In order to measure and control the transmit power in multi carrier wireless infrastructure, root mean square (RMS) power detection is needed. The traditional power detector uses diode detection or logarithmic amplifier. When the PAPR of the transmitted signal is not fixed, the traditional method can not accurately measure the power. Temperature stability of measurement circuit and linearity of geophone transfer function are very important. The technique described in this note can improve the temperature stability of the root mean square power detector and the linearity of its transfer function; In the dynamic range of more than 50dB, less than ± 3 dB.

Modern wireless transmitters generally require strict control of the transmitted radio frequency (RF) power. In wireless cellular networks, strict power control is the premise of setting cell size accurately to enhance coverage. In addition, when the actual transmit power is uncertain, the size of RF power amplifier (PA) must be very large for the sake of heat dissipation, which can be avoided by precise power control. For example, when the transmission power uncertainty of a 50W (47dbm) power amplifier is 1dB, in order to transmit power safely and avoid overheating, PA must be sized according to 63w (48dbm) power requirement.

Power measurement and control are also used in the receiver, usually in the intermediate frequency (if). The goal of this application is to measure and control the gain of the received signal to ensure that if amplifiers and analog-to-digital converters (ADCs) are not overdriven. Although the signal-to-noise ratio can be greatly improved by accurately measuring the received signal (generally called received signal strength indicator or RSSI), it is not as important as the transmitter; The former only aims to keep the received signal below a certain limit.

Root mean square RF power detector can measure RF power independently of signal PAPR or wave crest factor. This ability is very important when the PAPR of the measured signal is constantly changing. In the wireless cellular network, the number of calls carried by the cellular base station is constantly changing, so it is a common phenomenon that the signal PAPR is constantly changing; There are two specific reasons: one is that multiple carriers transmit at different power levels, the other is that the code domain power of a single CDMA carrier will change.

Figure 1. Modern wireless transmitters use RF power measurement and control technology to precisely adjust transmission power. In the receiver, power measurement can be used to prevent over drive of if and baseband devices, and greatly improve the signal-to-noise ratio.

**1 high dynamic range RMS DC converter**

Ad8362 is a root mean square DC converter, which can measure root mean square voltage in the range of 60dB or higher. The operating frequency range is from very low frequency to about 2.7ghz. Figure 2 shows the transfer function of the ad8362 at 2.2GHz, which reflects the transfer function relative to 50 Ω The relationship between the output voltage (V) and the input signal strength (DBM) at the time of resistance.

Figure 2 also shows the deviation of this transfer function from the best fit line. The slope and intercept of this line are obtained by performing linear regression on the measured data. After calculating the slope and intercept of this line, we can draw the error chart in DB scale. In Figure 2, the scale of this line is on the right axis.

Figure 2. The transfer function of the LMS DC converter shows a linear DB relationship between the output voltage (V) and the input signal (DB). The figure also shows the transfer function ripple and temperature drift (see the right axis for the scale).

The peak to peak amplitude is as high as 0.75db. This ripple leads to great uncertainty in measurement. It also shows that the transfer function varies with temperature. In this case, the temperature drift of the transfer function is mainly represented by the change of intercept (the slope is relatively stable).

**The principle of ad8362**

Figure 3 shows the block diagram of ad8362. The main component of ad8362 is a linear DB variable gain amplifier (VGA), which includes voltage controlled attenuator, fixed gain amplifier, low dynamic range RMS DC converter and error amplifier.

Figure 3. Log root mean square DC converter ad8362. The input signal of the RMS DC converter is applied to the VGA input. The VGA output is applied to the low dynamic range RMS DC converter. The output of the detector is compared with the set point voltage to generate an error signal which is fed back to the gain control input of VGA.

The input signal is applied to the VGA. The VGA output is applied to the low dynamic range RMS DC converter. The output of the detector is proportional to the RMS voltage of the VGA output signal.

The fixed reference voltage, also known as the target voltage, is applied to another low dynamic range RMS DC converter exactly the same. The outputs of the two detectors are applied to the error amplifier / integrator to generate the error signal. The output of the error amplifier is applied to the gain control input of VGA. The gain control transfer function of VGA is negative, that is, increasing the voltage will reduce the gain.

When a small input signal is applied to the circuit, the output voltage of the signal path detector will be very small, resulting in a smaller and smaller error signal driving the VGA. This error signal will continue to decrease, while the VGA gain will continue to increase until the output of the signal link detector is equal to that of the reference detector.

Similarly, large input signal will produce larger and larger error signal, which will lead to the decrease of VGA gain until the output voltage of signal path detector is equal to that of reference detector. In any case, when the system reaches equilibrium, the input voltage of root mean square DC converter will be established at the same value. Therefore, the low dynamic range RMS DC converter only needs a very small operating range to make the circuit work.

The transfer function of VGA is linear dB, that is, the dB gain is proportional to the v-scale control voltage. In this example, the slope of VGA gain control is about – 50mV / DB. Thus, a logarithmic transfer function (i.e. the relationship between VGA input and error amplifier output) suitable for the whole circuit is obtained, that is, the output voltage is proportional to the logarithm or root mean square value of the input voltage. Please note that the temperature stability of this gain control function is very important for the overall temperature stability of root mean square measurement.

**3 Gaussian interpolator**

Figure 2 shows a periodic ripple in the form of a consistency curve. The source of this ripple is Gaussian interpolator. The Gauss interpolator determines the node to collect the signal from the variable attenuator, and then applies the signal to the fixed gain amplifier, which constitutes the output stage of ad8362vga.

The simplified schematic diagram of attenuator and Gaussian interpolator circuit is shown in Figure 4. The input trapezoidal attenuator consists of several parts, each part attenuates the input signal by 6.33db. The signal is extracted from these parts by a variable transconductance stage. According to the control signal applied to the control port of the variable attenuator, the Gaussian interpolator determines which transconductance stage is effective, and then determines the attenuation applied to the input signal.

Figure 4. Ad8362vga attenuator and Gaussian interpolator. Although the existence of Gaussian interpolator realizes the continuous relationship between output voltage and control voltage, the relationship has periodic ripple.

The attenuation level between the contacts requires the adjacent transconductance stages to be effective at the same time, so as to generate the weighted average value of these contacts according to the strength of the transconductance unit. In order to make the contact slide along the attenuator, the conductance of adjacent transconductance stages changes in a certain way, which is the cause of the ripple observed in the consistency curve.

**4 filtering of error signal**

The square cell of the low dynamic range RMS DC converter produces a DC component and a component with twice the input frequency. This comes from the following trigonometric identity:

If the signal is a single frequency sine wave, the output of the square cell will be a DC component and a sine wave signal with double input frequency. The main pole of the error amplifier / integrator will filter out the double frequency component, leaving only the DC component.

If the input signal is a wideband signal, such as CDMA or WCDMA, the DC component will cover half of the bandwidth of the original signal. Therefore, after filtering out the double frequency component, the output of the circuit fed back to the VGA still contains obvious ripple, which is superimposed on the DC level as a noise like signal. The general method is to strengthen the filtering of the error amplifier to significantly reduce the noise of the output signal of the error amplifier. This will make the whole circuit produce noiseless output.

**5 elimination of transfer function ripple**

Figure 5 shows an optional configuration for the circuit to use this baseband noise to eliminate ripple. Compared with the circuit shown in Fig. 3, the external filter capacitance of the integrator is significantly reduced, but it is still quite large enough to perform effective root mean square calculation. When the wideband signal is applied to the input of the circuit, the output of the error amplifier contains obvious noise, but it is still centered on the correct root mean square output level. Set the noise level of the output end of the error amplifier to at least 300mV peak to peak. 300mV is the product of the DB distance between adjacent taps on the R-2R ladder network of VGA and the gain control slope of VGA (i.e. 50mV / DB) × 6dB）。 As long as the output noise level is at least 300 MV peak to peak, the actual value is not important.

Figure 5. Reducing the filter capacitance that is commonly used to reduce the square cell output noise. The noise is fed back to the VGA, causing the gain of the VGA to fluctuate within at least 6dB. This will often offset the ripple of VGA transfer function, and then offset the ripple of the whole circuit transfer function. The output noise of the squarer is filtered by external filter before measurement.

After simple filtering, the signal is fed back to the VGA control input. The noise in this signal causes the VGA gain to fluctuate around a central point. The gain control slope of VGA is 50 mV / DB. Therefore, the noise will make the instantaneous gain of VGA change about 6dB. The cursor of Gaussian interpolator moves back and forth on about one tap of R-2R ladder network.

The gain control voltage moves continuously on at least one tap of the Gaussian interpolator, so the relationship between the RMS signal strength of the VGA output and the VGA control voltage has nothing to do with the gain control ripple of the VGA. Now, the signal applied to the square cell is simply AM modulated. However, this modulation does not change the PAPR of the signal.

Due to the small capacitance of the filter, the RMS voltage at the output of the error amplifier will contain obvious peak to peak noise. Although the signal including noise is required to be fed back to the VGA gain control input, a simple filter can be used to filter the RMS voltage entering the external measurement node to produce a noise free RMS voltage.

Figure 6 shows the ripple reduction of the transfer function of the RMS DC converter. The noise level fed back to the VGA gain control terminal is 600mV peak to peak, which seems too large, because only enough noise is needed to adjust the gain control voltage within 6dB (a tap on the R-2R ladder network). However, as the call load of spread spectrum CDMA signal decreases, the PAPR of the signal also decreases. This will result in noise reduction at the detector output. Therefore, the peak to peak noise should be set so that it can always cover at least one tap on the R-2R ladder network. Please note that the peak value of the error function is about – 57dbm, which is caused by the measurement error of the high dynamic range RMS power meter head used to measure the power transmitted to the circuit.

Figure 6. Reduction of transfer function ripple of PAPR signal (single carrier WCDMA, test model 16, 2.2GHz). The peak at – 57dbm is caused by measurement error.

Fig. 7 shows the transfer function of the improved circuit when an unmodulated sine wave is applied. At this time, the ripple of transfer function does not decrease. As described above, when a sine wave is applied to the square cell, the output is a double frequency component and a DC level component. Sine wave belongs to narrow band signal, and there is no noise like voltage close to DC. After eliminating the double frequency component, no AC component can be used to adjust the gain control input of VGA in a certain range.

Fig. 7. Applying an unmodulated (2.2GHz) sine wave to the circuit, the transfer function ripple does not decrease because there is no baseband disturbance at the low dynamic range RMS detector output.

**6 injecting disturbance into vtgt**

Figure 8 shows a circuit that can be used in the above case. The disturbance signal needed to adjust the VGA is coupled to the reference voltage (also known as the target voltage). This will produce a disturbance at the output of the error amplifier and feed back to the VGA gain control input. The disturbance signal coupled to VREF signal can be either noise or sine wave.

Figure 8. Disturbance signal can be applied to vtgt pin. This technique is useful when the PAPR of the input signal is low (for example, sine wave). The disturbance signal can be sine wave or white noise.

Figure 9 shows the transfer function of the circuit when a sine wave is applied as the input signal. At this time, a 500mv peak to peak, 10kHz sine wave is superimposed on the vtgt voltage with a nominal value of 1vdc. The ripple reduction of transfer function is similar to that of WCDMA signal. The frequency of the disturbance signal is not very important. It should be set high enough to filter the output ripple easily and achieve the required impulse response time.

Figure 9. For the input signal with low PAPR, applying the disturbance signal to the vtgt input (500 MV PAP, 10 kHz, DC level = 1 V) can also reduce the ripple. In this example, the input signal is a 2.2GHz sine wave

**7 temperature compensation**

In addition to the measurement uncertainty caused by the ripple of the transfer function, the temperature drift of the device also leads to (greater) measurement uncertainty (Fig. 2). However, looking at a large number of devices (Figure 10), we can see that the trend of temperature drift is consistent. The lower the temperature, the higher the output voltage. However, the drift varies from device to device. In addition, the drift amplitude varies with frequency. The temperature drift diagrams of these devices at other frequencies are shown in the appendix.

Figure 10.2.2 statistical distribution of temperature drift of different devices at 2GHz (average value) ±( When the temperature is lower, the output voltage becomes higher; When the temperature is higher, the output voltage becomes lower. The temperature drift is mainly manifested as intercept movement.

Using the simple technique shown in FIG. 11, the temperature drift of the device can be further reduced. As mentioned above, the output voltage drift of ad8362 is mainly caused by intercept drift. With the increase of temperature, the whole transfer function will decrease, while the slope is quite stable. Therefore, the temperature drift has little to do with the input level. This method of temperature compensation based on the drift at a specific input level (such as 5dBm) will be effective in the full dynamic range (Fig. 12).

Figure 11. Adding a small offset voltage with positive temperature coefficient to the output voltage of the logarithmic amplifier can further reduce the low temperature offset of ad8362.

Figure 12. Using a simple intercept temperature compensation scheme, the temperature drift of ad8362 can be significantly reduced. In this case, the drift of 2.2GHz at 5dBm is compensated. Because the temperature drift is mainly the intercept movement, it can achieve good performance in the whole range.

The compensation scheme is very simple, relying on the precision temperature sensor tmp36 to drive one end of the resistance divider, ad8362 to drive the other end, and the output is located in the center tap. Tmp36 at 25 ° The output voltage is 750 MV and the temperature coefficient is 10 MV when the temperature is 10 ℃/ ° C。 With the increase of temperature, the output voltage of ad8362 decreases, while that of tmp36 increases. R1 and R2 should be selected to ensure that the voltage at the center of the resistance divider does not vary with temperature. In practice, R2 is much larger than R1, so the output voltage of the circuit is very close to the voltage of ad8362vout pin.

**8 select R1 and R2**

The resistance ratio R1 / R2 is determined by the temperature drift of ad8362 at the target frequency. Select the drift of a specific input level to achieve the best accuracy at that level. In the example shown, R1 and R2 are selected according to the drift of 5dBm input level. R1 and R2 are selected according to the following equation:

Among them, 10mV/ ° C is the temperature drift of tmp36, and MV is the temperature drift of ad8362/ ° C stands for. In DB/ ° The temperature drift expressed by C multiplied by the logarithmic slope can be converted to MV/ ° C。 For example, the drift at 900MHz is – 0.008db/ ° C (at 5dBm), multiply the slope by 50mV / DB to get – 0.4mv/ ° C。 Table I shows the calculation results of R2 and R1 values at 900 MHz, 1900 MHz and 2200 MHz.

Table I. calculation of R1 and R2

**9 ripple reduction and temperature compensation combined circuit**

Temperature compensation and transfer function ripple reduction can be combined to form a highly linear and temperature stable RMS detector.

The schematic diagram of the circuit is shown in Figure 13. The two compensation circuits are separated by an op amp buffer.

Figure 13. The disturbance reduction scheme and the temperature compensation scheme can be combined to form a circuit with low temperature drift and excellent transfer function linearity.

Figure 14 shows the circuit at 2.2GHz and – 40 GHz ° C、+25 ° C、+85 ° The transfer function measured at C. In the range of 60dB, the measurement error is about 0 ± 0.5dB。 As explained above, the error spike at about – 57dbm is caused by insufficient measurement of the input signal of ad8362 by the high dynamic range RMS power detector head used for measurement.

Figure 14. The measurement linearity of the circuit with the combination of ripple reduction scheme and temperature compensation scheme is about 60 dB ± 5 dB (the excessive error at low power is caused by measurement error).

**10 conclusion**

Ad8362 is a 60dB logarithmic trupwr ™ Although the geophone has excellent reference performance, its measurement accuracy can be further improved. The technology is simple and easy to use, involving resistance, capacitance and temperature sensor. The temperature drift between devices is repeatable, so these technologies can be used on a large scale.

**appendix**

Figure 15. Relationship between log rule consistency and input amplitude, average ±( 3 sigma), sine wave, frequency 900 MHz, temperature – 40 ℃ ° C、+25 ° C and + 85 ° C。

Figure 16. Relationship between log rule consistency and input amplitude, average ±( 3 sigma), sine wave, frequency 1900MHz, temperature – 40 ℃ ° C、+25 ° C and + 85 ° C。

**AD8362**

Complete and fully calibrated measurement / control system

Accurate RMS to DC conversion (50 Hz to 3.8 GHz)

The input dynamic range is greater than 65dB: − 52dbm to + 8dbm (50 dB) Ω)

It has nothing to do with waveform and modulation, such as GSM / CDMA / TDMA, etc

Linear DB output, adjusting proportion: 50mV / db

Consistency error: 0.5dB

All functions have excellent temperature and power stability

Working voltage: 4.5V to 5.5V (24Ma)

Power saving function: 1.3MW

Editor: hfy