Balancing GBWP and quiescent current for dissipation optimization
Minimizing power dissipation in analog applications requires a careful balance between GBWP and quiescent current.
Namrata Pandya, Microchip Technology Inc -- EDN, February 2, 2012
Although conceptually simple, operational amplifiers implement parametrically complex circuits that can pose numerous challenges to IC selection. Digital circuits dominate the power budgets of many familiar mains-powered system designs, and analog subsystems represent only a small fraction of the total dissipation. In these cases, your top priority for operational-amplifier selection is likely one or more signal-chain performance parameters. These parameters might include ac terms, such as distortion and broadband noise, or dc terms, such as input offset and offset drift.In energy-constrained applications for which you must wring out every last bit of unnecessary power dissipation, however, the temptation is to start by looking for the operational amplifier with the lowest quiescent current. Unfortunately, this intuitively reasonable approach all too often identifies numerous candidates that meet the application’s power requirement but not necessarily its GBWP (gain-bandwidth-product) needs.
For a given circuit topology, GBWP and quiescent current go hand in hand—essentially in direct proportion. The reasons for this behavior are several and involve the detailed topology of specific amplifiers. At the top level, however, consider that the operational amplifier you choose must charge and discharge internal capacitances at signal speed. The resulting displacement currents flow from the internal bias current of the amplifier, which determines the net quiescent current. Therefore, for a given topology, as bandwidth increases, the amplifier’s quiescent current must also increase.
A helpful figure of merit
The challenge for low-power design, then, is not simply to find low-power operational amplifiers but to find those that most efficiently provide bandwidth. A simple figure of merit to assess operational-amplifier bandwidth efficiency is the ratio of GBWP to quiescent current.
For example, a performance comparison and figure-of-merit
calculation for four devices of similar architecture—the Microchip MCP644X, MCP640X, MCP628X, and
MCP629X—shows a figure of merit that varies barely more than an octave, whereas the GBWP and quiescent current
vary by a little more than three orders of magnitude (Table
1 and references 1 through 3). Indeed, at the lower bandwidths,
the figure of merit for these devices is nearly constant.In practice, your selection process will focus, of course, on competing devices of similar GBWP—not a group covering several orders of magnitude. First, though, you must determine one key factor.
How much is enough?
The GBWP is an indication of an amplifier’s open-loop gain
as a function of frequency. The amplifier’s Bode plot, which
virtually all op-amp data sheets include, provides both the
open-loop and the phase responses versus frequency and is
a handy graphical tool for quickly assessing an amplifier’s
potential in your application. In this case, you need to
consider only the open-loop-gain component of the Bode
plot (Figure 1).Note that the open-loop dc-gain level extends only to very small frequencies before the amplifier’s dominant pole starts to roll off the open-loop-gain curve at a rate of 20 dB per decade. For most of the amplifier’s bandwidth, open-loop gain falls by a factor of 10 for every factor-of-10 increase in frequency. The product of gain and frequency at any point along this part of the curve, then, is a constant: GBWP.
When you choose the dc closed-loop gain of a noninverting-gain op-amp circuit, closed-loop bandwidth is approximately GBWP divided by dc closed-loop gain. For example, using the MCP644X, you might expect that you could take a gain of 100 and see a useful bandwidth of 90 Hz (Figure 2), as the following equations show:
The gain over frequency, which derives directly from Black’s formula (Reference 5), is expressed as
Loop transmission is the ratio of the open-loop gain to
the ideal closed-loop gain. As the loop transmission increases,
the gain in the first equation approaches the ideal gain in
the third equation. The loop transmission greatly influences
essentially all of the operational amplifier’s closed-loop
behaviors, including gain accuracy, linearity, distortion, output impedance, and, most notably, sensitivity to the
value of open-loop gain, which is not a tightly controlled
parameter (Figure 3).
As you push for lower and lower quiescent current, then,
you must be more careful in assessing your circuit’s GBWP
requirements to prevent degradation of your circuit’s performance.
As your application’s gain-accuracy requirement
grows, so does the loop-transmission requirement.As a general rule of thumb, you should ensure a minimum loop transmission of 10, which equals 20 dB, meaning that the open-loop gain is at least 10 times the forward, or closed-loop, gain. This limit keeps the gain error less than −1 dB, which suffices for most ac signal-processing applications. For more precise circuits, loop transmission of 100, or 40 dB, yields a gain error of only −1%, or −0.086 dB. Precision circuits, such as those for metrology applications, require even greater loop transmission. You can calculate the forward gain error as a function of loop transmission:
As figures 3 and 4 indicate, as signal frequency increases,
the amount of loop transmission falls off, due to the
downward trajectory of open-loop gain. As the flat dc-gain
plot approaches the open-loop-gain curve, the operational
amplifier’s performance begins to degrade.
A simple method of maintaining a fixed-loop transmission
is to add a single-pole lowpass filter to the amplifier’s
forward-transfer function (figures 5 and 6). This approach
will cost you only one capacitor and prevents the amplifier’s linearity, distortion, and dynamic-output impedance
from increasing at the upper end of the circuit’s bandwidth—important terms if you want the amplifier to feed,
for example, an ADC.In this example, an amplifier has a GBWP of 9 kHz, and
the application requires a gain factor of 100. The minimum
loop-transmission factor is 10. Multiplying these factors
yields the maximum signal bandwidth, which is a factor
of 1000 smaller than the GBWP, or 9 Hz. This value is a
factor of 10 below the 90 Hz that the first equation calculates
because that equation does not take into account the
selected loop transmission.
You often start your amplifier-selection process knowing the signal bandwidth, a forward gain, and a maximum gain-error requirement. From these data, you can calculate the required GBWP in two steps. First calculate the loop transmission from your maximum gain-error tolerance:
Beating the numbers
Consider a low-power application that requires a signal bandwidth of 20 kHz, a gain of 25, and a loop-transmission factor of 10. Multiplying these factors yields a GBWP of 5 MHz. Assume further that the MCP640X operational amplifier in Table 1 would be attractive with its GBWP/quiescent current figure of merit of 0.022, were it not for the fact that its GBWP does not meet the requirement. If you could find a faster amplifier with the same gain-bandwidth efficiency, then you could expect it to draw 225 μA—five times the current of the MCP640X for five times the bandwidth.
This scenario sounds good. Unfortunately, however, amplifier vendors don’t offer models with every conceivable GBWP, and different amplifier families use different topologies. Therefore, they offer different GBWP/quiescent-current figures of merit. If available amplifiers included only those in Table 1, your next stop would be the 5-MHz MCP628X, drawing 445 mA, which provides excellent performance but more than your application needs.
If power-dissipation optimization is a high priority, a small increase in circuit complexity can allow you to beat the numbers, in effect, by forming an amplifier that you can’t buy. Cascading two operational amplifiers provides a total gain that is the product of the individual stages but that draws current that is only the sum of the two amplifiers.
A cascade of two gain-of-five stages meets this application’s
gain requirements (Figure 7). The total quiescent
current for the circuit is 90 μA—an 81% savings over the
higher-current amplifier and a 60% savings over the hypothetical
5-MHz amplifier called for in the original analysis.
Many analog-signal-processing applications require only intermittent operation. For example, an ambient-light monitor requires only a fraction of a second to take a measurement, digitize the data, and transmit the data to a host processor. The data-density requirement for such a device may not demand continuous monitoring. It may perhaps require only one observation every couple of seconds. Between measurements, the system can disable the monitoring circuit to save power.
For example, if a light monitor can make, digitize, and transmit a measurement in, say, 10 msec and needs to do so, say, every 2 sec, then the measurement circuits can operate with a duty cycle of 0.5%. Neglecting leakage currents, this approach can reduce the average quiescent current by a corresponding factor of 200. You can implement the duty-cycle operation of operational amplifiers under digital control in one of two ways. You can power the amplifiers through an interruptible energy source, or you can use amplifiers that feature an enable pin.
Interruptible power sources come in three varieties,
depending on how much load current they must provide. For high-current applications, a power
converter or a regulator that features an
enable pin can isolate a block of circuitry.
For low-load currents, you can power a
block directly from a microcontroller’s
I/O pin, thereby eliminating the dedicated
power converter or regulator. For other
cases, you can use a microcontroller’s I/O
pin to control a pass element, such as a
discrete PMOS transistor.Whichever way you choose to power the circuit block, be sure to check the off-state leakage current of the block’s energy source and include that term in your power budget. This step is particularly important when powering circuits from small batteries or from energy-harvesting or -scavenging technologies.
The advantage of this approach is that you can use any amplifiers you want in the power-controlled block. The disadvantage is that it may be difficult to determine the time that the system must wait between powering up the block and using the settled accurate output of the analog subsystem.
The alternative is to use amplifiers that feature enable pins that turn off the amplifier, not just its output. These devices usually specify their turn-on time and can greatly enhance circuit efficiency by eliminating the need to pad your turn-on-time estimate.
Acknowledgment
This article originally appeared on EDN’s sister site, Planet Analog.
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Author’s biography
Namrata Pandya is a product-marketing engineer for the analog- and interface-products division of Microchip Technology Inc (Chandler, AZ). She is responsible for the strategic marketing of operational amplifiers, as well as tactical-marketing support for Microchip’s analog and interface products in the South Pacific and Association of Southeast Asian Nations. Before joining Microchip in 2007, Pandya spent two years with Cypress Semiconductor (San Jose, CA) in product marketing. She earned a bachelor’s degree in electrical engineering from Mumbai University (Mumbai, India) in August 2001 and a master’s degree in electrical engineering from San Jose State University (San Jose, CA) in December 2006.
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