ST AN2653 APPLICATION NOTE

AN2653

Application note

Operational amplifier stability compensation methods for capacitive loading applied to TS507

Introduction

Who has never experienced oscillations issues when using an operational amplifier? Opamps are often used in a simple voltage follower configuration. However, this is not the best configuration in terms of capacitive loading and potential risk of oscillations.

Capacitive loads have a big impact on the stability of operational amplifier-based applications. Several compensation methods exist to stabilize a standard op-amp. This application note describes the most common ones, which can be used in most cases.

The general theory of each compensation method is explained, and based on this, specific data is provided for the TS507. The TS507 is a high precision rail-to-rail amplifier, with very low input offset voltage, and a 1.9 MHz gain bandwidth product, which is available in SOT23-5 and SO-8 packages.

This document simplifies the task of designing an application that includes the TS507. It spares you the time-consuming effort of trying numerous combinations on bench, and it is also much more accurate than using Spice models which are not designed to study system stability, even though they can give a general trend.

November 2007

Rev 1

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www.st.com

Contents	AN2653

Contents

1	Stability basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		. 3
	1.1	Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	3
	1.2	Operational amplifier modeling for stability study . . . . . . . . . . . . . . . . . . . .	4
2	Stability in voltage follower configuration . . . . . . . . . . . . . . . . . . . . . . .		6
3	Out-of-the-loop compensation method . . . . . . . . . . . . . . . . . . . . . . . . . .		8
	3.1	Theoretical overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	8
	3.2	Application on the TS507 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	9
4	In-the-loop compensation method . . . . . . . . . . . . . . . . . . . . . . . . . . . .		12
	4.1	Theoretical overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	12
	4.2	Application on the TS507 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	12
5	Snubber network compensation method . . . . . . . . . . . . . . . . . . . . . . .		16
	5.1	Theoretical overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	16
	5.2	Application on the TS507 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	17
6	Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		20
7	Revision history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		21

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AN2653	Stability basics

1 Stability basics

1.1Introduction

Consider a linear system modeled as shown in Figure 1.

Figure 1. Linear system with feedback model

Vin

A

Vout

-

ß

The model in Figure 1 gives the following equation:

	Vout =	A		Vin
		----------------
		1 + Aβ
A	is named closed loop gain.
----------------
1 + Aβ

From this equation, it is evident that for Aβ = -1, the circuit is unstable (Vout is independent of Vin).

Aβ is the loop gain.

To evaluate it, the loop is opened and -Vr/Vs is calculated as shown in Figure 2.

Figure 2. Loop gain calculation

A Vout

-

Vs Vr ß

Opening the loop leads to the following equation:

Vr Aβ

–----- =

Vs

If a small signal Vs is sourced into the system, and if Vr comes back in phase with it with an amplitude above that of Vs (which means that Aβ is a real number greater than or equal to 1) then the system oscillates and is unstable.

This leads to the definition of the gain margin, which is the opposite of the loop gain (in dB) at the frequency for which its phase equals -180°. The bigger the gain margin, the more stable the system. In addition, the phase margin is defined as the phase of the loop gain plus 180° at the frequency for which its gain equals 0 dB. Therefore, from the value of Aβ it is possible to determine the stability of the system.

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Stability basics	AN2653

1.2Operational amplifier modeling for stability study

Figure 3 illustrates the definition of phase and gain margins in a gain configuration.

Figure 3. Illustration of phase and gain	Figure 4. TS507 open loop gain
margins

					Loop Gain											TS507 Open Loop Gain
	40								0			160									TS507 :	0
	0								-45			130									Vcc = 5 V	-30
																					Vicm = 2.5 V
						Gain Margin															T = 25 °C
Gain (dB)	-40								-90		Gain (dB)	100										-60	Phase (°)
	-80		Phase Margin						-135	Phase (°)		70										-90
												40										-120
	-120								-180
	-160								-225			10										-150
	-200								-270			-20										-180
	1.E+00	1.E+01	1.E+02	1.E+03	1.E+04	1.E+05	1.E+06	1.E+07	1.E+08				1.E-02	1.E-01	1.E+00	1.E+01	1.E+02	1.E+03	1.E+04	1.E+05	1.E+06	1.E+07
					Frequency (Hz)												Frequency (Hz)
					Gain	Phase											Gain	Phase

To apply this stability approach to operational amplifier based applications, it is necessary to know the gain of the operational amplifier when no feedback and no loads are used. It is the open loop gain (A(ω )) of the amplifier (shown in Figure 4 for the TS507). From this parameter, it is possible to model the amplifier and to study the stability of any gain configuration.

Figure 5. Equivalence between schematics and block diagram

The loop gain is:

Vr	= A( ω)	Rf	Rg
–V-----s			+ Rg
		------------------

This equation shows the impact of the gain on the stability: if Rf/Rg increases, the closed loop gain of the system increases and the loop gain decreases. Because the phase remains the same, the gain margin increases and stability is improved.

In addition, if you consider the case of a second order system such as the one shown in Figure 6, a decrease of the loop gain allows to pass the 0 dB axis before the second pole occurs. It minimizes the effect of the phase drop due to this pole, and as a result, the phase margin is higher. Therefore, a voltage follower configuration is the worst case for stability.

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AN2653	Stability basics

Figure 6. Impact of closed loop gain on stability

Gloop gain (dB)

Case 1

Case 2

0 f

Closed Loop Gain (Case1) < Closed Loop Gain (Case 2)

Another parameter that impacts stability is the amplifier output impedance Zo. Including this parameter in the model of the amplifier leads to the model shown in Figure 7.

Figure 7. Follower configuration model with Figure 8. TS507 output impedance Zo capacitive load for loop gain

calculation

TS507 Output Impedance (Zo)

	1.E+05								TS507 :	90
	1.E+04								Vcc = 5 V	45
Impedance (Ohm)									Vicm = 2,5 V
									T = 25 °C
	1.E+03									0	Phase (°)
	1.E+02									-45
	1.E+01									-90
	1.E+00									-135
	1.E-02	1.E-01	1.E+00	1.E+01	1.E+02	1.E+03	1.E+04	1.E+05	1.E+06	1.E+07

Frequency (Hz)

Impedance Phase

Zo is neither constant over frequency nor purely resistive. Figure 8 shows how the output impedance varies with the frequency in the case of the TS507. These variations complicate the stability study.

Finally, to study the stability of an op-amp based system, two parameters need to be taken into account in order to better fit reality: the amplifier open-loop gain and the amplifier output impedance. Then, a calculation of the loop gain indicates how stable the system is.

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Stability in voltage follower configuration	AN2653

2 Stability in voltage follower configuration

This section examines a voltage follower configuration because it is the worst case scenario for stability (compared with a gain configuration).

Figure 9. Voltage follower configuration	Figure 10. Closed loop gain measured for a
	voltage follower configuration

Voltage Follower Configuration - Closed Loop Gain

	20				TS507 :
	10				Vcc = 5 V
					Vicm = 2,5 V
					T = 25 °C
	0				RL = 10 kΩ
(dB)
	-10			Without CL
Gain
	-20
				CL=550 pF
	-30
	-40
	1.E+03	1.E+04	1.E+05	1.E+06	1.E+07

Frequency (Hz)

Gain without CL Gain with CL = 550 pF

In voltage follower configuration, the loop gain is:

Vr	=	A( ω)
–-----		-Z----o----	---------------------	-
Vs	1 +		+ jZoCL	ω
		R-----L-

The capacitive load adds a pole to the loop gain that impacts the stability of the system. The higher the frequency of this pole, the greater the stability. In fact, if the pole frequency is lower than or close to the unity gain frequency, the pole can have a significant negative impact on phase and gain margins. It means that the stability decreases when the capacitive load increases.

Without CL, the system is stable. However, Figure 11 and Figure 12 show, for the TS507, the oscillations due to instability with and without an AC input signal for a capacitive load of 550 pF. The oscillation frequency is in line with the peaking frequency observed in a closed loop gain configuration (approximately 1.9 MHz according to Figure 10).

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AN2653	Stability in voltage follower configuration
Figure 11. Input and output signals measured	Figure 12. Input and output signals measured
with grounded input	for an AC input signal

		Voltage Follower Configuration -							Voltage Follower -
		Output Signal with Input Grounded					0.2		Input and Output Signals
	0.08				TS507 :							TS507 :
	0.06				Vcc = 5 V		0.15					Vcc = 5 V
					Vicm = 2,5 V							Vicm = 2,5 V
					T = 25 °C							T = 25 °C
	0.04				RL = 10 kΩ		0.1					RL = 10 kΩ
(V)					CL = 550pF	(V)						CL = 550 pF
	0.02						0.05
Amplitude						Amplitude
	0						0
	-0.02						-0.05
	-0.04						-0.1
	-0.06						-0.15
	0.00	0.50	1.00	1.50	2.00		0	100	200	300	400	500
			Time (μs)						Time (μs)
			Output Signal	Input Signal					Output Signal	Input Signal

To remove this instability and work with higher capacitive loads, many compensation methods exist, and this application note examines some of them. By adding zeroes and poles to the loop gain, stability can be improved.

However, compensation components have to be chosen carefully. A compensation scheme can indeed improve stability, but can also lead the system to instability, depending on the choice of component values. Similarly, a compensation configuration can work for a specific load, but modifying this load can affect stability.

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