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 follow e r co nf igu r at ion . Howev er, this is not the b est 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 comp en sa tio n me th od is explained, and based on this, specific data is provided fo r the TS507. The TS507 is a high precision rail-to-rail amplifier, with very low input offset volta ge, 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 1/22

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

1.1 Introduction

Consider a linear system modeled as shown in Figure 1.

Figure 1. Linear system with feedback model

Vin Vout

The model in Figure 1 gives the following equation:

out

---------------- -

1Aβ+

---------------- -

1Aβ+

is named closed loop gain.

From this equation, it is e vident that f or Aβ = -1, the circuit is unstable (V V

Aβ is the loop gain.

⋅=

is independent of

out

To evaluate it, the loop is opened and -V

is calculated as shown in Figure 2.

r/Vs

Figure 2. Loop gain calculation

Vout

Opening the loop leads to the following equation:

If a small signal V amplitude above t hat of V then the system oscillates and is unstable.

This leads to the definition of the gain mar gin, 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.

is sourced into the system, and if Vr comes back in phase with it with an

(which means that Aβ is a real number g reater than or e qual to 1)

------– Aβ= V

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Stability basics AN2653

1.2 Operational 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

Gain (dB)

-40

-80

-120

-160

-200

Loop Gain

Phase Margin

1.E+00

1.E+01

1.E+02

1.E+03

Frequency (Hz )

Gain Phase

1.E+04

Gain Marg in

1.E+05

1.E+06

-45

-90

-135

-180

-225

-270

1.E+07

1.E+08

160

130

100

Phase (°)

Gain (dB)

-20

1.E-02

1.E-01

To apply this stability approach to operational amplifier based applications, it is necessary to know the gain of the operation al amplifier when no f e edbac k and n o loads are used. I t 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 b lock diagram

TS507 Open Loop Gain

1.E+00

1.E+01

1.E+02

Frequency (Hz )

Gain Phase

TS507 : Vcc = 5 V Vicm = 2.5 V T = 25 °C

1.E+03

1.E+04

1.E+05

-30

-60

-90

Phase (°)

-120

-150

-180

1.E+06

1.E+07

The loop gain is:

------– A ω() V

This equation shows the impact of the gain on the stability: if R loop gain of the system increases and the loop gain decrease s. 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 minimize s the ef fect of the phase drop due to t his po le, and as a result, the phase margin is higher. Therefore, a voltage follower configuration is the worst case for stability.

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------------------ -

⋅=

RfRg+

increases, the closed

f/Rg

AN2653 Stability basics

Figure 6. Impact of closed loop gain on stability

loop gain

(dB)

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

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

Figure 7. Follower configuration model with

capacitive load for loop gain calculation

Case 1

Case 2

. Including

Figure 8. TS507 output impedance Zo

TS507 Output Impedance (Zo)

1.E+05

1.E+04

1.E+03

1.E+02

Impedance ( Ohm)

1.E+01

1.E+00

TS507 : Vcc = 5 V Vicm = 2,5 V T = 25 °C

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

Frequency (Hz )

Impedanc e Phase

1.E+05

-45

-90

-135

1.E+06

1.E+07

Zo is neither constant over frequency nor purely resistive. Figure 8 shows how the output impedance varies with the frequ ency in t he case o f the TS507 . Thes e 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: th e amplifier open-loop g ain and the amplifier ou tput impedance. Then, a calculation of the loop gain indicates how stable the system is.

Phase (°)

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Stability in voltage follower configuration AN2653

2 Stability in voltage follower configuration

This section examines a v o ltage 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

-10

Gain (dB)

-20

-30

-40

Without CL

CL=550 pF

TS507 : Vcc = 5 V Vicm = 2,5 V T = 25 °C RL = 10 kΩ

1.E+03

1.E+04

Gain without CL Gain with CL = 550 pF

1.E+05

Frequency (Hz )

1.E+06

1.E+07

In voltage follower configuration, the loop gain is:

------–

----------------------------------------- -=

A ω()

------ - jZoCLω++ R

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 freq uency, 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 C

, the system is stable. Howe ver, Figure 11 and Figure 12 show , f or the TS507, t he

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

with grounded input

Voltage Follower Configuration -

0.08

0.06

0.04

Output Signal with Input Grounded

TS507 : Vcc = 5 V Vicm = 2,5 V T = 25 °C RL = 10 kΩ CL = 550pF

0.02

Amplitude (V)

-0.02

-0.04

-0.06

0.00 0.50 1.00 1.50 2.00

Time (μs)

Output Si gnal Input Signa l

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

However, compensation components have to be chos en 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 f or a specific load, but modifying this load can affect stability.

Figure 12. Input and output signals measured

for an AC input signal

Voltage Follower -

0.2

0.15

0.1

0.05

Amplitude (V)

-0.05

-0.1

-0.15 0 100 200 300 400 500

Input and Output Signals

Time (μs)

Output Si gnal Input Signal

TS507 : Vcc = 5 V Vicm = 2,5 V T = 25 °C RL = 10 kΩ CL = 550 pF

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