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Texas Instruments Understanding Open Loop Gain of the PGA900 DAC Gain Amplifier Application notes
Application Report
SLDA031 – April 2015
Understanding Open Loop Gain of the
PGA900 DAC Gain Amplifier
Miro Oljaca, Collin Wells, Tim Green ............................................. Enhanced Industrial and Precision Analog
ABSTRACT
The open-loop gain (AOL) of an operational amplifier is one of the most important specifications. Proper
understanding of AOL at DC and over frequency is crucial for the understanding of closed-loop gain,
bandwidth, and stability analysis.
This application note provides an in-depth understanding of the PGA900 AOL magnitude and phase over
frequency. The effects of temperature, power supply voltage, and semiconductor process variation on the
AOL curve were observed. The variation over these parameters was used to develop a worst-case model
that can be used to create robust designs.
1
2
3
4
5
6
7
8
Contents
PGA900 AOL .................................................................................................................. 2
Temperature Effects on PGA900 AOL ..................................................................................... 4
Output Load Effects on PGA900 AOL ................................................................................... 6
Power Supply Voltage Effects on PGA900 AOL .......................................................................... 8
Process Variation Effects on PGA900 AOL .............................................................................. 10
Worst-Case PGA900 AOL Variations ..................................................................................... 12
Conclusion .................................................................................................................. 14
References .................................................................................................................. 14
List of Figures
1
PGA900 Typical AOL(s) and Phase Response (φ(s)) over Frequency ................................................ 2
2
PGA900 AOL(s) vs Temperature............................................................................................ 4
3
PGA900 AOL_DC vs Temperature ............................................................................................ 4
4
PGA900 Unity-Gain Frequency vs Temperature ........................................................................ 5
5
PGA900 AOL(s) vs Output Load ............................................................................................ 6
6
PGA900 AOL_DC vs Output Load ............................................................................................ 6
7
PGA900 Unity-Gain Frequency vs Output Load ......................................................................... 7
8
PGA900 AOL(s) vs Power Supply Voltage ................................................................................ 8
9
PGA900 AOL_DC vs Power Supply
10
11
12
13
14
15
16
17
.......................................................................................... 8
PGA900 Unity Gain Frequency vs Power Supply ....................................................................... 9
PGA900 AOL(s) vs Process Variation .................................................................................... 10
PGA900 AOL_DC Change vs Process Variation .......................................................................... 10
PGA900 Unity Gain Frequency vs Process Variation ................................................................. 11
PGA900 Worst-Case AOL(s) vs Frequency .............................................................................. 12
PGA900 Worst-Case AOL_DC ............................................................................................... 12
PGA900 Worst-Case Unity Gain Frequency............................................................................ 13
PGA900 Worst-Case Phase Margin ..................................................................................... 13
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1
PGA900 AOL
1
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PGA900 AOL
Figure 1 shows the typical frequency behavior of the PGA900 AOL magnitude (AOL(s)) and phase (φ(s)).
225
200
180
AOL_DC
160
180
ƒ1
140
135
100
80
90
60
40
ƒu
ƒXZ1
0
0
ƒXZ2
-20
-40
1µ
45
ƒXP1
20
10µ
100µ
1m
10m
100m
1
10
100
Frequency (Hz)
1k
Phase (°)
Gain (dB)
120
ƒ,XP2
10k
100k
1M
10M
-45
100M
D001
Figure 1. PGA900 Typical AOL(s) and Phase Response (φ(s)) over Frequency
The frequency where AOL(s) = 1 V/V or 0 dB, is marked as ƒu in Figure 1; ƒu is defined in Equation 1.
ƒu = 1.8 MHz
(1)
AOL_DC is the DC change in output voltage (VOUT) versus the change in input offset voltage (VOS) as defined
in Equation 2.
V
A OLDCdB 20 u log10 OUT
VOS
A OLDCdB 195 dB
(2)
The frequency behavior of AOL(s) is largely defined by the low-frequency dominant pole located at
frequency ω1 or ƒ1. At the dominant pole frequency, AOL(s) has decreased 3 dB from AOL_DC and the phase
has shifted by –45°.
ƒ1= 0.37 mHz
(3)
A single-pole Laplace approximation to the AOL curve can be defined based on ƒ1, as shown in Equation 4.
A O L (s)
A OL
_ DC
1 s
Z1
where
•
•
s = jω
ω1 = 2πƒ1
(4)
The complete frequency behavior of the PGA900 AOL curve is additionally shaped by a midfrequency polezero pair, ƒXP1 and ƒXZ1, an additional zero at ƒXZ2 and a high-frequency triple-pole, ƒXP2. These frequencies
are listed below for the PGA900. The location of these poles and zero in the AOL(s) transfer function
determines the unity-gain crossover frequency (ƒu) of 1.8 MHz.
ƒXP1 = 142 kHz
ƒXZ1 = 274 kHz
ƒXZ2 = 1.24 MHz
ƒXP2 = 4.88 MHz
(5)
(6)
(7)
(8)
The complete analytical expression of AOL(s) and φ(s) are shown in Equation 9 and Equation 10.
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PGA900 AOL
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A OL (s)
\V
A OL _ DC
§
s ·§
s ·
¨1 ¸¨ 1 ¸
ZXZ1 ¹©
ZXZ2 ¹
©
§
s ·§
s ·§
s ·
¨1 ¸¨ 1 ¸¨ 1 ¸
Z1 ¹©
ZXP1 ¹©
ZXP2 ¹
©
3
§ s ·
§ s ·
§ s ·
§ s ·
§ s ·
± DUFWDQ ¨ ¸ ± DUFWDQ ¨
¸ DUFWDQ ¨
¸ DUFWDQ ¨
¸ ± u DUFWDQ ¨
¸
Z
Z
Z
Z
© 1¹
© XP1 ¹
© XZ1 ¹
© XZ2 ¹
© ZXP2 ¹
(9)
(10)
To create a robust design, it is important to understand how AOL(s) changes as the system operating
conditions change. System operating conditions that affect the performance of the AOL(s) curve include:
temperature, output load, power supply voltage, and process variation.
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3
Temperature Effects on PGA900 AOL
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Temperature Effects on PGA900 AOL
Gain (dB)
The PGA900 is specified over an extended operating temperature range of –40ºC to 150ºC. The operating
temperature affects both the DC and the frequency behavior of the PGA900 AOL(s) curve as shown in
Figure 2.
240
220
200
180
160
140
120
100
80
60
40
20
0
-20
-40
1P
±ƒ&
0°C
25°C
70°C
85°C
125°C
150°C
10P
100P
1m
10m
100m
1
10
100
Frequency (Hz)
1k
10k
100k
1M
10M
100M
D002
Figure 2. PGA900 AOL(s) vs Temperature
Figure 3 shows the temperature effects on AOL_DC. Over the operating temperature range, AOL_DC can vary
from 214 to 149 dB. The 65-dB change in AOL_DC results in changes in the accuracy of the closed-loop gain
at low-frequencies.
240
±ƒ&
0°C
25°C
70°C
85°C
125°C
150°C
220
Gain (dB)
200
180
160
140
120
1P
10P
100P
1m
Frequency (Hz)
10m
100m
D003
Figure 3. PGA900 AOL_DC vs Temperature
Figure 4 shows the variation of the unity-gain frequency, ƒu, over the operating temperature range. Over
the operating temperature of the PGA900, ƒu can vary from 1.26 to 2.75 MHz.
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Temperature Effects on PGA900 AOL
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8
±ƒ&
0°C
25°C
70°C
85°C
125°C
150°C
6
4
Gain (dB)
2
0
-2
-4
-6
-8
-10
1M
10M
Frequency (Hz)
D004
Figure 4. PGA900 Unity-Gain Frequency vs Temperature
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5
Output Load Effects on PGA900 AOL
3
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Output Load Effects on PGA900 AOL
Gain (dB)
The PGA900 is specified to drive output loads with up to 2.5 mA of source and sink current. The operating
output current, or better output load, affects both the DC and the frequency behavior of the PGA900 AOL(s)
curve as shown in Figure 5.
220
200
180
160
140
120
100
80
60
40
20
0
-20
-40
-60
1P
480
1k
2k
5k
10k
10P
100P
1m
10m
100m
1
10
100
Frequency (Hz)
1k
10k
100k
1M
20k
50k
100k
200k
10M
100M
D005
Figure 5. PGA900 AOL(s) vs Output Load
Figure 6 shows the output load effects on AOL_DC. Over the operating output load range, AOL_DC can vary
from 195 to 141 dB.
200
480
1k
2k
5k
10k
Gain (dB)
180
20k
50k
100k
200k
160
140
120
1P
10P
100P
1m
Frequency (Hz)
10m
100m
1
D006
Figure 6. PGA900 AOL_DC vs Output Load
Figure 7 shows the variation of the unity-gain frequency, ƒu, over the operating output load range. Over
the operating output load of the PGA900, ƒu can vary from 0.48 to 1.8 MHz.
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Output Load Effects on PGA900 AOL
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20
480
1k
2k
5k
10k
15
Gain (dB)
10
20k
50k
100k
200k
5
0
-5
-10
-15
-20
100k
1M
Frequency (Hz)
10M
D007
Figure 7. PGA900 Unity-Gain Frequency vs Output Load
Lower values of load resistance cause a greater impact on AOL due to the interaction of the open-loop
output impedance and the output load.
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Power Supply Voltage Effects on PGA900 AOL
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Power Supply Voltage Effects on PGA900 AOL
Gain (dB)
The PGA900 can operate over a wide range of the power supply voltages from 3.3 to 30 V. The power
supply voltage has minimal impact on AOL(s) as shown in Figure 8.
200
180
160
140
120
100
80
60
40
20
0
-20
-40
-60
1P
3.3 V
5V
10 V
15 V
20 V
25 V
30 V
10P
100P
1m
10m
100m
1
10
100
Frequency (Hz)
1k
10k
100k
1M
10M
100M
D008
Figure 8. PGA900 AOL(s) vs Power Supply Voltage
AOL_DC changes by less than 1 dB from 195.9 to 196.8 dB over the full power-supply voltage range, as
shown in Figure 9.
200
3.3 V
5V
10 V
15 V
20 V
25 V
30 V
199
198
Gain (dB)
197
196
195
194
193
192
191
190
1P
10P
100P
Frequency (Hz)
1m
D009
Figure 9. PGA900 AOL_DC vs Power Supply
Over the full power-supply voltage range, ƒu only changes from 1.7 to 1.8 MHz as shown in Figure 10.
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5
3.3 V
5V
10 V
15 V
20 V
25 V
30 V
4
3
Gain (dB)
2
1
0
-1
-2
-3
-4
-5
1M
10M
Frequency (Hz)
D010
Figure 10. PGA900 Unity Gain Frequency vs Power Supply
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Process Variation Effects on PGA900 AOL
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Process Variation Effects on PGA900 AOL
Gain (dB)
During manufacturing, semiconductor process parameters are subjected to variations that result in
performance differences in the final integrated circuits. Process corners represent the worst-case
variations of these semiconductor parameters. The effects of the manufacturing process corners on the
PGA900 AOL(s) are displayed in Figure 11.
220
200
180
160
140
120
100
80
60
40
20
0
-20
-40
1P
10P
100P
1m
10m
100m
1
10
100
Frequency (Hz)
1k
10k
100k
1M
10M
100M
D011
Figure 11. PGA900 AOL(s) vs Process Variation
Over the process corners, AOL_DC changes from 188.9 dB to 196.2 dB as shown in Figure 12.
200
198
196
Gain (dB)
194
192
190
188
186
184
182
180
1P
10P
100P
1m
Frequency (Hz)
D012
Figure 12. PGA900 AOL_DC Change vs Process Variation
Process variations result in changes of ƒu from 1.66 to 1.9 MHz as shown in Figure 13.
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Process Variation Effects on PGA900 AOL
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5
4
3
Gain (dB)
2
1
0
-1
-2
-3
-4
-5
1M
10M
Frequency (Hz)
D013
Figure 13. PGA900 Unity Gain Frequency vs Process Variation
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11
Worst-Case PGA900 AOL Variations
6
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Worst-Case PGA900 AOL Variations
Gain (dB)
The variations in the PGA900 AOL(s) due to temperature, power-supply voltage, and process variations for
a 200-kΩ load resistor can be combined together to understand the worst-case variations that may occur
in an application. The operating temperature results in the largest variations of AOL(s), while the powersupply voltage results in the smallest variations. Observe the worst-case PGA900 AOL(s) in Figure 14.
240
220
200
180
160
140
120
100
80
60
40
20
0
-20
-40
1P
10P
100P
1m
10m
100m
1
10
100
Frequency (Hz)
1k
10k
100k
1M
10M
100M
D014
Figure 14. PGA900 Worst-Case AOL(s) vs Frequency
Over all of the possible system variations, AOL_DC can change from 135 to 213 dB as shown in Figure 15.
220
210
200
Gain (dB)
190
180
170
160
150
140
130
120
1P
10P
100P
1m
10m
100m
1
10
100
Frequency (Hz)
1k
10k
100k
1M
10M
100M
D015
Figure 15. PGA900 Worst-Case AOL_DC
As shown in Figure 16, the system variations result in a worst-case change in ƒu from 1.2 to 3 MHz. This
variation can significantly impact the stability analysis of the PGA900 and must be taken into account
during the design process.
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Worst-Case PGA900 AOL Variations
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5
4
3
Gain (dB)
2
1
0
-1
-2
-3
-4
-5
1M
10M
Frequency (Hz)
D016
Figure 16. PGA900 Worst-Case Unity Gain Frequency
The corresponding phase responses for the curves shown in Figure 16 have been plotted in Figure 17.
The phase margin is the measure of the phase at ƒu for each of the curves. The worst-case system
variations cause the phase margin to change from the nominal value of 77.6° up to 79° and down to 56°.
135
Phase (°)
90
45
0
1M
10M
Frequency (Hz)
D017
Figure 17. PGA900 Worst-Case Phase Margin
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Conclusion
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Conclusion
The PGA900 AOL curve is shaped by a low-frequency dominant pole, a midfrequency pole-zero pair, an
additional zero, and a high-frequency triple pole. The complete PGA900 AOL curve is shown in Figure 1
and defined in Equation 1.
The typical magnitude and phase response of the AOL curve changes due to variations in the system
operating temperature, output load, power-supply voltage, and semiconductor processing. The changes in
AOL due to these varying application factors were presented in this note over the full operating range of the
PGA900. The results from the individual parameters were used to determine the worst-case changes that
may occur in a harsh industrial application. Table 1 lists the results of the individual application factors
along with the worst-case analysis. System designers can use this information to create a robust design
over the expected application operating conditions. The AOL characteristics and typical variations shown in
this application note are valid for any semiconductor operational amplifier on a CMOS process.
Table 1. Summary of PGA900 AOL and ƒu Shifts
Application Factor
8
Conditions
AOL
ƒc
MIN (dB)
MAX (dB)
MIN (MHz)
MAX (MHz)
Temperature
–45°C to 150°C
149
214
1.26
2.75
Output load
470 Ω to 200 kΩ
140
195
0.48
1.8
Power supply
3.3 to 30 V
195.9
196.8
1.7
1.8
Process variation
Weak-strong
188.9
196.2
1.66
1.9
Worst case
Power supply, temperature, process
135
213
1.2
3.0
References
1. John V. Wait, etc., Introduction to Operational Amplifier Theory and Applications, ISBN: 9780070677654
2. Thomas M. Frederiksen, Intuitive Operational Amplifiers: From Basics to Useful Applications, ISBN:
978-0070219670
3. George B. Rutkowski, Operational Amplifiers: Integrated and Hybrid Circuits, ISBN: 978-0-471-57718-8
4. Jerald G. Graeme, Optimizing Op Amp Performance, ISBN: 978-0071590280
5. Sergio Franco, Design With Operational Amplifiers And Analog Integrated Circuits, ISBN: 9780078028168
6. Miroslav Oljaca, Henry Surtihadi, Operational amplifier gain stability, Part 1: General system analysis
SLYT367
7. Miroslav Oljaca, Henry Surtihadi, Operational amplifier gain stability, Part 2: DC gain-error analysis
SLYT374
8. Miroslav Oljaca, Henry Surtihadi,Operational amplifier gain stability, Part 3: AC gain-error analysis
SLYT383
9. TI E2E forum, Solving Op Amp Stability Issues
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