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Automatic Linearity (IP3) Test with Built-in Pattern Generator and Analyzer

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. Purpose.

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Automatic Linearity (IP3) Test with Built-in Pattern Generator and Analyzer

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  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 ELEC5970-003/6970-003 (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 systems • Provides BIST-based measurement of • Amplifier linearity (IP3) • Gain and frequency response • Implemented in hardware • IP3, gain, and freq. response measured ELEC5970-003/6970-003 (Guest Lecture)

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

  4. Linear vs. Nonlinear Systems • A system is linear if for any inputs x1(t) and x2(t),x1(t)  y2(t), x2(t)  y2(t) and for all values of constants a and b, it satisfies a x1(t)+bx2(t)  ay1(t)+by2(t) • A system is nonlinear if it does not satisfy the superposition law. ELEC5970-003/6970-003 (Guest Lecture)

  5. Time Invariant vs. Time Variant Systems • 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-t)  y(t-t), for all value of t • A system is time variant if it does not satisfy the condition. ELEC5970-003/6970-003 (Guest Lecture)

  6. Memoryless Systems • A system is memoryless if its output does not depend on the past value of its input. • For a memoryless linear system,y(t) = αx(t) whereα is a function of time if the system is time variant. • For a memorylessnonlinear system, y(t) = α0 + α1x(t) + α2x²(t)+ α3x³(t) + ······ where ajare in general function of time if the system is time variant. ELEC5970-003/6970-003 (Guest Lecture)

  7. Dynamic Systems • A system is dynamic if its output depends on the past values of its input(s) or output(s). • For a linear, time-invariant, dynamic system, y(t) = h(t) * x(t), 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, ELEC5970-003/6970-003 (Guest Lecture)

  8. Effects of Nonlinearity • Harmonic Distortion • Gain Compression • Desensitization • Intermodulation • For simplicity, we limit our analysis to memoryless, time variant system. Thus, (3.1) ELEC5970-003/6970-003 (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 αj 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 An. ELEC5970-003/6970-003 (Guest Lecture)

  10. Output Voltage (dBV) 1dB 20logAin Effects of Nonlinearity – 1dB Compression Point • 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. ELEC5970-003/6970-003 (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. ELEC5970-003/6970-003 (Guest Lecture)

  12. Effects of Nonlinearity – Intermodulation • assume x(t) = A1cosω1t+ A2cosω2t two tone test • Expanding the right side and disregarding dc terms and harmonics, we obtain the following intermodulation products: • And these fundamental components: ELEC5970-003/6970-003 (Guest Lecture)

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

  14. ω2 ω1 ω1 ω2 ω ω 2ω2-ω1 2ω1-ω2 Effects of Nonlinearity – Intermodulation • Ofparticular interest are the third-order IM products at 2ω1-ω2 and 2 ω2-ω1. The key point here is that if the difference between ω1and ω2 is small, the 2 ω1-ω2 and 2 ω2-ω1 appear in the vicinity of ω1 and ω2. ELEC5970-003/6970-003 (Guest Lecture)

  15. Intermodulation -- Third Order Intercept Point (IP3) • Two-tune test: A1=A2=A and A is sufficiently small so that higher-order nonlinear terms are negligible and the gain is relatively constant and equal to α1. • As A increases, the fundamentals increases in proportion to A, whereas IM3 products increases in proportion to A³. ELEC5970-003/6970-003 (Guest Lecture)

  16. α1A OIP3 A 20logA IIP3 Intermodulation -- Third Order Intercept Point (IP3) • 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 IP3(IIP3), and the vertical coordinate is called the output referred IP3(OIP3). ELEC5970-003/6970-003 (Guest Lecture)

  17. Calculate IIP3 without Extrapolation ELEC5970-003/6970-003 (Guest Lecture)

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

  19. fclkFr 2N R N W fout= 1/fout 1/fout 1/fout 1/fout 1/fclk 1/fclk 1/fclk Typical DDS Architecture Digital Circuits Frequency Word Sine Lookup Table Low Pass Filter Accum -ulator D-to-A Conv. Sine Wave Fr clk ELEC5970-003/6970-003 (Guest Lecture)

  20. f1 f2 f2 f1 f2-f1 f1+f2 3f1 3f2 2f2-f1 2f1-f2 2f2 2f1 freq 7 8 0 2 4 6 8 10 12 14 16 18 20 22 24 freq Intermodulation • Two 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 critical • Very close to fundamental frequencies IM3 ELEC5970-003/6970-003 (Guest Lecture)

  21. 1A P ¾ 3A2 freq 21-2 1 2 22-1 Mathematical Foundation • Input 2-tone: x(t)=A1cos 1t + A2 cos 2t • Output of non-linear device: y(t)=α0+α1x(t)+α2x2(t)+α3x3(t)+ • Substituting x(t) into y(t): y(t) = ½α2(A12+A22) + [α1A1+¾α3A1(A12+2A22)]cos1t + [α1A2+¾α3A2(2A12+A22)]cos2t + ½α2(A12cos21t+A22cos22t) + α2A1A2[cos(1+2)t+cos(1-2)t] + ¼α3[A13cos31t+A22cos32t] + ¾α3{A12A2[cos(21+2)t+cos(21-2)t] +A1A22[cos(22+1)t+cos(22-1)t]} ELEC5970-003/6970-003 (Guest Lecture)

  22. 1A P ¾ 3A2 freq 21-2 1 2 22-1 Output Power (OIP3) IM3 20log(¾3A3) 20log(1A) P[dB] 2 IP3 fundamental P Input Power (IIP3) P/2 3rd-order Intercept Point (IP3) • IP3 is theoretical input power point where 3rd-order distortion and fundamental output lines intercept • IIP3[dBm]= +Pin[dBm] Practical measurement with spectrum analyzer ELEC5970-003/6970-003 (Guest Lecture)

  23. Sine Lookup Table 1 Low Pass Filter Accum -ulator #1 D-to-A Conv. Fr1  Sine Lookup Table 2 Accum -ulator #2 Fr2 2-tone Waveform 2-Tone Test Pattern Generator • Two DDS circuits generate two fundamental tones • Fr1 & Fr2 control frequencies tones • DDS outputs are superimposed using adder to generate 2-tone waveform for IP3 measurement ELEC5970-003/6970-003 (Guest Lecture)

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

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

  26. y(t) DC1 X  f2 1A P ¾ 3A2 freq f2 2f2-f1 slope = DC1  ½A221 DC1 Accumulator • y(t) x f2 DC1 ½A221 • Ripple in slope due to low frequency components • Longer accumulation reduces effect of ripple MATLAB Simulation Results Actual Hardware Results ELEC5970-003/6970-003 (Guest Lecture)

  27. 1A P ¾ 3A2 slope = DC2 3/8A12A223 freq f2 2f2-f1 y(t) DC2 Accumulator DC2 X • y(t) x 2f2-f1 DC2 3/8A12A223 • Ripple is bigger for DC2 • Signal is smaller • Test controller needs to obtain DC2 at integral multiple of 2f2-f1  2f2-f1 MATLAB Simulation Results Actual Hardware Results ELEC5970-003/6970-003 (Guest Lecture)

  28. Actual Hardware Results MATLAB Simulation Results BIST-based P Measruement • DC1 & DC2 are proportional to power at f2 & 2f2-f1 • Only need DC1 & DC2 from accumulators to calculate P = 20 log (DC1) – 20 log (DC2) ELEC5970-003/6970-003 (Guest Lecture)

  29. x(t)=cos(f2) x(t)=cos(f1)+cos(f2) f1 LUT1 Accum DUT DAC ADC y(t)  X X LUT2 Gain Freq Resp DC1 2f2-f1 DC2 DC2 Accum Accum LUT3 BIST Architecture • BIST-based IP3 measurement • Reduce circuit by repeating test sequence for DC2 • BIST-based Gain & Frequency Response is subset Output Response Analyzer Test Pattern Generator f2 Accum Accum ELEC5970-003/6970-003 (Guest Lecture)

  30. FPGA TPG/ORA PC DAC & ADC FPAA DUT Experimental Implementation of BIST • TPG, 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 FPAA • DAC-ADC PCB ELEC5970-003/6970-003 (Guest Lecture)

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

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

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

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

  35. Conclusion • BIST-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 compensation • Amplifier linearity (IP3) • Gain and frequency response • Measurements with hardware implementation • Accurately measures IP3 < 30dB • Measurements of IP3 > 30dB imply higher values ELEC5970-003/6970-003 (Guest Lecture)

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