Observer-Based Test in Analog/RF
Circuits
Sule Ozev
Arizona State University
Outline
 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
2
Introduction
 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
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
Statistical Training
x2
CUT1…N
f1…N(x)
y2 (1, N )
h( x2 , y2 )
y2 (1, N ), S (1, N )
Learning Machine
 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
6
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
Observer-based Testing of RF Transceivers
 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 loopback 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.
8
Transceiver System Response
Challenges:
- Full-path behavior of the system is complex
- Finding an analytical time domain solution is
not feasible
I out 
G
I (t  t d   tx   rx ) cos(c t d   d ) 
2
G
Q(t  t d   dtx   tx   rx ) sin( c t d   d  tx ) 
2
G
DCQtx (1  g tx ) sin( c t d   d  tx ) 
2
G
DC Itx cos(c t d   d )  DC Itx
2
Qout  
G
(1  g rx ) I (t  t d   tx   rx   drx ) sin( ct d   d   rx ) 
2
G
(1  g rx )(1  g tx )Q(t  t d   dtx   tx   rx   dtx ) cos(c t d   d   rx  tx ) 
2
G
G
DCQtx (1  g tx )(1  g rx ) cos(ct d   d  tx   rx )  DC Itx (1  g rx ) sin( ct d   d   rx )  DCQrx
2
2
Proposed Method
 Assuming
  ctd  d
Iout_I
Iout_Q
G
G
I (t  t d   tx   rx ) cos( )  (1  g tx )Q(t  t d   dtx   tx   rx ) sin(   tx ) 
2
2
G
1
DC Qtx (1  g tx ) sin(   tx )  DC Itx cos( )  DC Irx
Eq(1)
2
2
I out 
Using a special input we
have access to each part of
these equation in order to
find all the unknowns.
Iout_DC
Qout_I
Qout  
G
(1 grx )I(t  t d   tx   rx   drx )sin(   rx ) 
2
Qout_Q
G
(1 grx )(1 gtx )Q(t  t d   dtx   tx   rx   dtx )cos(  rx  tx ) 
2
G
1
DCQtx (1 gtx )(1 grx )cos(  tx  rx )  DC Itx (1 grx )sin(   rx )  DCQrx
2
2
Qout_DC
Eq(2)
Proposed Methodology
φ1
φ2
• 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.
Challenge: 6 distinct measurements
(Signal amplitude, DC offsets) in each
measurements but 9 unknowns.
Solution: Changing loop-back delay
generates more linearly independent
equation
11
Analytical Derivation:
 ratio based equations are proposed to analytically
find the system impairments:
1
I out I
2
.
2
I out
Q
1
I out I I outQ
1
I out
I : output signal amplitude on
A
2
1
Q
I out
out Q
I
. 1  B
2
I out I QoutQ
1
2
I out
Q
out I
I
.
C
2
1
I out I Qout I
I arm in φ1 phase while I arm at
the input is non-zero.
• Similar unknowns would be
removed in nominator and
denominator
• Left side of the equations
are determined by amplitude
measurement.
12
Analytical Derivation:
 Substituting from Eq(1) and Eq(2) and
simplifying we have 3 equations, 4 unknowns:
cos 1 sin(  2   tx )
.
A
cos  2 sin( 1   tx )
cos 1 cos( 2   rx   tx )
.
B
cos  2 cos(1   rx   tx )
cos 1 sin(  2   rx )
.
C
cos  2 sin( 1   rx )
• 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
13
Path Gain and Gain Mismatch
Calculation
 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:
G
g tx 
I out I
cos(1 )
I out
g rx 
Q
G. sin(    tx )
Qout I
 G. sin(    rx )
1
1
14
DC Offsets Calculation
 In next step we have 4 equation and 4 unknowns
for DC offsets
• All the coefficients are a function of already known parameters
. I 1  a DC  a DC  DC
Q1  b DC  b DC  DC
out DC
1
Qtx
2
Itx
Irx
2
I out
 a3 DCQtx  a4 DCItx  DCIrx
DC
out DC
1
Qtx
2
Itx
Qrx
2
Qout
 b3 DCQtx  b4 DCItx  DCQrx
DC
 Solving those equations:
DCQtx 
DC Itx 
1
2
1
1
(a3  a4 )( I out

I
)

(
a

a
)(
Q

Q
out DC
1
2
out DC
outDC )
DC
(b1  b2 )(a3  a4 )  (b3  b4 )(a1  a2 )
1
2
( I out

I
out DC )  (b1  b2 ) DCQtx
DC
(a1  a2 )
1
DCQrx  Qout
 a3 DCItx  b3 DCQtx
DC
1
DCIrx  I out
 a1 DCItx  b1 DCQtx
DC
15
Differential Delays Extraction
 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:
 drx 
 dtx 
arg( I out I )  arg( Qout I )
2f in
arg( I out I )  arg( I outQ )
2f in
16
Test Time
 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.
17
Hardware Measurement Set-up
 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.
18
Hardware Measurement Result:
Parameter
Actual
Computed
Error
Parameter
Actual
Computed
Error
TX Phase MM
1˚
1.58˚
0.58˚
TX Phase MM
4˚
5.87˚
1.87˚
RX Phase MM
2˚
1.76˚
0.24˚
RX Phase MM
2˚
1.25˚
0.75˚
TX Gain MM
10%
10.7%
0.7%
TX Gain MM
25%
25%
0%
RX Gain MM
25%
26.7%
1.7%
RX Gain MM
15%
16%
1%
Irx-Dcoffset
20mV
22.6mV
2.6mV
Irx-Dcoffset
-20mV
-18mV
2mV
Qrx-Dcoffset
15mV
12.5mV
2.5mV
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˚
• These results show the analytical
computation follows the actual
values.
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
• Measurements display slightly
higher error due to noise in the
system, equipment limitations,
and potential unmodeled
behavioral deviations.
19
Sensor-based Tx Testing
 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
20
System Model
Transmitter and BIST System level block diagram including modeled impairments:
Parameters
Parameters
Gain mismatch
gtx
Self mixing
delay
td
Phase Mismatch
φtx
LO frequency
ωc
TX DC offsets
DCItx,DCQtx
Path gain
G
Baseband time
skew
Tdtx
Self mixing
attenuation
K
Baseband
Delay
ttx
- Only amplitude
information is used to
determine target
parameters, which can
be easily obtained using
FFT at the desired
frequency locations.
21
Proposed Methodology
Transmitter output signal:
RFout (t )  G ( I (t   tx )  DC Itx ) cos(c t ) 
G (Q(t   dtx   tx )  DCQtx )(1  gtx ) sin( c t d   tx ))
Eq(1)
Detector output signal in terms of transmitter inputs:
2
2
1G 
G 
2
2
S out (t )    ( DC Itx  (1  g tx ) 2 DCQtx )     (1  g tx ) DC Itx DCQtx sin(  tx ) 
2 K 
K
2
2
G 
G  2
  ( DC Itx  (1  g tx ) sin(  tx ) DCQtx ) I (t   tx  t d )    I (t   tx  t d ) 
K
K
2
G 
  (1  g tx )( DC Itx sin(  tx )  (1  g tx ) DCQtx )Q (t   tx   dtx  t d ) 
K
2
1G 
2
2
  (1  g tx ) Q (t   tx   dtx  t d ) 
2 K 
2
G 
  (1  g tx ) sin(  tx ) I (t   tx  t d )Q (t   tx   dtx  t d )
K
The effect of impairments are
convoluted in the overall
signal and separation of
these parameters is not
straight forward.
Eq(2)

Proposed Methodology

A special test signal is designed to separate
out the effect of each impairment parameters:
I(t)  cos(w1t)

Q(t)  cos(w2t)
If the frequency of the two signals are distinct
then the information will be separated out to
DC, 1,2,21,22,12 ,12 as it is

shown in the figure.
- Signal amplitude in different frequencies:
1 G  1 1
   (  (1 gtx ) 2  DC Itx 2 
2 K  2 2
2
ADC
2
(1 gtx ) DC
2
Qtx
G 2
)    (1 gtx )DC Itx DCQtx sin( tx )
K 
G 2
G 2
Aw1    DC Itx    (1 gtx )DCQtx sin( tx )
K 
K 
Aw 2
G 2
G 2
   (1 gtx )DC Itx sin( tx )    (1 gtx ) 2 DCQtx
K 
K 
1 G 
A2w1   
4 K 
2
1 G 
   (1 gtx ) 2
4 K 
2
A2w 2
Aw1w 2
1 G 
   (1 gtx )sin( tx )
2 K 
Aw1w 2
2
1 G 
   (1 gtx )sin( tx )
2 K 
2
Proposed Methodology
 There are 7 equations, but there are 5 usable linearly independent
equations and 5 unknowns as:
• 21and 22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:
G 
   4  A2 w1
K
gtx 
A2 w 2
1G 
 
4 K 
2
1
Proposed Methodology
 Step3:
 Step4:




Aw1 w 2


 tx  sin 1 
2

1
G


   (1  gtx ) 
2 K

  

DC Itx 
DCQtx 
Aw1 (1  gtx )  Aw 2 sin(  tx )
2
G 
2
  (1  gtx ) cos ( tx )
K
Aw 2  Aw1 (1  gtx ) sin(  tx )
2
G 
2
2
  (1  gtx ) cos ( tx )
K
 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.
 drx
arg( 2 w1) arg( 2 w 2)


2 w1
2w 2
Hardware Measurements: Off-the Shelf
Components as TX and RX
Cases
Case1
Case2
Case3
Actual
Computed
Error
Gain MM
-5%
-5.1%
0.1%
Phase MM
1˚
1.1˚
0.1˚
DC Itx
10mV
12.6mV
2.6mV
DC Qtx
10mV
10.6mV
0.6mv
Gain MM
15%
16%
1.0%
Phase MM
4˚
4.37˚
0.37˚
DC Itx
20mV
23.2mV
3.2mV
DC Qtx
30mV
19.7mV
10.3mV
Gain MM
20%
21%
1%
Phase MM
5˚
5.47˚
0.47˚
DC Itx
10mV
10.5mV
0.5mV
DC 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.
26
Hardware Measurement Setup:
Bench Equipment as TX and RX
27
Measurement Results
28
Non-linearity Results
IIP3 of PA (dBm)
Actual
5.8
5.8
5.8
5.8
5.8
Case 1
Case 2
Case 3
Case 4
Case 5
Extracted
5.1
5.7
6.1
6.0
5.3
IQ Imbalance for the above measurements
Case 1
Case 2
Case 3 Case 4
Case 5
gtx
0
0.1
0.15
0.2
0.2
Phtx1 (deg)
0
1
4
5
3
Idc1 (V)
0
0.01
0.02
0.01
0
Qdc1 (V)
0
0.02
0.03
0.02
0
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