢ ⎥ ⎢ ⎥⎣ ⎦⎢ ⎥−⎢ ⎥⎣ ⎦
Resultant Z-matrix - CCVS
Macromodel
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Z-matrix of the composite CCVS
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-1oa oaf
L f oaia f S f
oa oa oaff
oa f oa f L ia S f
Loa oa oa oa oa
L f ia S f
Loa f
R RR 11 1 1 1 1A R R ARR R R R
A 1 1 1 1 R R RRRR R R R R A R R R
AgR R R R R1R R R R R
AIf g 1thenR R
⎡ ⎤⎛ ⎞⎡ ⎤ + ++ + − ⎢ ⎥⎜ ⎟⎢ ⎥ ⎝ ⎠⎢ ⎥⎢ ⎥ = ⎢ ⎥⎢ ⎥ ⎛ ⎞− + + ⎢ ⎥− + +⎢ ⎥ ⎜ ⎟⎢ ⎥⎣ ⎦ ⎝ ⎠⎣ ⎦−=⎛ ⎞⎛ ⎞
+ + + +⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠
Δ=?
Example
Design trans-resistance amplifier with a Z-matrix for a source resistance of 10 kW and a load resistance of 1kW Consider an Op Amp with input impedance of 1 MW, voltage gain
of 106, and output impedance of 100W The Op Amp is represented by Y-matrix
The feedback passive network is chosen to have an admittance matrix
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0 01k 0
⎡ ⎤⎢ ⎥− Ω⎣ ⎦
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1 S 0
10 S 10mS
µ⎡ ⎤⎢ ⎥⎣ ⎦
1mS 1mS1mS 1mS
−⎡ ⎤⎢ ⎥−⎣ ⎦
Resultant Z-matrix - CCVS
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1.2m 0.1m 0 01k 0.11m 1k 0
Ω Ω⎡ ⎤ ⎡ ⎤≈⎢ ⎥ ⎢ ⎥Ω Ω Ω⎣ ⎦ ⎣ ⎦
Feedback network
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The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again.The feedback passive network is chosen to have an admittance matrix
f
1mS 1mS1mS 1mS
R 1k
−⎡ ⎤⎢ ⎥−⎣ ⎦
= Ω
The composite Y-matrix
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( )( )
( )( )
4 4
ia ip S oa op L fa rp
7fa rp 2
ia ip S oa op L
1 S 1mS 0.1 mS 1 mS 1.1mS 1mS
10 S 1mS 10mS 1mS 1mS 10 S 12mS
Y Y Y Y Y Y Y Y
Y Y 10 1then 10S13.2Y Y Y Y Y Y
µ + + − −⎡ ⎤ ⎡ ⎤≈⎢ ⎥ ⎢ ⎥
− + +⎣ ⎦ ⎣ ⎦Δ= + + + + −
= Δ=+ + + +
?
CCVS
Rs=10k RL=1k Rf=1k
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General Amplifier (VCVS, CCVS, VCCS and CCCS)
An ideal general amplifier should have an immittance matrix
pf ◦ is finite and is the chosen
design parameter ◦ should be independent of
parameters of active device used
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f
0 0p 0⎡ ⎤⎢ ⎥⎣ ⎦
Available active devices
Pfa is very large All the three elements of immittance matrix have poor manufacturing tolerances can vary widely with temperature, time
and bias supply voltages
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ia
fa oa
p 0p p⎡ ⎤⎢ ⎥⎣ ⎦
Available active devices (contd.,)
This can be achieved by adding two matrices and inverting the resultant matrix
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( )
oa op rp1ia ip rp
fa fp oa op fa fp ia ip
p p pp p pp p p p p p p p
−+ −⎡ ⎤
⎢ ⎥+⎡ ⎤ Δ Δ⎢ ⎥=⎢ ⎥ ⎢ ⎥+ + − + +⎢ ⎥⎣ ⎦ ⎢ ⎥⎣ Δ Δ ⎦
Available active devices (contd.,)
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( ) ( ) ( ) ( ) ( )( )
( ) ( ) ( ) ( ) ( )( ) ( ) ( )
( )( ) ( )
rp
ia ip L ia ip oa op L
fa fp
ia ip oa op L oa op L
ia ip oa op L fa rp L
fa fp rpL
ia ip oa op
p1Composite p p 1 g p p p p 1 gInverted
p p 1Matrixp p p p 1 g p p 1 g
where p p p p 1 g p p when g 1
p p pwhere g isloopg
p p p p
−⎡ ⎤⎢ ⎥⎛ ⎞ + − + + −⎢ ⎥⎜ ⎟ = ⎢ ⎥⎜ ⎟ − +⎢ ⎥⎜ ⎟⎝ ⎠ ⎢ ⎥+ + − + −⎣ ⎦
Δ = + + − ≈ −
+=
+ +
?
1ia ip rp
fa fp oa oprp
ainwhich has to be negative
for negative feedback0 0p p p1 0p p p p p
− ⎡ ⎤+⎡ ⎤ ⎢ ⎥≈⎢ ⎥ ⎢ ⎥+ +⎢ ⎥⎣ ⎦ ⎢ ⎥⎣ ⎦
Available active devices (contd.,)
Choose a passive linear two-port network
We need to generate a matrix similar to from the two matrices
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ip rp
fp op
p pp p⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦
f
0 0p 0⎡ ⎤⎢ ⎥⎣ ⎦
ip rpia
fa oa fp op
p pp 0and
p p p p⎡ ⎤⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦ ⎣ ⎦
Conclusion
Design of feedback amplifiers Feedback Matrix
Voltage h g Current g h
Trans-conductance Z Y
Trans-resistance Y Z
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In the next lecture we shall discuss the design of voltage and current amplifiers and trans-conductance amplifiers
