Capacitive Loads. AN884 Datasheet 

AN884
Driving Capacitive Loads With Op Amps
Author: Kumen Blake
Microchip Technology Inc.
INTRODUCTION
Overview
Operational amplifiers (op amps) that drive large
capacitive loads may produce undesired results. This
application note discusses these potential problems. It
also offers simple, practical solutions to each of these
problems.
The circuit descriptions and mathematics are kept to a
minimum, with emphasis on understanding rather than
completeness. Simple models of op amp behavior help
achieve these goals. Simple equations are included to
help connect circuit design to overall circuit behavior.
Simple examples illustrate the concepts discussed.
They give concrete results that can be used to better
understand the theory. They are also practical to help
develop a feel for real world designs.
Purpose
This application note is for circuit designers using op
amps that drive capacitive loads. It assumes only a
basic understanding of circuit analysis.
This application note has the goal of helping circuit
designers quickly and effectively resolve capacitive
loading issues in op amp circuits. It focuses on building
a fundamental understanding of why problems occur,
and how to resolve these problems.
LINEAR RESPONSE
Capacitive loads affect an op amp’s linear response.
They change the transfer function, which affects AC
response and step response. If the capacitance is large
enough, it becomes necessary to compensate the op
amp circuit to keep it stable, and to avoid AC response
peaking and step response overshoot and ringing.
An op amp’s linear response is also critical in
understanding how it interacts with sampling
capacitors. These sampling capacitors present a non
linear, reactive load to an op amp. For instance, many
A/D converters (e.g., low frequency SAR and Delta
Sigma) have sampling capacitors at their inputs.
Simplified Op Amp AC Model
In order to understand how capacitive loads affect op
amps, we must look at the op amp’s output impedance
and bandwidth. The feedback network modifies the op
amp’s behavior; its effects are included in an equivalent
circuit model.
OP AMP MODEL
Figure 1 shows a simplified AC model of a voltage
feedback op amp. The openloop gain is represented
by the dependent source with gain AOL(s), where
s = jω = j2πf. The output stage is represented by the
resistor RO (openloop output resistance).
VINP
VE
VINM
RO
VEAOL(s)
VOUT
FIGURE 1:
Op Amp AC Model.
We will include gain bandwidth product (fGBP), the
openloop gain’s “second pole” (f2P) in our openloop
gain (AOL(s)) model. Low frequency effects are left out
for simplicity. f2P models the openloop gain’s reduced
phase (< 90°) at high frequencies due to internal
parasitics (see Section B.1 “Estimating f2P” for more
information).
EQUATION 1:
AOL(s) ≈ s(1+ωGsB⁄Pω2P)
© 2008 Microchip Technology Inc.
DS00884Bpage 1


AN884
CIRCUIT MODEL
Figure 2 shows the op amp in a noninverting gain, and
Figure 3 in an inverting gain. These circuits cover the
majority of applications.
MCP6XXX
VIN VOUT
FIGURE 2:
RG RF
Noninverting Gain Circuit.
MCP6XXX
VOUT
VIN
RG
RF
FIGURE 3:
Inverting Gain Circuit.
These circuits have different DC gains (K) and a DC
noise gain (GN). GN can be defined to be the gain from
the input pins to the output set by the feedback
network. It is also useful in describing the stability of op
amp circuits. These gains are:
EQUATION 2:
K = 1 + RF ⁄ RG ,
K = –RF ⁄ RG ,
GN = 1 + RF ⁄ RG
noninverting
inverting
Note: Some applications do not have constant
GN due to reactive elements (e.g.,
capacitors). More sophisticated design
techniques, or simulations, are required in
that case.
The op amp feedback loop (RF and RG) causes its
closedloop behavior to be different from its openloop
behavior. Gain bandwidth product (fGBP) and open
loop output impedance (RO) are modified by GN to give
closedloop bandwidth (f3dBA) and output impedance
(ZOUT). We can analyze the circuits in Figure 1,
Figure 2 and Figure 3 to give:
EQUATION 3:
f3dBA ≈ fGBP ⁄ GN
ZOUT = 1+AORLO(s)⁄GN
Figure 4 shows ZOUT’s behavior. At low frequencies, it
is constant because the openloop gain is constant. As
the openloop gain decreases with frequency, ZOUT
increases. Past f3dBA, the feedback loop has no more
effect, and ZOUT stays at RO. The peaking at GN = +1
is caused by the reduced phase margin due to f2P.
1000
MCP6271
100
10
1
0.1
0.01
GN = +1
GN = +10
GN = +100
0.001
10..E1 1.1E+ 11.E0+ 11.0E0+ 11.Ek+ 11.0Ek+ 110.E0+k 11.EM+ 11.0EM+
01 00 01 F0re2que0n3cy (H0z4) 05 06 07
FIGURE 4:
MCP6271’s ClosedLoop
Output Impedance vs. Frequency.
Figure 5 shows a simple AC model that approximates
this behavior. The amplifier models the no load gain
and bandwidth, while the inductor and resistor model
the output impedance vs. frequency.
MCP6XXX
K
VIN 1 + s/ω3dBA
LOUT
ROUT
ZOUT
VOUT
FIGURE 5:
Model.
Simplified Op Amp AC
ROUT is larger than RO because it includes f2P’s phase
shift effects, which are especially noticeable at low gain
(GN). The equations for LOUT and ROUT are:
EQUATION 4:
LOUT = RO ⁄ (2πf3dBA)
ROUT ≈ max(1–f3dBRAO⁄f2P,1/2)
DS00884Bpage 2
© 2008 Microchip Technology Inc.

Uncompensated AC Behavior
This section shows the effect load capacitance has on
op amp gain circuits. These results help distinguish
between circuit that need compensation and those that
do not.
THEORY
Figure 6 shows a noninverting gain circuit with an
uncompensated capacitive load. The inverting gain
circuit is a simple modification of this circuit. For small
capacitive loads and high noise gains (typically
CL/GN < 100 pF), this circuit works quite well.
MCP6XXX
VIN VOUT
CL
RG RF
FIGURE 6:
Load.
Uncompensated Capacitive
The feedback network (RF and RG) also presents a
load to the op amp output. This load (RFL) depends on
whether the gain is noninverting or inverting:
EQUATION 5:
RFL = RF + RG ,
RFL = RF ,
noninverting gain
inverting gain
Replacing the op amp in Figure 6 with the simplified op
amp AC model gives an LC resonant circuit (LOUT and
CL). When CL becomes large enough, ROUTRFL does
a poor job of dampening the LC resonance, which
causes peaking and step response overshoot. This
happens because the feedback loop’s phase margin is
reduced by both f2P and CL.
A simplified transfer function is:
EQUATION 6:
Where:
VOUT
VIN
≈
K
⁄
⎛
⎜
⎝
1
+
ωPsQP
+
s2⎟⎞
ω P2 ⎠
GN = 1 + RF ⁄ RG
K = GN ,
noninverting
K = 1 – GN , inverting
ωP = 2πfP = 1 ⁄ LOUTCL
QP = (ROUT RFL) ⋅ CL ⁄ LOUT
AN884
We can now use the equations in Appendix A: “2nd
Order System Response Model” to estimate the
overall bandwidth (f3dB), frequency response peaking
(HPK/GN), and step response overshoot (xmax). Note
that f3dB is not the same as the op amp’s no load, 3dB
bandwidth (f3dBA).
MCP6271 EXAMPLE
The equations above were used to generate the curves
in Figure 7 and Figure 8 for Microchip’s MCP2671 op
amp. The parameters used are from TABLE B1:
“Estimates of Typical Microchip Op Amp Parame
ters”.
20
MCP6271
15 GN = +1
10
5
CL = 10 nF
CL = 1 nF
CL = 100 pF
CL = 10 pF
0
5
10
15
20
1.1E0+k04
11.E0+00k5 Frequ1e.E1nM+c0y6(Hz) 1.1E0+M07
11.E0+0M08
FIGURE 7:
Estimate of MCP6271’s AC
Response with GN = +1.
40
35
30
25
20
15
10
5
0
1.E10+k04
MCP6271
CL = 100 nF
GN = +10
CL = 10 nF
CL = 1 nF
CL = 100 pF
1.1E0+00k5
1.E1M+06
1.1E0+M07
Frequency (Hz)
11.E0+00M8
FIGURE 8:
Estimate of MCP6271’s AC
Response with GN = +10.
The peaking (HPK/GN) should be near 0 dB for the best
overall performance. Keeping the peaking below 3 dB
usually gives enough design margin for changes in op
amp, resistor, and capacitor parameters over
temperature and process. However, the performance is
degraded.
© 2008 Microchip Technology Inc.
DS00884Bpage 3

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