The 741 Operational-Amplifier
1
Reference Bias Current : The 741 op-amp circuit.
Reference Bias Current
DC Analysis of the 741
Reference Bias Current
VCC
-VEE
Bias for input stage The 741 op-amp circuit.
Bias for input stage
IC10
Input Stage Bias
VBE 10
I C10  I S 10 e
VBE 11
I C11  I S 11e
ln I C10
I S 10
VT
 VBE10  VT
VT
 VBE11  VT ln
VBE11  VBE10  VT ln
I REF
I S 11
I
I REF
I
 VT ln C10  VT ln REF
I S 11
I S 10
I C10
+
VBE11
-
+
VBE10
-
++
-
IC10 can be determined by knowing IREF and R4
IC10
Biasing Input Stage : The 741 op-amp circuit.
IC1
IC3
IC2
IC4
The dc analysis of the 741 input stage.
npn β very high
Relationship IREF & IO
Base current IE/1+βP
Base currents add together
As  P  1
IC10  2I
A Simple BJT Current Source
8
Negative Feed-back Loop : 741 input stage.
Causes current pulled from Q8 to increase
For some reason I in Q1 & Q2 increases
Output current of Q8 Q9 correspondingly increase
Negative Feed back Loop
Since Ic10 remains constant, it forces
combined current of Q3 & Q4 to decrease
Input Stage : The 741 op-amp circuit.
IC7
The dc analysis of the 741 input stage, continued.
Ic5=I
6
1
5
2
Bias Current of Q7
3
7
4
The dc analysis of the 741 input stage, continued.
50 KΩ
The 741 op-amp circuit : SECOND STAGE
IC16
IC17
DC Analysis : Second Stage
Q13 is lateral pnp transistor
Q13B has a scale of 0.75 times that of Q12
IREF = 0.73 mA & βP>>1
IC13B = 550 µA & IC17 = 550 µA
IC13B=0.75 IREF
Neglect Base Current of Q23
IC17=IC13B
Output Stage Bias :
The 741 op-amp circuit.
The 741 output stage without the short-circuit protection devices.
Q13 is lateral pnp transistor
IS of Q13A is 0.25 times IS of Q12
Neglect Base current of Q14 & Q20
Base Current of Q23 is 180/50=36 μ A
Negligible as assumed
Output Stage Bias
Voltage VBE18 ≈ 0.6V
Current Thru R10=0.6/40k=15 µ A
+
VBB
-
14
20
Summary Collector Currents : 741 Op Amp
Small-signal analysis of the 741 input stage.
Collectors Q1 & Q2 connected to dc voltage so are grounded
Q3 & Q3 are biased by constant current source so are open cct
Small-signal analysis of the 741 input stage.
Input appears across four input resistors
vi vi
Rid   (   1)  4(   1)re
ib ie
The 741 op-amp circuit.
Small signal model :
The load circuit of the input stage.
The load circuit of the input stage
Q5 & Q6 are identical and their bases are tied together
So their collector currents are equal
The load circuit of the input stage
Output Resistance : 741 Op Amp
Ro1 is parallel equivalent of Ro4 & Ro6
Assume that common bases of Q3 & Q4
are at virtual ground
Com m on Base Circuit
Ro 4  ro 1  g m RE || r  ......equation 6.118
RE  re , ro  VA
I
,
Ro 4  10.5 M
Output Resistance Ro1
Output Resistance : 741 Op Amp
Assume that the base of Q6 is at virtual ground
Because signal is very small
Com m on Base Circuit
Ro 6  ro 1  g m RE || r  ......equation 6.118
RE  R2 , ro  VA
I
,
Ro 6  18.2 M
Output Resistance Ro1
Output Resistance : 741 Op Amp
Ro1 is parallel equivalent of Ro4 & Ro6
Ro1=Ro4||Ro6
Ro1=6.7 MΩ
Output Resistance Ro1
Figure 9.22 Small-signal equivalent circuit for the input stage of the 741 op amp.
Second Stage :The 741 op-amp circuit.
Figure 9.24 The 741 second stage prepared for small-signal analysis.
Input Resistance : Second Stage
Transconductance : Second Stage
Thus current through the output resistance of Q13B is zero
Output Resistance R02 : Second Stage
R02
Output Resistance R02 : Second Stage
Since the resistance between the base of Q17 and ground
is relatively small, The base is grounded and circuit is CB
R02
Output Resistance R02 : Second Stage
R02
Output Resistance R017
Since the resistance between the base of Q17 and ground
is relatively small, The base is grounded and circuit is CB
Figure 9.25 Small-signal equivalent circuit model of the second stage.
Figure 9.27 Thévenin form of the small-signal model of the second stage.
Open Circuit Voltage Gain =
Output Stage :The 741 op-amp circuit.
The 741 output stage.
The 741 output stage.
• Input from second stage
Q17
• Loaded with 2 kΩ resistor
• Q18 & Q19 and R10 provide
Class AB bias to output
stage.
• Q14 & Q20 are output
transistors
• Output stage is driven by
emitter follower Q23 acts
as buffer
Output Voltage
Limits
Maximum positive output voltage
vomax is limited by input circuit
Saturation of Q13A
vo max  VCC  VEC13 A  VBE14
Minimum negative output voltage
vomin is limited by input circuit
Saturation of Q17
Small Signal Model for the 741 output stage.
vo2=-Gm2R02vi2
Gm2 = 6.5mA/V & RO2 = 81kΩ
Rin3 is input resistance of the output stage with load RL
Input resistance Rin3 of output stage
Rin3
Rin
Rin3
vb 23

  23  1re 23  Rin    23 Rin
ib 23
Input resistance Rin
Rin=Rin20||Rout18
Suppose Q20 is conducting and
Q14 is cut-off
Rout18
Rin
Rin20
Input resistance Rin20
Rin20
Rin20
vb 20

  20  1re 20  RL    20 RL
ib 20
Input resistance Rout18
Rout18 is ro13A in series with output resistance of Q18
& Q19
Output resistance of Q18 & Q19
= 163 Ω
Rout18
ro13A >>Output resistance of Q18 & Q19
Rout18  r013 A
Input resistance Rin3 of the output stage
Rin3   23 Rin
Rin=Rin20||Rout18
Rout18
Rout18  r013 A
Rin
Rin3
Rin20  20 RL
Rin20
β20 = β23 = 50 ,
RL= 2kΩ, ro13A= 280kΩ
Rin3 = 3.7 MΩ
Small Signal Model for the 741 output stage.
Rin3 = 3.7 MΩ
Ro2 = 81 kΩ
Rin3 >> Ro2
So Rin3 will have little effect On the performance of the op
amp
= -515 V/V
Open Circuit Overall Voltage Gain Gvo
Small Signal Model for the 741 output stage.
Gvo3
vo

vo 2
RL  
Open Circuit Overall Voltage Gain Gvo
Gvo3
Q14 , Q20 & Q23 are common collector circuits, So gain is unity
Gvo3  1
vo

vo 2
RL  
Circuit for finding the output resistance Rout.
Exact Value of Rout will depend upon which transistor (Q14 or Q20) is conducting
Suppose Q20 Is conducting and Q14 is cut-off.
Input source feeding the output stage is grounded
Circuit for finding the output resistance Rout.
Rout
1
2
ve 23

ie 23
Output Short Circuit Protection Stage :The 741 op-amp circuit.
Output Short-Circuit Protection
• If any terminal of the IC is
short circuited to one of
the power supplies, IC
will burnout.
• Protection Circuit limits
the current in the output
transistors in the event of
short circuit.
Output Short-Circuit Protection
Against maximum current the op amp can source
• In normal case
– Current thru the emitter of
Q14 is 20mA, voltage drop
across R6 is approx 540mV
and Q15 is off
• In the event of short circuit,
– if current in the emitter of
Q14 exceeds 20mA, voltage
drop across R6 will increase
above 540mV and Q15 will
conduct.
• Robs some of the current
supplied by Q13A, thus
reducing the base current of
Q14.
• This limits the current that the
op amp supplies from the
output terminal in the
outward direction to 20mA.
Output Short-Circuit Protection
Against maximum current the op amp can source
• In normal case
– Current thru the emitter of
Q20 is 20mA, voltage drop
across R7 is approx 540mV
and Q21 is off
• In the event of short circuit,
– if current in the emitter of
Q20 exceeds 20mA, voltage
drop across R7 will increase
above 540mV and Q21 will
conduct.
• Robs some of the current
supplied by Q24, thus reducing
the base current of Q20.
• This limits the current that the
op amp supplies from the
output terminal in the inward
direction to 20mA.
Small Signal Gain
Gain is found from the cascade of the equivalent
circuits of the op amp
Frequency Response
Frequency Response
Cc
Frequency Response
Cc
Cc introduces a dominant low-frequency pole
Using Miller’s theorem, the effective capacitance
due to Cc between the base of Q16 and ground is
The total resistance between base of Q16 and ground is
Figure 9.32 Bode plot for the 741 gain, neglecting nondominant poles.
The convenience of use of internally compensated 741 is achieved at the expense of a great
reduction in open loop gain--- externally compensated op amp.
Slew Rate
Slew rate
SR 
t 

2CCVT
4VT
I
Gm1 
VT
re 
I

2re
SR 
4VT t
