c8 – electronic amplifiers. amplifiers withopamp.. electronic...electronic amplifiers modeling the...
TRANSCRIPT
-
ELECTRONIC DEVICESAssist. prof. Laura-Nicoleta IVANCIU, Ph.D.
C8 – Electronic amplifiers. Amplifiers with OpAmp.
-
2Laura-Nicoleta IVANCIU, Electronic devices
Contents
Electronic amplifiers Types of supply Power transfer and power balance Types of amplifiers VTC Modeling the voltage amplifier Amplifier performances Frequency response
Amplifiers with OpAmp Non-inverting amplifier Inverting amplifier
C8 – Electronic amplifiers. Amplifiers with OpAmp.
-
3Laura-Nicoleta IVANCIU, Electronic devices
Electronic amplifiers
Electronic amplifiers
C8 – Electronic amplifiers. Amplifiers with OpAmp.
Amplifier = active three-port network that delivers an output signal xo(t) (voltage or current) with the same shape as the input signal xi(t) and can provide more power, on an adequate load.
)()( tAxtx io =
Linear circuit: x0 proportional with xi
A0 non-inverting
A – amplification, gain
-
4Laura-Nicoleta IVANCIU, Electronic devices
Electronic amplifiers
Types of supply
C8 – Electronic amplifiers. Amplifiers with OpAmp.
Single source supply Two source supply (symmetric differential)
The supply is provided by dc voltage and/or current sources. Voltage sources are most commonly used.
-
5Laura-Nicoleta IVANCIU, Electronic devices
Electronic amplifiers
Power transfer and power balance
C8 – Electronic amplifiers. Amplifiers with OpAmp.
The average power of the output signal is greater than the average power of the input signal:
Pout > PinThe excess of the output power is taken from the supply sources.
Psupply + Pin = Pout + Pdissip
Psupply ≈ Pout + Pdissip
η =Pout/Psupply
!A step up transformer is not an amplifier!
Efficiency:
-
6Laura-Nicoleta IVANCIU, Electronic devices
Electronic amplifiers
Types of amplifiers
C8 – Electronic amplifiers. Amplifiers with OpAmp.
Based on the types of input/output signals (voltage/current):
voltage amplifier Av = vo/vI - dimensionless
current amplifier Ai = io/iI - dimensionless
transconductance amplifier Ai/v = io/vI – [S], [mS]
transresistance amplifier Av/i = vo/iI – [Ω], [kΩ]
-
7Laura-Nicoleta IVANCIU, Electronic devices
Electronic amplifiers
VTC
C8 – Electronic amplifiers. Amplifiers with OpAmp.
( )OHOLOv
OH
v
OLI
VVvA
VA
Vv
;
;;
∈
∈
amplification (active) region:
VOL = -VPS ; VOH = +VPS
rail-to-rail OpAmp: ( )PSPSO VVv +−∈ ;
general-purpose OpAamp V)2...V1;V2...V1( −++−∈ PSPSO VVv
ideal amplifier:
voltage-to-voltage, non-inverting amplifier, symmetric differential supply
-
8Laura-Nicoleta IVANCIU, Electronic devices
Electronic amplifiers
VTC
C8 – Electronic amplifiers. Amplifiers with OpAmp.
Signal transfer
Note: if the input signal is low enough for the amplifier to work in a linear region around the OP: small signal approximation
-
9Laura-Nicoleta IVANCIU, Electronic devices
Electronic amplifiers
Modeling the voltage amplifier
C8 – Electronic amplifiers. Amplifiers with OpAmp.
two-port networks: only the behavior of the input and output ports is explicitly taken into account, and the input-output signal transfer
valid regardless of the internal complexity of the amplifiers valid in the bandpass frequency domain
Linear controlled sources
active two-port network only one finite, non-zero parameter: forward transfer parameter (gain) the output signal is controlled by the input signal pseudo-sources
VCVS (voltage controlled voltage source)
vO = avvi
-
10Laura-Nicoleta IVANCIU, Electronic devices
Electronic amplifiers
Modeling the voltage amplifier
C8 – Electronic amplifiers. Amplifiers with OpAmp.
av – open circuit gainRi – draws current from viRo – deteriorates vo in the presence of loadi
ov v
va =
s
ov v
vA =
voL
L
is
iv aRR
RRR
RA++
=
Ideal amplifier?
Amplifier model
Amplifier model connected in a circuit
-
11Laura-Nicoleta IVANCIU, Electronic devices
Electronic amplifiers
Modeling the voltage amplifier
C8 – Electronic amplifiers. Amplifiers with OpAmp.
voL
L
is
iv aRR
RRR
RA++
=
s
ov v
vA =
Av is closer to the open circuit gain av when the voltage losses at the input (across Rs) and at the output (across Ro) are reduced.
Ri >> Rs – the source voltage is transferred to the input
Ro
-
12Laura-Nicoleta IVANCIU, Electronic devices
Electronic amplifiers
Amplifier performances
C8 – Electronic amplifiers. Amplifiers with OpAmp.
Gain (forward transfer factor) Analyze the circuit, by using circuit theorems and equation (Kirchhoff, Ohm, Millman) Express the output signal as a function of the input signal, then compute the gain
Input resistance
i
ii i
vR =
-
13Laura-Nicoleta IVANCIU, Electronic devices
Electronic amplifiers
Amplifier performances
C8 – Electronic amplifiers. Amplifiers with OpAmp.
Output resistance Set the input signal source to zero Connect a test source at the output
test
testo i
vR =
sc,o
open,oo i
vR =
open circuit short-circuit
#1
#2
-
14Laura-Nicoleta IVANCIU, Electronic devices
Electronic amplifiers
Frequency response
C8 – Electronic amplifiers. Amplifiers with OpAmp.
analyze the equivalent model of the amplifier including capacitive components too, by means of their complex impedances: 1/jωC
complex transfer function for the gain:
input and output impedances are now complex
)()(
)(ωω
ωjvjv
jAi
o=
)( ωjZi ( )ωjZo
Band-pass amplifier
Why does the gain decrease at low/high frequencies?
-
15Laura-Nicoleta IVANCIU, Electronic devices
Electronic amplifiers
Frequency response
C8 – Electronic amplifiers. Amplifiers with OpAmp.
internal capacitances (parasitic) of active devices => Av @ f
coupling/decoupling capacitors (tens of µF) => Av @ f (zero dc gain)
capacitive coupling at input
capacitive coupling of two amplifier stages
Direct coupling amplifier (LPF)
-
I. Utilization as comparator, in switching modevO ∈ {VOL ; VOH}
vD > 0, vO→ +∞, vO limited by the positive supply vO = VOH ≈ +VPSvD< 0, vO→ -∞, vO limited by the negative supply vO = VOL ≈ -VPS
II. Utilization as amplifiervO ∈ (VOL ; VOH)
It is mandatory that vD = 0, so then vO = a·vD = ∞·0 - indeterminationvD is kept at 0 by means of external components (R) arranged in a negative feedback (NF) configuration
16Laura-Nicoleta IVANCIU, Electronic devices
Amplifiers with OpAmp
Amplifiers with OpAmp
C8 – Electronic amplifiers. Amplifiers with OpAmp.
vO = avD = ∞·vD
C6 + C7
-
17Laura-Nicoleta IVANCIU, Electronic devices
Amplifiers with OpAmp
Amplifiers with OpAmp
C8 – Electronic amplifiers. Amplifiers with OpAmp.
NI
NF automatically keeps vD at zero
↓↑↑↑= − DODD vvvvv ,,,0
vO = avD
NI II Amplifier
vI ground non-inverting
ground vI inverting
vI1 vI2 differential
-
18Laura-Nicoleta IVANCIU, Electronic devices
Non-inverting amplifier
C8 – Electronic amplifiers. Amplifiers with OpAmp. Amplifiers with OpAmp
OvRRRv
21
1
+=−
021
1 =+
−=−= −+ OID vRRRvvvv
OI vRRRv
21
1
+= 1
21RR
vvA
I
Ov +==
-
19Laura-Nicoleta IVANCIU, Electronic devices
Non-inverting amplifier
C8 – Electronic amplifiers. Amplifiers with OpAmp. Amplifiers with OpAmp
Alternative method for computing Av
i
i
gain is set only by the ratio of two resistors (external components) the gain value: precise and stable the gain is independent of the OpAmp, it is not influenced by the technological
spread of the OpAmp’s parameters
0=Dv
Ivv =+ Ivv =
−
1
21RR
vv
AI
Ov +==The same current goes through R1 and R2
Direct consequences of NF for an OpAmp with very high intrinsic gain (a → ∞ for ideal op-amp):
-
20Laura-Nicoleta IVANCIU, Electronic devices
Non-inverting amplifier
C8 – Electronic amplifiers. Amplifiers with OpAmp. Amplifiers with OpAmp
Input and output resistances
0=∞
== open
sc
open O
O
Oo
vi
vRvI sees an open circuit, so Ri = ∞
Computed on the equivalent model
-
21Laura-Nicoleta IVANCIU, Electronic devices
Non-inverting amplifier
C8 – Electronic amplifiers. Amplifiers with OpAmp. Amplifiers with OpAmp
Example
vO(t) for triangular vI(t), 3 V amplitude, zero dc component
-
22Laura-Nicoleta IVANCIU, Electronic devices
Non-inverting amplifier
C8 – Electronic amplifiers. Amplifiers with OpAmp. Amplifiers with OpAmp
Adjustable gain
1
21R
PRAmaxv
++=
PRRA
minv ++=
1
21
1
21max R
RAv +=
0min
=vA
-
23Laura-Nicoleta IVANCIU, Electronic devices
Non-inverting amplifier
C8 – Electronic amplifiers. Amplifiers with OpAmp. Amplifiers with OpAmp
Voltage follower
total (full) NF no voltage gain (Av = 1) infinite current gain (Ai = ∞)
Voltage followers are used as a buffer stages between a source (or the output of a circuit) with high RO (can only supply low current) to a low RL (needs high current) – impedance matching.
IO vv = the output voltage follows the input voltage
-
24Laura-Nicoleta IVANCIU, Electronic devices
Inverting amplifier
C8 – Electronic amplifiers. Amplifiers with OpAmp. Amplifiers with OpAmp
0=+v
OI vRRRv
RRRv
21
1
21
2
++
+=−
0021
1
21
2 =+
−+
−=−= −+ OID vRRRv
RRRvvv
1
2
RR
vvA
I
Ov −==
-
25Laura-Nicoleta IVANCIU, Electronic devices
Inverting amplifier
C8 – Electronic amplifiers. Amplifiers with OpAmp. Amplifiers with OpAmp
Alternative method for computing Av
21 ii =1
10
Rvi I −=
21 Rv
Rv OI −=
22
0R
vi O
−=
1
2
RR
vv
AI
Ov −==
0=+v0=−v
virtual ground
−+ = vv=>
0=DvNF =>
-
26Laura-Nicoleta IVANCIU, Electronic devices
Inverting amplifier
C8 – Electronic amplifiers. Amplifiers with OpAmp. Amplifiers with OpAmp
Input and output resistances
Noninverting amplifier: Ri→∞
Inverting amplifier: Ri→ finite (units, tens of kΩ)
1RRi =
0=oR
The input source “sees” only R1 (the inverting input is virtual ground)
-
27Laura-Nicoleta IVANCIU, Electronic devices
Inverting amplifier
C8 – Electronic amplifiers. Amplifiers with OpAmp. Amplifiers with OpAmp
ExampleRi, Ro, AvvI range for active regionequivalent model
k101 == RRi0=oR
1010
100
1
2 −=−=−=RRAv
vI range: )V2.1;V2.1( +−
R1 = 10 K, R2 = 100K,
supply ±12 V
-
28Laura-Nicoleta IVANCIU, Electronic devices
Inverting amplifier
C8 – Electronic amplifiers. Amplifiers with OpAmp. Amplifiers with OpAmp
Voltage follower
IO vv −=
1−==I
Ov v
vA
RRi =
-
29Laura-Nicoleta IVANCIU, Electronic devices
Design example
C8 – Electronic amplifiers. Amplifiers with OpAmp. Amplifiers with OpAmp
Design an inverting amplifier with Ri > 8 kΩ and |Av| adjustable in the range [10, 18].
101
2min
==RRAv
181
2max
=+
=R
PRAv
12 10RR = 12 18RPR =+
What next?
-
30Laura-Nicoleta IVANCIU, Electronic devices
Design example
C8 – Electronic amplifiers. Amplifiers with OpAmp. Amplifiers with OpAmp
Design an inverting amplifier with Ri > 8 kΩ and |Av| adjustable in the range [10, 18].
12 10RR = 12 18RPR =+
kΩ81 ≥= RRi kΩ101 =RChoose
kΩ10010102 =⋅=RkΩ801001018 =−⋅=P
P = 100 kΩ will be used. Keeping R2 = 100 kΩ will result in:
kΩ1,1118
100100182
1 =+
=+
=PRR R2 = 100 kΩ P = 100kΩ
Verification: 1.9min
=vA 18max =vA Acceptable?
Solution 1
-
31Laura-Nicoleta IVANCIU, Electronic devices
Design example
C8 – Electronic amplifiers. Amplifiers with OpAmp. Amplifiers with OpAmp
Design an inverting amplifier with Ri > 8 kΩ and |Av| adjustable in the range [10, 18].
12 10RR =
Select
Verification: 18max
=vA
What if we began w/ P = 10kΩ?
Solution 2Ω= k100P
12 10RR =
12 18k100 RR =+Ω= k5.121RΩ= k1252R
10min
=vA
Ω>Ω== k8k5,12RRi
12 18RPR =+
-
32Laura-Nicoleta IVANCIU, Electronic devices
High gain and high input resistance
C8 – Electronic amplifiers. Amplifiers with OpAmp. Amplifiers with OpAmp
OPTIONAL
1RRi =
10201.01
10101
1010−=
⋅⋅
++
−=vA
same current through R1 and R21 same voltage across R3 and R21
+
+−==
31
2221
1
2221
RRRR
RRR
vvA
I
Ov
For
k1.0k,10k10k,1
322
211
====
RRRR
k1=iR
-
32Laura-Nicoleta IVANCIU, Electronic devices
SummaryThe little black bug (OpAmp) is also able to make: Amplifiers with OpAmp
Non-inverting amplifiers Inverting amplifiers
Next week: Summing and differential amplifiers with OpAmp.
To do: Homework 6
C8 – Electronic amplifiers. Amplifiers with OpAmp.
Slide Number 1Slide Number 2Slide Number 3Slide Number 4Slide Number 5Slide Number 6Slide Number 7Slide Number 8Slide Number 9Slide Number 10Slide Number 11Slide Number 12Slide Number 13Slide Number 14Slide Number 15Slide Number 16Slide Number 17Slide Number 18 Alternative method for computing AvSlide Number 20Slide Number 21Slide Number 22Slide Number 23Slide Number 24 Alternative method for computing AvSlide Number 26Slide Number 27Slide Number 28Slide Number 32