1. Oct. 7, 04ELEC5970-003/6970-003 (Guest Lecture)1 Automatic Linearity (IP3) Test with Built-in Pattern Generator and Analyzer Foster Dai, Charles Stroud, Dayu Yang Dept. of Electrical and Computer Engineering Auburn University

2. Oct. 7, 04ELEC5970-003/6970-003 (Guest Lecture)2 Purpose Develop Built-In Self-Test (BIST) approach using direct digital synthesizer (DDS) for functionality testing of analog circuitry in mixed-signal systemsDevelop Built-In Self-Test (BIST) approach using direct digital synthesizer (DDS) for functionality testing of analog circuitry in mixed-signal systems Provides BIST-based measurement ofProvides BIST-based measurement of –Amplifier linearity (IP3) –Gain and frequency response Implemented in hardwareImplemented in hardware –IP3, gain, and freq. response measured

3. Oct. 7, 04ELEC5970-003/6970-003 (Guest Lecture)3 Outline Overview of direct digital synthesizer (DDS)Overview of direct digital synthesizer (DDS) 3 rd order inter-modulation product (IP3)3 rd order inter-modulation product (IP3) BIST architectureBIST architecture –Test pattern generator –Output response analyzer Experimental resultsExperimental results –Implementation in hardware –IP3 Measurements

4. Oct. 7, 04ELEC5970-003/6970-003 (Guest Lecture)4 Linear vs. Nonlinear Systems A system is linear if for any inputs x 1 (t) and x 2 (t), x 1 (t)  y 2 (t), x 2 (t)  y 2 (t) and for all values of constants a and b, it satisfiesA system is linear if for any inputs x 1 (t) and x 2 (t), x 1 (t)  y 2 (t), x 2 (t)  y 2 (t) and for all values of constants a and b, it satisfies a x 1 (t)+bx 2 (t)  ay 1 (t)+by 2 (t) a x 1 (t)+bx 2 (t)  ay 1 (t)+by 2 (t) A system is nonlinear if it does not satisfy the superposition law.A system is nonlinear if it does not satisfy the superposition law.

5. Oct. 7, 04ELEC5970-003/6970-003 (Guest Lecture)5 A system is time invariant if a time shift in input results in the same time shift in output, namely,A system is time invariant if a time shift in input results in the same time shift in output, namely, if x(t)  y(t), then x(t-  )  y(t-  ), for all value of  if x(t)  y(t), then x(t-  )  y(t-  ), for all value of  A system is time variant if it does not satisfy the condition.A system is time variant if it does not satisfy the condition. Time Invariant vs. Time Variant Systems

6. Oct. 7, 04ELEC5970-003/6970-003 (Guest Lecture)6 Memoryless Systems A system is memoryless if its output does not depend on the past value of its input.A system is memoryless if its output does not depend on the past value of its input. For a memoryless linear system, y(t) = αx(t)For a memoryless linear system, y(t) = αx(t) w here  is a function of time if the system is time variant. w here  is a function of time if the system is time variant. For a memoryless nonlinear system,For a memoryless nonlinear system, y(t) = α 0 + α 1 x(t) + α 2 x²(t)+ α 3 x³(t) + ······ y(t) = α 0 + α 1 x(t) + α 2 x²(t)+ α 3 x³(t) + ······ where  j are in general function of time if the system is time variant. where  j are in general function of time if the system is time variant.

7. Oct. 7, 04ELEC5970-003/6970-003 (Guest Lecture)7 Dynamic Systems A system is dynamic if its output depends on the past values of its input(s) or output(s).A system is dynamic if its output depends on the past values of its input(s) or output(s). For a linear, time-invariant, dynamic system,For a linear, time-invariant, dynamic system, y(t) = h(t) * x(t), where h(t) denotes the impulse response. where h(t) denotes the impulse response. If a dynamic system is linear but time variant, its impulse response depends on the time origins, namely,If a dynamic system is linear but time variant, its impulse response depends on the time origins, namely,

8. Oct. 7, 04ELEC5970-003/6970-003 (Guest Lecture)8 Effects of Nonlinearity Harmonic DistortionHarmonic Distortion Gain CompressionGain Compression DesensitizationDesensitization IntermodulationIntermodulation For simplicity, we limit our analysis to memoryless, time variant system. Thus,For simplicity, we limit our analysis to memoryless, time variant system. Thus, (3.1)

9. Oct. 7, 04ELEC5970-003/6970-003 (Guest Lecture)9 Effects of Nonlinearity -- Harmonics If a single tone signal is applied to a nonlinear system, the output generally exhibits fundamental and harmonic frequencies with respect to the input frequency. In Eq. (3.1), if x(t) = Acosωt, then Observations: 1. even order harmonics result from α j with even j and vanish if the system has odd symmetry, i.e., differential circuits. 2. For large A, the nth harmonic grows approximately in proportion to A n.

10. Oct. 7, 04ELEC5970-003/6970-003 (Guest Lecture)10 Output Voltage (dBV) 1dB 20logA in 1-dB compression point is defined as the input signal level that causes small-signal gain to drop 1 dB. It’s a measure of the maximum input range. 1-dB compression point occurs around -20 to -25 dBm (63.2 to 35.6mVpp in a 50-Ω system) in typical frond-end RF amplifiers. Effects of Nonlinearity – 1dB Compression Point

11. Oct. 7, 04ELEC5970-003/6970-003 (Guest Lecture)11 Effects of Nonlinearity – Intermodulation Harmonic distortion is due to self-mixing of a single- tone signal. It can be suppressed by low-pass filtering the higher order harmonics. However, there is another type of nonlinearity -- intermodulation (IM) distortion, which is normally determined by a “two tone test”. When two signals with different frequencies applied to a nonlinear system, the output in general exhibits some components that are not harmonics of the input frequencies. This phenomenon arises from cross- mixing (multiplication) of the two signals.

12. Oct. 7, 04ELEC5970-003/6970-003 (Guest Lecture)12 assume x(t) = A 1 cosω 1 t+ A 2 cosω 2 t  two tone testassume x(t) = A 1 cosω 1 t+ A 2 cosω 2 t  two tone test Expanding the right side and disregarding dc terms and harmonics, we obtain the following intermodulation products:Expanding the right side and disregarding dc terms and harmonics, we obtain the following intermodulation products: And these fundamental components:And these fundamental components: Effects of Nonlinearity – Intermodulation

13. Oct. 7, 04ELEC5970-003/6970-003 (Guest Lecture)13 DC Term 1 st Order Terms 2 nd Order Terms 3 rd Order terms Effects of Nonlinearity – Intermodulation

14. Oct. 7, 04ELEC5970-003/6970-003 (Guest Lecture)14 Of particular interest are the third-order IM products at 2ω 1 -ω 2 and 2 ω 2 - ω 1. The key point here is that if the difference between ω 1 and ω 2 is small, the 2 ω 1 -ω 2 and 2 ω 2 -ω 1 appear in the vicinity of ω 1 and ω 2.Of particular interest are the third-order IM products at 2ω 1 -ω 2 and 2 ω 2 - ω 1. The key point here is that if the difference between ω 1 and ω 2 is small, the 2 ω 1 -ω 2 and 2 ω 2 -ω 1 appear in the vicinity of ω 1 and ω 2. ω1ω1 ω2ω2 ω ω1ω1 ω2ω2 2ω1-ω22ω1-ω2 2ω2-ω12ω2-ω1 ω Effects of Nonlinearity – Intermodulation

15. Oct. 7, 04ELEC5970-003/6970-003 (Guest Lecture)15 Intermodulation -- Third Order Intercept Point (IP3) Two-tune test: A 1 =A 2 =A and A is sufficiently small so that higher-order nonlinear terms are negligible and the gain is relatively constant and equal to α 1.Two-tune test: A 1 =A 2 =A and A is sufficiently small so that higher-order nonlinear terms are negligible and the gain is relatively constant and equal to α 1. As A increases, the fundamentals increases in proportion to A, whereas IM3 products increases in proportion to A³.As A increases, the fundamentals increases in proportion to A, whereas IM3 products increases in proportion to A³.

16. Oct. 7, 04ELEC5970-003/6970-003 (Guest Lecture)16 Plotted on a log scale, the intersection of the two lines is defined as the third order intercept point. The horizontal coordinate of this point is called the input referred IP 3 (IIP 3 ), and the vertical coordinate is called the output referred IP 3 (OIP 3 ).Plotted on a log scale, the intersection of the two lines is defined as the third order intercept point. The horizontal coordinate of this point is called the input referred IP 3 (IIP 3 ), and the vertical coordinate is called the output referred IP 3 (OIP 3 ). α1Aα1A A OIP3 IIP3 20logA Intermodulation -- Third Order Intercept Point (IP3)

17. Oct. 7, 04ELEC5970-003/6970-003 (Guest Lecture)17 Calculate IIP3 without Extrapolation

18. Oct. 7, 04ELEC5970-003/6970-003 (Guest Lecture)18 Direct Digital Synthesis (DDS) DDS  generating deterministic communication carrier/reference signals in discrete time using digital hardwareDDS  generating deterministic communication carrier/reference signals in discrete time using digital hardware –converted into analog signals using a DAC AdvantagesAdvantages –Capable of generating a variety of waveforms –High precision  sub Hz –Digital circuitry Small size  fraction of analog synthesizer sizeSmall size  fraction of analog synthesizer size Low costLow cost Easy implementationEasy implementation

19. Oct. 7, 04ELEC5970-003/6970-003 (Guest Lecture)19 Typical DDS Architecture 1/f out 1/f clk 1/f out 1/f clk 1/f out 1/f clk f out = f clk F r 2 N Accum-ulatorNFrequencyWordWSineLookupTableRLowPassFilter SineWave FrFrFrFr clk Digital Circuits D-to-AConv.

20. Oct. 7, 04ELEC5970-003/6970-003 (Guest Lecture)20 Intermodulation Intermodulation Two signals with different frequencies are applied to a nonlinear systemTwo signals with different frequencies are applied to a nonlinear system –Output exhibits components that are not harmonics of input fundamental frequencies Third-order intermodulation (IM3) is criticalThird-order intermodulation (IM3) is critical –Very close to fundamental frequencies IM3 f1f1f1f1 f2f2f2f2 7 8 freq f1f1f1f1 f2f2f2f2802461012141618202224 f2- f1f2- f1f2- f1f2- f1 f1+f2f1+f2f1+f2f1+f2 2f12f12f12f1 2f22f22f22f2 3f13f13f13f1 3f23f23f23f2 2f1- f22f1- f22f1- f22f1- f2 2f2- f12f2- f12f2- f12f2- f1 freq

21. Oct. 7, 04ELEC5970-003/6970-003 (Guest Lecture)21 Mathematical Foundation Input 2-tone:Input 2-tone: x(t)=A 1 cos  1 t + A 2 cos  2 t Output of non-linear device:Output of non-linear device: y(t)=α 0 +α 1 x(t)+α 2 x 2 (t)+α 3 x 3 (t)+  Substituting x(t) into y(t):Substituting x(t) into y(t): y(t) = ½α 2 (A 1 2 +A 2 2 ) + [α 1 A 1 +¾α 3 A 1 (A 1 2 +2A 2 2 )]cos  1 t + [α 1 A 2 +¾α 3 A 2 (2A 1 2 +A 2 2 )]cos  2 t + ½α 2 (A 1 2 cos2  1 t+A 2 2 cos2  2 t ) + α 2 A 1 A 2 [cos(  1 +  2 )t+cos(  1 -  2 )t] + ¼α 3 [A 1 3 cos3  1 t+A 2 2 cos3  2 t] + ¾α 3 {A 1 2 A 2 [cos(2  1 +  2 )t+cos(2  1 -  2 )t] +A 1 A 2 2 [cos(2  2 +  1 )t+cos(2  2 -  1 )t]} freq 1111 2222 22-122-122-122-1 21-221-221-221-2 ¾  3 A 2 1A1A1A1A PPPP

22. Oct. 7, 04ELEC5970-003/6970-003 (Guest Lecture)22 3rd-order Intercept Point (IP3) freq 1111 2222 22-122-122-122-1 21-221-221-221-2 ¾  3 A 2 1A1A1A1A PPPP Input Power (IIP3) IP3 20log(  1 A) Output Power (OIP3)  P/2 IM3 fundamental PPPP 20log(¾  3 A 3 ) IP3 is theoretical input power point where 3 rd -order distortion and fundamental output lines interceptIP3 is theoretical input power point where 3 rd -order distortion and fundamental output lines intercept IIP 3 [dBm]= +P in [dBm]IIP 3 [dBm]= +P in [dBm]  P[dB] 2 Practical measurement with spectrum analyzer

23. Oct. 7, 04ELEC5970-003/6970-003 (Guest Lecture)23 2-Tone Test Pattern Generator LowPassFilter 2-toneWaveform D-to-AConv. SineLookup Table 1 Fr1Fr1Fr1Fr1 Accum-ulator#1 SineLookup Table 2 Fr2Fr2Fr2Fr2 Accum-ulator#2  Two DDS circuits generate two fundamental tonesTwo DDS circuits generate two fundamental tones –F r 1 & F r 2 control frequencies tones DDS outputs are superimposed using adder to generate 2-tone waveform for IP3 measurementDDS outputs are superimposed using adder to generate 2-tone waveform for IP3 measurement

24. Oct. 7, 04ELEC5970-003/6970-003 (Guest Lecture)24 Actual 2-Tone IP3 Measurement DAC output x(t): DUT output y(t): PPPP Outputs of DAC and DUT taken with scope from our experimental hardware implementationOutputs of DAC and DUT taken with scope from our experimental hardware implementation Typical  P measurement requires expensive, external spectrum analyzerTypical  P measurement requires expensive, external spectrum analyzer –For BIST we need an efficient output response analyzer

25. Oct. 7, 04ELEC5970-003/6970-003 (Guest Lecture)25 Output Response Analyzer Multiplier/accumulator-based ORA Multiply the output response by a frequencyMultiply the output response by a frequency –N-bit multiplier, N = number of ADC bits Accumulate the multiplication resultAccumulate the multiplication result –N+M-bit accumulator for < 2 M clock cycle samples Average by # of clock cycles of accumulationAverage by # of clock cycles of accumulation –Gives DC value proportional to power of signal at freq AdvantagesAdvantages –Easy to implement –Low area overhead –Exact frequency control –More efficient than FFT X y(t) fxfxfxfx  DCmultiplieraccumulator

26. Oct. 7, 04ELEC5970-003/6970-003 (Guest Lecture)26 DC 1 Accumulator MATLAB Simulation Results Actual Hardware Results y(t) x f 2  DC 1  ½A 2 2  1y(t) x f 2  DC 1  ½A 2 2  1 Ripple in slope due to low frequency componentsRipple in slope due to low frequency components –Longer accumulation reduces effect of ripple freq f2f2f2f2 2f2-f12f2-f12f2-f12f2-f1 ¾  3 A 2 PPPP 1A1A1A1A X y(t) f2f2f2f2  DC 1 slope = DC 1  ½A 2 2  1

27. Oct. 7, 04ELEC5970-003/6970-003 (Guest Lecture)27 DC 2 Accumulator slope = DC 2  3 / 8 A 1 2 A 2 2  3 MATLAB Simulation Results Actual Hardware Results y(t) x 2 f 2 - f 1  DC 2  3 / 8 A 1 2 A 2 2  3y(t) x 2 f 2 - f 1  DC 2  3 / 8 A 1 2 A 2 2  3 Ripple is bigger for DC 2Ripple is bigger for DC 2 –Signal is smaller –Test controller needs to obtain DC 2 at integral multiple of 2 f 2 - f 1 freq f2f2f2f2 2f2-f12f2-f12f2-f12f2-f1 ¾  3 A 2 PPPP 1A1A1A1AX y(t) 2f2-f12f2-f12f2-f12f2-f1  DC 2

28. Oct. 7, 04ELEC5970-003/6970-003 (Guest Lecture)28 BIST-based  P Measruement DC 1 & DC 2 are proportional to power at f 2 & 2 f 2 - f 1DC 1 & DC 2 are proportional to power at f 2 & 2 f 2 - f 1 Only need DC 1 & DC 2 from accumulators to calculateOnly need DC 1 & DC 2 from accumulators to calculate  P = 20 log (DC 1 ) – 20 log (DC 2 ) MATLAB Simulation Results Actual Hardware Results

29. Oct. 7, 04ELEC5970-003/6970-003 (Guest Lecture)29 BIST Architecture X Test Pattern Generator Output Response Analyzer Analyzer LUT2 Accum f2f2f2f2 Accum x(t)=cos(f 1 )+cos(f 2 ) DC1 LUT1 f1f1f1f1 Accum  LUT3 2f 2 -f 1 Accum DAC DUT ADC y(t) X DC2 Accum DC2 GainFreqResp x(t)=cos(f 2 ) BIST-based IP3 measurementBIST-based IP3 measurement –Reduce circuit by repeating test sequence for DC 2 BIST-based Gain & Frequency Response is subsetBIST-based Gain & Frequency Response is subset

30. Oct. 7, 04ELEC5970-003/6970-003 (Guest Lecture)30 Experimental Implementation of BIST TPG, ORA, test controller, & PC interface circuitsTPG, ORA, test controller, & PC interface circuits –Three 8-bit DDSs and two 17-bit ORA accumulators –Implementation in Verilog –Synthesized into Xilinx Spartan 2S50 FPGA Amplifier device under test implemented in FPAAAmplifier device under test implemented in FPAA DAC-ADC PCBDAC-ADC PCB PC FPGATPG/ORA DAC & ADC FPAADUT

31. Oct. 7, 04ELEC5970-003/6970-003 (Guest Lecture)31 Hardware Results  P  14 BIST measures  P  14 Spectrum analyzer  P distribution for 1000 BIST measurement s BIST measurement s mean=13.97 dB,  =0.082

32. Oct. 7, 04ELEC5970-003/6970-003 (Guest Lecture)32 More Hardware Results BIST measures  P  22 Spectrum analyzer  P  22  P distribution for 1000 BIST measurements BIST measurements mean=21.7 dB,  =2.2

33. Oct. 7, 04ELEC5970-003/6970-003 (Guest Lecture)33 Measurements in Noisy Environment 14 dB  P BIST measurement in noisy environment 17 dB  P BIST measurement in less noisy environment

34. Oct. 7, 04ELEC5970-003/6970-003 (Guest Lecture)34 BIST IP3 Measurement Results Good agreement with actual values for  P < 30dBGood agreement with actual values for  P < 30dB For measured  P > 30dB, the actual  P is greaterFor measured  P > 30dB, the actual  P is greater –Good threshold since  P < 30dB is of most interest

35. Oct. 7, 04ELEC5970-003/6970-003 (Guest Lecture)35 Conclusion BIST-based approach for analog circuit functional testingBIST-based approach for analog circuit functional testing –DDS-based TPG –Multiplier/accumulator-based ORA Good for manufacturing or in-system circuit characterization and on-chip compensationGood for manufacturing or in-system circuit characterization and on-chip compensation –Amplifier linearity (IP3) –Gain and frequency response Measurements with hardware implementationMeasurements with hardware implementation –Accurately measures IP3 < 30dB –Measurements of IP3 > 30dB imply higher values