Log and limiting amps tame rowdy
communications signals
Bill Schweber - August 19, 1999
Engineers usually spend lots of time designing amplifiers that are linear to maintain
signal waveshape and dynamics throughout the signal chain. But the laws of physics make that goal
difficult in some situations, putting signals with 50 to 100 dB of dynamic range into the system. This
span forces designers to abandon the linear-amplifier model. Instead, your challenges are to avoid
signal-chain overload and to extract useful information from the signal.
Even these wide-dynamic-range applications have their differences. In some cases, the RF signal's
relatively low-frequency envelope is of interest, as you use its value to adjust receiver gain or
transmitter output level. Or, this signal represents a modulating waveform. In other situations, such
as radar-signal echo processing or fiber-optic receiver front ends, the system must demodulate an
amplitude-shift-keyed waveform to determine the absence or presence of a valid digital signal. In
these applications, the signal's amplitude is not of interest, but the signal's existence is. And, if its
existence is all that you're interested in, you may be able to use a basic limiting amplifier.
Select different types of logs
The output voltage of the logarithmic amp is proportional to the input-signal power—usually
expressed in decibels referred to 1 mW—reflecting the historical use of these amps in receiver signal
processing. Although a log amplifier is mathematically a simple function to express, commercial log
amps have several variations. These variations are due, in some part, to the virtues and limitations of
available technologies and are changing as IC process technology advances.
The detector log video amplifier (DLVA) detects the envelope of an RF signal using a linear-response
diode detector and then compresses the detector output in a subsequent video-bandwidth amplifier
stage to approximate a logarithmic transfer function. The DLVA has a wide operating-frequency
range—nearly 10 GHz, depending on the model—but a relatively limited dynamic range of about 30
to 40 dB. Some techniques, such as using two DLVAs in parallel (one with a preamp), can extend the
dynamic range to about 70 dB. The gain-bandwidth product of the video-amplifier section is a major
factor in DLVA performance because it affects rise time, recovery time, and sensitivity.
The successive detection log (video) amplifier (SDLA or SDLVA) offers a different approach. Here,
the amplifier uses an array of RF compression stages to replicate the desired transfer function. Each
stage, typically with 10 dB of dynamic range, couples to its own linear detector, and the outputs of
these detectors combine in a single video-amp stage to provide the output. With the SDLA/SDLVA,
the vendor can choose the dynamic range and dynamic performance of each stage to achieve a good
compromise in overall performance; by using enough stages in the array, it's possible to achieve
dynamic ranges greater than 100 dB with this architecture.
A third choice is the true log amplifier (TLA), which is the closest you'll get to implementing a pure
log function as a single-stage black box (see sidebar "It's not as easy as falling off a log"). The output
of the TLA is the input RF signal compressed by a log scale, and this output has both the amplitude
and phase information of the input, rather than just its envelope. For this reason, the TLA is often
useful in audio-band applications, such as sonar, in which amplitude and phase convey necessary
information.
The apparent simplicity of the logarithmic-amp I/O transfer functions obscures a basic fact: They
have a different set of terms and parameters, as well as figures of merit, than linear-amplifier
functions have (see sidebar "Clear up log confusion").
If you're interested only in determining whether a valid signal is present despite a range of possible
input values—so you can make a basic assessment—you may need to use a limiting amplifier. Unlike
a log amp, which implements a smooth but nonlinear mathematical function, the limiter is a gain
function that boosts all signals to a maximum output value (Figure 1); in some cases, this value can
be as much as 50 to 100 dB. By its design, the limiting amp destroys amplitude information, but it
preserves phase, frequency, and timing information, which is what you need when you're recovering
pulse-based information. Pulse-based information includes that in a fiber-optic link or in phase- and
frequency-modulated waveforms.
By itself, providing a high-gain function is not much of a challenge for an amplifier. The real problem
is that the output of any conventionally designed linear amplifier saturates when the input times the
gain achieves the maximum output value of the amplifier. Once it saturates, the amp takes a
relatively long time to discharge internally and to revert to a nonsaturated mode. During this time,
the amplifier is useless.
To overcome this saturation and consequential recovery-time problem, a limiter amp employs special
circuitry that gracefully transitions to its maximum value as the input signal begins to saturate the
output. Although the limiter output reaches its maximum, it never goes into debilitating saturation.
Instead, the limiting circuitry ensures that the output is at a maximum but does not get overdriven
despite the high gain. You can also think of a limiting amp as a high-gain block for signals reaching a
certain magnitude, but the amp automatically switches to unity or less-than-unity gain for signals
with magnitude near its maximum value.
Another fundamental difference exists between a log amp and a limiting amp. A log amp performs a
mathematical function, so there is a one-to-one mapping between input and output. You can, if you
wish, perform the antilog function to go back to the original signal; antilog-function modules are
commercially available, or you can configure one from some log amps. In contrast, the limiting
operation is not a mathematical function—although many people casually refer to it as such—and
you can't go back to your original-signal value after the limiter. This fact is not a problem, though,
because there is rarely a need for you to go back to this value.
Ironically, although the log function and the limiter are mathematically quite different, many log
amps also have a limiting output as a consequence of their design. In effect, you get both the log
amp and the limiting output for the price of one device, and you may need to use both in your system
architecture. For example, you can use the log output as a received-signal-strength indicator (RSSI)
or to control transmit power, while the limiter output can go to a phase detector or demodulator.
Internally, the log amp is inherently more complex and sophisticated than the limiter. The log amp
requires the IC designer to pay more attention to subtle error sources, such as temperature,
process, layout-crosstalk and -noise, and other variations. As a result, you see high-performance,
wide-dynamic-range log amps as stand-alone ICs and hybrid modules but not as part of larger, more
integrated ICs. In contrast, manufacturers often build limiter circuitry into analog front ends and
even mixed-signal ICs, achieving performance that is commensurate with the application.
Putting those logs to use
Because of their relatively esoteric function, their relatively high costs, the somewhat finicky
performance of earlier log amps, and the practical difficulties of successfully using any component
over an 80- to 100-dB dynamic range, log amplifiers have been limited to specific applications, such
as radar systems and some specialized communications links. Mass-market applications just didn't
need these amps or couldn't use them effectively except for RSSI or AGC functions over a limited
range and accuracy. In contrast, limiting amps have had much broader use but usually required
frequencies around only 100 MHz. (Recall the FM receiver, which had a limiter performing a key
circuit function, that Major EH Armstrong developed in the 1930s.)
This relatively narrow focus has changed with the advent of cellular systems. CDMA and Global
System for Mobile communications systems need to adjust their base-station power output to match
the distance to the target handsets and local conditions over 60 dB or more of power. This dynamic
power adjustment reduces the possibility that the base station will overload nearby handsets and
also reduces base-station power consumption and thermal loading. Similarly, the base station needs
the wide-ranging RSSI function to adjust re- ceived-channel gain and so maximize SNR and minimize
bit-error rate (BER) without using excessive gain, which may result in channel overload.
Log in with vendor offerings
Historically, the impetus for many wide-range, wide-band log amps came primarily from military and
aerospace applications. Vendors who dominated these markets still produce a range of logarithmic
amps in various configurations—often as enclosed, shielded assemblies complete with cable
connectors—in addition to a few pc-board-mount packages. Because these vendors generally use
hybrid technology as well as monolithic-microwave ICs (MMICs), they can customize or tune their
catalog designs to meet your specification combinations.
For example, Menlo Industries (www.menloindustries.com) offers DLVAs and SDLVAs for
frequencies from a mere 500 MHz to 18 GHz and dynamic range as high as 75 dB. The company's
MSDA-4816 SDLVA covers the 6- to 18-GHz range, with typical log linearity of ±1.2 dB. Rise time
and fall time are 10 and 20 nsec, respectively, and log slope is nominally 25 mV/dB.
Similarly, Miteq Corp (www.miteq.com) has standard and extended dynamic-range DLVAs operating
as high as 8 GHz. The company designed its extended-range FBLA-1.0/2.0-70BC unit for operation
from 1 to 2 GHz, with 65-dB dynamic range. Log slope is 20 mV/dB, and log linearity is ±1 dB. This
unit is specified over the –20 to +90°C range and features extensive specifications for many of its
first- and second-order operating parameters.
But IC makers haven't ignored the log market, either, and are even finding new applications for
older, still-useful parts. Burr-Brown's (www.burr-brown.com) LOG100 14-lead ceramic DIP handles a
six-decade input range of 1 nA to 1 mA and provides basic log output, as well as the log ratio of two
inputs and antilog functions. Although this device has relatively low bandwidth of less than 50 kHz,
many scientific applications, such as optical density and absorbency measurements and fiber-optic
power monitoring, need no more than this amount of bandwidth. The device includes internal, lasertrimmed resistors that let you select precise scale factors of 1, 3, or 5V/decade via pin selection.
Analog Devices (www.analog.com) offers an extensive line of IC log amps with devices that serve in
both power-measurement and demodulating applications. For example, the AD8307 92-dB-range log
amp (–75 to +17 dBm) operates from dc to 500 MHz from a 2.7 to 5.5V supply. Log linearity is ±0.3
dB to 100 MHz, increasing to just ±1 dB at 500 MHz, with a slope of 25 mV/dB.
Other members of this family include the AD8309 IC (Figure 2). Like the AD8307, the AD8309 has a
bandwidth to 500 MHz, but this bandwidth does not go as low as dc. However, this log amp has a
100-dB dynamic range and includes a limiter output in addition to the log output, so the same part
provides both RSSI and phase-detection outputs (Figure 3). This 16-lead IC uses six cascaded
amplifier/limiter cells with 12-dB gain each; an 18-dB-gain stage follows these cells. There are also
10 full-wave detectors in a row.
Targeting RF detection, transmitter-power-amplifier monitoring and control, and RSSImeasurements needs, the AD8313 log detector has a bandwidth of 0.1 to 2.5 GHz and 70-dB
dynamic range; the IC functions to 3.5 GHz. Equally important, accuracy of the log chain is ±1.0 dB
over 65-dB range and at 1.9 GHz, and the amplifier has a 40-nsec typical full-scale response.
If you need the limiting function rather than the log function, there is a selection of ASICs with an
integral limiter as well as stand-alone limiters. Many of these limiting amplifiers are also called
"limiting postamplifiers," because you use them after the fiber-optic PIN-diode transimpedance
amplifier converts weak, impinging, photon-induced current to a small voltage. These limiters
operate on differential signals and also include a loss-of-signal flag, which the limiter sets when the
input-signal differential magnitude falls below some user-set threshold. This threshold ranges from
half a millivolt to several hundred millivolts, depending on the application.
For example, Maxim's (www.maxim-ic.com) MAX3866 is a combined transimpedance preamplifier
and limiting postamplifier targeting 2.488-Gbps OC-48 synchronous-digital-hierarchy/synchronos-optical-network (SDH/ SONET) links (Figure 4). Although its minimum sensitivity is –22 dBm, the
3.3V IC with 1.8-GHz analog bandwidth withstands overdrive levels as high as +1.4 dBm.
Applied Micro Circuits Corp (www.amcc.com) offers a silicon-germanium limiting amp combined
with a quantizer, which also aims at clock recovery in fiber-optic links to the OC-48 rate. The
company's S3058 has sensitivity as low as ±1 mV p-p, with a 62-dB input dynamic range. You can set
the decision-threshold level at the input of the limiter at ±25% of nominal value to compensate for
the asymmetric noise that occurs in many fiber applications.
Burr-Brown offers a pair of similar limiting amps: the OPA668 and OPA689. The OPA668 is a 530MHz, unity-gain-stable IC; the OPA689 is stable for gains greater than 4 and has bandwidth of 280
MHz at gain of 6. These op amps operate linearly to within 30 mV of their output limits and recover
from limiting in 2.4 nsec; they also smoothly handle overdrive (Figure 5). The devices come in eightpin packages and operate from either a single 5V supply or a bipolar 5V supply.
The OC-48 GD16511 limiting amplifier from GiGA North America (www.giga.dk) handles differential
input signals from ±1 mV to ±1 V p-p, with a 3-GHz, 3-dB bandwidth. The single-supply IC comes in
a 5-mm-square 32-lead TQFP and yields BERs of less than 10–9 with signal magnitudes as low as ±3
mV.
Micrel-Synergy (www.synergysemi.com) also offers a stand-alone limiting amplifier. The SY88913
postamplifier is part of a three-IC chip set for fiber optics, but you can also use it as an independent
device. The 10-pin MSOP IC operates on bit streams to 1.25 Gbps and suits Gigabit Ethernet, Fibre
Channel, and SONET applications. It accepts signals as low as ±5 mV and delivers differential
positive-emitter-coupled-logic output data.
The Philips Semiconductors (www.semiconductors.philips.com) TZA3019-HL, a 2.5-Gbps
limiter/postamplifier is unusual because it is a dual-channel unit that contains an internal crossbar
switch between channels. Although this feature complicates the IC's design internally, it saves you
space and enhances system reliability, because you can switch channels between two external
transimpedance amplifiers. This capability lets you more easily implement a protection backup fiber
ring for redundancy and also lets you invoke algorithms that switch between and test parts of the
end-to-end path.
Broad-range vendor Mini-Circuits (www.minicircuits.com) offers a trio of similar limiters in its PLS
family, which cover 0.01 to 1 MHz, 0.1 to 150 MHz, and 100 to 900 MHz in overlapping ranges. The
highest frequency unit, the PLS-2, accepts input signals with magnitudes of 3 to 15 dBm and has
phase shift of less than 2° throughout the range. The lower frequency models have phase shift of 1°
or less.
If you are looking to go beyond the 2.4-Gbps OC-48 rate, Oki Semiconductor (www.okisemi.com) has
a GaAs fiber-optic chip set for 10-Gbps OC-192 rates that includes the GHAD4103 limiting amplifier.
Operating from –7V, this IC has typical gain of 12 dB and output amplitude of ±0.8V p-p. Limiting
action occurs when the input-signal power exceeds –25 dBm with a 4-dBm output; full-scale output
of 7 dBm occurs for inputs of –15 dBm.
Regardless of the parts or architecture you prefer, be sure to spend time studying the application
information that most vendors provide—and be wary if they don't provide such information. Make
sure that the temperature performance of the device you are considering is adequate for your
application; temperature performance is the area in which log amps and limiters are especially
prone to drift and parameter shift. Although log amps and limiters have a long and noble history in
signal-processing applications, each implementation and application has many subtleties of which
you should be aware. Don't hesitate to work with the vendor's log/limiter-amp applications experts to
make sure they understand your design goals and to understand how their parts interact with the
nature of your signal-processing constraints.
It's not as easy as falling off a log
In the digital, DSP-driven-algorithm world of today's design, you may think that
determining the logarithm of a signal value without using numerical calculation is a
throwback to an earlier era. But, doing it digitally is not a viable option for many
reasons, and you have to use a single all-analog function block.
Why not do it digitally? First, it would take considerable floating-point MIPS to
calculate the logarithm of signals with bandwidth of even 100 MHz, and calculations on
gigahertz signals would be impossible. Second, you'd need a very fast A/D converter
ahead of the DSP to convert the analog signal. Finally, even if these factors were not
obstacles, you would also need resolution of 12 bits to reach 72 dB of range under ideal
conditions. You would need 16 bits for 96 dB of range, which means using a costly,
power-hungry converter. And the design still wouldn't work! Just because the converter
has the resolution doesn't mean that your system would actually realize that resolution,
because the actual resolution of the A/D conversion for millivolt signals is different from
what it is for volt-level signals. You'd need to put a variable-gain stage ahead of the
converter, so, your design would be back to where it started in terms of signal-path
gain, range, and resolution.
So how do you get the logarithm without calculations? In short, making a crude log amp
from an analog component is relatively easy, but making an accurate, stable, and
repeatable one is tricky. Once you have the transistor past its threshold voltage of
about 0.6V (for a silicon device), the technique starts with the fundamental logarithmic
relationship between a transistor's applied collector current and the resulting baseemitter voltage. Unfortunately, this simple approach yields poor performance because
the voltage drifts with temperature, varies widely from unit-to-unit, and encounters
other obstacles. But this approach is a start, and circuit designers have used it as a
building block for wide-range, accurate, and low-cost ICs. ICs, which inherently provide
matched transistor pairs and other virtues, make it possible to build even better log
amps. (For an insightful tour through design maturation, check Reference 1.)
Another accepted technique is to use a diode detector in an active RC circuit that
resembles the basic passive diode-detector that crystal radios from the early years of
this century used. Although this approach works, the circuit is sensitive to temperature
drift, which affects absolute accuracy, and has only 20 to 30 dB of useful dynamic
range.
REFERENCE
1. Pease, Bob, "What's all this logarithmic stuff, anyhow?" Electronic Design, June 14,
1999.
Clear up log confusion
The transfer-function equation of a logarithmic amplifier is simple:
VOUT =VSLOPE log(VIN /VINTERCEPT ),
where you usually express the slope voltage in volts or millivolts per decade or per
decibel. (Recall that 20 dB equals 1 decade.)
From this equation, you see that the transfer function has only two parameters: the
slope voltage and the intercept voltage (Figure A). Unfortunately, log amps historically
had poor calibration for these parameters, so they often needed trimming in the
application. Vendors now more precisely calibrate their ICs, which thus yield fairly
accurate values for both parameters. These capabilities mean that you can use the log
amp for accurate measurements as well as for more general envelope detection.
When you are looking at specifications for a log amp, some specifications have familiar
names, but some do not. Bandwidth, for example, is the frequency range that the entire
log amp provides for the stated specifications, but bandwidth specifications also exist
for the internal amplifiers. These specifications tell you about the pulse rise and fall
times that the amplifier delivers.
One critical specification, log linearity, sounds like an oxymoron but isn't. It tells
you—using a best-fit straight line—the maximum deviation you will see, in decibels, of
the transfer-function line representing slope voltage.
References 1 through 5 provide a good discussion of the basic log-amp functions and
specs. After you understand them, you can start working through accuracy and error
budgets. Although this topic is not trivial for linear amplifiers, it becomes even more
complex for log amps in which, for example, you have to carefully measure and
interpret basic specs, such as rise and fall times.
You also need to consider device-to-device tolerance and variation to see what your
design can tolerate. Pay special attention to typical-versus-worst-case specs. Log amps
are not as consistent as linear devices, and you may decide to do an in-system
calibration in some cases; in other cases, such as some closed-loop designs, the
absolute calibration is not as critical as stability and repeatability.
REFERENCE
1. Ask the Applications Engineer—28, Analog Devices Inc.
2. Logarithmic amplifier Q&A, Analog Devices Inc.
3. Specification definitions for logarithmic amplifiers, Technical Note No. 35T001,
Miteq Corp.
4. Defining logarithmic amplifier accuracy, Technical Note No. 35T003, Miteq Corp.
5. Gilbert, Barrie and Eamon Nash, "Demodulating Log amps bolster wide-dynami-range measurements," Microwaves & RF, March 1998 (part 1) and April 1998 (part 2).
Author info
You can reach Technical Editor Bill Schweber at 1-617-558-4484, fax 1-617-558-4470
bill.schweber@cahners.com.