ETC AB-105

APPLICATION BULLETIN
®
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TUNING IN AMPLIFIERS
By Bonnie Baker
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Have you ever had the experience of designing an analog
gain block with an amplifier that is specified to be unity gain
stable only to find that it is oscillating out of control in your
circuit? Or have you ever replaced a stable voltage feedback
amplifier with a current feedback amplifier to find that the
current feedback amplifier immediately oscillates when
placed in the amplifier socket? Oscillation problems are a
nuisance to track down, particularly if there is no clear game
plan. When troubleshooting an oscillating amplifier circuit,
several questions come to mind, such as, has the feedback
loop been properly configured to insure stability? Have the
effects of loading the output of the amplifier been considered? Are the by-pass capacitors properly positioned on the
board in respect to the amplifier? Is the PCB layout executed
properly to avoid the ill effects of trace parasitics and crosstalk? This simple check-list with some general knowledge
about what determines amplifier stability, or lack thereof,
can help the designer identify oscillation problems and
implement effective, stable solutions.
applied. The selection of these components is dependent on
first and foremost the type of amplifier that is being used,
i.e., voltage feedback as opposed to current feedback amplifier. Once the amplifier type is known the stability equations
quickly fall out of simple calculations. Take, as an example,
an amplifier configured in a non-inverting circuit as shown
in Figure 1a. The amplifier is configured in a non-inverting
circuit where the low frequency gain is (1 + RF /RIN). Here,
RF and RIN are the low frequency equivalent impedance of
ZF and ZIN. In the case of Figure 1a, a voltage feedback
amplifier is used in the circuit. A current feedback amplifier
could be used instead while still achieving good circuit
stability.
The voltage feedback amplifier is the most prolific amplifier
on the market. Dependent on the characteristics of the
specific amplifier, they are used in high speed as well as
precision applications. Since the preferred frame of reference for most analog designers is the voltage feedback
amplifier, the stability analysis begins with the topology
shown in Figure 1a. This simplified block diagram illustrates many of the key characteristics needed in a frequency
analysis of the voltage feedback amplifier. Starting with the
input segment of the amplifier, the inputs to the voltage
When beginning the troubleshooting process, the first step
the designer should take determines whether or not the
resistors, capacitors and inductors that are used around the
amplifier’s input, feedback and output are appropriately
(a)
(b)
ZF
VOUT(s)
VIN(s)
CCM
–
=
(1 + ZF /ZIN)
1 + (1 + ZF /ZIN)/AOL(s)
GN
CC
Gain
VERR
CDIFF
+
VIN
+
VOUT
AOL(s)
AOL
OPA650
GN1
VERR
CCM
~20dB/decade
GN2
AOL(s) =
GDC
1 + rO CCs
, s = jw
VOUT = AOL(s) • VERR
VIN – VERR
ZIN
=
f1
f2
Frequency
VOUT – (VIN – VERR)
ZF
FIGURE 1a). The Model of a Voltage Feedback Amplifier Configured in a Non-Inverting Closed-Loop Configuration.
1b). Bode Plot Response of Various Closed-Loop Non-Inverting Systems Using a Voltage Feedback Amplifier.
©
1996 Burr-Brown Corporation
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VOLTAGE FEEDBACK AMPLIFIER ANALYSIS
DESIGNING AROUND THE AMPLIFIER
ZIN
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AB-105
Printed in U.S.A. October, 1996
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feedback amplifier are evenly matched. The input transistors
of this amplifier type could be bipolar (NPN or PNP), FET,
or CMOS, with the input differential capacitance and common-mode capacitance modeled as CDIFF and CCM, respectively. In most cases, the input bias currents are very close
to being the same magnitude and the difference between the
two input bias currents is usually small. Additionally, the
input impedances of the amplifier are close to equal and
relatively high. Input bias current can range from femto
amps, as in the case of the OPA129, to 100s of micro amps,
depending on the input transistors.
A small error voltage at the input of the amplifier is gained
by the open-loop gain, AOL(s), which is usually fairly high.
The open-loop gain is frequency dependent and starts rolling
off at a relatively low frequency. The resulting open-loop
voltage output is the product of the open-loop gain times the
input voltage error.
The voltage feedback amplifier can be analyzed across the
frequency spectrum in this non-inverting circuit. By using
the simple model shown in Figure 1, a second equation is
quickly derived from a nodal analysis. These calculations
assume there are no contributions to the frequency behavior
of the circuit from the input bias currents of the amplifier.
This is a good assumption for this small signal analysis in
the amplifier’s linear region.
The open-loop gain of the amplifier is modeled as a single
pole system, although there are typically multiple poles and
zeros at the higher frequencies. The single pole in the AOL(s)
equation represents the dominant pole. This formula is not
an accurate representation of the open-loop gain over the
entire frequency spectrum. Poles can be added to this transfer function with a capacitive or inductive load interacting
with the output resistance of the amplifier. In this example,
a single pole system is used to simplify the derivation. The
DC open-loop gain is symbolized with the variable, GDC.
The element, rO represents the effective impedance of the
open-loop gain equation. CC and rO are used to set the
frequency of the dominant pole.
Rigorous calculation of the transfer function reveals characteristics and limitations of the voltage feedback amplifier in
this closed-loop system.
As expected, the calculation in Figure 1b proves that the
closed-loop DC gain is equal to 1 + RF /RIN. At low frequencies the open-loop gain of the amplifier is sufficiently high
to allow for ignoring the gain error. As frequency increases,
AOL(s) begins to decrease and finally becomes the dominant
controlling factor in the gain of the circuit. The calculation
of the intersection of the open-loop gain, AOL(s) and the
noise gain (also called 1/β), GN = (1 + ZF /ZIN), gives a close
approximation to the bandwidth of the closed-loop amplifier
circuit. In the case of the OPA650 wideband, voltage feedback amplifier, the extrapolated zero crossing of the openloop gain is typically 180MHz and the DC open-loop gain is
typically 50dB. If ZF and ZIN are both equivalent to 402Ω,
the signal bandwidth of the circuit would be a theoretical
90MHz.
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Gain peaking, which is caused by the phase response of the
amplifier and the feedback circuit, can increase the bandwidth of the closed-loop system at the expense of decreased
stability. The criteria for stability is determined where the
closed-loop noise gain intersects the open-loop gain of the
amplifier. Generally, if the phase margin, at that frequency,
is smaller than a theoretical 45 degrees, the circuit can
oscillate given part-to-part variation. A conservative phase
margin is more like 60 degrees for flat frequency response.
The transfer function of the voltage feedback amplifier in a
non-inverting configuration is shown graphically in Figure
1b. The open-loop gain plot of the amplifier assumes a
single pole system. Although this is not totally realistic, the
generalization of closed-loop gain versus closed-loop bandwidth shown here is still true. As the closed-loop gain
increases, the closed-loop bandwidth decreases. The circuit
designer needs to take this characteristic under consideration
when selecting the right amplifier for his application.
Matched inputs may or may not be a benefit when using
voltage feedback amplifiers. The high impedance can be a
saving grace at times when line termination is otherwise
difficult. In addition, offset voltages and offset currents are
relatively low compared to the current feedback amplifier
topology. A possible disadvantage of the voltage feedback
amplifier is the intimate relationship between the bandwidth
and closed-loop gain.
CURRENT FEEDBACK AMPLIFIER ANALYSIS
The current feedback amplifier’s block diagram in Figure 2a
illustrates how this amplifier differs from the voltage feedback amplifier. The inputs to the current feedback amplifier
are not matched, consequently the input bias currents are
different along with the input impedances. Typically, the
current feedback amplifier’s input bias current is in the
micro ampere region. The ratio between the input bias
currents is dependent on the current feedback input stage
topology and can vary from ±2X to 5X. In the case of the
OPA658, the inverting input bias current is ±35mA(max)
and the non-inverting input bias current is ±30mA(max).
The inverting input generally has a higher input bias current
magnitude and very low input resistance (ideally zero) as
compared to the non-inverting input. On the other hand, the
non-inverting input is buffered, having a high impedance.
The buffer’s gain is approximately +1V/V and its bandwidth
is significantly wider than the bandwidth of the remaining
internal stages of the amplifier.
A small error current from the inverting input of the current
feedback amplifier is gained by the open-loop transimpedance
of the amplifier, Z(s), which is usually fairly high. The
resulting open-loop output voltage of the current feedback
amplifier is the product of the open-loop transimpedance
(Z(s)) times the input current error (IERR).
The current feedback amplifier can also be used in the noninverting circuit. By using the simple model shown in
Figure 2, a nodal analysis reveals a second equation. This
calculation assumes there are no contributions to the fre-
(a)
ZIN
(b)
ZF
VOUT(s)
VIN(s)
–
RS
IERR
≈1
Gain
Z(s)
+1
α(1 + ZF / ZIN)
1 + (ZF + RS (1+ ZF / ZIN)) / Z(s)
>>20dB/decade
VOUT
IERR
G1
VIN
G2
OPA658
+
=
G3
Z(s) =
RT
1 + RT CTs
, s = jw
VOUT = IERR • Z(s)
VIN
ZIN
=
VOUT – VIN
ZF
f1,f2,f3
Frequency
+ IERR
FIGURE 2a). The Model of a Current Feedback Amplifier Configured in a Non-Inverting Closed-Loop Configuration.
2b). Bode Plot Response of Various Closed-Loop Non-Inverting Systems Using a Current Feedback Amplifier.
quency behavior of the circuit from the input offset voltage
or buffer stage of the amplifier. Since this analysis assumes
the amplifier is operating in its linear region and this is a
small signal analysis, these are good assumptions.
where α represents the gain of the input buffer, which is
typically +0.996V/V as opposed to +1V/V. RS represents the
non-zero output impedance of the input buffer, which ranges
from 10 to 40Ω depending on the particular amplifier used.
The open-loop transimpedance of the amplifier is modeled
as a single pole system. The single pole in the equation on
the slide represents the dominant pole. This formula is not an
accurate representation of the open-loop transimpedance
over the entire frequency spectrum, however, it is adequate
for purposes of this discussion. The DC open-loop
transimpedance is symbolized with the variable, RT where
CT and RT are used to derive the dominant pole for the openloop transimpedance gain.
From this formula, it is easy to see the limitations on the
current feedback amplifier’s frequency response performance.
Because of the effects of RS, the closed-loop bandwidth does
vary slightly with changes in ZIN, however, the bandwidth
and stability is more dependent on the feedback impedance,
ZF, particularly with lower closed-loop gains.
The current feedback amplifier is easier to design with than
the voltage feedback amplifier as long as the correct feedback impedance is selected. The bandwidth and stability of
the current feedback amplifier in a closed-loop configuration
is dependent and adjustable with the feedback element. If the
wrong feedback impedance is used, the amplifier circuit
could oscillate.
Rigorous calculation of the transfer function reveals characteristics and limitations of the current feedback amplifier in
this closed-loop system.
The DC gain of this circuit is the same regardless of whether
a current feedback or voltage feedback amplifier is used.
The bandwidth for the closed-loop response, when a current
feedback amplifier is used, is dependent principally on the
feedback resistor, ZF, in conjunction with the transimpedance
of the amplifier. The resistor, ZIN , has minimal effect on the
bandwidth. This fundamental difference in the closed-loop
response between the two amplifier topologies allows for
each to have an advantage or disadvantage, as the case may
be, dependent on the circuit topology selected.
BY-PASS, BY-PASS, BY-PASS (Effectively)
By-pass capacitors are an absolute necessity in analog circuits. The selection of the proper capacitors and placement
could be as critical as insuring that the amplifier circuit is
designed for stability. Capacitors that are used to by-pass
power supplies must satisfy two important criteria: 1) filter
out high frequency noise from the power supplies, 2) serve
as a charge reservoir to deliver high frequency load current.
These two tasks can only be accomplished by using two
capacitors as opposed to one.
The transfer function of the closed-loop system shown in
Figure 2 is:
The first capacitor type mentioned above should be selected
to filter out higher frequency noise from the power supply at
the frequencies where the analog amplifier’s power supply
rejection is not good enough and the amplifier still has ample
α(1+ Z F / Z IN )
V OUT (s)
=
V IN (s) 1 + (Z F + R S (1 + Z F / Z IN )) / Z(s)
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open-loop gain. Appropriate values for this function is dependent on the amplifier and typically range from 0.01µF up to
1µF. A good by-pass value for the OPA130, which is a unity
gain stable, 1MHz bandwidth device, would be 0.1µF. Ceramic capacitors most appropriately serve this need as long as
they are positioned as close to the amplifier as possible.
References
1996 Design Seminar, Burr-Brown Corporation, LI-477.
Voltage-Feedback Amplifiers vs Current-Feedback Amplifiers: Bandwidth and Distortion Considerations, Application Bulletin, AB-091,
Tony Wang, Burr-Brown Corporation.
OPA678 Product Data Sheet, PDS-1136, Burr-Brown Corporation.
The second capacitor used in the circuit can provide a reservoir of charge for more than one amplifier in the circuit and
can be positioned a few inches away from the amplifier on the
board. Tantalum capacitors are a good choice for this function
and typical values range from 1µF to 10µF depending on the
circuit requirements.
LAYOUT DESIGNED FOR SUCCESS
Layout can make or break a circuit just as much as poor
design or improper by-passing techniques. Some basic guidelines for analog amplifier for layout are as follows:
1. Use a heavy copper ground plane on the component side of
the PC board to provide low inductance ground.
2. By-pass power supply pins directly at the active device.
Supply pins should not be left un-by-passed.
3. Signal paths should be short and direct. Passive components should have short lead lengths.
4. Parasitic inductance and capacitance should be avoided
particularly in high frequency circuits.
5. Capacitive loads can causes loop instability if not compensated for.
6. Terminate transmission loads in high speed circuits.
Unterminated lines can appear to the amplifier as a capacitive or inductive load. By terminating a transmission line
the characteristic impedance will appear as purely resistive.
7. Plug-in prototype boards and wire-wrap boards become
less and less satisfactory as the signal frequencies increase.
Use these breadboards with caution.
Analog circuit oscillation problems can be overcome with
careful thought up front in the design process. Oscillation
problems are difficult to solve, particularly if there is no clear
troubleshooting guide. In order to reduce the chances of
oscillations from the beginning, the checklist should include
design stability techniques, proper by-passing and appropriate
board layout methods. This simple checklist with some general knowledge about what determines amplifier stability, or
lack thereof, can help the designer identify oscillation problems and implement a stable amplifier circuit.
The information provided herein is believed to be reliable; however, BURR-BROWN assumes no responsibility for inaccuracies or omissions. BURR-BROWN assumes
no responsibility for the use of this information, and all use of such information shall be entirely at the user’s own risk. Prices and specifications are subject to change
without notice. No patent rights or licenses to any of the circuits described herein are implied or granted to any third party. BURR-BROWN does not authorize or warrant
any BURR-BROWN product for use in life support devices and/or systems.
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