Observer-Based Test in Analog/RF Circuits
Sule OzevArizona State University
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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
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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
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
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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
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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
2 (1, )y NCUT1…N
f1…N(x)
2x
Learning Machine
2 2( , )h x y),1(),,1(2 NSNy
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
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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
Transceiver System Response
ItxddcItx
txddctxQtx
txddcrxtxdtxd
ddcrxtxdout
DCtDCG
tgDCG
tttQG
tttIGI
)cos(2
)sin()1(2
)sin()(2
)cos()(2
QrxrxddcrxItxrxtxddcrxtxQtx
txrxddcdtxrxtxdtxdtxrx
rxddcdrxrxtxdrxout
DCtgDCGtggDCG
tttQggG
tttIgGQ
)sin()1(2
)cos()1)(1(2
)cos()()1)(1(2
)sin()()1(2
Challenges:- Full-path behavior of the system is complex
- Finding an analytical time domain solution is not feasible
Proposed Method Assuming ddct
IrxItxtxtxQtx
txrxtxdtxdtxrxtxdout
DCDCgDCG
ttQgGttIGI
)cos(21)sin()1(
2
)sin()()1(2
)cos()(2
Qout G2(1 grx)I(t td tx rx drx)sin( rx)
G2(1 grx)(1 gtx)Q(t td dtx tx rx dtx)cos( rx tx)
G2DCQtx (1 gtx)(1 grx)cos( tx rx)
12DCItx(1 grx)sin( rx)DCQrx
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.
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Proposed Methodology
• 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.
φ1
φ2
Challenge: 6 distinct measurements (Signal amplitude, DC offsets) in each measurements but 9 unknowns.Solution: Changing loop-back delay generates more linearly independent equation
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ratio based equations are proposed to analytically find the system impairments:
Analytical Derivation:
AI
I
II
Q
Q
I
I
out
out
out
out 1
2
2
1
.
BQ
Q
II
Q
Q
I
I
out
out
out
out 1
2
2
1
.
CQQ
II
I
I
I
I
out
out
out
out 1
2
2
1
.
• Similar unknowns would be removed in nominator and denominator• Left side of the equations are determined by amplitude measurement.
1IoutI : output signal amplitude on
I arm in φ1 phase while I arm at the input is non-zero.
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Substituting from Eq(1) and Eq(2) and simplifying we have 3 equations, 4 unknowns:
Analytical Derivation:
Atx
tx
)sin()sin(.
coscos
1
2
2
1
Btxrx
txrx
)cos()cos(.
coscos
1
2
2
1
Crx
rx
)sin()sin(.
coscos
1
2
2
1
• 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
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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
)cos( 1IoutIG
1)sin(.
tx
outtx G
Ig Q
1)sin(.
rx
outrx G
Qg I
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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
IrxItxQtxout DCDCaDCaIDC
211
IrxItxQtxout DCDCaDCaIDC
432
QrxItxQtxout DCDCbDCbQDC
211
QrxItxQtxout DCDCbDCbQDC
432
))(())(())(())((
21434321
1121
2143
aabbaabbQQaaIIaa
DC outDCoutoutoutQtx
DCDCDC
)()()(
21
2121
aaDCbbII
DC QtxoutoutItx
DCDC
QtxItxoutIrx DCbDCaIDCDC 111
QtxItxoutQrx DCbDCaQDCDC 331
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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
in
outoutdtx
in
outoutdrx
f
IIf
QI
QI
II
2
)arg()arg(2
)arg()arg(
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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
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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
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Hardware Measurement Result:Parameter Actual Computed Error
TX Phase MM 1˚ 1.58˚ 0.58˚
RX Phase MM 2˚ 1.76˚ 0.24˚
TX Gain MM 10% 10.7% 0.7%
RX Gain MM 25% 26.7% 1.7%
Irx-Dcoffset 20mV 22.6mV 2.6mV
Qrx-Dcoffset 15mV 12.5mV 2.5mV
Parameter Actual Computed Error
TX Phase MM 4˚ 5.87˚ 1.87˚
RX Phase MM 2˚ 1.25˚ 0.75˚
TX Gain MM 25% 25% 0%
RX Gain MM 15% 16% 1%
Irx-Dcoffset -20mV -18mV 2mV
Qrx-Dcoffset 10mV 9.4mV 0.6mV
Parameter Actual Computed Error
TX Phase MM 3˚ 5.43˚ 2.43˚
RX Phase MM 2˚ 1˚ 1˚
TX Gain MM 30% 29.3% 0.7%
RX Gain MM 15% 14.7% 0.3%
Irx-Dcoffset -15mV -14.8mV 0.2mV
Qrx-Dcoffset 10mV 9.4mV 0.6mV
• 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.
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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
System Model
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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 ParametersGain mismatch gtx
Self mixing delay
td
Phase Mismatch φtxLO frequency ωc
TX DC offsets DCItx,DCQtx Path gain GBaseband time skew
TdtxSelf mixing attenuation
K
Baseband Delay
ttx
Proposed Methodology
))sin()1)()(()cos())(()(
txdctxQtxtxdtx
cItxtxout
tgDCtQGtDCtIGtRF
)()()sin()1(
)()1(21
)())1()sin()(1(
)()())sin()1((
)sin()1())1((21)(
2
222
2
222
2222
2
ddtxtxdtxtxtx
ddtxtxtx
ddtxtxQtxtxtxItxtx
dtxdtxQtxtxtxItx
txQtxItxtxQtxtxItxout
ttQttIgKG
ttQgKG
ttQDCgDCgKG
ttIKGttIDCgDC
KG
DCDCgKGDCgDC
KGtS
Transmitter output signal:
Detector output signal in terms of transmitter inputs:
Eq(1)
The effect of impairments are convoluted in the overall signal and separation of these parameters is not straight forward.
Eq(2)
ADC 12GK
2
(12
12(1 gtx)
2 DCItx2
(1 gtx)2DC2Qtx )
GK
2
(1 gtx)DCItxDCQtx sin(tx)
Aw1 GK
2
DCItx GK
2
(1 gtx)DCQtx sin(tx)
Aw2 GK
2
(1 gtx)DCItx sin(tx)GK
2
(1 gtx)2DCQtx
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,1,2,21,22,12,12as it is
shown in the figure.
I(t) cos(w1t)
Q(t) cos(w2t)
A2w1 14GK
2
A2w2 14GK
2
(1 gtx)2
Aw1w2 12GK
2
(1 gtx)sin(tx)
Aw1 w2 12GK
2
(1 gtx)sin(tx)
- Signal amplitude in different frequencies:
Proposed Methodology
There are 7 equations, but there are 5 usable linearly independent equations and 5 unknowns as:• 21and22Have 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:
124 wAKG
1
41 2
22
KGAg w
tx
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.
)(cos)1(
)sin()1(
)(cos)1(
)sin()1(
222
12
22
21
txtx
txtxwwQtx
txtx
txwtxwItx
gKG
gAADC
gKG
AgADC
22)22arg(
12)12arg(
ww
ww
drx
)1(21
sin 2211
tx
wwtx
gKGA
Proposed Methodology
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Hardware Measurements: Off-the Shelf Components as TX and RX
Cases Actual Computed Error
Case1 Gain MM -5% -5.1% 0.1%Phase MM 1˚ 1.1˚ 0.1˚DC Itx 10mV 12.6mV 2.6mVDC Qtx 10mV 10.6mV 0.6mv
Case2 Gain MM 15% 16% 1.0%Phase MM 4˚ 4.37˚ 0.37˚DC Itx 20mV 23.2mV 3.2mVDC Qtx 30mV 19.7mV 10.3mV
Case3 Gain MM 20% 21% 1%Phase MM 5˚ 5.47˚ 0.47˚DC Itx 10mV 10.5mV 0.5mVDC Qtx 20mV 9.1mV 10.9mV
- 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
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Measurement Results
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Non-linearity Results
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IQ Imbalance for the above measurements Case 1 Case 2 Case 3 Case 4 Case 5gtx 0 0.1 0.15 0.2 0.2Phtx1 (deg) 0 1 4 5 3Idc1 (V) 0 0.01 0.02 0.01 0Qdc1 (V) 0 0.02 0.03 0.02 0
IIP3 of PA (dBm)
Actual ExtractedCase 1 5.8 5.1Case 2 5.8 5.7Case 3 5.8 6.1Case 4 5.8 6.0Case 5 5.8 5.3
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
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