Make short work of RF power measurement

RF fields are alive with the sound of music and abuzz with telephone conversation, paging signals, e-mail, and Internet traffic. RF products-and the need for RF power measurements-are proliferating in applications as diverse as traditional voice communication, WLANs, CDMA and G3 handsets, and electronic toll-collection systems.

By Joshua Israelsohn, Technical Editor -- EDN, August 3, 2000

If you've noticed your products hitting the open road in the push for all things portable, you may be understandably apprehensive about what's to come from the famed black art of RF engineering. But before you are gripped by fear and loathing on the RF-measurement trail, take a look at the variety of tools available to make short work of RF power measurement.

For analog-RF links, decades-old methods still work well, but when instrumentation designers implement them in modern meters, users benefit from simpler sensor and meter calibration, easier sensor swapping, and computer interfaces for data logging or offline analysis. Modern RF power meters are also smaller, lighter, and, in some cases, battery-powered, allowing you to make measurements in the field as simply and accurately as those you make in the lab.

Digital-RF links, particularly those exploiting spread-spectrum-modulation techniques, challenge traditional measurement methods. Processor-based RF meters allow measurements of digital links that previously required analyzers costing two to five times as much.

Meanwhile, the most sophisticated digital-RF techniques, such as CDMA (code-division multiple access) point the way toward the future: Manufacturers must build RF-power-measurement capability right into the radios, both handset and base station, as part of the RF-link control. The payoff is unprecedented RF-channel usage with excellent voice quality.

Ways and means

A number of good ways exist to measure RF power. They vary by the frequency band, power level, and modulation technique of the measured signal, as well as accuracy, size, and cost. For traditional analog signals, RF power measurement, either rms or peak, is fairly straightforward.

The most conceptually simple method uses a thermoelectric sensor (Figure 1, Reference 1). This approach is the closest to a direct implementation of the mathematical definition of rms power: the heating ability of an ac signal compared with that of a dc source. Here, a buffer amplifier drives a heating element with a replica of the RF input signal. The heating element is thermally intimate with, but electrically isolated from, a temperature sensor—typically a thermocouple. A servo amplifier drives a matching heater/sensor pair until, at equilibrium, the power the dc-servo delivers is equal to the power of the input RF signal.

The output voltage is equal to the rms value of the input voltage. You can calculate the power in the analog domain with additional circuitry, in the digital domain before display, or in logging and analysis applications, as a data-stream process: P_RF=V_O²/R, where P_RF is RF power, V_O is the sensor's output voltage, and R is the heater resistance.

Primary sources of error derive from tolerances on the heater resistors' absolute resistance, matching, and temperature coefficients. Because the absolute resistance shows up as a scaling factor in the power calculation, you have to calibrate the squaring function to a particular instance of probe. Thermocouple matching and thermal communication from one cell to another or from ambient to either or both cells add to the error budget. Fortunately, careful sensor design can minimize cell-to-cell thermal crosstalk, and sensor designs or meter interfaces can include ambient compensation or calibration. Commercially available sensors, paired with small benchtop or handheld power meters, can render all these errors small and make for a compact measurement capability.

An advantage of the thermoelectric-type RF sensor is that it correctly calculates rms values independently of crest factor (see sidebar "The rest about crest"). A key disadvantage is that thermoelectric sensors have relatively slow and nonadjustable response times determined by thermomechanical, not electrical, properties.

Diode sensors, on the other hand, swap these two characteristics (Figure 2). Fundamentally peak detectors, diode sensors can exhibit electrically adjustable dynamic behavior but require crest-factor compensation. This trait makes diode sensors both reasonably inexpensive and accurate if you use either known test signals or a good method of crest-factor estimation and if you know what crest-factor compensation the sensor and meter provide. In addition to faster and electrically adjustable response times, diode detectors offer as much as three orders of magnitude better noise performance, though these detectors are limited to small signals—often, 300 mW.

Between the thermoelectric and diode sensors, small commercially available meters can accommodate a range of signal frequencies, dynamic range, and waveform complexity. Examples of inexpensive power meters include the Boonton Electronics 4230A series benchtop instruments, which are available in half-rack, single-channel models (4231A) and two-channel models (4232A) (Figure 3). These instruments measure signal power from –70 to +44 dBm over 10 kHz to 100 GHz, depending on the sensor selected, at a rate as high as 200 readings/sec. The 4230 series meters automatically identify the sensor type (thermocouple or diode type) and read calibration data from an EEPROM built into the sensor adapters. The 4232 provides for simultaneous independent power measurements on each of its two channels and calculates their differences and ratios. Both models offer a GPIB interface as standard; RS-232 is optional. Like several other instruments in this price/performance class, these emulate older competing models for easy integration into ATE environments.

Also available from Boonton Electric, the 5230 series meters add voltage-measurement capability for signals of 10 Hz to 2.5 GHz (Figure 4). The single-channel 5231 and dual-channel 5232 meters operate over an amplitude range of 200 µV to 10V, depending on the sensor selected—300V when used with a companion divider—and automatically correct for sensor offsets. The 5232 allows simultaneous and independent voltage and power measurements. Like the 4230A series, the 5230 meters read calibration data from the sensor adapter.

Giga-tronics offers the model 3410A handheld RF power meter with a built-in field-replaceable sensor, covering 100 kHz to 2.6 GHz (Figure 5). This instrument has a measurement range of –60 to ±20 dBm, though because the sensor has a damage level of 23 dBm, users should be cautious about pushing the upper end of this instrument's capability with input waveforms that are not well-characterized and -controlled. The 3410A packs the power meter and sensor along with a frequency meter, a calibrator, an RS-232 interface, and an NiMH battery pack (for 3.5 to 8 hours of operation, depending on mode) all in a package weighing less than 2 lbs. Measurement accuracy is ±0.25 dB, including the built-in calibrator's residual error, and the 3 measurement noise is better than 200 pW (–67 dBm).

Using the directionals

Unlike measurements that terminate an RF signal, inline sensors need to distinguish between the forward and the reflected signals (see sidebar "Directional couplers"). An example of a portable RF-power meter designed to mate with inline directional sensors is the Bird model 5000 (Figure 6). This instrument measures 2 MHz to 3.6 GHz, 1W to 1 kW, depending on the sensor selected, with a rated accuracy of better than 0.25 dB. The model 5000 is also a good example of how the current flock of power meters have integrated signal-processing technologies to enable high-speed measurements of a variety of challenging waveforms, such as those used in PCS and HDTV with crest factors as high as 10, as well as traditional analog wireless.

he market for communications devices making use of digital modulation techniques is growing rapidly because these methods offer efficiencies significant to base-station operators and mobile users alike. Digitally modulated spread-spectrum systems pack a lot of information and users onto a single slice of an RF band and do so with good received-signal fidelity under a variety of conditions that have proven problematic for traditional analog methods. A good example is CDMA, which is particularly attractive because it allows both basestation and mobile systems to minimize their transmission power for a given message fidelity, and, in so doing, maximize the number of users who can share a channel. CDMA also allows for "soft-handoff," in which multiple base stations serve a single mobile user. These base stations operate at the same carrier frequency, as the mobile moves from one cell into the service area of another. Although CDMA may not be the last word in wireless communication, the kinds of strategies it exploits to maximize channel usage, battery life, and user mobility will likely appear in future communications systems as well.

Digital power to the people

The amount of information you can pack into a communications channel in a noisy environment has a theoretical limit described by CE Shannon (Reference 2):

where B_W is the channel bandwidth in hertz, C is the channel capacity in bits per second, S is the signal power, and N is the noise power.

Because RF applications are growing rapidly while the spectrum is stubbornly not, channel sharing is the only way users will be able to access airtime for many applications. One reason CDMA is gaining popularity is that it demonstrates a distinct advantage over FDMA (frequency-division multiple-access) and TDMA (time-division multiple-access) codings in how it manages channel sharing. Unlike the FDMA and TDMA, CDMA systems can tune their performance, trading between capacity and voice quality. This "elasticity" in performance depends on both base and mobile stations carefully assessing their received and controlling their transmitted RF power because to a given user's signal, operating in a shared channel, all other user's signals are sources of noise power.

For a given SNR, you can determine the number of users that can share a channel using the following equation (Reference 3):

where M is the number of users,  is a power-control accuracy factor; B_W is the channel bandwidth; R is the spreading signal rate; E_b is the bit energy; N_o is the noise spectral density; and k is a factor into which you heap spill-over noise from adjacent cells, typical-use factor (one does take a breath from time to time), and a factor to account for the benefit of directionally sectored cells

With practical values for  ranging from 0.5 to 0.9, getting the RF-power measurement and control under control is critical to both the signal and the economic performance of CDMA systems (see sidebar "How they do it: controlling CDMA-transmitter power"). The challenge is to implement a measurement function that can update the system every 1.25 msec or faster, with fractions of a decibel resolution, all in the waste space on a digital-wireless-handset pc board.

As easy as falling off a log

There is no wasted space on a digital-wireless-handset pc board.

nly a few practical means exist of assessing signal power with small circuits in spread-spectrum systems—most notably, diode detectors and logarithmic amplifiers. In modulation schemes that result in waveforms of reasonably constant crest factor, such as QPSK (quadrature phase-shift keying) and GMSK (Gaussian-filtered minimum-shift keying), diode detector circuits can perform well with crest-factor compensation.

Commercially available logarithmic amplifier ICs have the advantage of as much as five-times larger dynamic range, better temperature stability, and smaller footprints than diode detectors. Log amps, like diode detectors, are fundamentally voltage-sensing, not power-sensing, devices, even though manufacturers often calibrate both in power terms, usually dBm. The result is that both suffer from crest-factor errors, but, in a log amp's case, that error manifests itself as an intercept shift, which lends itself to comparatively simple compensation (Reference 4).

A good example of logarithmic amplifiers suitable for RF measurements is the AD8314 from Analog Devices for use with 100-MHz to 2.5-GHz signals with a dynamic range of 45 dB. The company based the device on the older AD8313's architecture, which sums eight 8-dB cells. The AD8314's structure, comprising four 10-dB segments, sacrifices dynamic range—45 versus 70 dB—and high-frequency log conformance but drops the power dissipation by a factor of three and halves the price as well.

The AD8314 also has a feature that makes it attractive in transmitter-control applications: In addition to the normal output signal, a dc voltage directly proportional to the log of the input RF-signal amplitude, a second output, V_DN, presents a signal of inverse polarity and twice the slope, which is offset so that at zero signal, it sits at 2.25V and decreases for increasing input signal (Figure 7). Connecting the V_DN signal to the gain-control port on the transmitter power amplifier and sampling the RF output back to the AD8314's inputs implement a closed-loop power-control system. This scheme takes a dc setpoint signal from a DAC or another source to set the output power.

Riding the crest to success

Unfortunately, when measuring CDMA signals with crest factors that can vary over more than two octaves, diode detectors and a log amplifiers both perform poorly. For example, in one comparison, a diode detector and a log amp were gauged against a laboratory thermoelectric sensor (Reference 5). A test CDMA signal with a crest factor of 3.5, simulating the reverse link, induced a 2-dB error in the diode detector and a 3.5-dB error in the log amp. With a crest factor of 16, representative of a forward-link signal, the errors of both exceeded 5 dB.

Another Analog Devices part, the AD8361 rms-to-dc converter, has received much recent attention as a solution to the problem posed by the crest-factor range in CDMA and could find a home in a variety of other RF power-measurement applications for frequencies as to 2.5 GHz. With a sine-wave error of only 2 dB over a 30-dB range, the AD8361 deviates only 0.2 dB more with an IS-95 CDMA reverse-link test signal and 1 dB more on the forward link. No other approach comes near this performance at a similar cost, size, or power dissipation.

As with many challenging measurements, it is advisable to have a number of ways to assess RF power in the lab. Knowing the limitations of each method is critical to evaluating measurement data. Small fixtures based on broadband ICs such as the AD8361 can be helpful in making benchtop diagnostic measurements and for setting up transfer standards in conjunction with traceable instrumentation. For a table of representative products, click Table 1.

The rest about crest A signal's crest factor is, by definition, the ratio of its peak value to its rms value. The crest factors of a few common waveforms appear in Table A. Though clearly a characteristic of the waveform, three questions about crest factor pop up (or should) every time you make an ac measurement. You can avoid making potentially large measurement errors by considering the measured signal's crest factor, the instrument's accuracy as a function of crest factor, and the instrument's crest-factor compensation. If the measurement front end reports a true rms value, independently of waveform (as does the thermoelectric sensor and rms-to-dc converter discussed in the main text), then there's no problem. However, many front ends do not. Several options exist, and knowing which one your instrumentation manufacturer took is critical to the correct interpretation of the reported value. The manufacturer may use one of the following options: True rms detection: Even if you're convinced that your instrumentation speaks the truth, know how its accuracy varies as you approach any of its limits. Peak detection/peak reporting: If you want the rms value, you need to determine the crest factor of the waveform of interest and divide it into the reading. Peak detection, calibrated to report rms for a particular waveform: Manufacturers usually calibrate these instruments for sine waves, and you must correct further for other waveforms. Capture and computation: In this approach, the incoming signal gets digitized, and rms values are computed. This approach works well as long your signal doesn't have high-frequency components to get caught up in the antialiasing filter or—worse still—have sufficient residual energy beyond the digitizer's Nyquist rate after the filter has done its work to cause errors. Signals with fast rise times and low duty cycles can challenge this type of instrument. What does your meter do? Don't take the front panel's word for it: Learn how its accuracy varies over its specified range of input frequency and amplitude and as a function of source impedance, symmetry, and even operating temperature if you're going to make measurements in the field. Each method of observing and presenting the value of an ac waveform has its limitations, which you need to be aware of if you're going to collect meaningful data. Either read the manual (doh!) or observe the meter with known test signals side by side with an oscilloscope. Better yet, do both! You can quickly gain important insights into how your instrument behaves over a range of signals of interest to you and your application. When you perform these benchtop investigations, remember that, for normalized (unit amplitude), simple, periodic waveforms, the crest factor and rms value are reciprocals.

Directional couplers The instantaneous voltage and current seen at a given point along a transmission line are given by (Reference 1):   and   where Z0 is the characteristic impedance, VF is the forward component, VR is the reflected component, the exponentials in t account for the phase versus time, and the exponentials in kx account for the phase versus position along the transmission line. Dividing through by , taking the real voltage and current seen at the selected point and relating them to the forward and reflected signal components, you get:   and   Figure A is a simplified schematic of a network, which combines these terms to directly reveal VF and VR . Such an implementation would not function at the frequencies that advanced communications systems occupy, but the lumped approximation serves as a good conceptual model, revealing the relationships between the various signal elements. If the designer chooses the capacitive divider ratio, A, the current transformer turns ratio, n, and sense resistance, R, such that R/n=AZ0 , then the voltages V1 and V2 at either end of the sense resistor are:   and   The magnitudes of these signals are simply V1 =2AVF and V2 =AVR . By selecting suitable values of A, designers can make inline sensors to measure extremely large power levels. A buffer followed by a thermoelectric, a diode, or another detector circuit completes the sensor, which to the transmission line, looks like an R/n2 series resistance. REFERENCE Hagen, Jon, Radio-Frequency Electronics , 1996, Cambridge University Press, New York, NY.

How they do it: controlling CDMA-transmitter power Back in the days when "radio" referred to the thing you listened to for news, weather, sports, and the hit parade, formulating a strategy to control transmitter power was a simple proposition: Control the peak radiated power to fit between the maximum, which the Federal Communications Commission set, and the minimum, which the station owner set. Conveniently, these values differed by about a half-decibel. Thus was born the transmitter AGC. Radio engineers also applied this concept to the program feed, giving rise to the Gates Sta-Level, the CBS Volumax, and a host of other signal processors whose sole purpose was to ensure that, along with the hits, you got all the power, all the time. The strategy worked well for one good reason: Transmitter operating frequencies, power levels, and antenna patterns were closely regulated as were their location: The transmitters were all bolted firmly to the ground; it had not yet occurred to anyone that putting them on wheels might be a good thing. Then it did. Why? A phone in every car Modern modulation schemes accommodate large numbers of transmitters operating in a small region on the same carrier frequency at the same time. TDMA (time-division multiple access) takes a microscopic view of time, dividing available messaging intervals into a number of "slots" and assigning messages to each one. FDMA (frequency-division multiple access) works in a similar fashion, dividing the modulation space into frequency bands, which can be allocated to users as they pass through a cell. CDMA (code-division multiple access) takes a different tack that results in some useful attributes: It assigns a different spectrum-spreading code to each message, the result of which is that every message appears as pseudorandom noise to every other message. How many messages can you pack onto a single carrier? It all depends on how much noise you are willing to tolerate. An increase in the noise energy accompanying the coded signal translates into an increase in the probability of a frame error, which corresponds to a decay in the decoded signal's SINAD (signal-to-noise-and-distortion) ratio. So unlike TDMA and FDMA, which have hard limits on the number of users a cell can support according to the number of slots, CDMA, as an interference-limited system, has no brick-wall limit. To minimize the contributed noise energy, a control strategy needs to minimize the transmitted power of all users. Meanwhile, a user struggling against all the random racket of the cosmos—or at least the racket occurring in his slice of the spectrum—knows that increasing transmitted power results in better SNR. The answer lies in a balance that manages the power levels of all radios to maximize the service level, or number of users, for a given service quality. In practice, the base station assesses service quality by tracking the frame-error rate and the burst-error length (number of consecutive frames with errors) for each mobile. How? Loops within loops CDMA implements a multipronged power-control strategy consisting of both open and closed loops operating on the reverse link (mobile to base station). The system works to maintain constant and equal received-signal strengths from each mobile, independently of distance, local topography, interference sources, or other challenges to signal propagation. The open-loop control uses the fact that the transmitter power should vary inversely with effective distance to the base station, and the base station's own signal strength (the forward link) is a good approximate measure of that effective distance. A measurement that the mobile must make on the forward-link signal determines the power level for a mobile's initial attempt to contact a base station, or probe. A problem with this method is that it makes a reverse-link power decision based on the forward-link behavior, and the two are not correlated. Once the mobile establishes contact with the base station, the mobile receives a traffic-channel assignment. From that point on, the base station sends power control data back to the mobile every 1.25 msec, based on the received strength of the mobile's signal. The control data has a 1-dB resolution. CDMA also implements forward-link transmitter power control, which takes into account information that the mobiles periodically report and compensates for adjacent-cell spillover. CDMA's "soft-handoff" procedure largely eliminates handoff noise as mobiles move from cell to cell. Because more than one base station can service a single radio at a given time, the handoff procedure has to include power control as well.

Author info

Contact Technical Editor Joshua Israelsohn at 1-617-558-4427, fax 1-617-558-4470, jisraelsohn@cahners.com.

 

 

REFERENCE

1.Kitchin, Charles, and L Counts, RMS to DC Conversion Application Guide, Second Edition, 1986, Analog Devices, Norwood, MA.

2. Shannon, CE, "Communication in the presence of noise," Proceedings of the IRE, No. 37, 1949, pg 10 to 21.

3. Garg, Vijay K, IS-95 CDMA and cdma2000, 2000, Prentice Hall, Saddle River, NJ.

4. Gilbert, Barrie, and E Nash, "Effect of signal waveform on the transfer function of a logarithmic amplifier," 1995, Analog Devices, Norwood, MA.

5. Greichen, John, "TruPwr detection IC solution: rms to dc conversion at RF," Analog Devices, Norwood, MA.