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 ampfor 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, R_{o}, 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 openloop 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 closedloop bandwidth. The closedloop bandwidth of a voltagefeedback op amp
circuit is equal to the op amp's bandwidth product (GBP, or unitygain frequency),
divided by the circuit's closed loop gain (A_{CL}).
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 "smallsignal 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 100pF capacitance at unity gain should be able to drive a 1000pF capacitance
at a gain of 10.
A few op amp data sheets specify the open loop output resistance (R_{o}),
from which you can calculate the frequency of gainthe added pole as described above.
The circuit will be stable if the frequency of the added pole (f_{P}) 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:
Noisegain manipulation: A powerful way to maintain stability in
lowfrequency applicationsoften overlooked by designersinvolves increasing the
circuit's closedloop gain (a/k/a "noise gain") without changing signal gain,thus
reducing the frequency at which the product of openloop 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/A_{NOISE}) 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 inputreferred voltage noise
and input offset voltage. The added dc offset can be eliminated by including C_{D}
in series with R_{D}, but the added noise is inherent with this technique.
The effective noise gain of these circuits with and without C_{D} are shown
in the figure.
C_{D}, when used, should be as large as feasible; its minimum value should
be 10 A_{NOISE}/(2 pR_{D}GBP) to keep the "noise pole" at least
a decade below the "noise bandwidth".
Outofloop 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 R_{X} should be such that the added zero
(f_{Z}) is at least a decade below the closed loop bandwidth of the op amp
circuit.With the addition of R_{X},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 R_{X} and R_{L}. If R_{L} 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 R_{L}
and R_{X} must equal the characteristic impedance of the cable (often 50ohms
or 75ohms) in order to avoid standing waves. So R_{X} is predetermined,
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.
Inloop compensation: If R_{L} 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 R_{X} inside the overall feedback loop, as shown
below. With this configuration, dc and lowfrequency feedback comes from the load
itself, allowing the signal gain from input to load to remain unaffected by the
voltage divider, R_{X} and R_{L}.
The added capacitor, C_{F}, in this circuit allows cancellation of the pole
and zero contributed by C_{L}. To put it simply, the zero from C_{F}
is coincident with the pole from C_{L}, and the pole from C_{F}
with the zero from C_{L}. 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 R_{O} is unknown. In this case, the design
procedure turns into a guessing gameand a prototyping nightmare.A word of caution
about SPICE:SPICE models of op amps don't accurately model openloop output resistance
(RO); so they cannot fully replace empirical design of the compensation network.
It is also important to note that C_{L} 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 C_{L} can vary significantly from
one load to the next. It is best to use the above circuit only when C_{L}
is part of a closed system.
One such application involves the buffering or inverting of a reference voltage,
driving a large decoupling capacitor. Here, C_{L} 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.
