Deciphering Electrical Characteristics in an

Op Amp Datasheet

Tim GreenLinear Applications ManagerTucson Divisiongreen_tim@ti.com

Op Amp Basics

-

+

-

+

Open Loop Gain

Rout

Rin

OUT+IN

-IN

-

+

Ideal Op Amp

OUT+IN

-IN

Infinite0 ohms

Infinite

Input Current = 0A

Input Current = 0A Ideal Op Amp

Ideal Operational Amplifier

• Zero input current• Infinite input resistance• Infinite open loop gain• Zero output resistance• Infinite Slew Rate

Op Amp Loop Gain Model

+

-

RF

RI

VIN

+

-

network

Aol+

-

VOUTVIN

VFBVOUT

VFB

RF

RI

=VFB/VOUT

VOUT

network

VOUT/VIN = Acl = Aol/(1+Aolβ)

If Aol >> 1 then Acl ≈ 1/β

Aol: Open Loop Gain

β: Feedback Factor

Acl: Closed Loop Gain

Ideal Operational Amplifier

Aol+

-

VOUTVINP

VINM

VOUT = (VINP – VINM) * AolVOUT / Aol – VINP = -VINM

If Aol = ∞ (for an Ideal Op Amp) then:-VINP = -VINM

orVINP = VINM

Ideal Operational Amplifier

For Ideal Op Amp

With Feedback and High Open Loop Gain:

+IN is forced to equal -IN

Non-Inverting Configuration

Irf = (Vout - Vin) / RF

Iri = Vin / RI

Iin- = 0A

Irf = Iri

(Vout - Vin) / RF = Vin / RI

Vout / Vin = 1 + RF/RI

-

+

Ideal Op Amp

Vout

RF 90kRI 10k

Vin 1 Vin

IrfIri

Iin- = 0A

1V 10V

Ideal Operational Amplifier

-

+

Ideal Op Amp

Vout

RF 90kRI 10k

Vin 1

Gnd

IrfIri

Iin- = 0A

0V -9V

Irf = (Vout - 0V) / RF

Iri = (0V-Vin) / RI

Iin- = 0A

Irf = Iri

(Vout - 0V) / RF = (0V-Vin) / RI

Vout / Vin = -RF/RI

For Ideal Op Amp

With Feedback and High Open Loop Gain:

+IN is forced to equal -IN

Inverting Configuration

Intuitive AC Op Amp Model

+

-

K(f)

VDIFF

IN+

IN-

RIN

RO

VO

VOUTx1

Input SpecificationsInput Bias Current (Ib) & Input Offset Current (Ios)Input Offset Voltage (Vos)Power Supply Rejection Ratio (PSRR): Referred-To-Input VosCommon 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 = 5pAIos = 4pA

Polarity is + or –Current into or out of inputs

-

+

Ideal Op Amp

Ib- 3p

Ib+ 7p

Vout

Ib = Ib+ + Ib-

2

Ib = 7pA + 3pA

2 = 5pA

Ios = Ib+ - Ib-

Ios = 7pA - 3pA = 4pA

Input Bias Current (Ib), Input Offset Current (Ios)

25C Specs in TableOften Curves for Temperature Specs Polarity is + or –

-

+

Ideal Op Amp

VoutR1 1M

+Vin

R2 1M

R3 1M

VIb 5.5u

Vout error = 11uV

Simplif ied VIb Model

VIb = VIb+ - VIb-

Non-Invverting Gain Creates Vout error

-

+

Ideal Op Amp

VoutRs 1M

+

Vin

RF 1M

RI 1M VIb- 1.5u

VIb+ 7u

Vout error = 11uV

Ib flow s through feedback and input resistors

Model as VIb+ and VIb-

Inverting and Non-Inverting Gains create Vout error

-

+

Ideal Op Amp

Ib- 3p

Ib+ 7p

VoutRs 1M

RF 1M

RI 1M

Vinm

Vinp

Vinm = 1.5uV

Vinp =7uV

Ib f low s through feedback and input resistors

View Vout and Vin as low impedance

Vinm = Ib- (RF // RI)

Vinp = Ib+ (Rs)

Vin

Vout

Input Bias Current (Ib) Vout Error

-

+

Idelal Op AmpIb- 3p

Ib+ 7p

VoutRs 1M

+

Vin

RF 1M

RI 1M

Ib causes errors at Vout

1

2

3 4

Input Offset Voltage (Vos) Vout Error

25C Specs in TableOften Histograms show distribution of VosPolarity is + or –

-

+

Ideal Op Amp

Vout

RF 1M

RI 1M

Vos 25u

Vout error = 50uV

Input Offset Voltage

Creates Vout error

Input Offset Voltage (Vos) Drift Vout Error

Vos Drift Specs in TableOften Histograms show

distribution of Vos DriftPolarity is + or -

-

+

Ideal Op Amp

Vout

RF 1M

RI 1M

Vos 25uVos_drift 60u

Vout error = 170uV

Initial Vos + Vos Drift creates Vout error

Operating Temperatue = 25C to 85CT = 85C - 25C = 60C

Vos_drift = T dVos

dT

Vos_drift = 60C 1uV/C = 60uV

Power Supply Rejection Ratio (PSRR) Vout Error

DC PSRR in TableDC PSRR Drift in TablePolarity is + or -

PSRR is an RTI (Referred-To-Input) specification Appears as Input Offset Voltage

-

+ +

Ideal Op Amp

Vcc 5

delta_Vcc 500m

RF 1M

RI 1M

Vos_PSRR 10u

Vout

Vout error = 20uV

PSSR DC = 20uV/V

delta_Vcc = 500mV (DC change in Vcc)

Vos_PSRR = PSSR DC delta_Vcc

Vos_PSRR = 20uV/V 500mV = 10uV

PSSR reflects as Vos_PSRR & creates Vout error

20kHz

Power Supply Rejection Ratio (PSRR) Vout Error AC PSRR in Curve

PSRR is an RTI (Referred-To-Input) specification Appears as Input Offset Voltage

-

+ +

Ideal Op Amp

Vcc 5

R4 1M

R5 1M

Vout

+ delta_Vcc_ac+

Vos_PSRR_ac

Vout error = 20uVpp @ 20kHz

100mVpp @ 20kHz10uVpp @ 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

Frequency of analysis = 20kHz

PSRR AC @ 20kHz = 80dB

Convert PSRR (dB) to PSRR (Linear Gain):

10(80dB/20) = 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

PSRR AC reflects as Vos_PSRR_ac & creates Vout error

Common Mode Voltage Range (Vcm)

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

Vin_CM = Voltage Common to Vinp & Vinm

VcmSame for DC & ACAC peak voltage < Vcm

-

+ +

Ideal Op Amp

Vcc 15

Vee 15

+

Vin

RF 1M

Vout

Vinm

Vinp

V = 2V max

V = 2V max-13V < Vin < +13V

Common Mode Rejection Ratio (CMRR) Vout Error

CMRR is an RTI (Referred-To-Input) specification Appears as Input Offset Voltage

CMRR DC in TablePolarity is + or -

CMRR DC reflects as Vos_CMRR & creates Vout error

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

-

+ +

Ideal Op Amp

V1 15

V2 15

RF 1M

RI 1M

Vout

Vin 5 Vos_CMRR 1.58u

Vout error = 3.16uV

CMRR DC = 130dB

Convert CMRR (dB) to CMRR (Linear Gain):

10(130dB/20) = 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

Common Mode Rejection Ratio (CMRR) Vout Error

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

CMRR AC reflects as Vos_CMRR_ac & creates Vout error

CMRR is an RTI (Referred-To-Input) specification Appears as Input Offset Voltage

AC CMRR in Curve

-

+ +

Ideal Op Amp

Vcc 15

Vee 15

RF 1M

RI 1M

Vout

+

Vin

+

Vos_CMRR_ac

Vout error = 400uVpp @ 1kHz

20Vpp @ 1kHz

200uVpp @ 1kHz

Frequency of Analysis = 1kHz

CMRR AC = 100dB @ 1kHz

Convert CMRR (dB) to CMRR (Linear Gain):

10(100dB/20) = 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

Vee

Vcc

-

+ +

Ideal Op Amp

Rdiff

Rcm

Rcm

Ccm

Cdiff

Ccm

-In

+In

Vout

RF 1M

RI 1M

Cin

Small Signal

Input Parasitics

Small SignalInput Parasitics

Rdiff > 200G for Bipolar InputsRcm > 40M for Bipolar InputsEven greater for JFET or MOSFET inputs

Ccm and Cdiff can be a problem:Ccm and Cdiff form CinCin & RF form a Loop Gain pole unwanted oscillations depending upon UGBW and value of RF.

Ccm, Cdiff in TableRcm, Rdiff in Table if specified

Input Noise: Current, Voltage (in, en)

Op Amp Noise Model

OPA277 Data

VVNN

IINN--IINN

++

Noise Model

(IN+ and IN- are not correlated)

Tina Simplified Model

*n

VU

1

*fA

U2

-

+

IOP1

INVN

Understanding The Spectrum:Total Noise Equation (Current or Voltage)

0.1 1 10 100 1k 10k1

10

100

1k

10k

100k

)V

olt

age

No

ise

(nV

/H

z

1/f Noise Region(Pink Noise Region)

White Noise Region(Broadband Noise Region)

en1/f calculation

fHfL

Frequency (Hz)

enBB calculation

enT = √[(en1/f)2 + (enBB)2]

where:enT = Total rms Voltage Noise in volts rms en1/f = 1/f voltage noise in volts rmsenBB = Broadband voltage noise in volts rms

fP fBF

Small Signal BW

Noise BW

Skirt of1-Pole FilterResponse

Brickwall

Frequency (f)

0

0.1fP 10fP

-20

-40

-80

Fil

ter

Att

en

ua

tio

n (

dB

)

Skirt of2-Pole FilterResponse

Skirt of3-Pole FilterResponse

Real Filter Correction vs Brickwall Filter

where: fP = roll-off frequency of pole or polesfBF = equivalent brickwall filter frequency

Number of Poles in Filter

KnAC Noise Bandwidth Ratio

1 1.57

2 1.22

3 1.16

4 1.13

5 1.12

AC Noise Bandwidth Ratios for nth Order Low-Pass Filters

Real Filter Correction vs Brickwall Filter

BWn = (fH)(Kn) Effective Noise Bandwidth

Broadband Noise Equation

enBB = (eBB)(√[BWn])

where:enBB = Broadband voltage noise in volts rmseBB = Broadband voltage noise density ; usually in nV/√HzBWn = Noise bandwidth for a given system

BWn = (fH)(Kn)

where:BWn = noise bandwidth for a given systemfH = upper frequency of frequency range of operationKn = “Brickwall” filter multiplier to include the “skirt” effects of a low pass filter

eBB

1/f Noise Equation

en1/f = (e1/f@1Hz)(√[ln(fH/fL)])

where:en1/f = 1/f voltage noise in volts rms over frequency range of operatione1/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

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

e1/f@1Hz

Example Noise Calculation

Given:OPA627 Noise Gain of 101

Find (RTI, RTO): Voltage NoiseCurrent NoiseResistor Noise

V1 15

V2 15

-

+ +U1 OPA627/BB

R1 100kR2 1k+

VG1

VF1

Unity Gain Bandwidth = 16MHz

Closed Loop Bandwidth = 16MHz / 101 = 158kHz

Voltage Noise Spectrum and Noise Bandwidth

50nV/rt-Hz

5nV/rt-Hz

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.

Gain

Req = R1 || Rf

*

Rf 3k

-

+

IOP1

VF1

*fA

U2

R1 1k Rf 3k

-

+

IOP1

VF1

*fA

U2

R1 1k

en-out= Gain x (in)x(Req)en-in= (in)x(Req)

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

Noise Spectral Density vs. Resistance

Resistance (Ohms)

Noi

se S

pect

ral D

ensi

ty v

s. R

esis

tanc

e

nV/r

t-H

z

10 100 1 103

1 104

1 105

1 106

1 107

0.1

1

10

100

1 103

468.916

0.347

4 1.38065 1023 25 273.15( ) X 10

9

4 1.38065 1023 125 273.15( ) X 10

9

4 1.38065 1023 55 273.15( ) X 10

9

10710 X

1000

10 100 1 103

1 104

1 105

1 106

1 107

0.1

1

10

100

1 103

468.916

0.347

4 1.380651023 25 273.15( ) X 10

9

4 1.380651023 125 273.15( ) X 10

9

4 1.380651023 55 273.15( ) X 10

9

10710 X

25C

125C

-55C

en density = √√ (4kTKR)

Resistor Noise – Thermal Noise

eenr = √(4kT = √(4kTKKRRΔΔf) f)

where:where:

R = Req = R1||RfR = Req = R1||Rf

ΔΔf = BWf = BWnn

eenr = √(4 ( = √(4 (1.38E-23) (273 + 25) (0.99k)((273 + 25) (0.99k)(248kHz)) = 2010nV rms

Example Resistor Noise Calculation

Gain

Req = R1 || Rf

*

R1 2kR2 1k

-

+

IOP1

VF1

*nV

U1

*nV

U1

RfR1

en-out= Gain x (√(4kTR√(4kTRΔΔf)f))en-in= √(4kTR√(4kTRΔΔf)f)

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

Peak-to-PeakAmplitude

Probability of Havinga 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%

Relation of Peak-to-Peak Value of AC Noise Voltage to rms Value

*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 < 10HzGiven 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) & PhaseSlew Rate (SR)Total Harmonic Distortion + Noise (THD+N)Settling Time (ts)

Open Loop Gain & Phase

Gain-Bandwidth Product = UGBW (Unity Gain Bandwidth)

G=1 Stable Op Amps

5.5MHz

Open-Loop Voltage Gain at DCLinear operation conditions NOT the same as Voltage Output Swing to Rail

Vout/Vin:Gain Accuracy & Frequency Response

fcl

1/Beta

Vout/Vin

-

+

Real Op Amp

Vout

+

Vin

R2 9k

R3 1k

Aol at any Frequency:

Aol_f = UGBW / f

Aol @ 1kHz = 5.5MHz / 1kHz = 5500

Aol @ 1kHz = 20LOG10(5500) = 74.8dB

Gain Accuracy at any frequency:

Frequency of analysis for Gain Accuracy = 1kHz

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%

Vout/ Vin Frequency Response

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

Slew Rate Slew Rate Measurement:10% to 90% of Vout

Slew Rate &Full Power Bandwidth orMaximum 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) = 2fVop(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) = 2fVop(1e-6)

2 = 2f(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 FrequencyFundamental f = 99% Vout AmplitudeHarmonics due to Op Amp non-linearitiesNoise due to Op Amp Input Noise (en, in)

Harmonics + Noise < 1% of Vout

Settling Time

Note: Settling Time includes Slew Rate time

SlewRate

Settling Time

Settling TimeLarge Signal effects:Slew Rate

Small Signal effectsLarge Gain = Less closed loop BandwidthLarge Gain = Less Loop Gain (AolB) to correct for errorsLarge Gain = Longer Settling Time

Output Specifications

Voltage Output Swing from RailShort 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 RailHigher Current Load Farther from RailHigher Current Load Larger VsatVsat = Vs - Vout

+25C Curve:Op Amp Aol is degraded if on curveOp Amp Aol is okay if left of curve

12

1

2

Short Circuit Current (Isc)

Output shorted Current Limit engagedFor Graph shown TJ max is okayIf 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

+

-

RDIFF

xAol

RO-IN

+IN

-

+

VE

Op Amp Model

1A

VOUT

VO

RF

RI

IOUTVFB

ROUT = VOUT/IOUTFrom: Frederiksen, Thomas M. Intuitive Operational Amplifiers. McGraw-Hill Book Company. New York. Revised Edition. 1988.

Definition of Terms:

RO = Op Amp Open Loop Output Resistance

ROUT = Op Amp Closed Loop Output Resistance

ROUT = RO / (1+Aolβ)

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

+

-

+

- RO

Data Sheet Aol CL

+

-

RFRI

100k 100k

1F

OPA452

VIN

VOUT

28.7

Extra Pole in Aol Plot due to RO & CL:

fpo1 = 1/(2∙П∙RO∙CL)

fpo1 = 1/(2∙П∙28.7Ω∙1μF)

fpo1 = 5.545kHz

Create a new “Modified Aol” Plot

RO & CL: OPA542 Modified Aol First Order

1 10 100 1K 10K 100k 1M 10M

Frequency (Hz)

Ga

in (

dB

)

-60

-40

-20

0

20

40

60

80

100

120OPA452

Aol

Modified Aoldue to CL

fpo1

1/ fcl

40dB/DecadeRate-Of-Closure

STABLE

Zo (Open Loop Output Impedance)Cap Load Drive

OPA376 and many other Single Supply Op Amps Open Loop Output Impedance is not Purely Resistive

As Cap Load increases Loop Gain Phase Margin decreases and we see the transient response for Cap Load increase in overshoot for OPA376

For about 500pF Load Capacitance Small-Signal Overshoot is 50%

2nd Order Transient Curves

Fro

m:

Do

rf,

Ric

ha

rd C

. M

od

ern

Co

ntr

ol

Sy

ste

ms

. A

dd

iso

n-W

es

ley

P

ub

lis

hin

g C

om

pa

ny

. R

ea

din

g,

Ma

ss

ac

hu

se

tts

. T

hir

d E

dit

ion

, 1

98

1.

Signal overshoot of 50% or normalized signal output of 1.5 yields a Damping ratio ( ) of 0.2

2nd Order Damping Ratio vs Phase MarginF

rom

: D

orf

, R

ich

ard

C.

Mo

de

rn C

on

tro

l S

ys

tem

s.

Ad

dis

on

-We

sle

y

Pu

bli

sh

ing

Co

mp

an

y.

Re

ad

ing

, M

as

sa

ch

us

ett

s.

Th

ird

Ed

itio

n,

19

81

.

Damping ratio ( ) of 0.2 yields 23.5 degrees of phase margin for AC Loop Stability

23.5o

Closed Loop Output ImpedanceFor 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

Closed Loop Output impedance gives an indication of what source impedance the closed loop op amp will have to drive loads over frequency

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)

Quiescent Current:Supply Current to operate the op ampDoes NOT include load current

-

+ +Real Op Amp

IQ

IQ

-Vs

+Vs

Vout

Temperature Range Specifications

Specified Range

Operating Range

Thermal Resistance (JA)

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 (JA)

Thermal Resistance (JA)

JA will be used with ambient temperature TA and internal

total power dissipation PD to compute maximum op amp junction temperature TJ

Thermal Model

PD

RθJA

TA

TJ

TA

Thermal model with no heat sink

Analogous to an electrical circuit

TJ= PD( RθJA) + TA

T – is analogous to voltage

R – is analogous to resistance

P – is analogous to current

PD = PIQ + POUT

PD = Total Power Dissipated

PIQ = Power Dissipated due to IQ

POUT = Power Dissipated in Output Stages

IQ Power Dissipation (PIQ)

Vout

+Vs

-Vs

IQ

IQ

-

+ +Real Op Amp

PIQ = [+Vs - (-Vs) ] IQ

DC Normal Maximum Power Dissipation in Output Stage (POUT)

-

+ +Real Op Amp

IQ

IQ

-Vs

+Vs

VoutVin

RFRI

RL

Iout_DC

POUT_DC = Vs2

4 RL

Vout = 1

2 Vs

DC Short Circuit Maximum Power Dissipation in Output Stage (POUT)

-

+ +Real Op Amp

IQ

IQ

-Vs

+Vs

VF1

RFRI

+

VG1

Isc

POUT_SHORT = Vs Isc

-

+ +Real Op Amp

IQ

IQ

-Vs

+Vs

Vout

RFRI

RL

+

Vin

Iout_AC

Pc(Push-Pull) vs Vload for an AC Sinusoidal Signal

0

0.05

0.1

0.15

0.2

0.25

0.3

0 1 2 3 4 5

V(load) peak AC Sinusoidal Voltage

P(P

us

h P

ull

Ou

tput

Tra

ns

isto

rs)

AC Normal Maximum Power Dissipation in Output Stage (POUT)

For AC Sinusoidal Signals

POUT_AC = 2 Vs2

2 RL

Vout peak = 2 Vs

POUT_AC = 2 Vs2

2 RL

Vout peak = 2 Vs

-

+ +Real Op Amp

IQ

IQ

Vcc 5

Vout

RFRI

RL

+

Vin

Iout_AC

AC Normal Maximum Power Dissipation in Output Stage (POUT)

For AC Sinusoidal Signals

-

+ +Real Op Amp

IQ

IQ

-Vs 2.5

+Vs 2.5

Vout

RFRI

RL

+

Vin

Iout_AC

AC Maximum Power Dissipation Formula based on symmetrical dual supplies

To use formula for single supply circuits set +Vs = +(Vcc/2) and -Vs = -(Vcc/2)

as shown.

Vcc

-Vs = -(Vcc/2)

+Vs = (Vcc/2)

POUT_AC = 2 Vs2

2 RL

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 MaxFor 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 SearchVoltage? Current? Speed?

+

-

Current?

Voltage?

Sp

eed

?

Supply Voltage?Input Offset Voltage?Output Swing Voltage?

Supply Current?Output Current?Input Bias Current?

SSBW @ G=?Slew Rate? SR(V/us)=2pifVOP1e-6

where: f=Hz

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