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. Contents 1 PGA900 AOL .................................................................................................................. 2 2 Temperature Effects on PGA900 AOL ..................................................................................... 4 3 Output Load Effects on PGA900 AOL ................................................................................... 6 4 Power Supply Voltage Effects on PGA900 AOL .......................................................................... 8 5 Process Variation Effects on PGA900 AOL .............................................................................. 10 6 Worst-Case PGA900 AOL Variations ..................................................................................... 12 7 Conclusion .................................................................................................................. 14 8 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 .......................................................................................... 8 10 PGA900 Unity Gain Frequency vs Power Supply ....................................................................... 9 11 PGA900 AOL(s) vs Process Variation .................................................................................... 10 12 PGA900 AOL_DC Change vs Process Variation .......................................................................... 10 13 PGA900 Unity Gain Frequency vs Process Variation ................................................................. 11 14 PGA900 Worst-Case AOL(s) vs Frequency.............................................................................. 12 15 PGA900 Worst-Case AOL_DC ............................................................................................... 12 16 PGA900 Worst-Case Unity Gain Frequency............................................................................ 13 17 PGA900 Worst-Case Phase Margin ..................................................................................... 13 All trademarks are the property of their respective owners. SLDA031–April 2015 Understanding Open Loop Gain of the PGA900 DAC Gain Amplifier 1 Submit Documentation Feedback Copyright © 2015, Texas Instruments Incorporated PGA900 AOL www.ti.com 1 PGA900 AOL Figure 1 shows the typical frequency behavior of the PGA900 AOL magnitude (AOL(s)) and phase (φ(s)). 200 225 180 AOL_DC 160 180 ƒ1 140 120 135 100 80 90 Phase (°) Gain (dB) 60 40 ƒ 45 XP1 ƒ 20 u ƒ 0 XZ1 0 -20 ƒXZ2 ƒ,XP2 -40 -45 1µ 10µ 100µ 1m 10m 100m 1 10 100 1k 10k 100k 1M 10M 100M Frequency (Hz) 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 20u log OUT OLDCdB 10 VOS A 195 dB OLDCdB (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 OL_DC A ( s ) OL s 1 Z 1 where • s = jω • ω1 = 2πƒ1 (4) The complete frequency behavior of the PGA900 AOL curve is additionally shaped by a midfrequency pole- zero 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 (5) ƒXZ1 = 274 kHz (6) ƒXZ2 = 1.24 MHz (7) ƒXP2 = 4.88 MHz (8) The complete analytical expression of AOL(s) and φ(s) are shown in Equation 9 and Equation 10. 2 Understanding Open Loop Gain of the PGA900 DAC Gain Amplifier SLDA031–April 2015 Submit Documentation Feedback Copyright © 2015, Texas Instruments Incorporated www.ti.com PGA900 AOL §ss ·§ · ¨11 ¸¨ ¸ ©ZZ ¹© ¹ A (s) A XZ1 XZ2 OL OL _DC 3 §s ·§ s ·§ s · ¨1 ¸¨ 1 ¸¨ 1 ¸ ZZZ ©1 ¹© XP1 ¹© XP2 ¹ (9) §·s §· s §· s §· s §· s \ V ± DUFWDQ¨¸ ± DUFWDQ ¨¸ DUFWDQ ¨¸ DUFWDQ ¨¸ ± u DUFWDQ ¨¸ ©¹ZZZZZ1 ©¹ XP1 ©¹ XZ1 ©¹ XZ2 ©¹ XP2 (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. SLDA031–April 2015 Understanding Open Loop Gain of the PGA900 DAC Gain Amplifier 3 Submit Documentation Feedback Copyright © 2015, Texas Instruments Incorporated Temperature Effects on PGA900 AOL www.ti.com 2 Temperature Effects on PGA900 AOL 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 0°C 25°C 180 70°C 160 85°C 140 125°C 120 150°C 100 80 Gain (dB) Gain 60 40 20 0 -20 -40 1P 10P 100P 1m 10m 100m 1 10 100 1k 10k 100k 1M 10M 100M Frequency (Hz) 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 ±& 0°C 220 25°C 70°C 85°C 200 125°C 150°C 180 Gain (dB) Gain 160 140 120 1P 10P 100P 1m 10m 100m Frequency (Hz) 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. 4 Understanding Open Loop Gain of the PGA900 DAC Gain Amplifier SLDA031–April 2015 Submit Documentation Feedback Copyright © 2015, Texas Instruments Incorporated www.ti.com Temperature Effects on PGA900 AOL 8 ±& 6 0°C 25°C 4 70°C 85°C 2 125°C 150°C 0 -2 Gain (dB) Gain -4 -6 -8 -10 1M 10M Frequency (Hz) D004 Figure 4. PGA900 Unity-Gain Frequency vs Temperature SLDA031–April 2015 Understanding Open Loop Gain of the PGA900 DAC Gain Amplifier 5 Submit Documentation Feedback Copyright © 2015, Texas Instruments Incorporated Output Load Effects on PGA900 AOL www.ti.com 3 Output Load Effects on PGA900 AOL 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. 220 200 480 20k 180 1k 50k 2k 100k 160 5k 200k 140 10k 120 100 80 60 Gain (dB) Gain 40 20 0 -20 -40 -60 1P 10P 100P 1m 10m 100m 1 10 100 1k 10k 100k 1M 10M 100M Frequency (Hz) 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 20k 1k 50k 2k 100k 180 5k 200k 10k 160 Gain (dB) Gain 140 120 1P 10P 100P 1m 10m 100m 1 Frequency (Hz) 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. 6 Understanding Open Loop Gain of the PGA900 DAC Gain Amplifier SLDA031–April 2015 Submit Documentation Feedback Copyright © 2015, Texas Instruments Incorporated www.ti.com Output Load Effects on PGA900 AOL 20 480 20k 15 1k 50k 2k 100k 10 5k 200k 10k 5 0 Gain (dB) Gain -5 -10 -15 -20 100k 1M 10M Frequency