1. Copyright 2008, AgrawalLectures 16-17: RF Testing1 VLSI Testing Lectures 16 and 17: RF Test Dr. Vishwani D. Agrawal James J. Danaher Professor of Electrical and Computer Engineering Auburn University, Alabama 36849, USA vagrawal@eng.auburn.edu http://www.eng.auburn.edu/~vagrawal IIT Delhi, Aug 1, 4-5PM and Aug 3, 2012, 3-4PM

2. References 1. S. Bhattacharya and A. Chatterjee, "RF Testing," Chapter 16, pages 745-789, in System on Chip Test Architectures, edited by L.-T. Wang, C. E. Stroud and N. A. Touba, Amsterdam: Morgan-Kaufman, 2008. 2. M. L. Bushnell and V. D. Agrawal, Essentials of Electronic Testing for Digital, Memory & Mixed-Signal VLSI Circuits, Boston: Springer, 2000. 3. J. Kelly and M. Engelhardt, Advanced Production Testing of RF, SoC, and SiP Devices, Boston: Artech House, 2007. 4. B. Razavi, RF Microelectronics, Upper Saddle River, New Jersey: Prentice Hall PTR, 1998. 5. J. Rogers, C. Plett and F. Dai, Integrated Circuit Design for High- Speed Frequency Synthesis, Boston: Artech House, 2006. 6. K. B. Schaub and J. Kelly, Production Testing of RF and System-on- a-chip Devices for Wireless Communications, Boston: Artech House, 2004. 2 Lectures 16-17: RF TestingCopyright 2008, Agrawal

3. An RF Communications System 3 Duplexer LNA PA LO VGA Phase Splitter Phase Splitter Digital Signal Processor (DSP) ADC DAC 90° 0° RFIFBASEBAND Superheterodyne Transceiver Lectures 16-17: RF TestingCopyright 2008, Agrawal

4. An Alternative RF Communications System 4 Duplexer LNA PA LO Phase Splitter Phase Splitter Digital Signal Processor (DSP) ADC DAC 90° 0° RF BASEBAND Zero-IF (ZIF) Transceiver Lectures 16-17: RF TestingCopyright 2008, Agrawal

5. Components of an RF System  Radio frequency  Duplexer  LNA: Low noise amplifier  PA: Power amplifier  RF mixer  Local oscillator  Filter  Intermediate frequency  VGA: Variable gain amplifier  Modulator  Demodulator  Filter  Mixed-signal  ADC: Analog to digital converter  DAC: Digital to analog converter  Digital  Digital signal processor (DSP) 5 Lectures 16-17: RF TestingCopyright 2008, Agrawal

6. LNA: Low Noise Amplifier  Amplifies received RF signal  Typical characteristics:  Noise figure2dB  IP3– 10dBm  Gain15dB  Input and output impedance50Ω  Reverse isolation20dB  Stability factor> 1  Technologies:  Bipolar  CMOS  Reference: Razavi, Chapter 6. 6 Lectures 16-17: RF Testing Copyright 2008, Agrawal

7. PA: Power Amplifier  Feeds RF signal to antenna for transmission  Typical characteristics:  Output power+20 to +30 dBm  Efficiency30% to 60%  IMD– 30dBc  Supply voltage3.8 to 5.8 V  Gain20 to 30 dB  Output harmonics– 50 to – 70 dBc  Power controlOn-off or 1-dB steps  Stability factor> 1  Technologies:  GaAs  SiGe  Reference: Razavi, Chapter 9. 7 Lectures 16-17: RF Testing Copyright 2008, Agrawal

8. Mixer or Frequency (Up/Down) Converter  Translates frequency by adding or subtracting local oscillator (LO) frequency  Typical characteristics:  Noise figure12dB  IP3+5dBm  Gain10dB  Input impedance50Ω  Port to port isolation10-20dB  Tecnologies:  Bipolar  MOS  Reference: Razavi, Chapter 6. 8 Lectures 16-17: RF Testing Copyright 2008, Agrawal

9. LO: Local Oscillator  Provides signal to mixer for down conversion or upconversion.  Implementations:  Tuned feedback amplifier  Ring oscillator  Phase-locked loop (PLL)  Direct digital synthesizer (DDS) 9 Lectures 16-17: RF Testing Copyright 2008, Agrawal

10. SOC: System-on-a-Chip  All components of a system are implemented on the same VLSI chip.  Requires same technology (usually CMOS) used for all components.  Components not implemented on present-day SOC:  Antenna  Power amplifier (PA) 10 Lectures 16-17: RF Testing Copyright 2008, Agrawal

11. RF Tests  Basic tests  Scattering parameters (S-parameters)  Frequency and gain measurements  Power measurements  Power efficiency measurements  Distortion measurements  Noise measurements 11 Lectures 16-17: RF Testing Copyright 2008, Agrawal

12. Scattering Parameters (S-Parameters)  An RF function is a two-port device with  Characteristic impedance (Z 0 ):  Z 0 = 50Ω for wireless communications devices  Z 0 = 75Ω for cable TV devices  Gain and frequency characteristics  S-Parameters of an RF device  S 11 : input return loss or input reflection coefficient  S 22 : output return loss or output reflection coefficient  S 21 : gain or forward transmission coefficient  S 12 : isolation or reverse transmission coefficient  S-Parameters are complex numbers and can be expressed in decibels as 20 × log | S ij | 12 Lectures 16-17: RF TestingCopyright 2008, Agrawal

13. Active or Passive RF Device 13 RF Device Port 1 (input) Port 2 (output) a1a1 a2a2 b1b1 b2b2 Input return lossS 11 = b 1 /a 1 Output return lossS 22 = b 2 /a 2 GainS 21 = b 2 /a 1 IsolationS 12 = b 1 /a 2 Lectures 16-17: RF Testing Copyright 2008, Agrawal

14. S-Parameter Measurement by Network Analyzer 14 a1a1 b1b1 Digitizer Directional couplers a2a2 b2b2 Digitizer Directional couplers DUT Lectures 16-17: RF Testing Copyright 2008, Agrawal

15. Application of S-Parameter: Input Match  Example: In an S-parameter measurement setup, rms value of input voltage is 0.1V and the rms value of the reflected voltage wave is 0.02V. Assume that the output of DUT is perfectly matched. Then S 11 determines the input match:  S 11 = 0.02/0.1 = 0.2, or 20 × log (0.2) = –14 dB.  Suppose the required input match is –10 dB; this device passes the test.  Similarly, S 22 determines the output match. 15 Lectures 16-17: RF Testing Copyright 2008, Agrawal

16. Gain (S 21 ) and Gain Flatness  An amplifier of a Bluetooth transmitter operates over a frequency band 2.4 – 2.5GHz. It is required to have a gain of 20dB and a gain flatness of 1dB.  Test: Under properly matched conditions, S 21 is measured at several frequencies in the range of operation:  S 21 = 15.31 at 2.400GHz  S 21 = 14.57 at 2.499GHz  From the measurements:  At 2.400GHz, Gain = 20×log 15.31 = 23.70 dB  At 2.499GHz, Gain = 20×log 14.57 = 23.27 dB  Result: Gain and gain flatness meet specification. Measurements at more frequencies in the range may be useful. 16 Lectures 16-17: RF Testing Copyright 2008, Agrawal

17. Power Measurements  Receiver  Minimum detectable RF power  Maximum allowed input power  Power levels of interfering tones  Transmitter  Maximum RF power output  Changes in RF power when automatic gain control is used  RF power distribution over a frequency band  Power-added efficiency (PAE)  Power unit: dBm, relative to 1mW  Power in dBm= 10 × log (power in watts/0.001 watts)  Example: 1 W is 10×log 1000 = 30 dBm  What is 2 W in dBm? 17 Lectures 16-17: RF Testing Copyright 2008, Agrawal

18. Harmonic Measurements  Multiples of the carrier frequency are called harmonics.  Harmonics are generated due to nonlinearity in semiconductor devices and clipping (saturation) in amplifiers.  Harmonics may interfere with other signals and must be measured to verify that a manufactured device meets the specification. 18 Lectures 16-17: RF Testing Copyright 2008, Agrawal

19. Power-Added Efficiency (PAE)  Definition: Power-added efficiency of an RF amplifier is the ratio of RF power generated by the amplifier to the DC power supplied:  PAE = ΔP RF / P DC where  ΔP RF =P RF (output) – P RF (input)  P dc =V supply × I supply  Important for power amplifier (PA).  1 – PAE is a measure of heat generated in the amplifier, i.e., the battery power that is wasted.  In mobile phones PA consumes most of the power. A low PAE reduces the usable time before battery recharge. 19 Lectures 16-17: RF Testing Copyright 2008, Agrawal

20. PAE Example  Following measurements are obtained for an RF power amplifier:  RF Input power=+2dBm  RF output power=+34dBm  DC supply voltage=3V  DUT current=2.25A  PAE is calculated as follows:  P RF (input)= 0.001 × 10 2/10 = 0.0015W  P RF (output)= 0.001 × 10 34/10 = 2.5118W  P dc = 3× 2.25= 6.75W  PAE= (2.5118 – 0.00158)/6.75 = 0.373 or 37.2% 20 Lectures 16-17: RF Testing Copyright 2008, Agrawal

21. Distortion and Linearity  An unwanted change in the signal behavior is usually referred to as distortion.  The cause of distortion is nonlinearity of semiconductor devices constructed with diodes and transistors.  Linearity:  Function f(x) = ax + b, although a straight-line is not referred to as a linear function.  Definition: A linear function must satisfy:  f(x + y) = f(x) + f(y), and  f(ax) = a f(x), for all scalar constants a 21 Lectures 16-17: RF Testing Copyright 2008, Agrawal

22. Linear and Nonlinear Functions 22 x f(x) slope = a b f(x) = ax + b x f(x) b f(x) = ax 2 + b x f(x) slope = a f(x) = ax Lectures 16-17: RF Testing Copyright 2008, Agrawal

23. Generalized Transfer Function  Transfer function of an electronic circuit is, in general, a nonlinear function.  Can be represented as a polynomial:  v o = a 0 + a 1 v i + a 2 v i 2 + a 3 v i 3 + · · · ·  Constant term a 0 is the dc component that in RF circuits is usually removed by a capacitor or high- pass filter.  For a linear circuit, a 2 = a 3 = · · · · = 0. 23 Electronic circuit vovo vivi Lectures 16-17: RF Testing Copyright 2008, Agrawal

24. Effect of Nonlinearity on Frequency  Consider a transfer function, v o = a 0 + a 1 v i + a 2 v i 2 + a 3 v i 3  Let v i = A cos ωt  Using the identities (ω = 2πf):  cos 2 ωt = (1 + cos 2ωt)/2  cos 3 ωt = (3 cos ωt + cos 3ωt)/4  We get,  v o =a 0 + a 2 A 2 /2 + (a 1 A + 3a 3 A 3 /4) cos ωt + (a 2 A 2 /2) cos 2ωt + (a 3 A 3 /4) cos 3ωt 24 Lectures 16-17: RF Testing Copyright 2008, Agrawal

25. Problem for Solution  A diode characteristic is, I = I s ( e αV – 1)  Where, V = V 0 + v in, V 0 is dc voltage and v in is small signal ac voltage. I s is saturation current and α is a constant that depends on temperature and design parameters of diode.  Using the Taylor series expansion, express the diode current I as a polynomial in v in. 25 V I 0 – I s Lectures 16-17: RF Testing Copyright 2008, Agrawal

26. Linear and Nonlinear Circuits and Systems  Linear devices:  All frequencies in the output of a device are related to input by a proportionality, or weighting factor, independent of power level.  No frequency will appear in the output, that was not present in the input.  Nonlinear devices:  A true linear device is an idealization. Most electronic devices are nonlinear.  Nonlinearity in amplifier is undesirable and causes distortion of signal.  Nonlinearity in mixer or frequency converter is essential. 26 Lectures 16-17: RF Testing Copyright 2008, Agrawal

27. Types of Distortion and Their Tests  Types of distortion:  Harmonic distortion: single-tone test  Gain compression: single-tone test  Intermodulation distortion: two-tone or multitone test  Testing procedure: Output spectrum measurement 27 Lectures 16-17: RF Testing Copyright 2008, Agrawal

28. Harmonic Distortion  Harmonic distortion is the presence of multiples of a fundamental frequency of interest. N times the fundamental frequency is called Nth harmonic.  Disadvantages:  Waste of power in harmonics.  Interference from harmonics.  Measurement:  Single-frequency input signal applied.  Amplitudes of the fundamental and harmonic frequencies are analyzed to quantify distortion as:  Total harmonic distortion (THD)  Signal, noise and distortion (SINAD) 28 Lectures 16-17: RF Testing Copyright 2008, Agrawal

29. Problem for Solution  Show that for a nonlinear device with a single frequency input of amplitude A, the nth harmonic component in the output always contains a term proportional to A n. 29 Lectures 16-17: RF Testing Copyright 2008, Agrawal

30. Total Harmonic Distortion (THD)  THD is the total power contained in all harmonics of a signal expressed as percentage (or ratio) of the fundamental signal power.  THD(%) = [(P 2 + P 3 + · · · ) / P fundamental ] × 100%  Or THD(%) = [(V 2 2 + V 3 2 + · · · ) / V 2 fundamental ] × 100%  Where P 2, P 3,..., are the power in watts of second, third,..., harmonics, respectively, and P fundamental is the fundamental signal power,  And V 2, V 3,..., are voltage amplitudes of second, third,..., harmonics, respectively, and V fundamental is the fundamental signal amplitude.  Also, THD(dB) = 10 log THD(%)  For an ideal distortionless signal, THD = 0% or – ∞ dB 30 Lectures 16-17: RF Testing Copyright 2008, Agrawal

31. THD Measurement  THD is specified typically for devices with RF output.  Separate power measurements are made for the fundamental and each harmonic.  THD is tested at specified power level because  THD may be small at low power levels.  Harmonics appear when the output power of an RF device is raised. 31 Lectures 16-17: RF Testing Copyright 2008, Agrawal

32. Gain Compression  The harmonics produced due to nonlinearity in an amplifier reduce the fundamental frequency power output (and gain). This is known as gain compression.  As input power increases, so does nonlinearity causing greater gain compression.  A standard measure of Gain compression is “1-dB compression point” power level P 1dB, which can be  Input referred for receiver, or  Output referred for transmitter 32 Lectures 16-17: RF Testing Copyright 2008, Agrawal

33. Linear Operation: No Gain Compression 33 time LNA or PA Amplitude frequency Power (dBm) f1f1 frequency Power (dBm) f1f1 Lectures 16-17: RF Testing Copyright 2008, Agrawal

34. Cause of Gain Compression: Clipping 34 time LNA or PA Amplitude frequency Power (dBm) f1f1 frequency Power (dBm) f1f1 f2f2 f3f3 Lectures 16-17: RF Testing Copyright 2008, Agrawal

35. Effect of Nonlinearity  Assume a transfer function, v o = a 0 + a 1 v i + a 2 v i 2 + a 3 v i 3  Let v i = A cos ωt  Using the identities (ω = 2πf):  cos 2 ωt = (1 + cos 2ωt)/2  cos 3 ωt = (3 cos ωt + cos 3ωt)/4  We get,  v o =a 0 + a 2 A 2 /2 + (a 1 A + 3a 3 A 3 /4) cos ωt + (a 2 A 2 /2) cos 2ωt + (a 3 A 3 /4) cos 3ωt 35 Lectures 16-17: RF Testing Copyright 2008, Agrawal

36. Gain Compression Analysis  DC term is filtered out.  For small-signal input, A is small  A 2 and A 3 terms are neglected  v o = a 1 A cos ωt, small-signal gain, G 0 = a 1  Gain at 1-dB compression point, G 1dB = G 0 – 1  Input referred and output referred 1-dB power: P 1dB(output) – P 1dB(input) = G 1dB = G 0 – 1 36Lectures 16-17: RF TestingCopyright 2008, Agrawal

37. 1-dB Compression Point 37 1 dB Input power (dBm) Output power (dBm) 1 dB Compression point P 1dB(input) P 1dB(output) Slope = gain Linear region (small-signal) Compression region Lectures 16-17: RF TestingCopyright 2008, Agrawal

38. Testing for Gain Compression  Apply a single-tone input signal: 1. Measure the gain at a power level where DUT is linear. 2. Extrapolate the linear behavior to higher power levels. 3. Increase input power in steps, measure the gain and compare to extrapolated values. 4. Test is complete when the gain difference between steps 2 and 3 is 1dB.  Alternative test: After step 2, conduct a binary search for 1-dB compression point. 38 Lectures 16-17: RF Testing Copyright 2008, Agrawal

39. Example: Gain Compression Test  Small-signal gain, G 0 = 28dB  Input-referred 1-dB compression point power level, P 1dB(input) = – 19 dBm  We compute:  1-dB compression point Gain, G 1dB = 28 – 1 = 27 dB  Output-referred 1-dB compression point power level, P 1dB(output) =P 1dB(input) + G 1dB =– 19 + 27 =8 dBm 39 Lectures 16-17: RF Testing Copyright 2008, Agrawal

40. Intermodulation Distortion  Intermodulation distortion is relevant to devices that handle multiple frequencies.  Consider an input signal with two frequencies ω 1 and ω 2 : v i = A cos ω 1 t + B cos ω 2 t  Nonlinearity in the device function is represented by v o = a 0 + a 1 v i + a 2 v i 2 + a 3 v i 3, neglecting higher order terms  Therefore, device output is v o = a 0 + a 1 (A cos ω 1 t + B cos ω 2 t)DC and fundamental + a 2 (A cos ω 1 t + B cos ω 2 t) 2 2 nd order terms + a 3 (A cos ω 1 t + B cos ω 2 t) 3 3 rd order terms 40 Lectures 16-17: RF Testing Copyright 2008, Agrawal

41. Problems to Solve  Derive the following: v o =a 0 + a 1 (A cos ω 1 t + B cos ω 2 t) + a 2 [ A 2 (1+cos 2ω 1 t)/2 + AB cos (ω 1 +ω 2 )t + AB cos (ω 1 – ω 2 )t + B 2 (1+cos 2ω 2 t)/2 ] + a 3 (A cos ω 1 t + B cos ω 2 t) 3  Hint: Use the identity:  cos α cos β = [cos(α + β) + cos(α – β)] / 2  Simplify a 3 (A cos ω 1 t + B cos ω 2 t) 3 41 Lectures 16-17: RF Testing Copyright 2008, Agrawal

42. Two-Tone Distortion Products  Order for distortion product mf 1 ± nf 2 is |m| + |n| 42 Nunber of distortion productsFrequencies OrderHarmonicIntermod.TotalHarmonicIntrmodulation 22242f 1, 2f 2 f 1 + f 2, f 2 – f 1 32463f 1, 3f 2 2f 1 ± f 2, 2f 2 ± f 1 42684f 1, 4f 2 2f 1 ± 2f 2, 2f 2 – 2f 1, 3f 1 ± f 2, 3f 2 ± f 1 528105f 1, 5f 2 3f 1 ± 2f 2, 3f 2 ± 2f 1, 4f 1 ± f 2, 4f 2 ± f 1 6210126f 1, 6f 2 3f 1 ± 3f 2, 3f 2 – 3f 1, 5f 1 ± f 2, 5f 2 ± f 1, 4f 1 ± 2f 2, 4f 2 ± 2f 1 7212147f 1, 7f 2 4f 1 ± 3f 2, 4f 2 – 3f 1, 5f 1 ± 2f 2, 5f 2 ± 2f 1, 6f 1 ± f 2, 6f 2 ± f 1 N22N – 22NNf 1, Nf 2..... Lectures 16-17: RF Testing Copyright 2008, Agrawal

43. Problem to Solve Write Distortion products tones 100MHz and 101MHz Order Harmonics (MHz) Intermodulation products (MHz) 2200, 2021, 201 3300, 30399, 102, 301, 302 4400, 4042, 199, 203, 401, 402, 403 5500, 50598, 103, 299, 304, 501, 503, 504 6600, 606 3, 198, 204, 399, 400, 405, 601, 603, 604, 605 7700, 707 97, 104, 298, 305, 499, 506, 701, 707, 703, 704, 705, 706 43 Intermodulation products close to input tones are shown in bold. Lectures 16-17: RF Testing Copyright 2008, Agrawal

44. Second-Order Intermodulation Distortion 44 frequency DUT Amplitude f1f1 f2f2 frequency Amplitude f1f1 f2f2 2f 1 2f 2 f 2 – f 1 Lectures 16-17: RF Testing Copyright 2008, Agrawal

45. Higher-Order Intermodulation Distortion 45 frequency DUT Amplitude f1f1 f2f2 frequency Amplitude f1f1 f2f2 2f 1 2f 2 3f 1 3f 2 2f 1 – f 2 2f 2 – f 1 Third-order intermodulation distortion products (IMD3) Lectures 16-17: RF Testing Copyright 2008, Agrawal

46. Problem to Solve  For A = B, i.e., for two input tones of equal magnitudes, show that:  Output amplitude of each fundamental frequency, f 1 or f 2, is 9 a 1 A + — a 3 A 3 ≈ a 1 A 4 4  Output amplitude of each third-order intermodulation frequency, 2f 1 – f 2 or 2f 2 – f 1, is 3 — a 3 A 3 4 46 Lectures 16-17: RF Testing Copyright 2008, Agrawal

47. Third-Order Intercept Point (IP3)  IP3 is the power level of the fundamental for which the output of each fundamental frequency equals the output of the closest third-order intermodulation frequency.  IP3 is a figure of merit that quantifies the third-order intermodulation distortion.  Assuming a 1 >> 9a 3 A 2 /4, IP3 is given by a 1 IP3 = 3a 3 IP3 3 / 4 IP3 = [4a 1 /(3a 3 )] 1/2 47 a 1 A 3a 3 A 3 / 4 A Output IP3 Lectures 16-17: RF Testing Copyright 2008, Agrawal

48. Test for IP3  Select two test frequencies, f 1 and f 2, applied in equal magnitude to the input of DUT.  Increase input power P 0 (dBm) until the third-order products are well above the noise floor.  Measure output power P 1 in dBm at any fundamental frequency and P 3 in dBm at a third-order intermodulation frquency.  Output-referenced IP3:OIP3 = P 1 + (P 1 – P 3 ) / 2  Input-referenced IP3:IIP3 = P 0 + (P 1 – P 3 ) / 2 =OIP3 – G Because, Gain for fundamental frequency, G = P 1 – P 0 48 Lectures 16-17: RF Testing Copyright 2008, Agrawal

49. IP3 Graph 49 f 1 or f 2 20 log a 1 A slope = 1 Input power = 20 log A dBm Output power (dBm) 2f 1 – f 2 or 2f 2 – f 1 20 log (3a 3 A 3 /4) slope = 3 OIP3 IIP3 P1P1 P3P3 P0P0 (P 1 – P 3 )/2 Lectures 16-17: RF Testing Copyright 2008, Agrawal

50. Example: IP3 of an RF LNA  Gain of LNA = 20 dB  RF signal frequencies: 2140.10MHz and 2140.30MHz  Second-order intermodulation distortion: 400MHz; outside operational band of LNA.  Third-order intermodulation distortion: 2140.50MHz; within the operational band of LNA.  Test:  Input power, P 0 = – 30 dBm, for each fundamental frequency  Output power, P 1 = – 30 + 20 = – 10 dBm  Measured third-order intermodulation distortion power, P 3 = – 84 dBm  OIP3 = – 10 + [( – 10 – ( – 84))] / 2 = + 27 dBm  IIP3 = – 10 + [( – 10 – ( – 84))] / 2 – 20 = + 7 dBm 50 Lectures 16-17: RF Testing Copyright 2008, Agrawal

51. What is Noise?  Noise in an RF system is unwanted random fluctuations in a desired signal.  Noise is a natural phenomenon and is always present in the environment.  Effects of noise:  Interferes with detection of signal (hides the signal).  Causes errors in information transmission by changing signal.  Sometimes noise might imitate a signal falsely.  All communications system design and operation must account for noise. 51 Lectures 16-17: RF Testing Copyright 2008, Agrawal

52. Describing Noise  Consider noise as a random voltage or current function, x(t), over interval – T/2 < t < T/2.  Fourier transform of x(t) is X T (f).  Power spectral density (PSD) of noise is power across 1Ω S x (f) = lim [ E{ |X T (f)| 2 } / (2T) ]volts 2 /Hz T→∞ This is also expressed in dBm/Hz. 52 Lectures 16-17: RF Testing Copyright 2008, Agrawal

53. Thermal Noise  Thermal (Johnson) noise: Caused by random movement of electrons due to thermal energy that is proportional to temperature.  Called white noise due to uniform PSD over all frequencies.  Mean square open circuit noise voltage across R Ω resistor [Nyquist, 1928]: v 2 =4hfBR / [exp(hf/kT) – 1]  Where  Plank’s constant h = 6.626 × 10 34 J-sec  Frequency and bandwidth in hertz = f, B  Boltzmann’s constant k = 1.38 × 10 – 23 J/K  Absolute temperature in Kelvin = T 53 Lectures 16-17: RF Testing Copyright 2008, Agrawal

54. Problem to Solve  Given that for microwave frequencies, hf << kT, derive the following Rayleigh-Jeans approximation: v 2 =4kTBR  Show that at room temperature (T = 290K), thermal noise power supplied by resistor R to a matched load is ktB or – 174 dBm/Hz. 54 v = (4kTBR) 1/2 R R Noisy resistor Matched load Lectures 16-17: RF TestingCopyright 2008, Agrawal

55. Other Noise Types  Shot noise [Schottky, 1928]: Broadband noise due to random behavior of charge carriers in semiconductor devices.  Flicker (1/f) noise: Low-frequency noise in semiconductor devices, perhaps due to material defects; power spectrum falls off as 1/f. Can be significant at audio frequencies.  Quantization noise: Caused by conversion of continuous valued analog signal to discrete-valued digital signal; minimized by using more digital bits.  Quantum noise: Broadband noise caused by the quantized nature of charge carriers; significant at very low temperatures (~0K) or very high bandwidth ( > 10 15 Hz).  Plasma noise: Caused by random motion of charges in ionized medium, possibly resulting from sparking in electrical contacts; generally, not a concern. 55Lectures 16-17: RF TestingCopyright 2008, Agrawal

56. Measuring Noise  Expressed as noise power density in the units of dBm/Hz.  Noise sources:  Resistor at constant temperature, noise power = kTB W/Hz.  Avalanche diode  Noise temperature:  T n = (Available noise power in watts)/(kB) kelvins  Excess noise ratio (ENR) is the difference in the noise output between hot (on) and cold (off) states, normalized to reference thermal noise at room temperature (290K):  ENR = [k( T h – T c )B]/(kT 0 B) = ( T h / T 0 ) – 1  Where noise output in cold state is takes same as reference.  10 log ENR ~ 15 to 20 dB 56 Lectures 16-17: RF Testing Copyright 2008, Agrawal

57. Signal-to-Noise Ratio (SNR)  SNR is the ratio of signal power to noise power. 57 Input signal: low peak power, good SNR S i /N i Output signal: high peak power, poor SNR S o /N o G Noise floor Frequency (Hz) Power (dBm) GS i /N i S o /N o Lectures 16-17: RF Testing Copyright 2008, Agrawal

58. Noise Factor and Noise Figure  Noise factor (F) is the ratio of input SNR to output SNR:  F = (S i /N i ) / (S o /N o ) = N o / ( GN i ), when S i = 1W and G = gain of DUT = N o / ( GN i ), when S i = 1W and G = gain of DUT = N o /( kT 0 BG), when N i = kT 0 B for input noise source = N o /( kT 0 BG), when N i = kT 0 B for input noise source  F ≥ 1  Noise figure (NF) is noise factor expressed in dB:  NF = 10 log F dB  0 ≤ NF ≤ ∞ 58 Lectures 16-17: RF Testing Copyright 2008, Agrawal

59. Cascaded System Noise Factor  Friis equation [Proc. IRE, July 1944, pp. 419 – 422]: 59 F 2 – 1 F 3 – 1 F n – 1 F sys = F 1 + ——— +——— + · · · · + ——————— G 1 G 1 G 2 G 1 G 2 · · · G n – 1 Gain = G 1 Noise factor = F 1 Gain = G 2 Noise factor = F 2 Gain = G 3 Noise factor = F 3 Gain = G n Noise factor = F n Lectures 16-17: RF Testing Copyright 2008, Agrawal

60. Measuring Noise Figure: Cold Noise Method  Example: SOC receiver with large gain so noise output is measurable; noise power should be above noise floor of measuring equipment.  Gain G is known or previously measured.  Noise factor, F = N o / (kT 0 BG), where  N o is measured output noise power (noise floor)  B is measurement bandwidth  At 290K, kT 0 = – 174 dBm/Hz  Noise figure, NF = 10 log F = N o (dB) – ( – 174 dBm/Hz) – B(dB) – G(dB) = N o (dB) – ( – 174 dBm/Hz) – B(dB) – G(dB)  This measurement is also done using S-parameters. 60 Lectures 16-17: RF Testing Copyright 2008, Agrawal

61. Y – Factor  Y – factor is the ratio of output noise in hot (power on) state to that in cold (power off) state.  Y=N h / N c =N h / N 0  Y is a simple ratio.  Consider, N h = kT h BG and N c = kT 0 BG  Then N h – N c = kBG( T h – T 0 ) or kBG = ( N h – N c ) / ( T h – T 0 )  Noise factor, F = N h /( kT 0 BG) = ( N h / T 0 ) [ 1 / (kBG) ] = ( N h / T 0 ) ( T h – T 0 ) / (N h – N c ) = ( N h / T 0 ) ( T h – T 0 ) / (N h – N c ) =ENR / (Y – 1) =ENR / (Y – 1) 61 Lectures 16-17: RF Testing Copyright 2008, Agrawal

62. Measuring Noise Factor: Y – Factor Method  Noise source provides hot and cold noise power levels and is characterized by ENR (excess noise ratio).  Tester measures noise power, is characterized by its noise factor F 2 and Y-factor Y 2.  Device under test (DUT) has gain G 1 and noise factor F 1.  Two-step measurement:  Calibration: Connect noise source to tester, measure output power for hot and cold noise inputs, compute Y 2 and F 2.  Measurement: Connect noise source to DUT and tester cascade, measure output power for hot and cold noise inputs, compute compute Y 12, F 12 and G 1.  Use Friis equation to obtain F 1. 62 Lectures 16-17: RF Testing Copyright 2008, Agrawal

63. Calibration  Y 2 = N h2 / N c2, where  N h2 = measured power for hot source  N c2 = measured power for cold source  F 2 = ENR / (Y 2 – 1) 63 Noise source ENR Tester (power meter) F 2, Y 2 Lectures 16-17: RF Testing Copyright 2008, Agrawal

64. Cascaded System Measurement  Y 12 = N h12 / N c12, where  N h12 = measured power for hot source  N c12 = measured power for cold source  F 12 = ENR / ( Y 12 – 1 )  G 1 = ( N h12 – N c12 ) / ( N h2 – N c2 ) 64 Noise source ENR Tester (power meter) F 2, Y 2 DUT F 1, Y 1, G 1 F 12, Y 12 Lectures 16-17: RF Testing Copyright 2008, Agrawal

65. Problem to Solve  Show that from noise measurements on a cascaded system, the noise factor of DUT is given by F 2 – 1 F 1 = F 12 – ——— G 1 G 1 65 Lectures 16-17: RF Testing Copyright 2008, Agrawal

66. Phase Noise  Phase noise is due to small random variations in the phase of an RF signal. In time domain, phase noise is referred to as jitter.  Understanding phase: 66 φ amplitude noise tt V sin ωt[V + δ(t)] sin [ωt + φ(t)] phase noise δ Frequency (rad/s) ω ω Lectures 16-17: RF Testing Copyright 2008, Agrawal

67. Effects of Phase Noise  Similar to phase modulation by a random signal.  Two types:  Long term phase variation is called frequency drift.  Short term phase variation is phase noise.  Definition: Phase noise is the Fourier spectrum (power spectral density) of a sinusoidal carrier signal with respect to the carrier power. L(f) = P n /P c (as ratio) =P n in dBm/Hz – P c in dBm (as dBc) =P n in dBm/Hz – P c in dBm (as dBc)  P n is RMS noise power in 1-Hz bandwidth at frequency f  P c is RMS power of the carrier 67 Lectures 16-17: RF Testing Copyright 2008, Agrawal

68. Phase Noise Analysis 68 [V + δ(t)] sin [ωt + φ(t)]= [V + δ(t)] [sin ωt cos φ(t) + cos ωt sin φ(t)] ≈ [V + δ(t)] sin ωt + [V + δ(t)] φ(t) cos ωt In-phase carrier frequency with amplitude noise White noise δ(t) corresponds to noise floor Quadrature-phase carrier frequency with amplitude and phase noise Short-term phase noise corresponds to phase noise spectrum Phase spectrum, L(f) = S φ (f)/2 Where S φ (f) is power spectrum of φ(t) Lectures 16-17: RF Testing Copyright 2008, Agrawal

69. Phase Noise Measurement  Phase noise is measured by low noise receiver (amplifier) and spectrum analyzer:  Receiver must have a lower noise floor than the signal noise floor.  Local oscillator in the receiver must have lower phase noise than that of the signal. 69 Frequency (Hz) Power (dBm) Receiver noise floor Receiver phase noise Signal spectrum Lectures 16-17: RF TestingCopyright 2008, Agrawal

70. Phase Noise Measurement 70 DUT Pure tone Input (carrier) carrier offset Hz Spectrum analyzer power measurement Power (dBm) over resolution bandwith (RBW) Lectures 16-17: RF Testing Copyright 2008, Agrawal

71. Phase Noise Measurement Example  Spectrum analyzer data:  RBW = 100Hz  Frequency offset = 2kHz  P carrier = – 5.30 dBm  P offset = – 73.16 dBm  Phase noise, L(f) = P offset – P carrier – 10 log RBW =– 73.16 – ( – 5.30) – 10 log 100 =– 73.16 – ( – 5.30) – 10 log 100 = – 87.86 dBc/Hz = – 87.86 dBc/Hz  Phase noise is specified as “ – 87.86 dBc/Hz at 2kHz from the carrier.” 71 Lectures 16-17: RF Testing Copyright 2008, Agrawal

72. Problem to Solve  Consider the following spectrum analyzer data:  RBW = 10Hz  Frequency offset = 2kHz  P carrier = – 3.31 dBm  P offset = – 81.17 dBm  Determine phase noise in dBc/Hz at 2kHz from the carrier. 72 Lectures 16-17: RF Testing Copyright 2008, Agrawal

73. References, Again 1. S. Bhattacharya and A. Chatterjee, "RF Testing," Chapter 16, pages 745-789, in System on Chip Test Architectures, edited by L.-T. Wang, C. E. Stroud and N. A. Touba, Amsterdam: Morgan-Kaufman, 2008. 2. M. L. Bushnell and V. D. Agrawal, Essentials of Electronic Testing for Digital, Memory & Mixed-Signal VLSI Circuits, Boston: Springer, 2000. 3. J. Kelly and M. Engelhardt, Advanced Production Testing of RF, SoC, and SiP Devices, Boston: Artech House, 2007. 4. B. Razavi, RF Microelectronics, Upper Saddle River, New Jersey: Prentice Hall PTR, 1998. 5. J. Rogers, C. Plett and F. Dai, Integrated Circuit Design for High-Speed Frequency Synthesis, Boston: Artech House, 2006. 6. K. B. Schaub and J. Kelly, Production Testing of RF and System-on-a- Chip Devices for Wireless Communications, Boston: Artech House, 2004. 73 Lectures 16-17: RF TestingCopyright 2008, Agrawal