Improving RF Power Measurement Accuracy Using Logarithmic Amplifiers and MCUs

Accurate RF power management is a hot topic in modern wireless transmitters, with many benefits ranging from power amplifier protection in base stations to extended battery life in mobile applications. RF power monitors, such as logarithmic amplifiers, allow RF power measurement systems to monitor and dynamically adjust transmit power over a wide range. Although the accuracy of power monitoring has improved significantly in recent years, applications such as those requiring high-power transmissions can be significantly affected by even small changes in 0 dB power monitoring errors. This has led to a continuous improvement in detector performance.

Combining a logarithmic amplifier with a temperature sensor is a viable design temperature compensation solution to significantly reduce the effects of the two main error factors in RF power management - temperature and manufacturing process variations. In some cases, the temperature compensation hardware is integrated into the power detection chip.

RF Power Management Overview

Accurate base station RF power management is very important, and driving the transmit power amplifier beyond the required output power level will cause great losses. Excessive current consumption not only leads to increased costs but also causes heat dissipation problems that require additional heat dissipation measures. In extreme cases, overdriving the power amplifier can cause reliability problems caused by burnout failures.

Another benefit of accurate base station RF power management also extends to mobile transmitters because they have similar requirements. With the ability to accurately control output power, mobile devices can minimize power current expenditures. For example, RF power management allows the transmitted power to be precisely limited to the minimum required power level, thereby reducing battery current. Accurately controlling power will extend talk time while also allowing mobile transmitters to comply with cellular standards.

Figure 1 shows a block diagram of a typical RF power management circuit. The transmit signal path consists of three consecutive units: baseband, radio frequency (RF) transmission, and power amplifier. Before the transmit signal reaches the antenna, a portion of the transmit signal is sampled by a bidirectional coupler. The sampled RF power is sent to the power detector, where it is converted to a DC voltage. The output voltage of the power detector is digitized and sent to a digital signal processor (DSP) or microcontroller (MCU). Once the digitized power measurement is obtained, a decision can be made based on the relationship between the measured output power and the required output power. The MCU can adjust the output power using a digital-to-analog converter (DAC) and a variable gain amplifier (VGA) to drive the power control of the signal path - whether it is a baseband signal, RF signal or power amplifier. Once the measured output power is balanced with the required output power, the RF power management loop will reach a steady state. At the same time, a temperature sensor is introduced as an input to the MCU to increase temperature compensation capabilities. A similar RF power management loop can be implemented using only analog circuits in the transmitter.

Figure 1. RF power management circuits use logarithmic amplifiers to take advantage of their wide detection range, which is linear in dB.

Historically, diode detectors have been used in RF power management circuits to adjust transmit power. They provide good temperature performance at high input power values, but performance deteriorates at low input powers. Even with temperature compensation circuits, diode detectors provide only a small detection range due to temperature performance degradation at low input powers. A popular alternative to diode detectors is the demodulating logarithmic amplifier. Logarithmic amplifiers provide an easy to use RF power detection response that is linear in dB and has a wide dynamic range.

Logarithmic Amplifier

Figure 2 shows a progressive compression logarithmic amplifier. In this example, there are four 10 dB cascaded limiting amplifiers forming a progressive compression chain. Five full-wave rectified detector cells convert the RF signal voltage to a current—one detector cell at the RF input and the other four at the output of the amplifier stage. The detector cells produce currents proportional to the voltage signal amplitude, and these currents are summed to approximate a logarithmic function. A high gain stage is used to convert the sum of the incoming currents to a voltage. Five detector cells across four 10 dB amplifiers allow the logarithmic amplifier to have a 50 dB detection range.

Figure 2. Five detectors connected between four 10 dB amplifiers allow the progressive compression log amp to achieve a 50 dB detection range.

Figure 3 shows the transfer function of a 60 dB dynamic range, 1 MHz to 8 GHz bandwidth log amp at 2.2 GHz. There is a linear relationship between the RF output power and its output voltage, that is, as the input power increases, the corresponding output voltage increases linearly in dB. The figure also includes a logarithmic conformance error curve. This logarithmic conformance error curve is used to further examine the performance of the logarithmic amplifier. In the linear region of the detection range represented by the bright gray line, the slope of the transfer function and its intercept with the x-axis can be calculated. This information provides a simple ideal model to compare with the actual response of the logarithmic amplifier. The ideal linear reference model is shown in the figure as a dotted line. The ideal linear model is compared with the actual response curve to produce a logarithmic conformance error curve (in dB).

Figure 3. An ideal reference model calculated in the linear region of the log amp’s detection range is compared to its actual response curve. The comparison yields a logarithmic conformance error curve.

The method for calculating the log amp conformance error is similar to the two-point calibration method used in RF power management system calibration. During product testing, two known RF signal strengths are selected within the linear range of the detector. Using the resulting output voltage, the slope and intercept response characteristics can be calculated and stored in nonvolatile memory to establish a simple linear equation. Using the linear function in dB units and the measured detector voltage, it is easy to calculate the transmitted power in the field. The important advantages of using a two-point calibration are reduced cost and shortened test time. However, this calibration method is only possible due to the linear performance of the log amp.

Because calibration is usually done at one temperature, the quantitative effect of temperature on the detector is very important. The change in the accuracy of a logarithmic detector with temperature can be expressed as the conformance error. Figure 4 shows the transfer function at 900 MHz for a 45 dB logarithmic amplifier operating up to 3.5 GHz. Included in the figure are the transfer functions at -40ºC and +85ºC, as well as the logarithmic conformance error versus temperature. Because of the so-called two-point calibration situation, three linearity conformance error curves are generated using the same 25ºC linear reference.

Figure 4. Logarithmic conformance error for a single device at 900 MHz shows ±0.5dB accuracy over temperature.

The transfer function of the log amp at 25°C ambient temperature has a slope of 50.25 dB/V and an intercept (the point where the extension of the linear reference line intersects the x-axis) of -51.6 dBm. The 25°C curve fluctuates around the 0 dB error line, however, with smaller slope and intercept shifts at both end temperatures. The logarithmic conformance error of a single device remains within ±0.5 dB over the operating temperature range and 40 dB detection range. The temperature drift at +85°C is the limiter of the dynamic range. Although a single device may have good accuracy over the operating temperature range, the inherent small variations between devices caused by the semiconductor manufacturing process can prove to be an obstacle to accurate RF power management.

Figure 5 shows the distribution of logarithmic conformance error for 70 devices. A wide range of devices was sampled to account for variations caused by the manufacturing process. Each device had three temperature curves calibrated to a 25°C linear reference. Although there was significant variation from device to device, the distribution was very close. The overall distribution of devices had ±1 dB accuracy over the operating temperature range and a detection range of more than 40 dB. Temperature compensation was introduced due to the repeatable drift from device to device.

Figure 5. The logarithmic conformance errors vary significantly between devices, but their overall distributions are very similar.

Wireless communication standards typically require transmit power detection schemes to have ±1-dB and ±2-dB accuracy, with relaxed restrictions at extreme temperatures. The initial accuracy of log amps is sufficient to meet most standards without fine tuning. Nevertheless, log amps have many distinct advantages that exceed the RF power management requirements dictated by the various standards.

How can MCU compensate for errors?

As discussed previously, the MCU can effectively adjust the transmit power using the bias voltage of the transmit signal path. By adding a temperature sensor, the MCU can further improve the accuracy of the RF power management system. As long as the detector has a repeatable temperature drift, compensation for errors in certain measurements is possible. Compensation algorithms that take into account environmental changes can be integrated into the MCU's decision-making process to significantly reduce or eliminate manufacturing process and temperature variations. For example, if a power detector has a repeatable temperature drift, a compensation algorithm can be used to eliminate the expected error at a known temperature.

Figure 6 shows the logarithmic conformance error curves for a number of log amps. At 3.5 GHz, the temperature drift extends from +1 dB to -4 dB. The overall distribution of the devices at -40°C closely follows the curve at 25°C. In contrast, the distribution at +85°C has shifted by 2.5 dB and is no longer parallel to the distribution at 25°C. Although the temperature drift at this frequency is large, the distributions at each specific temperature remain very close. Because of the repeatability of these drifts, a compensation scheme can be implemented that significantly improves accuracy.

Figure 6. The temperature drift distribution at +85°C at 3.5 GHz shifts and is no longer parallel to the 25°C distribution.
The trendline through the linear region of the +85°C log conformance curve represents the error model for that temperature.

Most temperature drift occurs between +25°C and +85°C. An error function that is universal for all temperatures can be built for various temperature ranges using a temperature scaling factor, k(T), where k(T) is a function of temperature. Combining the compensation error function with the temperature scaling factor function results in the combination shown in Figure 7. As the temperature increases, the scaling factor changes, thereby eliminating the error caused by the increase in temperature drift.

Figure 7. Using the compensated error function to cancel out the error caused by temperature variation.
Using error compensation improves the logarithmic conformance error over the entire temperature range.

Figure 8. Laser-trimmed log amps use analog compensation circuitry to achieve accurate RF power management rather than digital compensation.

in conclusion

Using accurate RF power management, base stations and cell phone transmitters can benefit from power amplifier protection and reduced power consumption, far exceeding the requirements of cellular standards. Using a stable logarithmic amplifier and temperature sensor, the MCU can compensate for temperature drift errors to improve the overall accuracy of the RF power management system. The logarithmic amplifier is closely dependent on temperature distribution, so it allows simple error compensation. Two-point calibration for moderate temperature drift enables accurate RF power management with ±0.5-dB accuracy over the entire temperature range.