1. Deciphering Electrical Characteristics in an Op Amp Datasheet
The Operational Amplifier (Op Amp) is often the key analog gain block in acquiring and scaling real world signals in any data acquisition system. To predict system accuracy when using op amps it is important to understand the op amp data sheet and how individual specifications affect both the DC and AC transfer accuracy through the op amp.
Tim Green
Linear Applications Manager
Tucson Division

2. Op Amp Basics
Before we can decipher op amp specifications and how they affect accuracy when using op amps it is essential that we understand what an op amp is and how it works.

3. Ideal Operational Amplifier
Zero input current
Infinite input resistance
Infinite open loop gain
Zero output resistance
Infinite Slew Rate
An Ideal Operational Amplifier introduces no errors in a system. There is no input signal loading since it has infinite input impedance resulting in zero input bias current. There will be no closed loop gain error due to infinite open loop gain. There is no input to output delay due to infinite slew rate. Because of zero output resistance there is no output loading effects due to output current or swing to the supply limitations.

4. Op Amp Loop Gain Model
The Op Amp Loop Gain Model allows us to analyze how an op amp functions with Open Loop Gain (Aol) and Feedback (b). Classical control theory allows us to derive the formula for Closed Loop Gain (Acl) in terms of the op amp parameter Aol and the external feedback network. (b). If Aol is very large the external feedback network (b) accurately determines closed loop gain.

5. Ideal Operational Amplifier
VOUT = (VINP – VINM) * Aol
VOUT / Aol – VINP = -VINM
An important concept for op amps is that, when operating in the linear region, the +input and –input are forced to be equal to each other due to feedback (b) and Open Loop Gain (Aol). This effect is sometimes called a “virtual ground” from the inverting op amp gain configuration where the +input is tied to ground and therefore the –input is forced to zero volts or “virtual ground”.
If Aol = ∞ (for an Ideal Op Amp) then:
-VINP = -VINM or
VINP = VINM

6. Ideal Operational Amplifier
Using our derived concepts of how an op amp operates and assuming an ideal op amp we can derive the theoretical gain equation for Vout/Vin for a non-inverting op amp configuration. With infinite Aol and an external feedback network the op amp +input and –input are forced to equal each other. From nodal analysis we easily derive the standard non-inverting gain equation for an op amp of Vout/Vin = 1 + RF/RI.

7. Ideal Operational Amplifier
Using our derived concepts of how an op amp operates and assuming an ideal op amp we can derive the theoretical gain equation for Vout/Vin for an inverting op amp configuration. With infinite Aol and an external feedback network the op amp +input and –input are forced to equal each other. In the inverting gain configuration the +input is ground and therefore the +input is forced to zero volts or to “virtual ground”. From nodal analysis we easily derive the standard inverting gain equation for an op amp of Vout/Vin = - RF/RI.

8. Intuitive AC Op Amp Model
As we begin to analyze op amp specifications our ideal op amp will be transformed into a real world op amp. Effective real input resistance will cause currents to flow into or out of the +input an –input. The open loop gain will not be infinite and will in fact decrease markedly over frequency. There will be an effective output resistance, which is not zero ohms, that will cause reduction in Vout with output current. In addition the real op amp will not instantaneously respond to large voltage changes on the input due to lack of infinite slew rate.

9. 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)
There are many op amp specifications for a real op amp which will create errors at the output of the op amp. Some of these error sources are related directly to the input characteristics of the op amp. Some others are specified as Referred-To-Input (RTI) errors. All input errors will be gained up to the output of the op amp by the closed loop gain of the op amp.

10. Input Bias Current (Ib), Input Offset Current (Ios)
Input bias current is the input current into or out of the +input and –input of the op amp required for the input stages of the op amp to function properly. Unless specified the current could be either into or out of the op amp inputs. Industry standard definition of input bias current is the average of current into the +input and –input. Input offset current is defined as the difference between the input bias current of the +input and the input bias current of the –input.
Ib = 5pA
Ios = 4pA
Polarity is + or –
Current into or out of inputs

11. Input Bias Current (Ib), Input Offset Current (Ios)
25C Specs in Table
Often Curves for Temperature Specs
Polarity is + or –
Input Bias Current and Input Offset Current are usually specified in the Electrical Characteristics Table for 25C operation. Often the change in input bias current over temperature is shown as a curve in the Typical Characteristics

12. Input Bias Current (Ib)  Vout Error2 1 3 4
Input bias current flows through any resistance on the +input or –input of the op amp. This current flow creates an offset voltage on the input to the op amp and will be multiplied by the op amp closed loop gain as an error voltage at the output. To analyze this additional offset voltage set all voltage sources in the circuit to zero volts. Set the op amp output to zero volts since it is viewed as low impedance at DC. For the non-inverting op amp configuration this results in the Ib- flowing through the parallel combination of RF and RI. Ib+ flows through the input source resistance, Rs. Two offset voltages, Vb+ and Vb-, on the op amp inputs can be created. The equivalent offset voltage error due to Ib can be lumped into Vb = Vb+ - Vb- and this lumped offset voltage is gained up as an error on Vout by the closed loop gain of the op amp.

13. Input Offset Voltage (Vos)  Vout Error
25C Specs in Table
Often Histograms show distribution of Vos
Polarity is + or –
Input Offset Voltage is the inherent offset voltage due to non-ideal devices and mis-matches inside of the real op amp. The effect of this can be see with the op amp in inverting configuration and the +input grounded. Ideally Vout would be zero volts. For the real op amp Vout becomes Vos times closed loop gain. The input offset voltage can be either positive or negative. Often the data sheet will include an Offset Voltage Distribution histogram to indicate how the Offset Voltage typically varies over a wide number of units.

14. Input Offset Voltage (Vos) Drift  Vout Error
Vos Drift Specs in Table
Often Histograms show distribution of Vos Drift
Polarity is + or -
Offset Voltage Drift is an additional input offset voltage which is added to Vos depending upon the operating temperature of the op amp relative to 25C. A distribution of the Vos Drift may be shown in histogram form to indicate how Vos Drift will typically be different over a wide number of parts.

15. Power Supply Rejection Ratio (PSRR)  Vout Error
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
Power Supply Rejection Ratio is the error induced at the output of the op amp as the op amp power supply varies. PSRR is an RTI (Referred-To-Input) specification. Changes in the power supply voltage will appear as a input offset voltage. This additional input offset voltage will be gained up by the closed loop gain of the op amp and appear as an error in Vout.

16. Power Supply Rejection Ratio (PSRR)  Vout Error
AC PSRR in Curve
20kHz
PSRR also has a frequency component to it as well as the DC effect. To analyze the error at Vout for a given power supply ripple frequency and amplitude we need to use the PSRR vs Frequency plot. At the given frequency of analysis PSRR will be given in dB. This dB unit is converted to a voltage “gain” from the power supply to the input of the op amp as PSSR is an RTI (Referred-To-Input) specification. This voltage “gain” is actually an attenuation and so the reciprocal of this gain becomes the attenuation factor. Once the attenuation factor is converted to a convenient uV/V number it is easy to reflect the PSRR AC to the input as an offset voltage which will be gained up by the closed loop gain of the op amp and appear as an error at Vout.
PSRR is an RTI (Referred-To-Input) specification
Appears as Input Offset Voltage

17. Common Mode Voltage Range (Vcm)
Same for DC & AC
AC peak voltage < Vcm
Common Mode Voltage Range is how close we may push both inputs of the op amp towards either supply rail and still expect linear behavior out of the op amp. This is easiest seen by putting the op amp in a non-inverting gain where as +input varies towards either supply so does the –input.

18. Common Mode Rejection Ratio (CMRR)  Vout Error
CMRR DC in Table
Polarity is + or -
Common Mode Rejection Ratio is the error induced at the output of the op amp as both of the op amp inputs vary with the same voltage on them. This is easily seen by configuring the op amp in non-inverting gain. CMRR is an RTI (Referred-To-Input) specification. Changes in the Common Mode input voltage of the op amp will appear as a input offset voltage. This additional input offset voltage will be gained up by the closed loop gain of the op amp and appear as an error in Vout.
CMRR is an RTI (Referred-To-Input) specification
Appears as Input Offset Voltage

19. Common Mode Rejection Ratio (CMRR)  Vout Error
AC CMRR in Curve
CMRR also has a frequency component to it as well as the DC effect. To analyze the error at Vout for a given Common Mode input frequency and amplitude we need to use the CMRR vs Frequency plot. At the given frequency of analysis CMRR will be given in dB. This dB unit is converted to a voltage “gain” from the common mode input of the op amp to the non-inverting input of the op amp as CMRR as an RTI (Referred-To-Input) specification. This voltage “gain” is actually an attenuation and so the reciprocal of this gain becomes the attenuation factor. Once the attenuation factor is converted to a convenient uV/V number it is easy to reflect the CMRR AC to the input as an offset voltage which will be gained up by the closed loop gain of the op amp and appear as an error at Vout.
CMRR is an RTI (Referred-To-Input) specification
Appears as Input Offset Voltage

20. Small Signal Input Parasitics
Ccm, Cdiff in Table
Rcm, Rdiff in Table if specified
Rdiff > 200GW for Bipolar Inputs
Rcm > 40MW for Bipolar Inputs
Even greater for JFET or MOSFET inputs
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.
Real op amps have Small Signal Input Parasitics in the form of common mode and differential input resistances and capacitances. Usually, the resistances are so large they are not a source of problems. However, the input capacitances can interact with large values of the feedback resistor, RF, and form an unwanted loop gain pole which will result in excessive ringing, long settling times, or sustained oscillations.

21. Input Noise: Current, Voltage (in, en)
Since real op amps use real transistors (Bipolar, JFET, or MOSFET) the inputs can become a dominant source of noise. The magnitude of this noise which will be reflected to the output of the op amp is directly dependent upon both the closed loop gain and the closed loop bandwidth of the op amp.

22. Op Amp Noise Model Noise Model (IN+ and IN- are not correlated)
OPA277 Data VN
IN-
IN+
Tina Simplified Model
This slide show the typical op-amp noise model. In some cases it is important to have two separate current noise sources as shown in the upper left. In other cases a single noise source between the inputs is adequate. The noise sources represent the spectral density curves. VN IN

23. Understanding The Spectrum: Total Noise Equation (Current or Voltage)
enT = √[(en1/f)2 + (enBB)2]
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
The noise analysis technique we use will compute the effect of the 1/f region and the broadband region separately. These two results will be added together with the root sum of squares. An important concept in noise analysis is adding noise values. Noise cannot be added algebraically (e.g. 3+5=8). Noise must be added as a vector (e.g. sqrt(3^2 + 5^2) = 5.83). It is important to note that this relationship applies to uncorrelated random noise. If the noise source is correlated a different formula applies.

24. Real Filter Correction vs Brickwall Filter
where:
fP = roll-off frequency of pole or poles
fBF = equivalent brickwall filter frequency
A low pass filter can be converted to a brickwall filter. Note that the brick wall is a rectangle. Also note that as the order of a filter increases it approaches the brickwall shape (e.g. 3 order or 3-pole filter is closer to the brick wall then first order or 1-pole filter). The brickwall filter bandwidth is computed by taking the 3db bandwidth and multiplying by a factor. As the order of the filter increases the number approaches 1.

25. 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
Some brickwall conversion factors are shown in the table. To convert a first order low pass filter to a brickwall filter you multiply the 3db cutoff frequency by Note that the 5th order filter is practically a brickwall (i.e. the conversion factor is close to 1).

26. 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
The BWn formula converts the 3 dB point to the brick wall filter (i.e. noise bandwidth ). The enBB formula allows you to compute the total broad band noise over the bandwidth bounded by fH.

27. 1/f Noise Equation e1/f@1Hz e1/f@1Hz = (e1/f@f)(√[f]) where:
= normalized noise at 1Hz (usually in nV)
= 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 =
where:
en1/f = 1/f voltage noise in volts rms over frequency range of operation
= 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
The equation is used to normalize the reading on the 1/f curve to 1Hz. In this example this procedure is not required; however, some curves to not show a 1Hz point. The en1/f equation uses the result from the previous equation and the bandwidth to compute the total 1/f noise.

28. Example Noise Calculation
Given:
OPA627
Noise Gain of 101
Find (RTI, RTO):
Voltage Noise
Current Noise
Resistor Noise
We will examine an OPA627 in a non-inverting configuration as a definition-by-example on computing op amp noise. The total noise at the output will be the sum of op-amp voltage noise, op-amp current noise, and resistor noise.

29. Voltage Noise Spectrum and Noise Bandwidth
50nV/rt-Hz
5nV/rt-Hz
The left hand curve is the voltage spectral density curve. It has a 1/f and broadband region. The right hand curve is the open loop gain (Aol) curve. The bandwidth of the circuit is determined by the Aol curve because there is no other filter. The calculation shows that the bandwidth is 158kHz; this can also be seen graphically.
Unity Gain Bandwidth = 16MHz
Closed Loop Bandwidth = 16MHz / 101 = 158kHz

30. Example 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: =
= (50nV/√Hz)(√1Hz) = 50nV
en1/f = 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
Now that we have all the equations for the op-amp voltage noise let’s compute it for this example. Inspection of the results shows that the 1/f noise component is not significant in this example. This is fairly typical of wide bandwidth examples. Also note that the results are added using root sum of squares.

31. Example Current Noise Calculation
Note: This example amp doesn’t have 1/f component for current noise.
en-in= (in)x(Req)
en-out= Gain x (in)x(Req)
Now that we have the op-amp voltage noise component, let’s compute the effect of current noise. For this example the current noise flows through the parallel combination of R1 || Rf. So the current noise is multiplied by the equivalent noise resistor to generate an input noise source.

32. 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
Here are the numbers. For this example the noise current is very small (fA/rt-Hz). The equivalent input resistance is also small (approximately = 1k). The result is an extremely small noise voltage is developed. For all practical purposes we could neglect this number, but we will included it for completeness.

33. 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 = oC + TC
Random motion of charges within a resistor generate noise. The equation shown above gives the total rms noise generated by a resistor.

34. Resistor Noise – Thermal Noise
Noise Spectral Density vs. Resistance
en density = √ (4kTKR)
Noise Spectral Density vs. Resistance
nV/rt-Hz
Peak to Peak noise, such as that as seen on an oscilloscope can be estimated by applying a scale factor to RMS noise calculations. This chart was generated using the equation given in the last slide. Note that the equation was divided by the square root of bandwidth to give a spectral density. This chart is useful because it gives you a quick way of comparing resistor noise to op-amp noise. Most op-amps specify noise in nV/rtHz. So, for example a very low noise amplifier may have a 1nV/rtHz noise. This corresponds to approximately 70ohms on the curve above. Thus, for this example, op-amp you should try to keep resistance below 70ohms.
Resistance (Ohms)

35. Example Resistor Noise Calculation
enr = √(4kTKRΔf)
where:
R = Req = R1||Rf
Δf = BWn
enr = √(4 (1.38E-23) ( ) (0.99k)(248kHz)) = 2010nV rms
en-in= √(4kTRΔf)
en-out= Gain x (√(4kTRΔf))
The equivalent resistance is also used to compute the total thermal nose for a resistor. In this example the thermal noise is significant (2010nV rms).

36. 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
Peak to Peak noise, such as that as seen on an oscilloscope can be estimated by applying a scale factor to RMS noise calculations. Now we have all three components. We can add them together using the root sum of squares. This gives us the total output rms noise. What is the peak to peak? See the next slide.

37. Calculating Noise Vpp from Noise Vrms *Common Practice is to use:
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%
Peak to Peak noise, such as that as seen on an oscilloscope can be estimated by applying a scale factor to RMS noise calculations. Common practice is to use x6 or x6.6 with a very small probability that that noise of a larger amplitude than that computed will be seen.
*Common Practice is to use:
Peak-to-Peak Amplitude = 6 X rms

38. 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
A figure of merit with regards to noise performance of an op amp is presented in most data sheets as a curve and table specification of peak-to-peak noise. This is a measured noise number over a low frequency, narrow bandwidth (0.1Hz to 10Hz). The test uses a 0.1Hz Second-Order High-Pass filter and a 10Hz Fourth-Order Low Pass filter at the output of the op amp.

39. Frequency Response Specifications
Open Loop Gain (Aol) & Phase
Slew Rate (SR)
Total Harmonic Distortion + Noise (THD+N)
Settling Time (ts)
Frequency Response Specifications will allow us to predict gain accuracy of the op amp at any frequency of interest, Large signal AC performance, step response through the op amp, sinewave distortion on the output of the op amp, and settling time for a large step change on the input.

40. Gain-Bandwidth Product = UGBW (Unity Gain Bandwidth)
Open Loop Gain & Phase
Open-Loop Voltage Gain at DC
Linear operation conditions NOT the same as Voltage Output Swing to Rail
Open Loop Gain & Phase will be used to compute gain accuracy at any frequency of interest as well as how stable the op amp is when the loop is closed with feedback for a resistive load. Open Loop Gain is usually measured with Vout a specified drop away from the power supply rails. The op amp may be capable of swinging closer to the rails than where the Open Loop Gain is specified but the op amp will not have as high of open loop gain and other non-linearities may occur.
Gain-Bandwidth Product = UGBW (Unity Gain Bandwidth)
G=1 Stable Op Amps
5.5MHz

41. Vout/Vin: Gain Accuracy & Frequency Response
fcl
1/Beta
Vout/Vin
To compute the gain accuracy at any frequency for an op amp closed loop circuit requires that we have the Aol curve and know the closed loop gain of the op amp. From our loop gain op amp model we have the relationship between Vout/Vin = Aol / (1+Aol*b). If the Unity Gain Bandwidth (UGBW) is know it is easy to compute the magnitude of Aol at any frequency of interest. With this and the compute b from the closed loop gain components gain accuracy at any frequency is predicted.

42. Slew Rate Slew Rate Measurement: 10% to 90% of Vout
Slew Rate is a large signal transfer function of an op amp. It is a rate-of-change of the output for a large step voltage on the input. The accepted measurement points for delta Vout are 10% and 90%. The delta t (time) it takes to transition between these two voltage points is used to compute slew rate.

43. Slew Rate & Full Power Bandwidth or Maximum Output Voltage vs Frequency
Slew Rate is also used to determine the frequency and magnitude limitations of passing a large signal sinewave through an op amp. Maximum Output Voltage vs Frequency plot shows these frequency-amplitude limitations. This curve is also know as Power Bandwidth or Full Power Bandwidth curve.

44. THD + Noise
Larger Closed Loop Gain  Loop Gain to correct for Op Amp Non-Linearities and Noise
THD + Noise is a figure of merit describing how pure an output sinewave is for an input sinewave at a given frequency. As gain increase there is less loop gain available to correct for internal non-linearities and noise.

45. 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
A representative Spectrum Analyzer plot helps define THD + Noise. For a THD + Noise = 1% the output amplitude contains 99% of the input signal. Harmonics at various frequencies shown are due to internal non-linearities of the op amp. The noise level is lower than either the Harmonics or the Fundamental input frequency. The total corruption of the input sinewave on Vout is THD + Noise = 1%.

46. Note: Settling Time includes Slew Rate time
Settling time is a combination of both large signal (Slew Rate) and small signal (Closed Loop Bandwidth, Aol, Loop Gain) parameters. Settling time is important in data acquisition systems for the input to an A/D converter to be accurate and settled before a conversion takes place. A fast settling time is needed if there is a multiplexer in front of the op amp to read many different input signals into an A/D Converter.
Note: Settling Time includes Slew Rate time

47. 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
Settling Time vs Closed Loop Gain shows that as higher gains are used longer settling times can be expected since there is less and less loop gain to correct for errors the higher the closed loop gain used.

48. Output Specifications
Voltage Output Swing from Rail
Short Circuit Current (Isc)
Open Loop Output Impedance (Zo)
Closed Loop Output Impedance (Zout)
Capacitive Load Drive
Output Specifications are used to determine the op amp capability to drive large signals into loads. In addition the small signal open loop output impedance, along with Aol, directly affect the Capacitive Load Drive of the op amp.

49. 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
Op Amp Aol is okay if left of curve 2 1 1 2
Voltage Output Swing from Rail is an indication of output voltage swing capability of the op amp as it has to provide current into a load. The larger current required for the load the further away from the rails the op amp will swing. This curve is based on saturating the output transistors to get as close to the rails as possible. If one is trying to operate on a point directly on top of one of these curves then there is potential for higher gain errors as this is in anon-linear region of the output stage of the op and Aol is degraded.

50. 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
Short circuit current is the maximum current limit of what the op amp can drive through its output stage. These internally current-limited levels change with temperature. If this is a condition which can happen in a given application internal power dissipation and maximum junction temperature should be analyzed to ensure a reliable design.

51. Open Loop Output Impedance (Zo) Closed Loop Output Impedance (Zout)
Capacitive Load Drive
Open Loop Output Impedance, combined with Aol, directly determine the Capacitive Load Drive capability of an op amp. The Closed Loop Output Impedance can be used as a relative number for source impedance for driving loads over frequency.

52. 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)
The definition and relationship between ROUT and RO are detailed here. ROUT is RO reduced by loop gain. Here we define the op amp model used for the derivation of ROUT from RO. This simplified op amp model focuses solely on the basic DC characteristics of an op amp. A high input resistance (100MΩ to GΩ), RDIFF develops an error voltage across it, VE, due to the voltage differences between -IN and +IN. The error voltage , VE, is amplified by the open loop gain factor Aol and becomes VO. In series with VO to the output, VOUT, is RO, the open loop output resistance.
From: Frederiksen, Thomas M. Intuitive Operational Amplifiers.
McGraw-Hill Book Company. New York. Revised Edition

53. 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.
ROUT and RO differences are clearly described here.

54. RO & CL: Modified Aol Model
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
Modified Aol Model
Our stability analysis of the effects of capacitive loading on an op amp will be simplified by the introduction of the “Modified Aol Model”. As shown in this slide the data sheet Aol curve is followed by the op amp output resistance, RO. The capacitive load, CL, in conjunction with RO will form an additional pole in the Aol plot and may be represented by a new “Modified Aol” plot as shown in the next slide.

55. RO & CL: OPA542 Modified Aol First Order
In this slide we create the “Modified Aol” curve. We readily see that, with just resistive feedback and low gains, we have an UNSTABLE op amp circuit design since the 1/β curve intersects the “Modified Aol” curve at a rate-of-closure which is 40dB/decade.

56. 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
The larger RO is the less Capacitive load on the output can be driven without large overshoot and ringing in a transient response. Many low power op amps have small signal, AC open loop output Impedance (Zo) that is not resistive which makes driving capacitive loads more tricky. On the Small-Signal Overshoot vs Load Capacitance we see that 50% overshoot will occur for a Load Capacitance of about greater than 500pF.
For about 500pF Load Capacitance Small-Signal Overshoot is 50%

57. 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.
Transient response curves for second order systems are shown above for different damping factors. A signal overshoot of 50% can be viewed as normalized signal output of 1.5 which correlates to a 0.2 damping ratio.

58. 2nd Order Damping Ratio vs Phase Margin
From: Dorf, Richard C. Modern Control Systems. Addison-Wesley Publishing Company. Reading, Massachusetts. Third Edition, 1981.
Phase margin versus damping factor are shown above for second order systems. For a damping ratio of 0.2 there is only about 23.5 degrees of phase margin for AC Loop Stability.
Damping ratio ( z ) of 0.2 yields 23.5 degrees
of phase margin for AC Loop Stability
23.5o

59. Closed Loop Output Impedance
For Bipolar, Emitter-Follower Output Op amps like OPA177, open loop output impedance = RO (purely resistive inside UGBW)
Since ROUT = RO/(1+Aolb) 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
Closed Loop Output Impedance varies with closed loop gain since it is determined by loop gain (Aol*b). The higher the closed loop gain the less the loop gain and the higher ZO becomes. Closed Loop Output Impedance vs Frequency provides a good idea as to the op amp output’s source impedance to drive a load over frequency.

60. Power Supply Specifications
Specified Voltage Range (VS)
Operating Voltage Range (VS)
Quiescent Current (IQ)
Power Supply Specifications define the voltages that the op amp can operate at accurately. Quiescent current is the constant current draw from the supplies for the op amp to operate. Battery powered applications seek low IQ parts.

61. 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
Specified Voltage Range is the range over which the op amp can be powered with data sheet specifications being met. Operating Voltage Range is larger that than the Specified Voltage Range and although the op amp may still be functional there can be degraded performance such as lower Aol, reduced Output Swing to Rail, etc.

62. Quiescent Current (IQ)
Supply Current to operate the op amp
Does NOT include load current
Quiescent current is the current required from the power supplies to operate the op amp as linear gain block without any load current.

63. Temperature Range Specifications
Specified Range
Operating Range
Thermal Resistance (QJA)
Temperature Range Specifications define the temperature range over which the op amp can operate per the data sheet specifications. Thermal Resistance is an important parameter which allows direct computation of the junction temperature, TJ, of the op amp in a given application.

64. 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
Specified Temperature Range is the range over which the op amp can be powered with data sheet specifications being met. Operating Temperature Range is larger that than the Specified Temperature Range and although the op amp may still be functional there can be degraded performance such as lower Aol, reduced Output Swing to Rail, etc.

65. Thermal Resistance (QJA)
Thermal Resistance is an important parameter in determining the operating junction temperature, TJ, of an op amp in a specific application. The second computation need is internal power dissipation.

66. 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 Resistance is a measure of the resistance the semiconductor op amp to remove heat from its junction. To determine the junction temperature, TJ, we will need to know the ambient temperature, TA, and the internal power dissipation, PD.

67. Thermal model with no heat sink Analogous to an electrical circuit
PD = PIQ + POUT
PD = Total Power Dissipated
PIQ = Power Dissipated due to IQ
POUT = Power Dissipated in Output Stages
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
The Thermal Model for determining TJ, junction temperature, is based on electrical components representing temperature, heat flow, and thermal resistance.

68. IQ Power Dissipation (PIQ)
IQ Power Dissipation is simply the quiescent current, IQ, times the power supplies connected to the op amp.

69. DC Normal Maximum Power Dissipation in Output Stage (POUT)
For resistive loads the DC Maximum Power Dissipation in Output Stage occurs when Vout = ½ * Vs for normal operation into a resistive load. This is not a short circuit condition.

70. DC Short Circuit Maximum Power Dissipation in Output Stage (POUT)
If the application requires a short circuit condition and the maximum junction temperature is to be checked during a short circuit condition then POUT_SHORT = Vs * Isc where Isc is the short circuit specification of the op amp.

71. AC Normal Maximum Power Dissipation in Output Stage (POUT)
For AC Sinusoidal Signals
For resistive loads the sinewave AC Maximum Power Dissipation in Output Stage occurs when Vout = (2 * Vs) / pi for normal operation into a resistive load. This is not a short circuit condition.

72. AC Normal Maximum Power Dissipation in Output Stage (POUT)
For AC Sinusoidal Signals
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)
If an op amp is being used on a single supply you can use the formula for AC Maximum Power Dissipation by converting the single supply application to an “equivalent power dissipation in the output stage model”. To do this simple convert the single supply application to a dual supply application with the positive supply, +Vs = +(Vcc/2) and the negative supply, -Vs = -(Vcc/2). Use the equation in the lower left of the slide with Vs = Vcc/2.
-Vs = -(Vcc/2)

73. Absolute Maximum Rating

74. Absolute Maximum Rating
The Absolute Maximum Rating Table describes the key maximum conditions that the op amp can operate under. Operating an op amp at these levels continuously is not advisable from a robust, reliable application or from a long Mean-Time-To-Failure (MTTF).
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.

75. Op Amp Selection Tip

76. Choosing an Op Amp? Focus on Key Concerns for Application to Narrow Search Voltage? Current? Speed?
To narrow the search for an op amp for your application, among the numerous op amps and numerous specifications, analyze your key requirements at the board or system level from the perspective of Voltage, Current and Speed. In each of these main categories try to narrow which sub-parameter is the most important to help narrow the op amp search.

77. References

78. 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”
Tim Green, Senior Applications Engineer, Texas Instruments
“Operational Amplifier Stability: Parts 1-9 of 15”