Observer-Based Test in Analog/RF Circuits Sule Ozev Arizona State University

 Introduction  Challenges facing characterization, production test, and built-in test for integrated RF/Analog circuits  Observer based test  Application of observer based test for RF transceivers Outline 2

 Each manufactured device needs to be electrically tested for defects and process deviations  These tests often require measurement of hundreds of parameters related to the performance of the device  Each measurement may require a different set-up  The inputs are specified to excite certain characteristics, and the output is analyzed for one performance parameter at a time  Targeted parameter measurements often complicate load board design and result in long test times  These measurement set-up are often not amenable to on-chip implementation due to complexity Introduction 3

Observer-based testing  Overall behavior of the system includes all of its parameters  If excited and analyzed in the right manner, his behavior can be used to measure multiple parameters at once, often with less complex test signals  To facilitate such an approach, the observer (i.e. an input-output model) of the complex system needs to be defined  Using the observer functions, test signals can be designed to target multiple parameters 4

Modeling Approaches  Two approaches are prevalent for the modeling of the system Statistical modeling: learning the behavior by observing the input-output signals of a set of sample devices Analytical modeling: deriving the necessary mathematical expressions from ground up 5

6 Statistical Training  Learning machine can be linear or non-linear Linear regression Non-linear regression Neural networks, etc.  For statistical training, samples of CUT are necessary –Simulations –Manufactured samples  Excitation plays an important role in establishing the statistical model CUT 1…N f 1…N (x) Learning Machine

Analytical Derivation  Requires larger manual effort in model derivation  Provides a comprehensive model of the system (i.e. not limited to a population)  Excitation patterns can be determined by setting conditions on the observation patterns 7

 Deriving the full model of the system enables us to Determine the best excitation patterns to decouple parameters of interest Identify which parameters can be measured under which conditions Identify the parameters that are linearly dependent and cannot be decoupled (or find solutions for such problems)  Application of model-based testing to Tx-Rx loop: Low-frequency signal analysis An analytical technique to measure IQ imbalances in the loop- back mode Excite the system with sinusoidal-based test signal. Test signal is designed to separate the effect of impairments. Use a programmable delay in the loopback path, to generate linearly independent measurements. Calculations based on ratio of measured amplitudes to eliminate uncertainty in the path. Observer-based Testing of RF Transceivers 8

Transceiver System Response Challenges: - Full-path behavior of the system is complex - Finding an analytical time domain solution is not feasible

Proposed Method  Assuming Iout_I Iout_Q Qout_I Qout_Q Iout_DC Qout_DC Eq(1) Eq(2 ) Using a special input we have access to each part of these equation in order to find all the unknowns.

Proposed Methodology 11 Cross talk is due to fact that RF and LO signals are not fully synchronized and IQ imbalance in the system. Since signals are decoupled in time domain, the amplitudes can be measured directly. φ1φ1 φ2φ2 Challenge: 6 distinct measurements (Signal amplitude, DC offsets) in each measurements but 9 unknowns. Solution: Changing loop-back delay generates more linearly independent equation

 ratio based equations are proposed to analytically find the system impairments: Analytical Derivation: 12 Similar unknowns would be removed in nominator and denominator Left side of the equations are determined by amplitude measurement. : output signal amplitude on I arm in φ 1 phase while I arm at the input is non-zero.

 Substituting from Eq(1) and Eq(2) and simplifying we have 3 equations, 4 unknowns: Analytical Derivation: 13 The absolute value of the loop-back phase is not important as long as the two phases are different and the difference is known. So we will have 3 equations and 3 unknowns. Solving these 3 equations we will have φ1, transmitter phase mismatch as well as phase mismatch in receiver. These equations have 2 sets of answers that we pick the right one by using already known information and checking the part of equation that is not used

 Calculating phase unknowns. We can find independent equations for all other unknowns.  Substituting the extracted phases, we can calculate path gain as well as gain mismatch in transmitter and receiver as follow: Path Gain and Gain Mismatch Calculation 14

 In next step we have 4 equation and 4 unknowns for DC offsets All the coefficients are a function of already known parameters.  Solving those equations: DC Offsets Calculation 15

 In order to find the differential delays between I and Q channels we are using the phase of the signal on input signal frequency in each part of the output. Using Eq(1) and Eq(2) we have: Differential Delays Extraction 16

 Data processing time is dominated by the 128-point FFT to determine the amplitudes.  In order to increase accuracy and reduce errors due to noise, measurements are repeated 5 times and average the FFT amplitudes and phase measurements.  The total test time for our approach to compute all of these impairments thus is 1.9 ms on a 2.4GHz computer. Test Time 17

 In order to evaluate the accuracy of the computation method in presence of unmodeled effects, an experiments is conducted on a hardware platform.  A simple transceiver structure is formed out of discrete components. Hardware Measurement Set-up 18

Hardware Measurement Result: 19 ParameterActualComputedError TX Phase MM1˚1.58˚0.58˚ RX Phase MM2˚1.76˚0.24˚ TX Gain MM10%10.7%0.7% RX Gain MM25%26.7%1.7% Irx-Dcoffset20mV22.6mV2.6mV Qrx-Dcoffset15mV12.5mV2.5mV ParameterActualComputedError TX Phase MM4˚5.87˚1.87˚ RX Phase MM2˚1.25˚0.75˚ TX Gain MM25% 0% RX Gain MM15%16%1% Irx-Dcoffset-20mV-18mV2mV Qrx-Dcoffset10mV9.4mV0.6mV ParameterActualComputedError TX Phase MM3˚5.43˚2.43˚ RX Phase MM2˚1˚ TX Gain MM30%29.3%0.7% RX Gain MM15%14.7%0.3% Irx-Dcoffset-15mV-14.8mV0.2mV Qrx-Dcoffset10mV9.4mV0.6mV These results show the analytical computation follows the actual values. Measurements display slightly higher error due to noise in the system, equipment limitations, and potential unmodeled behavioral deviations.

 Design-for-test (or Built-in-self-test) is desirable for testing RF devices for both on-chip and production testing  Most DFT/BIST techniques convert the RF signal to low-frequency equivalent for processing –Simple test set-up –Feasible on chip analysis –No RF signal analysis  Model-based testing can be used to derive a complete response and find ways to de-embed parameters of interest Sensor-based Tx Testing 20

System Model 21 Transmitter and BIST System level block diagram including modeled impairments: - Only amplitude information is used to determine target parameters, which can be easily obtained using FFT at the desired frequency locations. Parameters Gain mismatch g tx Self mixing delay tdtd Phase Mismatch φ tx LO frequency ωcωc TX DC offsets DC Itx,DC Qtx Path gain G Baseband time skew T dtx Self mixing attenuation K Baseband Delay t tx

Proposed Methodology Transmitter output signal: Detector output signal in terms of transmitter inputs: The effect of impairments are convoluted in the overall signal and separation of these parameters is not straight forward.

 A special test signal is designed to separate out the effect of each impairment parameters:  If the frequency of the two signals are distinct then the information will be separated out to DC,                  as it is shown in the figure. - Signal amplitude in different frequencies: Proposed Methodology

 There are 7 equations, but there are 5 usable linearly independent equations and 5 unknowns as:   and   Have the same amplitude. DC terms is not usable, as the blocks offset will be added to DC term and the LO leakage will self mix with itself and show up on DC term.  Impairment Calculation Steps:  Step1 - Path Gain:  Step2 – Gain imbalance: Proposed Methodology

 Step3:  Step4:  Calculating time skews: The envelope signal phase is a function of delays in the baseband path. So measuring the difference of these delays will give us the time skews. Proposed Methodology

Hardware Measurements: Off-the Shelf Components as TX and RX 26 CasesActualComputedError Case1 Gain MM -5%-5.1%0.1% Phase MM 1˚1.1˚0.1˚ DC Itx 10mV12.6mV2.6mV DC Qtx 10mV10.6mV0.6mv Case2 Gain MM 15%16%1.0% Phase MM 4˚4.37˚0.37˚ DC Itx 20mV23.2mV3.2mV DC Qtx 30mV19.7mV10.3mV Case3 Gain MM 20%21%1% Phase MM 5˚5.47˚0.47˚ DC Itx 10mV10.5mV0.5mV DC Qtx 20mV9.1mV10.9mV - Measurements display slight error due to: - Noise in the system, - Equipment limitations. However the errors are well within acceptable range.

Hardware Measurement Setup: Bench Equipment as TX and RX 27

Measurement Results 28

Non-linearity Results 29

Conclusions  Observer-based test provides an efficient way to characterize the performance of analog/RF devices  Observer models can be developed statistically or analytically, or through a hybrid of the two  In-field testing can also be enabled by enforcing the observer to work with simpler test signals and low-frequency analysis  Demonstration on RF transceivers shows that the test time can be reduced from 500ms to below 10ms 30