Instructions
DISCLAIMER: For educational purposes only.
Condensed from the Analog Dialogue article
by Grayson King
Usually, driving large capacitive loads is not a matter of choice: most
often it's an unwanted parasitic, such as the capacitance of a length of
coaxial cable. However, situations do arise where it's desirable to decouple a
dc voltage at the output of an op amp-for example,when an op amp is used to
invert a reference voltage and drive a dynamic load. In this case, you might
want to place bypass capacitors directly on the output of an op amp. Either
way, a capacitive load affects the op amp's performance.
In fact, load capacitance can turn your amplifier into an oscillator. Op
amps have an inherent output resistance, Ro, which, in conjunction
with a capacitive load, forms an additional pole in the amplifier's transfer
function. As the Bode plot shows, at each pole the amplitude slope becomes more
negative by 20 dB/ decade. Notice how each pole adds as much as -90° of
phase shift. We can view instability from either of two perspectives. Looking
at amplitude response on the log plot,circuit instability occurs when the sum
of open-loop gain and feedback attenuation is greater than unity. Similarly,
looking at phase response, an op amp will tend to oscillate at a frequency
where loop phase shift exceeds -180°, if this frequency is below the
closed-loop bandwidth. The closed-loop bandwidth of a voltage-feedback op amp
circuit is equal to the op amp's bandwidth product (GBP, or unity-gain
frequency), divided by the circuit's closed loop gain (ACL).
Phase margin of an op amp circuit can be thought of as the amount of
additional phase shift at the closed loop bandwidth required to make the
circuit unstable (i.e., phase shift + phase margin = -180°). As phase
margin approaches zero, the loop phase shift approaches -180° and the op
amp circuit approaches instability. Typically, values of phase margin much less
than 45° can cause problems such as "peaking" in frequency response, and
overshoot or "ringing" in step response. In order to maintain conservative
phase margin, the pole generated by capacitive loading should be at least a
decade above the circuit's closed loop bandwidth. When it is not, consider the
possibility of instability.
The first step in managing potential instability is to determine whether the
op amp can safely drive the load on its own. Many op amp data sheets specify a
"capacitive load drive capability". Others provide typical data on
"small-signal overshoot vs. capacitive load". In looking at these figures,
you'll see that the overshoot increases exponentially with added load
capacitance. As it approaches 100%, the op amp approaches instability. If
possible, keep it well away from this limit. Also notice that this graph is for
a specified gain. For a voltage feedback op amp, capacitive load drive
capability increases proportionally with gain. So aVF op amp that can safely
drive a 100-pF capacitance at unity gain should be able to drive a 1000-pF
capacitance at a gain of 10.
A few op amp data sheets specify the open loop output resistance
(Ro), from which you can calculate the frequency of gain-the added
pole as described above. The circuit will be stable if the frequency of the
added pole (fP) is more than a decade above the circuit's
bandwidth.
If the op amp's data sheet doesn't specify capacitive load drive or open
loop output resistance, and has no graph of overshoot versus capacitive load,
then to assure stability you must assume that any load capacitance will require
some sort of compensation technique. There are many approaches to stabilizing
standard op amp circuits to drive capacitive loads. Here are a few:
Noise-gain manipulation: A powerful way to maintain
stability in low-frequency applications-often overlooked by designers-involves
increasing the circuit's closed-loop gain (a/k/a "noise gain") without changing
signal gain,thus reducing the frequency at which the product of open-loop gain
and feedback attenuation goes to unity. Some circuits to achieve this, by
connecting RD between the op amp inputs, are shown below. The "noise gain" of
these circuits can be arrived at by the given equation.
Since stability is governed by noise gain rather than by signal gain, the
above circuits allow increased stability without affecting signal gain. Simply
keep the "noise bandwidth" (GBP/ANOISE) at least a decade below the
load generated pole to guarantee stability.
One disadvantage of this method of stabilization is the additional output
noise and offset voltage caused by increased amplification of input-referred
voltage noise and input offset voltage. The added dc offset can be eliminated
by including CD in series with RD, but the added noise is
inherent with this technique. The effective noise gain of these circuits with
and without CD are shown in the figure.
CD, when used, should be as large as feasible; its minimum value
should be 10 ANOISE/(2 pRDGBP) to keep the "noise pole"
at least a decade below the "noise bandwidth".
Out-of-loop compensation: Another way to stabilize an op
amp for capacitive load drive is by adding a resistor, RX, between the op amp's
output terminal and the load capacitance, as shown below. Though apparently
outside the feedback loop, it acts with the load capacitor to introduce a zero
into the transfer function of the feedback network, thereby reducing the loop
phase shift at high frequencies.
To ensure stability, the value of RX should be such that the
added zero (fZ) is at least a decade below the closed loop bandwidth
of the op amp circuit.With the addition of RX,circuit performance
will not suffer the increased output noise of the first method, but the output
impedance as seen by the load will increase. This can decrease signal gain, due
to the resistor divider formed by RX and RL. If
RL is known and reasonably constant, the results of gain loss can be
offset by increasing the gain of the op amp circuit.
This method is very effective in driving transmission lines. The values of
RL and RX must equal the characteristic impedance of the
cable (often 50ohms or 75ohms) in order to avoid standing waves. So
RX is pre-determined, and all that remains is to double the gain of
the amplifier in order to offset the signal loss from the resistor divider.
Problem solved.
In-loop compensation: If RL is either unknown or
dynamic, the effective output resistance of the gain stage must be kept low. In
this circumstance, it may be useful to connect RX inside the overall
feedback loop, as shown below. With this configuration, dc and low-frequency
feedback comes from the load itself, allowing the signal gain from input to
load to remain unaffected by the voltage divider, RX and
RL.
The added capacitor, CF, in this circuit allows cancellation of
the pole and zero contributed by CL. To put it simply, the zero from
CF is coincident with the pole from CL, and the pole from
CF with the zero from CL. Therefore, the overall transfer
function and phase response are exactly as if there were no capacitance at all.
In order to assure cancellation of both pole/ zero combinations, the above
equations must be solved accurately. Also note the conditions; they are easily
met if the load resistance is relatively large.
Calculation is difficult when RO is unknown. In this case, the
design procedure turns into a guessing game-and a prototyping nightmare.A word
of caution about SPICE:SPICE models of op amps don't accurately model open-loop
output resistance (RO); so they cannot fully replace empirical design of the
compensation network.
It is also important to note that CL must be of a known (and
constant) value in order for this technique to be applicable. In many
applications, the amplifier is driving a load "outside the box," and
CL can vary significantly from one load to the next. It is best to
use the above circuit only when CL is part of a closed system.
One such application involves the buffering or inverting of a reference
voltage, driving a large decoupling capacitor. Here, CL is a fixed
value, allowing accurate cancellation of pole/zero combinations. The low dc
output impedance and low noise of this method (compared to the previous two)
can be very beneficial. Furthermore, the large amount of capacitance likely to
decouple a reference voltage (often many microfarads) is impractical to
compensate by any other method.
All three of the above compensation techniques have advantages and
disadvantages. You should know enough by now to decide which is best for your
application. All three are intended to be applied to "standard", unity gain
stable, voltage feedback op amps. Read on to find out about some techniques
using special purpose amplifiers.
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