Texas Instruments | Understanding Open Loop Output Impedance of the PGA900 DAC Gain Amplifier (Rev. A) | Application notes | Texas Instruments Understanding Open Loop Output Impedance of the PGA900 DAC Gain Amplifier (Rev. A) Application notes

Texas Instruments Understanding Open Loop Output Impedance of the PGA900 DAC Gain Amplifier (Rev. A) Application notes
Application Report
SLDA033A – May 2015 – Revised May 2015
Understanding Open Loop Output Impedance of the
PGA900 DAC Gain Amplifier
Miro Oljaca, Collin Wells, Tim Green ............................................. Enhanced Industrial and Precision Analog
ABSTRACT
The open-loop output impedance (ZO) of an operational amplifier is one of the most important
specifications. Proper understanding of ZO over frequency is crucial for the understanding of loop gain,
bandwidth, and stability analysis.
This application note provides an in-depth understanding of the PGA900 ZO magnitude over frequency.
The effects of temperature, power supply voltage, and semiconductor process variation on the ZO curve
were observed. The variation over these parameters was used to develop a worst-case model that can be
used to create robust designs.
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2
3
4
5
6
7
8
Contents
PGA900 ZO ...................................................................................................................
Temperature Effects on PGA900 ZO ......................................................................................
Power Supply Effects on the PGA900 ZO.................................................................................
Common-Mode Voltage Effects on PGA900 .............................................................................
Process Variation Effects on PGA900 ZO.................................................................................
Worst Case ...................................................................................................................
Conclusion ....................................................................................................................
References ...................................................................................................................
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3
4
5
6
7
8
8
List of Figures
1
PGA900 Typical Magnitude of the Open-Loop Output Impedance ZO ................................................ 2
2
PGA900 Typical Phase of the Open-Loop Output Impedance ZO ..................................................... 2
3
PGA900 ZO(s) vs Temperature............................................................................................. 3
4
PGA900 ZO(s) vs Power Supply Voltage ................................................................................. 4
5
PGA900 ZO(s) vs Common-Mode Voltage
6
PGA900 ZO(s) vs Process Variation ....................................................................................... 6
7
PGA900 Worst-Case ZO(s) vs Frequency ................................................................................ 7
8
PGA900 Minimum and Maximum ZO(s) from Worst-Case Results .................................................... 7
...............................................................................
5
List of Tables
1
Summary of PGA900 ZO .................................................................................................... 8
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1
PGA900 ZO
1
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PGA900 ZO
Figure 1 shows the typical frequency behavior of the PGA900 ZO magnitude, |ZO(s)|. The PGA900 ZO
phase (φ(s)) is shown in Figure 2.
10M
1M
RLOW_F
CLOW_F
ZO (Ω)
100k
RHIGH_F
10k
1k
100
RMID_F
10
1
1E-6
1E-5
1E-4
1E-3
1E-2
1E-1
1E+0
1E+1
1E+2
Frequency (Hz)
CHIGH_F
LO
1E+3
1E+4
1E+5
1E+6
1E+7
1E+8
D001
Figure 1. PGA900 Typical Magnitude of the Open-Loop Output Impedance Z O
90
45
Phase (q)
0
-45
-90
-135
1E-6
1E-5
1E-4
1E-3
1E-2
1E-1
1E+0
1E+1
1E+2
Frequency (Hz)
1E+3
1E+4
1E+5
1E+6
1E+7
1E+8
D002
Figure 2. PGA900 Typical Phase of the Open-Loop Output Impedance ZO
The PGA900 operational amplifier features a three-stage output stage architecture which results in the
three distinct ZO regions that can be seen in the ZO magnitude. At low frequencies the ZO curve is defined
by a low frequency resistance value, RLOW_F. As frequency increases ZO becomes capacitive and ZO in that
region is defined by a low frequency capacitance value, CLOW_F. At mid-frequencies, the ZO becomes
resistive again and is defined by a mid-frequency resistance value, RMID_F. ZO then becomes inductive and
2
Understanding Open Loop Output Impedance of the PGA900 DAC Gain
Amplifier
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Temperature Effects on PGA900 ZO
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will be defined by an open-loop inductance value, LO. This inductive region is the most important for
stability analysis because capacitive loading on the output can interact with the inductance resulting in
stability issues that are difficult to compensate. The inductive region turns resistive again at higher
frequencies and can be defined by a high frequency resistance value, RHIGH_F. Finally, at the high
frequencies near the end of the region of interest ZO turns capacitive again and can be defined by a
capacitance, CHIGH_F.
Nominal values for the PGA900 operational amplifier ZO are listed below:
• RLOW_F = 4.87 MΩ
• CLOW_F = 1.57 mF
• RMID_F = 4.09 Ω
• LO = 1.23 mH
• RHIGH_F = 1.03 kΩ
• CHIGH_F = 20.14 pF
To create a robust design, it is important to understand how |ZO(s)| changes as the system operating
conditions change. System operating conditions that affect the performance of the |ZO(s)| curve includes:
temperature, power supply voltage, common-mode voltage and process variation.
2
Temperature Effects on PGA900 ZO
The PGA900 is specified over an extended operating temperature range of –40ºC to 150ºC. The operating
temperature affects the frequency behavior of the PGA900 ZO(s) over the full range of the curve as shown
in Figure 3.
100M
±qC
0qC
25qC
70qC
85qC
125qC
150qC
10M
1M
ZO (:)
100k
10k
1k
100
10
1
1E-6
1E-5
1E-4
1E-3
1E-2
1E-1
1E+0
1E+1
1E+2
Frequency (Hz)
1E+3
1E+4
1E+5
1E+6
1E+7
1E+8
D003
Figure 3. PGA900 ZO(s) vs Temperature
The ZO parameter variations due to temperature are listed below:
• RLOW_F = 2.46 − 32.88 MΩ
• CLOW_F = 0.82 − 9.46 mF
• RMID_F = 2.54 − 35.89 Ω
• LO = 0.96 − 1.86 mH
• RHIGH_F = 0.84 − 1.46 kΩ
• CHIGH_F = 19.49 − 20.20 pF
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3
Power Supply Effects on the PGA900 ZO
3
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Power Supply Effects on the PGA900 ZO
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 ZO(s) as shown in Figure 4.
10M
3.3 V
5V
10 V
15 V
20 V
25 V
30 V
1M
100k
ZO (:)
10k
1k
100
10
1
1E-6
1E-5
1E-4
1E-3
1E-2
1E-1
1E+0
1E+1
1E+2
Frequency (Hz)
1E+3
1E+4
1E+5
1E+6
1E+7
1E+8
D004
Figure 4. PGA900 ZO(s) vs Power Supply Voltage
The ZO parameter variations due to power supply voltage are listed below:
• RLOW_F = 3.3 − 6.02 MΩ
• CLOW_F = 1.55 − 1.68 mF
• RMID_F = 3.83 − 4.14 Ω
• LO = 1.11 − 1.25 mH
• RHIGH_F = 0.94 − 1.04 kΩ
• CHIGH_F = 19.32 − 20.52 pF
4
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Common-Mode Voltage Effects on PGA900
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4
Common-Mode Voltage Effects on PGA900
The common-mode voltage of the PGA900 has some minimal effects on the ZO(s) as shown in Figure 5.
10M
0.24 V
0.48 V
0.72 V
0.96 V
1.2 V
1M
100k
ZO (:)
10k
1k
100
10
1
1E-6
1E-5
1E-4
1E-3
1E-2
1E-1
1E+0
1E+1
1E+2
Frequency (Hz)
1E+3
1E+4
1E+5
1E+6
1E+7
1E+8
D005
Figure 5. PGA900 ZO(s) vs Common-Mode Voltage
The ZO parameter variations due to common-mode voltage are listed below:
• RLOW_F = 0.15 − 4.87 MΩ
• CLOW_F = 1.56 − 1.88 mF
• RMID_F = 4.09 − 4.20 Ω
• LO = 1.23 − 1.40 mH
• RHIGH_F = 0.93 − 1.03 kΩ
• CHIGH_F = 20.14 − 24.31 pF
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5
Process Variation Effects on PGA900 ZO
5
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Process Variation Effects on PGA900 ZO
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 ZO(s) are displayed in Figure 6.
10M
1M
100k
ZO (:)
10k
1k
100
10
1
1E-6
1E-5
1E-4
1E-3
1E-2
1E-1
1E+0
1E+1
1E+2
Frequency (Hz)
1E+3
1E+4
1E+5
1E+6
1E+7
1E+8
D006
Figure 6. PGA900 ZO(s) vs Process Variation
The ZO parameter variations due to process variation are listed below:
• RLOW_F = 0.35 − 5.95 MΩ
• CLOW_F = 0.66 − 3.02 mF
• RMID_F = 3.07 − 5.64 Ω
• LO = 1.1 − 1.26 mH
• RHIGH_F = 1.01 − 1.07 kΩ
• CHIGH_F = 8.23 − 22.79 pF
6
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Worst Case
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6
Worst Case
The variations in the PGA900 ZO(s) due to temperature and process variations 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 ZO(s), while the power-supply voltage results in the smallest variations.
The worst-case PGA900 ZO(s) can be observed in Figure 7.
10M
1M
100k
ZO (:)
10k
1k
100
10
1
1E-6
1E-5
1E-4
1E-3
1E-2
1E-1
1E+0
1E+1
1E+2
Frequency (Hz)
1E+3
1E+4
1E+5
1E+6
1E+7
1E+8
D007
Figure 7. PGA900 Worst-Case ZO(s) vs Frequency
Taking the envelope of the minimum and maximum ZO(s) worst case results shows the possible variation
of ZO(s) over several common application factors. The results are displayed in Figure 8.
10M
Min
Typ
Max
1M
100k
ZO (:)
10k
1k
100
10
1
1E-6
1E-5
1E-4
1E-3
1E-2
1E-1
1E+0
1E+1
1E+2
Frequency (Hz)
1E+3
1E+4
1E+5
1E+6
1E+7
1E+8
D008
Figure 8. PGA900 Minimum and Maximum ZO(s) from Worst-Case Results
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Conclusion
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The ZO parameter variations due to worst case are listed below:
• RLOW_F = 0.22 − 5.95 MΩ
• CLOW_F = 0.002 − 15.81 mF
• RMID_F = 1.86 − 69.28 Ω
• LO = 0.84 − 2.17 mH
• RHIGH_F = 0.83 − 1.49 kΩ
• CHIGH_F = 17.76 − 22.69 pF
7
Conclusion
The PGA900 ZO curve is shaped by three resistive regions, two capacitive regions and one inductive
region. The complete PGA900 ZO curve is shown in Figure 1 and Figure 2.
The ZO curve changes due to variations in the system operating temperature, power-supply voltage,
common-mode voltage, and semiconductor processing. The changes in ZO due to these varying
application factors were presented in this article 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. The results of the individual application factors along with the worst-case analysis
are listed in Table 1. System designers can use this information to create a robust design over the
expected application operating conditions.
Table 1. Summary of PGA900 ZO
Application
Factor
8
Conditions
RLOW_F
CLOW_F
RMID_F
LO
RHIGH_F
CHIGH_F
Temperature
–45 to 150°C
–49/+575%
–48/+503%
–38/+778%
–22/+51%
–18/+42%
–3/+0%
Power supply
3.3 to 30 V
–32/+24%
–1/+7%
–6/+1%
–10/+2%
–9/+1%
–4/+2%
Commonmode voltage
0.24 to 1.2 V
–97/+22%
–1/+20%
–0/+3%
–0/+14%
–10/+0%
–0/+21%
Process
variation
Weak-strong
–93/+22%
–58/+92%
–25/+38%
–11/+2%
–2/+4%
–9/13%
Worst case
Temperature,
Process
–95/+22%
–100/+907%
–55/+1594%
–32/+76%
–19/+45%
–12/+13%
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. Miro Oljaca, Collin Wells, Tim Green, Understanding Open Loop Gain of the PGA900 DAC Gain
Amplifier, SLDA031
7. TI E2E forum, Solving Op Amp Stability Issues
8
Understanding Open Loop Output Impedance of the PGA900 DAC Gain
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Revision History
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Revision History
Changes from Original (May 2015) to A Revision ........................................................................................................... Page
•
•
Corrected graph axis titles ............................................................................................................... 2
Added description preceding nominal values.......................................................................................... 3
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Revision History
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