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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