CN0374

The frequency range of the circuit can be extended to lower frequencies by using the ADL5387 30 MHz to 2 GHz quadrature demodulator.

Depending on the specific application, the amplifier between the demodulator and ADC may or may not be necessary. The ADL5380 can interface directly to the AD7903 because the common-mode voltages of both devices are compatible. If using an alternative ADC with a common-mode voltage that is not within the range of the demodulator, an amplifier is necessary to achieve the level translation with minimal power loss.

The AD798x and AD769x family of ADCs can be used as alternatives to the AD7903.

As shown in Figure 3, the receiver subsystem is implemented using the ADL5380-EVALZ, ADA4940-2ACP-EBZ, EVAL-AD7903SDZ, and EVAL-SDP-CB1Z evaluation kits. These circuit components are optimized for interconnection in the subsystem. Two high frequency, phase-locked input sources provide the RF and LO input signals.

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

Receiver Subsystem Error Calibration

The receiver subsystem contains three major error sources: offset, gain, and phase.

The individual differential dc magnitudes of the I and Q channels have sinusoidal relationships with respect to the relative phase of the RF and LO signals. As a result, the ideal dc magnitude of the I and Q channels can be calculated as follows:

As the phase moves through the polar grid, some locations ideally produce the same voltage. For example, the voltage on the I (cosine) channel should be identical with phase shifts of +90° or −90°. However, a constant phase shift error, independent of the relative phase of RF and LO, causes the subsystem channel to generate different results for input phases that should produce the same dc magnitude. This is illustrated in Figure 4 and Figure 5, where two different output codes are generated when the input should be at 0 V. In this case, the −37° phase shift is much larger than expected in a real-world system containing phase-locked loops. The result is +90° actually appearing as +53°, and −90° as −127°.

Results were gathered in 10° steps from −180° to +180°, with the uncorrected data generating the elliptical shapes shown in Figure 4 and Figure 5. This error can be accounted for by determining the amount of additional phase shift present in the system. Table 2 shows that the system phase shift error is constant throughout the transfer function.

System Phase Error Calibration

With a step size of 10°, the average measured phase shift error was −37.32° for the system shown in Figure 3. With this additional phase shift known, the adjusted subsystem dc voltages can now be calculated. The variable φ_{PHASE_SHIFT} is defined as the average observed additional system phase shift. The dc voltage generated in the phase-compensated signal chain can be computed as

Equation 5 and Equation 6 provide the target input voltage for a given phase setting. The subsystem has now been linearized, and the offset error and gain error can now be corrected. The linearized I and Q channel results can also be seen in Figure 4 and Figure 5. A linear regression on the data sets generates the best fit line shown in the figures. This line is the measured subsystem transfer function for each conversion signal chain.

System Offset and Gain Error Calibration

The offset of each signal chain within the receiver subsystem is ideally 0 LSB; however, the measured offsets were −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

The results in Figure 4 and Figure 5 show that that measured slopes were 6315.5 and 6273.1 for the I and Q channels, respectively. These slopes must be adjusted to correct the system gain error. Correcting for gain error and offset error ensures that the signal magnitude computed using Equation 1 matches the ideal signal magnitude. The offset correction is the opposite of the measured offset error:

The gain error correction coefficient is

The received conversion result can be corrected by

The calibrated dc input voltage of the subsystem is calculated as

Use Equation 11 on both the I and Q channels to compute the perceived analog input voltage for each subsystem signal chain. These fully adjusted I and Q channel voltages are used to compute the RF signal amplitude as defined by the individual dc signal magnitudes. To evaluate the accuracy of the full calibration routine, convert the collected results to ideal subsystem voltages produced at the output of the demodulator as if no phase shift error were present; multiply the average dc magnitude computed previously by the sinusoidal fraction of the measured phase at each trial with the computed phase shift error removed. The calculation is as follows:

where:

φPHASE_SHIFT is the phase error previously computed. Average Post Calibration Magnitude is the dc magnitude result from Equation 1 that has been compensated for offset error and gain error.

Table 3 shows the results of the calibration routine at various target phase inputs for the 0 dBm RF input amplitude case. The calculations performed in Equation 12 and Equation 13 are the correction factors to be built into any system intended to sense phase and magnitude in the manner described in this circuit note.

Figure 6 is a histogram of the measured absolute phase error showing better than 1° accuracy for every 10° step from −180° to +180°.

For accurate phase measurements at any given input level, the perceived phase shift error (φ_{PHASE_SHIFT}) of RF relative to LO must be constant. If the measured phase shift error begins to change as a function of the target phase step (θ_TARGET) or amplitude, the calibration routine presented in this section begins to lose accuracy. Evaluation results at room temperature show that the phase shift error is relatively constant for RF amplitudes ranging from a maximum of 11.6 dBm to approximately −20 dBm at 900 MHz.

Figure 7 shows the dynamic range of the receiver subsystem along with the corresponding amplitude-induced additional phase error. As the input amplitude decreases past −20 dBm, the phase error calibration accuracy begins to degrade. The system user must determine the acceptable level of signal chain error to determine the minimum acceptable signal magnitude.

The results shown in Figure 7 were collected with a 5 V ADC reference. The magnitude of the ADC reference can be reduced, providing a smaller quantization level for the system, which provides an incremental improvement in phase error accuracy for small signals but increases the chance for system saturation. To increase system dynamic range, another option is to implement an oversampling scheme that increases the noise-free bit resolution of the ADC. Every doubling in samples averaged provides a ½ LSB increase in system resolution. The oversampling ratio for a given resolution increase is calculated as follows:

where N is the number of bits increase.

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

The AD7903 evaluation software is available with a calibration routine that allows the user to correct the ADC output results for the three sources of error: phase, gain, and offset. The user must collect uncorrected results with their system to determine the calibration coefficients calculated in this circuit note. Figure 8 shows the Amp/Phase Panel tab of the GUI with the calibration coefficients highlighted. When the coefficients are determined, this tab can also be used to deliver phase and magnitude results from the demodulator. The polar plot provides a visual indication of the observed RF input signal. The amplitude and phase calculations are performed using Equation 1 and Equation 2. The oversampling ratio can be controlled by adjusting the number of samples per capture using the Num Samples drop-down box.

Equipment Needed

The following equipment are used to evaluate the circuit.

• A Windows^® XP, Windows Vista (32-bit), or Windows 7 (32-bit) PC with USB port.
• The ADL5380-EVALZ, EVAL-AD7903SDZ, and EVAL-SDP-CB1Z evaluation boards.
• Two RF signal generators with phase control (such as the R&S SMT06).
• A digital multimeter.
• 5 V and 9 V power supplies.
• The AD7903 evaluation software, used to digitally process the resulting magnitude and phase information.