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Volume 36, Number 5, September-October, 2002
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Detecting Fast RF Bursts Using Log Amps
by Yuping Toh
(yuping.toh@analog.com)
INTRODUCTION
Monolithic
logarithmic amplifiers (log amps) can handle signals with dynamic
ranges up to 100 dB. They are capable of responding to RF bursts that are
as short in duration as a few tens of nanoseconds. However, when
demodulating logarithmic amplifiers are used to detect fast RF bursts,
strange tails sometimes appear at the output when the applied burst shuts
off. An example of this was seen in a log amp tutorial article that
appeared online in Analog Dialogue 33-3 (1999), and in print in
Volume 33. This article explains a common cause of these tails and offers
suggestions on how to eliminate them.
Understanding Demodulating Logarithmic
Amplifiers
The first thing to understand about log amps
is that, while they provide information about power, they actually respond
to voltage. In communications technology, the term log amp
generally refers to a device that outputs a voltage that is proportional
to the logarithm of the envelope of the input signal, scaled to base-10. A
power ratio of 100:1 corresponds to 20 decibels (dB)—or a voltage ratio of
10:1 into a given impedance.
Another important factor relating to log amps and output tails: Log
amps have high sensitivity to very small changes in amplitude at the low
end of their operating range. Figure 1 shows the typical relationship
between the input and output of a log amp. For every 10 × increase in the
peak-to-peak voltage at the input, the output increases by 500 mV. This
means that, when inputs are in the single-digit mV range, a very small
change in the input voltage will result in a significant change in the
output voltage.
Figure 1. Input bursts and their associated log
amp outputs.
Using Logarithmic Amplifiers for RF Pulse
Detection
When an RF burst is the input to a
demodulating log amp, the output will be a voltage pulse. This can be fed
into a comparator to determine the presence or absence of the RF burst, or
the amplitude of the RF burst can be determined by measuring the amplitude
of the log amp output voltage.
Figure 2 shows examples of the strange tails that are sometimes
seen at the end of otherwise fast and accurate log amp output-voltage
pulses. These undesirable tails can cause false readings in radar and
other systems where the shape of the detected pulse provides vital
information about the target.
Figure 2a shows a stationary tail. Figure 2b shows a tail that is
jittery, moving up and down the falling edge of the ideal rectangular
pulse. Note that there are instances where the tail does not occur, but
falls directly to the bottom without a kink in the response.
2a
(return
to Input Coupling) (return to Results)
2b
Figure 2. Tail at the output of a
log amp in response to RF bursts.
Understanding the
Tail
The tails in these two cases are caused by
different mechanisms. The stationary tail in Figure 2a is caused by the
poor quality of the RF burst applied to the input of the log amp. While
not apparent on the modest voltage and time scales of an oscilloscope, the
RF burst does not shut off instantaneously, but instead decays
exponentially. Figure 3 shows an exaggerated picture of the input signal
and the log amp response. Remember that log amps are highly sensitive to
small changes in voltage at the low end of their dynamic range. Thus, the
small, almost imperceptible, exponential decay of the RF burst causes a
linear tail. The exponential decay is predictable and repeatable; it is
due to the gating mechanism of the signal generator. This accounts for the
stationary tail at the log amp output. The only solution to this form of
tail is to obtain a signal generator that will shut off to zero more
rapidly.
Figure 3. Slow signal settling-the cause of the
stationary tail of Figure 2a.
The rest of this article will assume that a good-quality RF burst
generator is used—and that the tail is jittery and not stationary.
Input Coupling
The type
of jitter shown in Figure 2b is typically the result of improper input
interfacing to the demodulating log amp. Most logarithmic amplifiers are
designed to be driven differentially, but most RF signals are
single-ended. There are several options for performing the single-ended to
differential conversion necessary to inject the RF signal into the log
amp, as shown in Figure 4. INHI and INLO are the log amp's differential
input pins.
(return
to 50-ohm)
Figure 4. Three passive broadband single-ended
to differential input interfaces for a logarithmic
amplifier.
Figure 4a shows a balun (balance-unbalance-transformer)
interface. This is the best method, as it generates a good-quality, truly
differential signal at the inputs of the log amp. Use of a balun will
eliminate the tails, provided that the size and added cost entailed are
acceptable, given the design constraints.
Two popular alternatives involve RC networks. They occupy less board
area than a balun and cost less, but they require care to avoid tails. An
external shunt resistor is placed on either the device side (Figure 4b) or
the input side (Figure 4c) of the capacitors to provide a controlled
impedance at the device—usually 50 ohms.
Ideal Signals
Consider
first the circuit in Figure 4b (we will return to the somewhat similar
circuit of Figure 4c later on). This circuit does not convert the
single-ended input signal to a differential signal. Instead, the ac
component of the RF signal is allowed to pass through to INHI, while INLO
sees a low-pass-filtered version of the signal. Ideally, the signal at
INLO will have the same dc average as the signal at INHI. Both INHI and
INLO are typically biased by the same internally generated reference
voltage, as shown in Figure 5.
Figure 5. Ideal signals at INHI and INLO when
using circuit shown in figure 4b.
Imperfect Signals
The
signals shown in Figure 5 are idealized. The real low-pass filter will
attenuate the signal from INHI to INLO, but will not completely eliminate
it, and there will be residual traces of the input signal at INLO. Figure
6 shows an exaggerated picture of the signals at INHI and INLO. It can be
seen that the real signal at INLO is a highly attenuated version of INHI
with a 90-degree phase lag.
Figure 6. A closer look at signals at IMHI and
INLO when using circuit shown in Figure 4b.
Looking into the input port, the input signal sees a high-pass filter
to INHI. This means that any changes occurring above the corner frequency
formed by RC1 will pass unattenuated to INHI. Thus, when the RF
burst turns on suddenly from an off state, the voltage at INHI will track
the input. The same will be true for when the RF burst turns off: the
voltage at INHI will shut off immediately.
INLO, on the other hand, is a low-pass-filtered version of INHI; as a
result, it will be an attenuated version of the voltage at INHI,
phase-shifted by 90 degrees. When the RF burst is shut off, the voltage at
INHI will settle immediately—but the voltage at INLO will not. It will
instead undergo a single time-constant decay, with its time constant
defined by RC2. This is illustrated in the magnified section of
Figure 6 (note that the scale of the INLO signal has been exaggerated for
effect).
Source of the Tail
The
tail is the result of the exponential decay of the signal at INLO. While
INLO is decaying exponentially, INHI is off. The small differential input
that the log amp sees between INHI and INLO is enough to result in a
significant amount of output voltage. (Remember that the log amps are
highly sensitive to small input amplitude changes.)
Further evidence that the tail is the result of exponential signal
behavior at the input is given by the linear nature of the tails. When the
log of an exponentially decaying voltage is generated, the result is a
straight line with a negative slope. The jitter in the output occurs when
the pulse rate and the RF frequency are not integer multiples of one
other. Because of this, the RF signal is not always cut off at the same
place in its period. The point in a period where the RF is shut off will
establish the initial condition for the exponential decay. When the RF is
shut off exactly as it crosses the zero-axis, INLO will be at a peak and
the tail will start at its highest point. If the RF is shut off at a peak,
then INLO will be zero and there will be no tail at all. Switching
randomly between these two extremes will cause the jitter that is seen in
the tail.
Cutting the Tail Off
The
tail problem described above can be solved by making sure that the RC time
constants formed by R, C1, and C2 are set
appropriately. The critical time constant is that of the low-pass formed
between R and C2. The value of R is typically chosen to be
about 50 ohms for matching purposes. For convenience, C1 and
C2 are often chosen to be equal, though not
always.
C2 must be chosen to be small enough so that the
exponential decay is faster than the response time of the log amp,
typically specified as the 10% to 90% risetime of the log amp output to a
step increase in the input power. This number establishes the maximum rate
of change of the output voltage. As long as the exponential decay at INLO
is faster than the maximum rate of change, the
output will be limited by the log amp's own slew rate, and the tail will
not appear. This analysis dictates that C2 be as small
as possible.
But if C2 is made as small as possible, and C1 is
made equal, the corner frequency of the high-pass filter formed by R and
C1 will be pushed so far out that it might attenuate the
desired RF signal as it travels from the input to INHI. To ensure that
INHI is not attenuated going from the input to INHI, C1 must be
chosen so that the product of R and C1 forms a corner frequency
that is below the RF frequency. This dictates that C1 should be
large.
Within these bounds, C1 and C2 can be made equal,
or they may be chosen to be different for optimum results.
Should the
50-ohm Resistor be on the Signal
Side or the Device Side?
The analysis so far has
centered on Figure 4b. The circuit in Figure 4c is similar, except that
the input resistor is on the input side of the capacitors. Remember that
the input impedances of the log amps are typically much higher than the 50
ohm of the termination resistor. If the 50-ohm resistor is placed on the device
side of the capacitors C1 and C2, as in Figure 4b,
the net impedance between INHI and INLO is about 50 ohms. But if the
termination resistor is placed on the input side of C1 and C2
(Figure 4c), the impedance between INHI and INLO is the input impedance of
the device.
The problem with having the termination resistor on the signal side is
that the higher internal resistance of the device will require a much
smaller value of C2 to ensure elimination of the tails. Also,
if the input resistance is not predictable, varying with the semiconductor
manufacturing process, the choices for C1 and C2 may
not always ensure tail-free operation.
Thus, placing the termination resistor on the device side of the
capacitors is preferred.
Results
Figure 7 shows
the result of choosing the proper capacitance values. The output shown in
Figure 2b was taken with 10-nF input capacitors, while the output in
Figure 7 was taken with 1-nF capacitors. A factor of 10 capacitance
reduction has made a huge improvement in the output quality!
Figure 7. Tail-free output of a DLA
after a change in capacitor values.
CONCLUSION
The
performance of demodulating log amps need not be hampered by the presence
of tails. They occur because of poor-quality signal sources or because of
the improper selection of component values in the input interface. The
most effective solution for the first form of tail is to obtain a better
source of bursts. The second type of tail can be dealt with using proper
interfacing circuits. Techniques include the use of baluns and passive RC
circuits, as described here. Active solutions, such as single-ended to
differential amplifiers are also available to the designer (but they were
not covered here). Whatever method is chosen, it is important to keep in
mind the issues discussed here.
FOR FURTHER
INFORMATION
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