RF-to-bits solution provides precise phase and amplitude data for materials analysis applications

Introduction

When analyzing materials at remote sites where it is not possible to place a probe into the material, high frequency transceivers provide a viable method for accurately quantifying the volume fraction of the material without the detrimental effects of direct contact with the material. Quadrature demodulators provide a powerful new method for measuring amplitude and phase shift in these applications. The receiver signal chain discussed here uses the ADL5380 wideband quadrature demodulator, the ADA4940-2 ultra-low power, low distortion, fully differential ADC driver, and the AD7903 dual-channel, differential, 16-bit, 1 MSPS PulSAR ADC to provide accurate data while ensuring safe and economical operation.

In the receiver shown in Figure 1, a continuous wave signal is sent from the transmit (Tx) antenna, through the material to be analyzed, and reaches the receive (Rx) antenna. The received signal will be attenuated and phase shifted relative to the original transmitted signal. This amplitude change and phase shift can be used to determine the media content.

Figure 1. Receiver functional block diagram

The amplitude and phase shift can be directly related to the transmittance and reflectance properties of the component, as shown in Figure 2. For example, in an oil-gas-water flow, the dielectric constant, loss, and dispersion are high for water, low for oil, and very low for gas.

Figure 2. Transmittance and reflectance of different homogeneous media

Receiver Subsystem Implementation

The receiver subsystem shown in Figure 3 converts the RF signal into a digital signal for accurate amplitude and phase measurement. The signal chain consists of an orthogonal demodulator, a dual-channel differential amplifier, and a dual-channel differential SAR ADC. The main purpose of this design is to obtain high-precision phase and amplitude measurement results under the condition of high-frequency RF input with large dynamic range.

Figure 3. Simplified receiver subsystem for material analysis.

Quadrature Demodulator

The quadrature demodulator provides an in-phase (I) signal and a quadrature (Q) signal that is exactly 90° out of phase. The I and Q signals are vector quantities, so the amplitude and phase shift of the received signal can be calculated using trigonometric identities, as shown in Figure 4. The local oscillator (LO) input is the original transmitted signal, and the RF input is the received signal. The demodulator generates a sum and difference term. The two signals are exactly the same frequency, ωLO = ωRF, so the result is that the high frequency sum term is filtered out and the difference term resides at DC. The phase of the received signal is φRF, which is different from the phase of the transmitted signal, φLO. This phase shift, φLO – φRF, is a result of the dielectric constant of the medium and helps determine the material content.

Figure 4. Measuring amplitude and phase using a quadrature demodulator.

Real I/Q demodulators have many imperfections, including quadrature phase errors, gain imbalance, LO-RF leakage, etc., all of which degrade the demodulated signal. To select a demodulator, first determine the RF input frequency range, amplitude accuracy, and phase accuracy requirements.

The ADL5380 operates from a single 5 V supply and accepts RF or IF input frequencies from 400 MHz to 6 GHz, making it an ideal choice for receiver signal chains. Depending on the configuration, it can provide 5.36 dB of voltage conversion gain, and its differential I and Q outputs can drive a 2.5 V pp differential signal into a 500 Ω load. At 900 MHz, its noise figure is 10.9 dB, IP1dB is 11.6 dBm, and the third-order intercept point (IIP3) is 29.7 dBm, with excellent dynamic range; while the amplitude balance of 0.07 dB and the phase balance of 0.2° can achieve outstanding demodulation accuracy. It is manufactured using an advanced SiGe bipolar process and is available in a miniature 4 mm × 4 mm, 24-lead LFCSP package. [page]

ADC Drivers and High Resolution Precision ADCs

The ADA4940-2 fully differential dual-channel amplifier has excellent dynamic performance and adjustable output common mode, making it ideal for driving high-resolution dual-channel SAR ADCs. The device operates from a single 5 V supply and provides ±5 V differential outputs at 2.5 V common mode. It can provide a gain of 2 (6 dB) and drive the ADC input to full scale according to the configuration. The RC filter (22 Ω/2.7 nF) helps limit noise and reduce kickback from the capacitive DAC at the ADC input. It is manufactured using a proprietary SiGe complementary bipolar process and is available in a tiny 4 mm × 4 mm, 24-lead LFCSP package.

The AD7903 dual-channel, 16-bit, 1 MSPS successive approximation ADC has excellent accuracy, with a full-scale gain error of ±0.006% and an offset error of ±0.015 mV. The device operates from a single 2.5 V supply and consumes only 12 mW at 1 MSPS. The main goal of using a high-resolution ADC is to achieve ±1° phase accuracy, especially when the dc amplitude of the input signal is small. The 5 V reference required by the ADC is generated by the ADR435 low-noise reference.

The receiver subsystem is implemented using the ADL5380-EVALZ, EB-D24CP44-2Z, EVAL-AD7903SDZ, and EVAL-SDP-CB1Z evaluation kits as shown in Figure 5. These circuit components are optimized for interconnection in the subsystem. Two high frequency phase-locked input sources provide the RF and LO input signals.

Figure 5. Receiver subsystem evaluation platform.

Table 1 summarizes the input and output voltage levels of the various components in the receiver subsystem. At the RF input of the demodulator, a signal of 11.6 dBm produces an input within –1 dB of the ADC full-scale range. The table assumes a 500 Ω load, 5.3573 dB conversion gain, –4.643 dB power gain for the ADL5380, and 6 dB gain for the ADA4940-2. The calibration procedure and performance results for this receiver subsystem are discussed in subsequent sections.

Table 1. Input and output voltage levels for receiver subsystem components

RF Input	ADL5380 Output		AD7903 Input
(dBm)	(dBm)	(V  p-p)	(dBFS)
11.6	6.957	4.455	–1.022
0	–4.643	1.172	–12.622
–20	–24.643	0.117	–32.622
–40	–44.643	0.012	–52.622
–68	–72.643	466 m	–80.622

Receiver Subsystem Error Calibration

There are three main sources of error in the receiver subsystem: offset, gain, and phase.

The individual differential DC amplitudes of the I and Q channels have a sinusoidal relationship to the relative phases of the RF and LO signals. Therefore, the ideal DC amplitudes of the I and Q channels can be calculated as follows:

As the phase shifts through the polar coordinates, some locations should ideally produce the same voltage. For example, the voltage on the I (cosine) channel should be the same for a +90° or –90° phase shift. However, a constant phase shift error (independent of the relative phase of the RF and LO) can cause the subsystem channels to produce different results for input phases that should produce the same DC amplitude. This is shown in Figures 6 and 7, where two different output codes are produced when the input should be 0 V. In this case, the –37° phase shift is much larger than expected for a real system with a phase-locked loop. As a result, +90° actually appears as +53° and –90° appears as –127°.

The results were collected in 10 steps from –180° to +180°, where the uncorrected data produced the ellipses shown in Figures 6 and 7. This error can be accounted for by determining the amount of additional phase shift in the system. Table 2 shows that the system phase shift error is constant over the entire transfer function range.

Table 2. Summary of Measured Phase Shift of Receiver Subsystem at 0-dBm RF Input Amplitude

Input Phase RF to LO	Average I channel output code	Average Q channel output code	I Channel Voltage	Q channel voltage	Measured phase	Measured receiver
						Subsystem Phase Shift
–180°	–5851.294	4524.038	–0.893	0.69	+142.29°	–37.71°
–90°	–4471.731	–5842.293	–0.682	–0.891	–127.43°	–37.43°
0°	5909.982	–4396.769	0.902	–0.671	–36.65°	–36.65°
+90°	4470.072	5858.444	0.682	0.894	+52.66°	–37.34°
+180°	–5924.423	4429.286	–0.904	0.676	+143.22°	–36.78°

System Phase Error Calibration

For the system shown in Figure 5, the average measured phase shift error is –37.32° when the step size is 10°. Knowing this additional phase shift, the adjusted subsystem DC voltage can be calculated. The variable φPHASE_SHIFT is defined as the average value of the observed additional system phase shift. The DC voltage generated in the phase compensation signal chain can be calculated as follows:

For a given phase setting, Equation 5 and Equation 6 provide the target input voltage. Now that the subsystem has been linearized, the offset and gain errors can be corrected. The linearized I and Q channel results are shown in Figure 6 and Figure 7. A linear regression calculation on the data set produces the best fit line shown in the figure. The fit line is the measured subsystem transfer function for each conversion signal chain. [page]

Figure 6. Linearized I channel results

Figure 7. Linearized Q channel results

System O_set error and gain error calibration

The ideal offset of each signal chain in the receiver subsystem should be 0 LSB, however, the measured offsets are –12.546 LSB and –22.599 LSB for the I and Q channels, respectively. The slope of the best fit line represents the slope of the subsystem. The ideal subsystem slope can be calculated as follows:

The results in Figure 6 and Figure 7 show that the measured slopes for the I and Q channels are 6315.5 and 6273.1, respectively. These slopes must be adjusted to correct for system gain error. Correcting for gain error and offset error ensures that the signal amplitude calculated using Equation 1 matches the ideal signal amplitude. Offset correction is the inverse of the measured offset error:

To calculate the sensed analog input voltages for each subsystem signal chain, use Equation 11 on the I and Q channels. Use these fully scaled I and Q channel voltages to calculate the RF signal amplitudes defined by each DC signal amplitude. To evaluate the accuracy of the entire calibration procedure, the collected results can be converted to the ideal subsystem voltages that would be produced at the modulator output assuming no phase shift errors. This can be accomplished by multiplying the average DC amplitude calculated previously by the measured phase sine fraction for each trial (minus the calculated phase shift error). The calculation is as follows:

The φ phase shift is the phase error calculated previously, and the average calibrated magnitude is the DC magnitude result from Equation 1, compensated for offset and gain errors. Table 3 shows the results of the calibration procedure for various target phase inputs at 0 dBm RF input amplitude. The correction factors calculated by Equation 12 and Equation 13 are to be integrated into any system designed to detect phase and magnitude in the manner shown here.

Receiver Subsystem Evaluation Results

Table 3. Results achieved at some target phase inputs for 0 dBm RF input amplitude.

Target Phase	I channel fully calibrated input voltage	Q channel fully corrected input voltage	Fully phase corrected results	Absolute measured phase error
–180°	-1.172 V	+0.00789 V	–180.386°	0.386°
–90°	–0.00218 V	-1.172 V	–90.107°	0.107°
0°	+1.172 V	+0.0138 V	+0.677°	0.676°
+90°	+0.000409 V	+1.171 V	+89.98°	0.020°
+180°	-1.172 V	+0.0111 V	+180.542°	0.541°

Figure 8 shows a histogram of the measured absolute phase error, where the accuracy is better than 1° for every 10° step from –180° to +180°.

Figure 8. Histogram of measured absolute phase error at 0 dBm input level (phase step size of 10°)

In order to accurately measure phase at any given input level, the perceived phase shift error (ϕPHASE_SHIFT) of RF relative to LO should be constant. If the measured phase shift error starts to change as a function of the target phase step size (ϕTARGET) or amplitude, the accuracy of the calibration procedure presented here will begin to degrade. Evaluation results at room temperature show that the phase shift error remains relatively constant for RF amplitudes ranging from a maximum of 11.6 dBm to a minimum of approximately –20 dBm at 900 MHz. [page]

Figure 9 shows the dynamic range of the receiver subsystem and the additional phase error caused by the corresponding amplitude. As the input amplitude drops below –20 dBm, the phase error calibration accuracy begins to degrade. The system user needs to determine the acceptable level of signal chain error to determine the minimum acceptable signal amplitude.

Figure 9. Dynamic range of the receiver subsystem and the corresponding additional phase error.

The results shown in Figure 9 were collected using a 5 V ADC reference. The amplitude of this ADC reference can be reduced, providing the system with a smaller quantization level. This will slightly improve phase error accuracy under small signal conditions, but increase the chance of system saturation. Another good option to increase the dynamic range of the system is to use an oversampling scheme, which can increase the noise-free bit resolution of the ADC. Each doubling of the samples for averaging results in a ½ LSB increase in system resolution. The oversampling ratio for a given resolution increment is calculated as follows:

Oversampling reaches a point of diminishing returns when the noise amplitude is no longer sufficient to randomly change the ADC output code with each sample. At this point, the effective resolution of the system can no longer be increased. The reduction in bandwidth due to oversampling is not a big problem because the system is measuring signals with slowly changing amplitudes.

The AD7903 evaluation software provides a calibration routine that allows the user to correct the ADC output for three error sources: phase, gain, and offset. The user is required to collect the uncorrected results of the system to determine the calibration coefficients calculated in this article. Figure 10 shows the graphical user interface with the calibration coefficients highlighted. Once the coefficients are determined, this panel can be used to calculate the phase and amplitude of the demodulator. The polar coordinates provide a visual representation of the observed RF input signal. The amplitude and phase calculations are calculated using Equations 1 and 2. The oversampling ratio can be controlled by adjusting the number of samples captured at each time using the "Num Samples" drop-down box.

Figure 10. Receiver subsystem calibration GUI

in conclusion

This article discusses the key challenges faced in remote sensing applications and proposes a new solution using the ADL5380, ADA4940-2, and AD7903 receiver subsystem to accurately and reliably measure material content. The proposed signal chain features a wide dynamic range, achieving a measurement range of 0° to 360° with better than 1° accuracy at 900 MHz.