Copyright 2008, Copyright 2008, Agrawal Agrawal Lectures 16-17: RF Lectures 16-17: RF Testing Testing 1 VLSI Testing VLSI Testing Lectures 16 and 17: RF Test Lectures 16 and 17: RF Test Dr. Vishwani D. Agrawal Dr. Vishwani D. Agrawal James J. Danaher Professor of Electrical and James J. Danaher Professor of Electrical and Computer Engineering Computer Engineering Auburn University, Alabama 36849, USA Auburn University, Alabama 36849, USA [email protected]http://www.eng.auburn.edu/~vagrawal IIT Delhi, Aug 1, 4-5PM and Aug 3, IIT Delhi, Aug 1, 4-5PM and Aug 3, 2012, 3-4PM 2012, 3-4PM
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 [email protected] http://www.eng.auburn.edu/~vagrawal IIT Delhi, Aug 1, 4-5PM and Aug 3, 2012, 3 -4PM. References. - PowerPoint PPT Presentation
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IIT Delhi, Aug 1, 4-5PM and Aug 3, 2012, 3-4PMIIT Delhi, Aug 1, 4-5PM and Aug 3, 2012, 3-4PM
ReferencesReferences1.1. S. Bhattacharya and A. Chatterjee, "RF Testing," Chapter 16, pages S. Bhattacharya and A. Chatterjee, "RF Testing," Chapter 16, pages
745-789, in 745-789, in System on Chip Test ArchSystem on Chip Test Architectures, edited by L.-T. Wang, itectures, edited by L.-T. Wang, C. E. Stroud and N. A. Touba, Amsterdam: Morgan-Kaufman, 2008.C. E. Stroud and N. A. Touba, Amsterdam: Morgan-Kaufman, 2008.
2.2. M. L. Bushnell and V. D. Agrawal, M. L. Bushnell and V. D. Agrawal, Essentials of Electronic Testing for Essentials of Electronic Testing for Digital, Memory & Mixed-Signal VLSI CircuitsDigital, Memory & Mixed-Signal VLSI Circuits, Boston: Springer, , Boston: Springer, 2000.2000.
3.3. J. Kelly and M. Engelhardt, J. Kelly and M. Engelhardt, Advanced Production Testing of RF, SoC, Advanced Production Testing of RF, SoC, and SiP Devicesand SiP Devices, Boston: Artech House, 2007., Boston: Artech House, 2007.
4.4. B. Razavi, B. Razavi, RF MicroelectronicsRF Microelectronics, Upper Saddle River, New Jersey: , Upper Saddle River, New Jersey: Prentice Hall PTR, 1998.Prentice Hall PTR, 1998.
5.5. J. Rogers, C. Plett and F. Dai, J. Rogers, C. Plett and F. Dai, Integrated Circuit Design for High-Integrated Circuit Design for High-Speed Frequency SynthesisSpeed Frequency Synthesis, Boston: Artech House, 2006., Boston: Artech House, 2006.
6.6. K. B. Schaub and J. Kelly, K. B. Schaub and J. Kelly, Production Testing of RF and System-on-Production Testing of RF and System-on-a-chip Devices for Wireless Communicationsa-chip Devices for Wireless Communications, Boston: Artech House, , Boston: Artech House, 2004.2004.
PA: Power AmplifierPA: Power Amplifier Feeds RF signal to antenna for transmissionFeeds RF signal to antenna for transmission Typical characteristics:Typical characteristics:
Output powerOutput power +20 to +30 dBm+20 to +30 dBm EfficiencyEfficiency 30% to 60%30% to 60% IMDIMD – 30dBc– 30dBc Supply voltageSupply voltage 3.8 to 5.8 V3.8 to 5.8 V GainGain 20 to 30 dB20 to 30 dB Output harmonicsOutput harmonics – 50 to – 70 dBc– 50 to – 70 dBc Power controlPower control On-off or 1-dB stepsOn-off or 1-dB steps Stability factorStability factor > 1> 1
Mixer or Frequency (Up/Down) ConverterMixer or Frequency (Up/Down) Converter
Translates frequency by adding or subtracting Translates frequency by adding or subtracting local oscillator (LO) frequencylocal oscillator (LO) frequency
Typical characteristics:Typical characteristics: Noise figureNoise figure 12dB12dB IP3IP3 +5dBm+5dBm GainGain 10dB10dB Input impedanceInput impedance 5050ΩΩ Port to port isolationPort to port isolation 10-20dB10-20dB
Basic testsBasic tests Scattering parameters (S-parameters)Scattering parameters (S-parameters) Frequency and gain measurementsFrequency and gain measurements Power measurementsPower measurements Power efficiency measurementsPower efficiency measurements
Scattering Parameters (S-Parameters)Scattering Parameters (S-Parameters) An RF function is a two-port device withAn RF function is a two-port device with
ZZ00 = 50 = 50ΩΩ for wireless communications devices for wireless communications devices
ZZ00 = 75 = 75ΩΩ for cable TV devices for cable TV devices
Gain and frequency characteristicsGain and frequency characteristics
S-Parameters of an RF deviceS-Parameters of an RF device SS1111 : input return loss or input reflection coefficient : input return loss or input reflection coefficient
SS2222 : output return loss or output reflection coefficient : output return loss or output reflection coefficient
SS2121 : gain or forward transmission coefficient : gain or forward transmission coefficient
SS12 12 : isolation or reverse transmission coefficient : isolation or reverse transmission coefficient
S-Parameters are complex numbers and can be S-Parameters are complex numbers and can be expressed in decibels as 20 × log | Sexpressed in decibels as 20 × log | S ijij | | 1212Lectures 16-17: RF TestingLectures 16-17: RF TestingCopyright 2008, AgrawalCopyright 2008, Agrawal
Active or Passive RF DeviceActive or Passive RF Device
Application of S-Parameter: Input Application of S-Parameter: Input MatchMatch
Example: In an S-parameter measurement Example: In an S-parameter measurement setup, rms value of input voltage is 0.1V and the setup, rms value of input voltage is 0.1V and the rms value of the reflected voltage wave is 0.02V. rms value of the reflected voltage wave is 0.02V. Assume that the output of DUT is perfectly Assume that the output of DUT is perfectly matched. Then Smatched. Then S1111 determines the determines the input matchinput match::
Gain (SGain (S2121) and Gain Flatness) and Gain Flatness An amplifier of a Bluetooth transmitter operates over a An amplifier of a Bluetooth transmitter operates over a
frequency band 2.4 – 2.5GHz. It is required to have a gain of frequency band 2.4 – 2.5GHz. It is required to have a gain of 20dB and a gain flatness of 1dB.20dB and a gain flatness of 1dB.
Test: Under properly matched conditions, STest: Under properly matched conditions, S2121 is measured at is measured at
several frequencies in the range of operation:several frequencies in the range of operation:
SS2121 = 15.31 at 2.400GHz = 15.31 at 2.400GHz
SS2121 = 14.57 at 2.499GHz = 14.57 at 2.499GHz
From the measurements:From the measurements: At 2.400GHz, Gain = 20×log 15.31 = 23.70 dBAt 2.400GHz, Gain = 20×log 15.31 = 23.70 dB At 2.499GHz, Gain = 20×log 14.57 = 23.27 dBAt 2.499GHz, Gain = 20×log 14.57 = 23.27 dB
Result: Gain and gain flatness meet specification. Result: Gain and gain flatness meet specification. Measurements at more frequencies in the range may be Measurements at more frequencies in the range may be useful.useful.
Power MeasurementsPower Measurements ReceiverReceiver
Minimum detectable RF powerMinimum detectable RF power Maximum allowed input powerMaximum allowed input power Power levels of interfering tonesPower levels of interfering tones
TransmitterTransmitter Maximum RF power outputMaximum RF power output Changes in RF power when automatic gain control is usedChanges in RF power when automatic gain control is used RF power distribution over a frequency bandRF power distribution over a frequency band Power-added efficiency (PAE)Power-added efficiency (PAE)
Power unit: dBm, relative to 1mWPower unit: dBm, relative to 1mW Power in dBmPower in dBm = 10 × log (power in watts/0.001 watts)= 10 × log (power in watts/0.001 watts) Example: 1 W is 10×log 1000 = 30 dBmExample: 1 W is 10×log 1000 = 30 dBm What is 2 W in dBm?What is 2 W in dBm?
Multiples of the carrier frequency are called Multiples of the carrier frequency are called harmonics.harmonics.
Harmonics are generated due to nonlinearity in Harmonics are generated due to nonlinearity in semiconductor devices and clipping (saturation) semiconductor devices and clipping (saturation) in amplifiers.in amplifiers.
Harmonics may interfere with other signals and Harmonics may interfere with other signals and must be measured to verify that a manufactured must be measured to verify that a manufactured device meets the specification.device meets the specification.
Power-Added Efficiency (PAE)Power-Added Efficiency (PAE) Definition: Power-added efficiency of an RF amplifier is Definition: Power-added efficiency of an RF amplifier is
the ratio of RF power generated by the amplifier to the DC the ratio of RF power generated by the amplifier to the DC power supplied:power supplied:
PAE = PAE = ΔΔPPRFRF / P / PDCDC where where ΔPΔPRFRF == PPRFRF(output) – P(output) – PRFRF(input)(input)
PPdcdc == VVsupply supply × I× Isupplysupply
Important for power amplifier (PA).Important for power amplifier (PA). 1 – PAE is a measure of heat generated in the amplifier, 1 – PAE is a measure of heat generated in the amplifier,
i.e., the battery power that is wasted.i.e., the battery power that is wasted. In mobile phones PA consumes most of the power. A low In mobile phones PA consumes most of the power. A low
PAE reduces the usable time before battery recharge.PAE reduces the usable time before battery recharge.
PAE ExamplePAE Example Following measurements are obtained for an RF Following measurements are obtained for an RF
power amplifier:power amplifier: RF Input powerRF Input power == +2dBm+2dBm RF output powerRF output power == +34dBm+34dBm DC supply voltageDC supply voltage == 3V3V DUT currentDUT current == 2.25A2.25A
PAE is calculated as follows:PAE is calculated as follows: PPRFRF(input)(input) = 0.001 × 10= 0.001 × 102/102/10 = 0.0015W= 0.0015W
Distortion and LinearityDistortion and Linearity An unwanted change in the signal behavior is An unwanted change in the signal behavior is
usually referred to as usually referred to as distortiondistortion.. The cause of distortion is nonlinearity of The cause of distortion is nonlinearity of
semiconductor devices constructed with diodes and semiconductor devices constructed with diodes and transistors.transistors.
Linearity:Linearity: Function f(x) = ax + b, although a straight-line is not Function f(x) = ax + b, although a straight-line is not
referred to as a linear function.referred to as a linear function. Definition: A linear function must satisfy:Definition: A linear function must satisfy:
f(x + y) = f(x) + f(y), andf(x + y) = f(x) + f(y), and f(ax) = a f(x), for all scalar constants af(ax) = a f(x), for all scalar constants a
Generalized Transfer FunctionGeneralized Transfer Function Transfer function of an electronic circuit is, in Transfer function of an electronic circuit is, in
general, a nonlinear function.general, a nonlinear function. Can be represented as a polynomial:Can be represented as a polynomial:
vvoo = a = a00 + a + a11 v vii + a + a22 v vii22 + a + a33 v vii
33 + · · · · + · · · ·
Constant term aConstant term a00 is the dc component that in RF is the dc component that in RF
circuits is usually removed by a capacitor or high-pass circuits is usually removed by a capacitor or high-pass filter.filter.
For a linear circuit, aFor a linear circuit, a22 = a = a33 = · · · · = 0. = · · · · = 0.
Effect of Nonlinearity on FrequencyEffect of Nonlinearity on Frequency Consider a transfer function, vConsider a transfer function, voo = a = a00 + a + a11 v vii + a + a22 v vii
22 + a + a33 v vii33
Let vLet vii = A cos = A cos ωωtt
Using the identities (Using the identities (ωω = 2 = 2ππf):f): coscos22 ωωt = (1 + cos 2t = (1 + cos 2ωωt)/2t)/2 coscos33 ωωt = (3 cos t = (3 cos ωωt + cos 3t + cos 3ωωt)/4t)/4
We get,We get,
vvoo == aa00 + a + a22AA22/2 + (a/2 + (a11A + 3aA + 3a33AA33/4) cos /4) cos ωωtt
+ (a+ (a22AA22/2) cos 2/2) cos 2ωωt + (at + (a33AA33/4) cos /4) cos
Problem for SolutionProblem for Solution A diode characteristic is, I = IA diode characteristic is, I = Iss ( e ( eααVV – 1) – 1)
Where, V = VWhere, V = V00 + v + vinin, V, V00 is dc voltage and v is dc voltage and v inin is small signal ac is small signal ac
voltage. Ivoltage. Iss is saturation current and is saturation current and αα is a constant that is a constant that
depends on temperature and design parameters of diode.depends on temperature and design parameters of diode. Using the Taylor series expansion, express the diode current I Using the Taylor series expansion, express the diode current I
Linear and Nonlinear Circuits and Linear and Nonlinear Circuits and SystemsSystems
Linear devices:Linear devices: All frequencies in the output of a device are related to input by All frequencies in the output of a device are related to input by
a proportionality, or weighting factor, independent of power a proportionality, or weighting factor, independent of power level.level.
No frequency will appear in the output, that was not present in No frequency will appear in the output, that was not present in the input.the input.
Nonlinear devices:Nonlinear devices: A true linear device is an idealization. Most electronic devices A true linear device is an idealization. Most electronic devices
are nonlinear.are nonlinear. Nonlinearity in amplifier is undesirable and causes distortion Nonlinearity in amplifier is undesirable and causes distortion
of signal.of signal. Nonlinearity in mixer or frequency converter is essential.Nonlinearity in mixer or frequency converter is essential.
Types of Distortion and Their TestsTypes of Distortion and Their Tests
Types of distortion:Types of distortion: Harmonic distortion: single-tone testHarmonic distortion: single-tone test Gain compression: single-tone testGain compression: single-tone test Intermodulation distortion: two-tone or multitone testIntermodulation distortion: two-tone or multitone test
Harmonic DistortionHarmonic Distortion Harmonic distortion is the presence of multiples of a Harmonic distortion is the presence of multiples of a
fundamental frequency of interest. fundamental frequency of interest. NN times the times the fundamental frequency is called fundamental frequency is called NNth harmonic.th harmonic.
Disadvantages:Disadvantages: Waste of power in harmonics.Waste of power in harmonics. Interference from harmonics.Interference from harmonics.
Measurement:Measurement: Single-frequency input signal applied.Single-frequency input signal applied. Amplitudes of the fundamental and harmonic Amplitudes of the fundamental and harmonic
frequencies are analyzed to quantify distortion as:frequencies are analyzed to quantify distortion as: Total harmonic distortion (THD)Total harmonic distortion (THD) Signal, noise and distortion (SINAD)Signal, noise and distortion (SINAD)
Show that for a nonlinear device with a single Show that for a nonlinear device with a single frequency input of amplitude frequency input of amplitude AA, the , the nnth harmonic th harmonic component in the output always contains a term component in the output always contains a term proportional to proportional to AAnn..
Total Harmonic Distortion (THD)Total Harmonic Distortion (THD) THD is the total power contained in all harmonics of a signal THD is the total power contained in all harmonics of a signal
expressed as percentage (or ratio) of the fundamental signal expressed as percentage (or ratio) of the fundamental signal power.power.
THD is specified typically for devices with RF THD is specified typically for devices with RF output.output.
Separate power measurements are made for the Separate power measurements are made for the fundamental and each harmonic.fundamental and each harmonic.
THD is tested at specified power level becauseTHD is tested at specified power level because THD may be small at low power levels.THD may be small at low power levels. Harmonics appear when the output power of an RF Harmonics appear when the output power of an RF
Gain CompressionGain Compression The harmonics produced due to nonlinearity in an The harmonics produced due to nonlinearity in an
amplifier reduce the fundamental frequency power amplifier reduce the fundamental frequency power output (and gain). This is known as output (and gain). This is known as gain gain compressioncompression..
As input power increases, so does nonlinearity As input power increases, so does nonlinearity causing greater gain compression.causing greater gain compression.
A standard measure of Gain compression is “1-dB A standard measure of Gain compression is “1-dB compression point” power level Pcompression point” power level P1dB1dB, which can be, which can be Input referred Input referred for receiver, orfor receiver, or Output referred Output referred for transmitterfor transmitter
Effect of NonlinearityEffect of Nonlinearity Assume a transfer function, vAssume a transfer function, voo = a = a00 + a + a11 v vii + a + a2 2 vvii
22
+ a+ a33 v vii33
Let vLet vii = A cos = A cos ωωtt
Using the identities (Using the identities (ωω = 2 = 2ππf):f): coscos22 ωωt = (1 + cos 2t = (1 + cos 2ωωt)/2t)/2 coscos33 ωωt = (3 cos t = (3 cos ωωt + cos 3t + cos 3ωωt)/4t)/4
We get,We get, vvoo = = aa00 + a + a22AA22/2 + (a/2 + (a11A + 3aA + 3a33AA33/4) cos /4) cos ωωtt
+ (a+ (a22AA22/2) cos 2/2) cos 2ωωt + (at + (a33AA33/4) cos /4) cos
Testing for Gain CompressionTesting for Gain Compression Apply a single-tone input signal:Apply a single-tone input signal:
1.1. Measure the gain at a power level where DUT is Measure the gain at a power level where DUT is linear.linear.
2.2. Extrapolate the linear behavior to higher power Extrapolate the linear behavior to higher power levels.levels.
3.3. Increase input power in steps, measure the gain Increase input power in steps, measure the gain and compare to extrapolated values.and compare to extrapolated values.
4.4. Test is complete when the gain difference between Test is complete when the gain difference between steps 2 and 3 is 1dB.steps 2 and 3 is 1dB.
Alternative test: After step 2, conduct a binary Alternative test: After step 2, conduct a binary search for 1-dB compression point.search for 1-dB compression point.
Example: Gain Compression TestExample: Gain Compression Test
Small-signal gain, GSmall-signal gain, G00 = = 28dB28dB
Input-referred 1-dB compression point power level,Input-referred 1-dB compression point power level,
PP1dB(input)1dB(input) = = – 19 dBm– 19 dBm
We compute:We compute: 1-dB compression point Gain, G1-dB compression point Gain, G1dB1dB = 28 – 1 = 27 dB = 28 – 1 = 27 dB
Output-referred 1-dB compression point power level, Output-referred 1-dB compression point power level, PP1dB(output) 1dB(output) == PP1dB(input)1dB(input) + G + G1dB1dB
Intermodulation DistortionIntermodulation Distortion Intermodulation distortion is relevant to devices that handle Intermodulation distortion is relevant to devices that handle
multiple frequencies.multiple frequencies.
Consider an input signal with two frequencies Consider an input signal with two frequencies ωω11 and and ωω22::
vvii = A cos = A cos ωω11t + B cos t + B cos ωω22tt
Nonlinearity in the device function is represented byNonlinearity in the device function is represented by
vvoo = a = a00 + a + a11 v vii + a + a22 v vii22 + a + a33 v vii
33, , neglecting higher order termsneglecting higher order terms
Therefore, device output isTherefore, device output is
vvoo = a = a00 + a + a11 (A cos (A cos ωω11t + B cos t + B cos ωω22t)t) DC and fundamentalDC and fundamental
+ a+ a22 (A cos (A cos ωω11t + B cos t + B cos ωω22t)t)22 22ndnd order terms order terms
+ a+ a33 (A cos (A cos ωω11t + B cos t + B cos ωω22t)t)33 33rdrd order terms order terms
Third-Order Intercept Point (IP3)Third-Order Intercept Point (IP3) IP3 is the power level of the fundamental for which the IP3 is the power level of the fundamental for which the
output of each fundamental frequency equals the output output of each fundamental frequency equals the output of the closest third-order intermodulation frequency.of the closest third-order intermodulation frequency.
IP3 is a figure of merit that quantifies the third-order IP3 is a figure of merit that quantifies the third-order intermodulation distortion.intermodulation distortion.
Assuming aAssuming a11 >> 9a >> 9a33 A A22 /4, IP3 is given by /4, IP3 is given by
Example: IP3 of an RF LNAExample: IP3 of an RF LNA Gain of LNA = 20 dBGain of LNA = 20 dB RF signal frequencies: 2140.10MHz and 2140.30MHzRF signal frequencies: 2140.10MHz and 2140.30MHz Second-order intermodulation distortion: 400MHz; outside Second-order intermodulation distortion: 400MHz; outside
operational band of LNA.operational band of LNA. Third-order intermodulation distortion: 2140.50MHz; within the Third-order intermodulation distortion: 2140.50MHz; within the
operational band of LNA.operational band of LNA. Test:Test:
Input power, PInput power, P00 = – 30 dBm, for each fundamental frequency = – 30 dBm, for each fundamental frequency
Noise in an RF system is unwanted random fluctuations in a desired Noise in an RF system is unwanted random fluctuations in a desired signal.signal.
Noise is a natural phenomenon and is always present in the Noise is a natural phenomenon and is always present in the environment.environment.
Effects of noise:Effects of noise: Interferes with detection of signal (hides the signal).Interferes with detection of signal (hides the signal). Causes errors in information transmission by changing signal.Causes errors in information transmission by changing signal. Sometimes noise might imitate a signal falsely.Sometimes noise might imitate a signal falsely.
All communications system design and operation must account for All communications system design and operation must account for noise.noise.
Consider noise as a random voltage or current Consider noise as a random voltage or current function, x(t), over interval – T/2 < t < T/2.function, x(t), over interval – T/2 < t < T/2.
Fourier transform of x(t) is XFourier transform of x(t) is XTT(f).(f).
Power spectral density (PSD) of noise is power Power spectral density (PSD) of noise is power across 1across 1ΩΩ
Plank’s constant h = 6.626 × 10Plank’s constant h = 6.626 × 103434 J-sec J-sec Frequency and bandwidth in hertz = f, BFrequency and bandwidth in hertz = f, B Boltzmann’s constant k = 1.38 Boltzmann’s constant k = 1.38 ×× 10 10 – 23 – 23 J/K J/K Absolute temperature in Kelvin = TAbsolute temperature in Kelvin = T
Other Noise TypesOther Noise Types Shot noise [Schottky, 1928]: Broadband noise due to random Shot noise [Schottky, 1928]: Broadband noise due to random
behavior of charge carriers in semiconductor devices.behavior of charge carriers in semiconductor devices. Flicker (1/f) noise: Low-frequency noise 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 perhaps due to material defects; power spectrum falls off as 1/f. Can be significant at audio frequencies.be significant at audio frequencies.
Quantization noise: Caused by conversion of continuous valued Quantization noise: Caused by conversion of continuous valued analog signal to discrete-valued digital signal; minimized by using analog signal to discrete-valued digital signal; minimized by using more digital bits.more digital bits.
Quantum noise: Broadband noise caused by the quantized nature of Quantum noise: Broadband noise caused by the quantized nature of charge carriers; significant at very low temperatures (~0K) or very charge carriers; significant at very low temperatures (~0K) or very high bandwidth ( > 10high bandwidth ( > 101515 Hz). Hz).
Plasma noise: Caused by random motion of charges in ionized Plasma noise: Caused by random motion of charges in ionized medium, possibly resulting from sparking in electrical contacts; medium, possibly resulting from sparking in electrical contacts; generally, not a concern.generally, not a concern.
Measuring NoiseMeasuring Noise Expressed as noise power density in the units of dBm/Hz.Expressed as noise power density in the units of dBm/Hz. Noise sources:Noise sources:
Resistor at constant temperature, noise power = kTB W/Hz.Resistor at constant temperature, noise power = kTB W/Hz. Avalanche diodeAvalanche diode
Noise temperature:Noise temperature: TTnn = (Available noise power in watts)/(kB) kelvins = (Available noise power in watts)/(kB) kelvins
Excess noise ratio (ENR) is the difference in the noise output Excess noise ratio (ENR) is the difference in the noise output between hot (on) and cold (off) states, normalized to between hot (on) and cold (off) states, normalized to reference thermal noise at room temperature (290K):reference thermal noise at room temperature (290K): ENR = [k( TENR = [k( Thh – T – Tc c )B]/(kT)B]/(kT00B) = ( TB) = ( Thh / T / T00) – 1) – 1
Where noise output in cold state is takes same as reference.Where noise output in cold state is takes same as reference. 10 log ENR ~ 15 to 20 dB10 log ENR ~ 15 to 20 dB
Signal-to-Noise Ratio (SNR)Signal-to-Noise Ratio (SNR) SNR is the ratio of signal power to noise power.SNR is the ratio of signal power to noise power.
Noise Factor and Noise FigureNoise Factor and Noise Figure Noise factor (F) is the ratio of input SNR to output SNR:Noise factor (F) is the ratio of input SNR to output SNR:
F = (SF = (Sii /N /Nii) / (S) / (Soo /N /Noo))
= N= Noo / ( GN / ( GNii ), when S ), when Sii = 1W and G = gain of DUT = 1W and G = gain of DUT
= N= Noo /( kT /( kT00 BG), when N BG), when Nii = kT = kT00 B for input noise B for input noise
sourcesource F ≥ 1F ≥ 1
Noise figure (NF) is noise factor expressed in dB:Noise figure (NF) is noise factor expressed in dB: NF = 10 log F dBNF = 10 log F dB 0 ≤ NF ≤ ∞0 ≤ NF ≤ ∞
Cascaded System Noise FactorCascaded System Noise Factor Friis equation [Proc. IRE, July 1944, pp. 419 – 422]:Friis equation [Proc. IRE, July 1944, pp. 419 – 422]:
Example: SOC receiver with large gain so noise output is Example: SOC receiver with large gain so noise output is measurable; noise power should be above noise floor of measurable; noise power should be above noise floor of measuring equipment.measuring equipment.
Gain G is known or previously measured.Gain G is known or previously measured.
Noise factor, F = NNoise factor, F = No o / (kT/ (kT00BG), whereBG), where NNoo is measured output noise power (noise floor) is measured output noise power (noise floor)
B is measurement bandwidthB is measurement bandwidth
This measurement is also done using S-parameters.This measurement is also done using S-parameters.6060Lectures 16-17: RF TestingLectures 16-17: RF Testing
Copyright 2008, AgrawalCopyright 2008, Agrawal
Y – FactorY – Factor Y – factor is the ratio of output noise in hot (power on) state to that in cold (power Y – factor is the ratio of output noise in hot (power on) state to that in cold (power
off) state.off) state.
YY == NNh h / N/ Ncc
== NNhh / N / N00
Y is a simple ratio.Y is a simple ratio.
Consider, NConsider, Nh h = kT= kThhBG and NBG and Ncc = kT = kT00BGBG
Then NThen Nhh – N – Ncc = kBG( T = kBG( Thh – T – T00 ) or kBG = ( N ) or kBG = ( Nhh – N – Ncc ) / ( T ) / ( Thh – T – T00 ) )
Noise factor, F = Noise factor, F = NNhh /( kT /( kT00 BG) = ( N BG) = ( Nhh / T / T00 ) [ 1 / (kBG) ] ) [ 1 / (kBG) ]
== ( N ( Nhh / T / T00 ) ( T ) ( Thh – T – T00 ) / (N ) / (Nhh – N – Ncc ) )
Measuring Noise Factor: Y – Factor MethodMeasuring Noise Factor: Y – Factor Method
Noise source provides hot and cold noise power levels and is Noise source provides hot and cold noise power levels and is characterized by ENR (excess noise ratio).characterized by ENR (excess noise ratio).
Tester measures noise power, is characterized by its noise factor FTester measures noise power, is characterized by its noise factor F22
and Y-factor Yand Y-factor Y22..
Device under test (DUT) has gain GDevice under test (DUT) has gain G11 and noise factor F and noise factor F11..
Two-step measurement:Two-step measurement: Calibration: Connect noise source to tester, measure output Calibration: Connect noise source to tester, measure output
power for hot and cold noise inputs, compute Ypower for hot and cold noise inputs, compute Y22 and F and F22..
Measurement: Connect noise source to DUT and tester Measurement: Connect noise source to DUT and tester cascade, measure output power for hot and cold noise inputs, cascade, measure output power for hot and cold noise inputs, compute compute Ycompute compute Y1212, F, F12 12 and Gand G11..
Use Friis equation to obtain FUse Friis equation to obtain F11..
Show that from noise measurements on a Show that from noise measurements on a cascaded system, the noise factor of DUT is cascaded system, the noise factor of DUT is given bygiven by
Phase NoisePhase Noise Phase noise is due to small random variations in the phase of an Phase noise is due to small random variations in the phase of an
RF signal. In time domain, phase noise is referred to as RF signal. In time domain, phase noise is referred to as jitterjitter.. Understanding phase:Understanding phase:
Effects of Phase NoiseEffects of Phase Noise Similar to phase modulation by a random signal.Similar to phase modulation by a random signal. Two types:Two types:
Long term phase variation is called Long term phase variation is called frequency driftfrequency drift.. ShShort term phase variation is ort term phase variation is phase noisephase noise..
Definition: Phase noise is the Fourier spectrum (power spectral density) Definition: Phase noise is the Fourier spectrum (power spectral density) of a sinusoidal carrier signal with respect to the carrier power.of a sinusoidal carrier signal with respect to the carrier power.
L(f) = L(f) = PPnn /P /Pc c (as ratio) (as ratio)
== PPnn in dBm/Hz – P in dBm/Hz – Pcc in dBm (as dBc) in dBm (as dBc)
PPnn is RMS noise power in 1-Hz bandwidth at frequency f is RMS noise power in 1-Hz bandwidth at frequency f
PPcc is RMS power of the carrier is RMS power of the carrier
[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 noiseWhite noise δ(t) corresponds to noise floor
Quadrature-phase carrier frequency with amplitude and phase noiseShort-term phase noise corresponds to phase noise spectrum Phase spectrum, L(f) = Sφ(f)/2Where Sφ(f) is power spectrum of φ(t)
Phase Noise MeasurementPhase Noise Measurement Phase noise is measured by low noise receiver Phase noise is measured by low noise receiver
(amplifier) and spectrum analyzer:(amplifier) and spectrum analyzer: Receiver must have a lower noise floor than the signal noise Receiver must have a lower noise floor than the signal noise
floor.floor. Local oscillator in the receiver must have lower phase noise Local oscillator in the receiver must have lower phase noise
Consider the following spectrum analyzer data:Consider the following spectrum analyzer data: RBW = 10HzRBW = 10Hz Frequency offset = 2kHzFrequency offset = 2kHz
PPcarriercarrier = – 3.31 dBm = – 3.31 dBm
PPoffsetoffset = – 81.17 dBm = – 81.17 dBm
Determine phase noise in dBc/Hz at 2kHz from Determine phase noise in dBc/Hz at 2kHz from the carrier.the carrier.
References, AgainReferences, Again1.1. S. Bhattacharya and A. Chatterjee, "RF Testing," Chapter 16, pages S. Bhattacharya and A. Chatterjee, "RF Testing," Chapter 16, pages
745-789, in 745-789, in System on Chip Test ArchSystem on Chip Test Architectures, edited by L.-T. Wang, itectures, edited by L.-T. Wang, C. E. Stroud and N. A. Touba, Amsterdam: Morgan-Kaufman, 2008.C. E. Stroud and N. A. Touba, Amsterdam: Morgan-Kaufman, 2008.
2.2. M. L. Bushnell and V. D. Agrawal, M. L. Bushnell and V. D. Agrawal, Essentials of Electronic Testing for Essentials of Electronic Testing for Digital, Memory & Mixed-Signal VLSI CircuitsDigital, Memory & Mixed-Signal VLSI Circuits, Boston: Springer, 2000., Boston: Springer, 2000.
3.3. J. Kelly and M. Engelhardt, J. Kelly and M. Engelhardt, Advanced Production Testing of RF, SoC, Advanced Production Testing of RF, SoC, and SiP Devicesand SiP Devices, Boston: Artech House, 2007., Boston: Artech House, 2007.
4.4. B. Razavi, B. Razavi, RF MicroelectronicsRF Microelectronics, Upper Saddle River, New Jersey: , Upper Saddle River, New Jersey: Prentice Hall PTR, 1998.Prentice Hall PTR, 1998.
5.5. J. Rogers, C. Plett and F. Dai, J. Rogers, C. Plett and F. Dai, Integrated Circuit Design for High-Integrated Circuit Design for High-Speed Frequency SynthesisSpeed Frequency Synthesis, Boston: Artech House, 2006., Boston: Artech House, 2006.
6.6. K. B. Schaub and J. Kelly, K. B. Schaub and J. Kelly, Production Testing of RF and System-on-a-Production Testing of RF and System-on-a-Chip Devices for Wireless CommunicationsChip Devices for Wireless Communications, Boston: Artech House, , Boston: Artech House, 2004.2004.