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Deciphering Electrical Characteristics
in an
Op Amp Datasheet
Tim Green
Linear Applications Manager
Tucson Division
[email protected]
Op Amp Basics
Ideal Operational Amplifier
•
•
•
•
•
Zero input current
Infinite input resistance
Infinite open loop gain
Zero output resistance
Infinite Slew Rate
Ideal Op Amp
+IN
+
-IN
-
Input Current = 0A
+IN
Rin
Infinite
-IN
Input Current = 0A
OUT
Open Loop Gain
Infinite
+
+
-
-
Rout
0 ohms
Ideal Op Amp
OUT
Op Amp Loop Gain Model
network
RF
network
RI
=VFB/VOUT
VOUT
VFB
VOUT
RF
+
+
VFB
VIN
RI
-

VOUT/VIN = Acl = Aol/(1+Aolβ)
If Aol >> 1 then Acl ≈ 1/β
Aol: Open Loop Gain
VIN
+

Aol
VOUT
β: Feedback Factor
Acl: Closed Loop Gain
Ideal Operational Amplifier

VINM
VINP
+

Aol
VOUT = (VINP – VINM) * Aol
VOUT / Aol – VINP = -VINM
If Aol = ∞ (for an Ideal Op Amp) then:
-VINP = -VINM
or
VINP = VINM
VOUT
Ideal Operational Amplifier
Irf = (Vout - Vin) / RF
Iri = Vin / RI
Iin- = 0A
Non-Inverting Configuration
Irf = Iri
(Vout - Vin) / RF = Vin / RI
Vout / Vin = 1 + RF/RI
For Ideal Op Amp
With Feedback and High Open Loop Gain:
+IN is forced to equal -IN
Ideal Op Amp
+
Vin 1
Vin 1V
Vout 10V
-
Iin- = 0A
RI 10k
RF 90k
Iri
Irf
Ideal Operational Amplifier
Irf = (Vout - 0V) / RF
Iri = (0V-Vin) / RI
Iin- = 0A
Inverting Configuration
For Ideal Op Amp
With Feedback and High Open Loop Gain:
+IN is forced to equal -IN
Irf = Iri
(Vout - 0V) / RF = (0V-Vin) / RI
Vout / Vin = -RF/RI
Ideal Op Amp
+
Gnd 0V
Vout -9V
-
Iin- = 0A
RI 10k
Vin 1
RF 90k
Iri
Irf
Intuitive AC Op Amp Model
VO
RO
K(f)
IN+
x1
RIN
IN-
+
-
VDIFF
VOUT
Input Specifications
Input Bias Current (Ib) & Input Offset Current (Ios)
Input Offset Voltage (Vos)
Power Supply Rejection Ratio (PSRR): Referred-To-Input Vos
Common Mode Voltage Range (Vcm)
Common Mode Rejection Ratio (CMRR): Referred-To-Input Vos
Small Signal Input Parasitics: Input Capacitance, Input Resistance
Input Noise: Current, Voltage (in, en)
Input Bias Current (Ib), Input Offset Current (Ios)
Ib- 3p
Ib =
Ideal Op Amp
-
Ib =
Vout
Ib+ + Ib2
7pA + 3pA
2
= 5pA
+
Ios = Ib+ - IbIos = 7pA - 3pA = 4pA
Ib+ 7p
Ib = 5pA
Ios = 4pA
Polarity is + or –
Current into or out of inputs
Input Bias Current (Ib), Input Offset Current (Ios)
25C Specs in Table
Often Curves for Temperature Specs
Polarity is + or –
Input Bias Current (Ib)  Vout Error
2
Vinm = 1.5uV
Vinm
1
RF 1M
RF 1M
Vout
Ib- 3p
Ib- 3p
RI 1M
Ideal Op Amp
Idelal Op Amp
RI 1M
-
Rs 1M
Vout
Rs 1M
Vout
+
+
+
Vin
Ib+ 7p
Vin
Ib causes errors at Vout
Ib+ 7p
Vinp
Vinp =7uV
3
Ib flow s through feedback and input resistors
View Vout and Vin as low impedance
Vinm = Ib- (RF // RI)
Vinp = Ib+ (Rs)
VIb- 1.5u
RI 1M
Ideal Op Amp
Ideal Op Amp
R3 1M
+
VIb+ 7u
Ib flow s through feedback and input resistors
Model as VIb+ and VIbInverting and Non-Inverting Gains create Vout error
Vout
R1 1M
Vout error = 11uV
+
+
Vout
Rs 1M
Vin
4
R2 1M
RF 1M
Vin
+
Vout error = 11uV
VIb 5.5u
Simplified VIb Model
VIb = VIb+ - VIbNon-Invverting Gain Creates Vout error
Input Offset Voltage (Vos)  Vout Error
25C Specs in Table
Often Histograms show distribution of Vos
Polarity is + or –
RF 1M
Ideal Op Amp
RI 1M
Vout
+
Vos 25u
Input Offset Voltage
Creates Vout error
Vout error = 50uV
Input Offset Voltage (Vos) Drift  Vout Error
Vos Drift Specs in Table
Often Histograms show
distribution of Vos Drift
Polarity is + or -
RF 1M
Ideal Op Amp
RI 1M
Vout
Vos_drift 60u Vos 25u
+
Vout error = 170uV
Initial Vos + Vos Drift creates Vout error
Operating Temperatue = 25C to 85C
T = 85C - 25C = 60C
dVos
Vos_drift = T
dT
Vos_drift = 60C 1uV/C = 60uV
Power Supply Rejection Ratio (PSRR)  Vout Error
RF 1M
DC PSRR in Table
DC PSRR Drift in Table
Polarity is + or PSRR is an RTI (Referred-To-Input) specification
Appears as Input Offset Voltage
Ideal Op Amp
RI 1M
+
Vout
+
Vout error = 20uV
Vos_PSRR 10u
delta_Vcc 500m
PSSR DC = 20uV/V
delta_Vcc = 500mV (DC change in Vcc)
Vos_PSRR = PSSR DC delta_Vcc
Vos_PSRR = 20uV/V 500mV = 10uV
Vcc 5
PSSR reflects as Vos_PSRR & creates Vout error
Power Supply Rejection Ratio (PSRR)  Vout Error
AC PSRR in Curve
Frequency of analysis = 20kHz
PSRR AC @ 20kHz = 80dB
Convert PSRR (dB) to PSRR (Linear Gain):
(80dB/20)
10
= 10,000
PSRR is an attenuation so 1V gets attenuated by x10,000
1/10,000 = 1e-4V/V
Now convert numerator to uV:
(1e-4V) (1uV/1e-6V) = 1e-4uV / 1e-6 = 100uV:
PSRR AC @ 20kHz = 100uV/V
20kHz
R4 1M
Ideal Op Amp
R5 1M
PSRR AC reflects as Vos_PSRR_ac & creates Vout error
PSRR is an RTI (Referred-To-Input) specification
Appears as Input Offset Voltage
+
Vos_PSRR_ac
10uVpp @ 20kHz
+
Vout
Vout error = 20uVpp @ 20kHz
+
+
PSSR AC @ 20kHz = 100uV/V
delta_Vcc_ac = 100mVpp (AC change in Vcc @ 20kHz)
Vos_PSRR_ac = PSSR AC delta_Vcc_ac
Vos_PSRR_ac = 100uV/V 100mVpp = 10uVpp
-
delta_Vcc_ac
100mVpp @ 20kHz
Vcc 5
Common Mode Voltage Range (Vcm)
Vin_CM = Voltage Common to Vinp & Vinm
Vcm
Same for DC & AC
AC peak voltage < Vcm
Vinm
Vee 15
V = 2V max
Ideal Op Amp
-
Vinp
+
Vout
+
+
Common Mode Voltage Range
For: Non-Inverting Gain Vinp = Vinm
So: Vin_CM = Vin
From Vcm spec Vin must stay 2V aw ay from either
supply for op amp to operate as a linear gain block
RF 1M
Vin
-13V < Vin < +13V
V = 2V max
Vcc 15
Common Mode Rejection Ratio (CMRR)  Vout Error
CMRR DC in Table
Polarity is + or -
CMRR DC reflects as Vos_CMRR & creates Vout error
CMRR DC = 130dB
Convert CMRR (dB) to CMRR (Linear Gain):
RF 1M
(130dB/20)
10
= 3.16e+6
CMRR is an attenuation so 1V gets attenuated by x3.16e+6
1/3.16e+6 = 3.16e-7V/V
Now convert numerator to uV:
(31.6e-7V) (1uV/1e-6V) = 3.16e-7uV / 1e-6 = 0.316uV:
CMRR DC = 0.316uV/V
CMRR DC = 0.316uV/V
Vin = 5V for Non-Inverting Gain Vin =Vcm
Vcm = 5V
Vos_CMRR = CMRR DC Vcm
Vos_CMRR = 0.316uV/V 5V = 1.58uV
CMRR is an RTI (Referred-To-Input) specification
Appears as Input Offset Voltage
V2 15
Ideal Op Amp
RI 1M
+
Vin 5
Vos_CMRR 1.58u
Vout
+
Vout error = 3.16uV
V1 15
Common Mode Rejection Ratio (CMRR)  Vout Error
AC CMRR in Curve
Frequency of Analysis = 1kHz
CMRR AC = 100dB @ 1kHz
Convert CMRR (dB) to CMRR (Linear Gain):
(100dB/20)
10
= 100,000
CMRR is an attenuation so 1V gets attenuated by x100,000
1/100,000 = 1e-5V/V
Now convert numerator to uV:
(1e-5V) (1uV/1e-6V) = 1e-5uV / 1e-6 = 10uV:
CMRR AC = 10uV/V @ 1kHz
RF 1M
RI 1M
CMRR AC reflects as Vos_CMRR_ac & creates Vout error
CMRR is an RTI (Referred-To-Input) specification
Appears as Input Offset Voltage
Vee 15
Ideal Op Amp
200uVpp @ 1kHz
Vos_CMRR_ac
+
+
CMRR AC = 10uV/V @1kHz
Vin = 20Vpp for Non-Inverting Gain Vin =Vcm_ac
Vcm_ac = 20Vpp
Vos_CMRR_ac = CMRR AC Vcm_ac
Vos_CMRR_ac = 10uV/V 20Vpp = 200uVpp
Vin
20Vpp @ 1kHz
+
Vout
+
Vout error = 400uVpp @ 1kHz
Vcc 15
Cin
Small Signal
Input Parasitics
RF 1M
Vee
RI 1M
Ccm, Cdiff in Table
Rcm, Rdiff in Table if specified
Ccm
Rcm
Cdiff
Rdiff
+
+In
Ccm
Rdiff > 200GW for Bipolar Inputs
Rcm > 40MW for Bipolar Inputs
Even greater for JFET or MOSFET inputs
Ideal Op Amp
-
-In
Vout
+
Rcm
Small Signal
Input Parasitics
Vcc
Ccm and Cdiff can be a problem:
Ccm and Cdiff form Cin
Cin & RF form a Loop Gain pole  unwanted oscillations depending upon UGBW and value of RF.
Input Noise: Current, Voltage (in, en)
Op Amp Noise Model
Noise Model
OPA277 Data
(IN+ and IN- are not correlated)
VN
IN+
IN-
IOP1
Tina Simplified Model
U1
nV
*
VN
-
fA
IN
*
+
Understanding The Spectrum:
Total Noise Equation (Current or Voltage)
1/f Noise Region
(Pink Noise Region)
White Noise Region
(Broadband Noise Region)
Voltage Noise (nV/ Hz )
100k
enT = √[(en1/f)2 + (enBB)2]
10k
1k
100
10
1
0.1
fL
where:
enT = Total rms Voltage Noise in volts rms
en1/f = 1/f voltage noise in volts rms
enBB = Broadband voltage noise in volts rms
1
10
100
1k
10k
Frequency (Hz)
enBB calculation
en1/f calculation
fH
Real Filter Correction vs Brickwall Filter
where:
fP = roll-off frequency of pole or poles
fBF = equivalent brickwall filter frequency
Noise BW
Small Signal BW
0
Filter Attenuation (dB)
Skirt of
1-Pole Filter
Response
Skirt of
2-Pole Filter
Response
-20
Skirt of
3-Pole Filter
Response
-40
Brickwall
-80
0.1fP
fP fBF
Frequency (f)
10fP
AC Noise Bandwidth Ratios for nth Order Low-Pass Filters
BWn = (fH)(Kn) Effective Noise Bandwidth
Real Filter Correction vs Brickwall Filter
Number of Poles in
Filter
Kn
AC Noise Bandwidth Ratio
1
1.57
2
1.22
3
1.16
4
1.13
5
1.12
Broadband Noise Equation
eBB
BWn = (fH)(Kn)
where:
BWn = noise bandwidth for a given system
fH = upper frequency of frequency range of operation
Kn = “Brickwall” filter multiplier to include the “skirt” effects of a low pass filter
enBB = (eBB)(√[BWn])
where:
enBB = Broadband voltage noise in volts rms
eBB = Broadband voltage noise density ; usually in nV/√Hz
BWn = Noise bandwidth for a given system
1/f Noise Equation
e1/f@1Hz
e1/f@1Hz = (e1/f@f)(√[f])
where:
e1/f@1Hz = normalized noise at 1Hz (usually in nV)
e1/f@f = voltage noise density at f ; (usually in nV/√Hz)
f = a frequency in the 1/f region where noise voltage density is known
en1/f = (e1/f@1Hz)(√[ln(fH/fL)])
where:
en1/f = 1/f voltage noise in volts rms over frequency range of operation
e1/f@1Hz = voltage noise density at 1Hz; (usually in nV)
fH = upper frequency of frequency range of operation
(Use BWn as an approximation for fH)
fL = lower frequency of frequency range of operation
Example Noise Calculation
R2 1k
Given:
OPA627
Noise Gain of 101
R1 100k
V1 15
-
+
+
VG1
VF1
+
U1 OPA627/BB
V2 15
Find (RTI, RTO):
Voltage Noise
Current Noise
Resistor Noise
Voltage Noise Spectrum and Noise Bandwidth
50nV/rt-Hz
5nV/rt-Hz
Unity Gain Bandwidth = 16MHz
Closed Loop Bandwidth = 16MHz / 101 = 158kHz
Example Voltage Noise Calculation
Voltage Noise Calculation:
Broadband Voltage Noise Component:
BWn ≈ (fH)(Kn)
(note Kn = 1.57 for single pole)
BWn ≈ (158kHz)(1.57) =248kHz
enBB = (eBB)(√BWn)
enBB = (5nV/√Hz)(√248kHz) = 2490nV rms
1/f Voltage Noise Component:
e1/f@1Hz = (e1/f@f)(√f)
e1/f@1Hz = (50nV/√Hz)(√1Hz) = 50nV
en1/f = (e1/f@1Hz)(√[ln(fH/fL)]) Use fH = BWn
en1/f = (50nV)(√[ln(248kHz/1Hz)]) = 176nV rms
Total Voltage Noise (referred to the input of the amplifier):
enT = √[(en1/f)2 + (enBB)2]
enT = √[(176nV rms)2 + (2490nV rms)2] = 2496nV rms
Example Current Noise Calculation
Note: This example amp doesn’t have 1/f component for current noise.
en-in= (in)x(Req)
R1 1k
en-out= Gain x (in)x(Req)
Rf 3k
Gain
IOP1
U2
-
fA
*
VF1
Req = R1 || Rf
+
*
Example Current Noise Calculation
Broadband Current Noise Component:
BWn ≈ (fH)(Kn)
BWn ≈ (158kHz)(1.57) =248kHz
inBB = (iBB)(√BWn)
inBB = (2.5fA/√Hz)(√248kHz) = 1.244pA rms
Req = Rf || R1 = 100k || 1k = 0.99k
eni = (In)( Req) = (1.244pA)(0.99k) = 1.23nV rms
Since the Total Voltage noise is envt = 2496nV rms
the current noise can be neglected.
neglect
Resistor Noise – Thermal Noise
The mean- square open- circuit voltage (e) across a resistor (R) is:
en = √ (4kTKRΔf)
where:
TK is Temperature (ºK)
R is Resistance (Ω)
f is frequency (Hz)
k is Boltzmann’s constant
(1.381E-23 joule/ºK)
en is volts (VRMS)
To convert Temperature Kelvin to
TK = 273.15oC + TC
0
1  10
468.916 1000
3
en density = √ (4kTKR)
1 10
468.916
3
100
 23
  ( 25  273.15 )  X   10 9
 23
  ( 125  273.15 )  X   10 9
 23
  (  55  273.15 )  X   10 9
nV/rt-Hz
0
Noise Spectral Density vs. Resistance
Noise Spectral Density vs. Resistance
0
Resistor Noise – Thermal Noise
100
10
 23
 4 1.3806510
 9

 ( 25 273.15)  X  10

25C
 23
9
 4 1.3806510

 ( 125 273.15)  X  10

10
125C
1
 23
9
 4 1.3806510

 (  55 273.15)  X  10

-55C
0.347
1
0.1
10
10
100
1  10
3
1  10
X
4
1  10
5
Resistance (Ohms)
1  10
6
1  10
7
10
7
0.347 0.1
10
10
Example Resistor Noise Calculation
enr = √(4kTKRΔf)
where:
R = Req = R1||Rf
Δf = BWn
enr = √(4 (1.38E-23) (273 + 25) (0.99k)(248kHz)) = 2010nV rms
* U1
en-out= Gain x (√(4kTRΔf))
Gain
nV
R1Rf
2k
nV
R2R1
1k
* U1
en-in= √(4kTRΔf)
IOP1
-
VF1
Req = R1 || Rf
+
*
Total Noise Calculation
Voltage Noise From Op-Amp RTI:
env = 2510nV rms
Current Noise From Op-Amp RTI (as a voltage):
eni = 1.24nV rms
Resistor Noise RTI:
enr = 2020nV rms
Total Noise RTI:
en in = √((2510nV)2 + ((1.2nV)2 + ((2010nV)2) = 3216nV rms
Total Noise RTO:
en out = en in x gain = (3216nV)(101) = 325uV rms
Calculating Noise Vpp from Noise Vrms
Relation of Peak-to-Peak Value of AC Noise Voltage to rms Value
Peak-to-Peak
Amplitude
Probability of Having
a Larger Amplitude
2 X rms
32%
3 X rms
13%
4 X rms
4.6%
5 X rms
1.2%
6 X rms *
0.3%
6.6 X rms
0.1%
*Common Practice is to use:
Peak-to-Peak Amplitude = 6 X rms
Voltage Noise (f = 0.1Hz to 10Hz)  Low Frequency
Low frequency noise spec and curve:
Over specific frequency range:
0.1Hz < f < 10Hz
Given as Noise Voltage in pp units
Measured After Bandpass Filter:
0.1Hz Second−Order High−Pass
10Hz Fourth−Order Low−Pass
Frequency Response
Specifications
Open Loop Gain (Aol) & Phase
Slew Rate (SR)
Total Harmonic Distortion + Noise (THD+N)
Settling Time (ts)
Open Loop Gain & Phase
Open-Loop Voltage Gain at DC
Linear operation conditions NOT the same as Voltage Output Swing to Rail
Gain-Bandwidth Product = UGBW
(Unity Gain Bandwidth)
G=1 Stable Op Amps
5.5MHz
Vout/Vin:
Gain Accuracy & Frequency Response
R2 9k
Real Op Amp
R3 1k
-
+
Vout
+
Vin
fcl
Aol at any Frequency:
Aol_f = UGBW / f
1/Beta
Vout/Vin
Aol @ 1kHz = 5.5MHz / 1kHz = 5500
Aol @ 1kHz = 20LOG10(5500) = 74.8dB
Gain Accuracy at any frequency:
Vout/ Vin Frequency Response
Frequency of analysis for Gain Accuracy = 1kHz
1/ = 10
20LOG10(10) = 20dB
Vout / Vin =
Aol
1+Aol
fcl is w here Aol = 1
f > fcl: Loop Gain < 1 so Vout/Vin = Aol
Vout / Vin =
Aol
1+Aol
Vout / Vin = 5500 / (1+ 5500 0.1)
Vout/ / Vin = 9.98185
Vout / Vin ideal = 10
Gain Error = ((10 - 9.98185) / 10) 100 = 0.18%
Slew Rate
Slew Rate Measurement:
10% to 90% of Vout
Slew Rate &
Full Power Bandwidth
or
Maximum Output Voltage vs Frequency
Maximum Rate of change of sinew ave is at zero cross
Highest Frequency Op Amp can track sinew ave limited by:
Frequency, Output Voltage, Slew Rate
SR (V/us) = 2 f Vop (1e-6)
w here:
SR = Slew Rate in V/us
f = frequency of interest
Vop = Vout peak voltage
Given Slew Rate = 2V/us
What is max f for sinew ave of 2.5Vpp?
SR (V/us) = 2 f Vop (1e-6)
2 = 2 f (2.5Vpp/2) (1e-6)
Solving for f:
fmax = 254.6kHz
THD + Noise
Larger Closed Loop Gain  Loop
Gain to correct for Op Amp
Non-Linearities and Noise
THD + Noise = 1% Example
Fundamental f = Input Frequency
Fundamental f = 99% Vout Amplitude
Harmonics due to Op Amp non-linearities
Noise due to Op Amp Input Noise (en, in)
Harmonics + Noise < 1% of Vout
Settling Time
Slew
Rate
Note: Settling Time includes Slew Rate time
Settling Time
Settling Time
Large Signal effects:
Slew Rate
Small Signal effects
Large Gain = Less closed loop Bandwidth
Large Gain = Less Loop Gain (AolB) to correct for errors
Large Gain = Longer Settling Time
Output Specifications
Voltage Output Swing from Rail
Short Circuit Current (Isc)
Open Loop Output Impedance (Zo)
Closed Loop Output Impedance (Zout)
Capacitive Load Drive
Voltage Output
Swing From Rail
Loaded Vout swing from Rail
Higher Current Load  Farther from Rail
Higher Current Load  Larger Vsat
Vsat = Vs - Vout
+25C Curve:
Op Amp Aol is degraded if on curve 1
Op Amp Aol is okay if left of curve 2
2
1
Short Circuit Current (Isc)
Output shorted  Current Limit engaged
For Graph shown TJ max is okay
If using larger voltages (i.e. +5V, Gnd)
use Short-Circuit Current values
& analyze power dissipation and TJ max
Open Loop Output Impedance (Zo)
Closed Loop Output Impedance (Zout)
Capacitive Load Drive
Op Amp Model for Derivation of ROUT
Definition of Terms:
RO = Op Amp Open Loop Output Resistance
ROUT = Op Amp Closed Loop Output Resistance
ROUT = RO / (1+Aolβ)
RF
RI
RO
-IN
RDIFF
VFB
VE
xAol
+
VO
IOUT
-
1A
+
+IN
VOUT
Op Amp Model
From: Frederiksen, Thomas M. Intuitive Operational Amplifiers.
McGraw-Hill Book Company. New York. Revised Edition. 1988.
ROUT = VOUT/IOUT
ROUT vs RO
•
RO does NOT change when Closed Loop feedback is used
•
ROUT is the effect of RO, Aol, and β controlling VO
– Closed Loop feedback (β) forces VO to increase or decrease
as needed to accommodate VO loading
– Closed Loop (β) increase or decrease in VO appears at VOUT as
a reduction in RO
– ROUT increases as Loop Gain (Aolβ) decreases
Note: Some op amps have ZO characteristics other than pure
resistance (RO) – consult data sheet / manufacturer.
RO & CL: Modified Aol Model
RI
RF
100kW
100kW
OPA452
-
Da
+
fpo1 = 1/(2∙П∙RO∙CL)
fpo1 = 5.545kHz
Create a new “Modified Aol” Plot
RO
+
28.7W
ol
et A
+ ta She
Extra Pole in Aol Plot due to RO & CL:
fpo1 = 1/(2∙П∙28.7Ω∙1μF)
-
VIN
-
VOUT
CL
1F
RO & CL: OPA542 Modified Aol First Order
120
OPA452
Aol
100
80
Gain (dB)
60
fpo1
40
STABLE
40dB/Decade
Rate-Of-Closure
20
fcl
1/
0
-20
Modified Aol
due to CL
-40
-60
1
10
100
1K
10K
Frequency (Hz)
100k
1M
10M
Zo (Open Loop Output Impedance)
Cap Load Drive
As Cap Load increases Loop Gain Phase
Margin decreases and we see the
transient response for Cap Load
increase in overshoot for OPA376
OPA376 and many other Single Supply
Op Amps Open Loop Output
Impedance is not Purely Resistive
For about 500pF Load Capacitance
Small-Signal Overshoot is 50%
From: Dorf, Richard C. Modern Control Systems. Addison-Wesley
Publishing Company. Reading, Massachusetts. Third Edition, 1981.
2nd Order Transient Curves
Signal overshoot of 50% or normalized
signal output of 1.5 yields a Damping
ratio ( z) of 0.2
From: Dorf, Richard C. Modern Control Systems. Addison-Wesley
Publishing Company. Reading, Massachusetts. Third Edition, 1981.
2nd Order Damping Ratio vs Phase Margin
Damping ratio ( z) of 0.2 yields 23.5 degrees
of phase margin for AC Loop Stability
23.5o
Closed Loop Output Impedance
Closed Loop Output impedance gives an
indication of what source impedance
the closed loop op amp will have to
drive loads over frequency
For Bipolar, Emitter-Follower Output Op
amps like OPA177, open loop output
impedance = RO (purely resistive
inside UGBW)
Since ROUT = RO/(1+Aol) and RO is
resistive ROUT looks opposite of Aol
and increase at higher frequencies
Power Supply Specifications
Specified Voltage Range (VS)
Operating Voltage Range (VS)
Quiescent Current (IQ)
Specified and Operating Voltage Range (VS)
For 2.2V < VS < 5.5V data sheet
specifications will be met
For 2 < VS < 2.2V the op amp will still
function but all data sheet
specifications may not be met
i.e. Output Swing to Rail, Aol, etc may be
degraded
Quiescent Current (IQ)
+Vs
IQ
+
+
Vout
Real Op Amp
IQ
-Vs
Quiescent Current:
Supply Current to operate the op amp
Does NOT include load current
Temperature Range
Specifications
Specified Range
Operating Range
Thermal Resistance (QJA)
Specified and Operating Temperature Range
For -40C < TA < +125C data sheet
specifications will be met
For +125C < TA < +150C the op amp will still
function but all data sheet specifications
may not be met
i.e. Output Swing to Rail, Aol, etc may be
degraded
Thermal Resistance (QJA)
Thermal Resistance (QJA)
QJA will be used with ambient
temperature TA and internal
total power dissipation PD to
compute maximum op amp
junction temperature TJ
Thermal Model
PD = PIQ + POUT
PD = Total Power Dissipated
PIQ = Power Dissipated due to IQ
POUT = Power Dissipated in Output Stages
TJ
Thermal model with no heat sink
Analogous to an electrical circuit
PD
RθJA
TJ= PD( RθJA) + TA
T – is analogous to voltage
R – is analogous to resistance
TA
TA
P – is analogous to current
IQ Power Dissipation (PIQ)
PIQ = [+Vs - (-Vs) ] IQ
+Vs
IQ
+
+
Vout
Real Op Amp
IQ
-Vs
DC Normal Maximum Power Dissipation in Output Stage (POUT)
+Vs
Vout =
IQ
+
Real Op Amp
+
1
2
Vs
Iout_DC
Vout
Vin
IQ
RL
-Vs
RI
RF
POUT_DC =
Vs
2
4 RL
DC Short Circuit Maximum Power Dissipation in Output Stage (POUT)
+Vs
IQ
+
+
Real Op Amp
+
POUT_SHORT = Vs Isc
Isc
VF1
VG1
IQ
-Vs
RI
RF
AC Normal Maximum Power Dissipation in Output Stage (POUT)
For AC Sinusoidal Signals
+Vs
IQ
Vout peak =
POUT_AC =
2 Vs
2
+
+
2 Vs
2
Real Op Amp
+
Iout_AC
Vout
Vin
RL
IQ
RL
-Vs
Pc(Push-Pull) vs Vload for an AC Sinusoidal Signal
RI
P(Push Pull Output Transistors)
0.3
0.25
0.2
0.15
POUT_AC =
0.1
Vout peak =
2 Vs
2 Vs
2
2
RL
0.05
0
0
1
2
3
V(load) peak AC Sinusoidal Voltage
4
5
RF
AC Normal Maximum Power Dissipation in Output Stage (POUT)
For AC Sinusoidal Signals
AC Maximum Power Dissipation Formula
based on symmetrical dual supplies
Vcc
Vcc 5
To use formula for single supply circuits
set +Vs = +(Vcc/2) and -Vs = -(Vcc/2) as
shown.
IQ
+
+
Real Op Amp
Iout_AC
+
Vout
Vin
IQ
RL
+Vs 2.5
+Vs = (Vcc/2)
IQ
+
RF
+
RI
Real Op Amp
+
Iout_AC
Vout
Vin
IQ
RL
POUT_AC =
2 Vs
2
2
RL
-Vs 2.5
RI
RF
-Vs = -(Vcc/2)
Absolute Maximum Rating
Absolute Maximum Rating
For Long-Term Reliable Operation use Op Amp below the Absolute Maximum Ratings
Heat is semiconductor’s worst enemy – Keep TJ at least 25C less than TJ Max
For this op amp be sure to limit current into the input terminals to 10mA during electrical
overstress conditions.
Op Amp Selection Tip
Choosing an Op Amp?
Focus on Key Concerns for Application to Narrow Search
Voltage? Current? Speed?
Cu
rre
SSBW @ G=?
Slew Rate?
SR(V/us)=2pifVOP1e-6
where: f=Hz
Speed?
-
nt?
Supply Current?
Output Current?
Input Bias Current?
+
?
e
g
a
t
l
o
V
Supply Voltage?
Input Offset Voltage?
Output Swing Voltage?
References
References
Jim Karki, Senior Applications Engineer, Texas Instruments
“Understanding Operational Amplifier Specifications” White Paper: SLOA011
John Brown, Strategic Marketing Engineer (Retired), Texas Instruments
“How to Use TI/BB Data Sheet Specs for Op Amps and IAs” Internal White Paper
Art Kay, Senior Applications Engineer, Texas Instruments
“Analysis and Measurement of Intrinsic Noise in Op Amp Circuits: Parts 1-7”
http://www.en-genius.net/site/zones/audiovideoZONE/technical_notes/avt_022508
Tim Green, Senior Applications Engineer, Texas Instruments
“Operational Amplifier Stability: Parts 1-9 of 15”
http://www.en-genius.net/site/zones/acquisitionZONE/technical_notes/acqt_121106