Calibration Uncertainty for the PM AM Noise Standards

1 Page 1 NIST Special Publication 250-90 Calibration Uncertainty for the NIST PM /AM Noise Standards Ar chita Hati Craig Nelson Neil Ashby David Howe Carrier USB L SB USB LS B US B LSB US B LSB Carrier Open at page → 2 Page 2 he National Institute of Standards and Technology was established in 1988 by Congress to “assist industry in the development of technology ... needed to improve product quality, to modernize manufacturing processes, to e... Open at page → 3 Page 3 NIST Special Publication 250-90 Calibration Uncertainty for the NIST PM/AM Noise Standards Archita Hati Craig Nelson Neil Ashby David Howe Time and Frequency Division Physical Measurement Laboratory National Institute of... Open at page → 4 Page 4 Certain commercial entities, equipment, or materials may be identified in this document in order to describe an experimental procedure or concept adequately. Such identification is not intended to imply recommendation or... Open at page → 5 Page 5 iii Contents 1 Introduction ............................................................................................................................. 1 2 AM and PM noise - Basic concepts .............................. Open at page → 6 Page 6 iv Notations Acronym Meaning AM Amplitude Modulation BPF Bandpass Filter BW Bandwidth dB Decibel dBm Decibel relative to 1 milliwatt DDPNMS Direct Digital Phase Noise Measurement System FFT Fast Fourier Transform IF Inte... Open at page → 7 Page 7 v spectral density function σC Combined fractional uncertainty σLR Uncertainty due the long-term reproducibility of the PM/AM noise standard between calibration cycles σN-FFTAve Uncertainty due to the number of FFT avera... Open at page → 8 Page 8 vi u C Combined uncorrelated uncertainty U Expanded uncertainty v(t) Instantaneous voltage fluctuations V 0 Peak voltage of the carrier signal V Baseband Folded double-sideband down-converted voltage of the PM/AM noise s... Open at page → 9 Page 9 1 1 Introduction In this document, we provide the total (or combined) uncertainty of phase modulation (PM) and amplitude modulation (AM) noise measurement of the NIST portable noise standard calculated from the individua... Open at page → 10 Page 10 2 2 AM and PM noise - Basic concepts In this section we briefly describe the basic concept of phase-modulated (PM) noise and amplitude-modulated (AM) noise and their characterization in the frequency domain [5-8]. We als... Open at page → 11 Page 11 3 L(f) includes the fluctuations from only one sideband of the carrier, and hence it is a single- sideband unit of measure. When L(f) is expressed in the form 10log[L(f)], its unit is dBc/ Hz, that is dB below the carrie... Open at page → 12 Page 12 4 where β is the phase-modulation index (or peak phase deviation, also denoted by ∆φpeak). The second exponential term in the curly bracket is a periodic signal with period 2 π/ωm and can be expanded by the exponential F... Open at page → 13 Page 13 5 ( ) peak 0 2 S d 0.1 rad .f f φ ∞ <<∫ (13) However, the practical values for the lower and upper integration limits, f L and f U, are respectively the reciprocal of the measurement time and system half-bandwidth. The c... Open at page → 14 Page 14 6 sidebands, each having average power γ 2 /4. If there is a similar amount of uncorrelated white noise power in the lower sideband at “ν 0- f”, it also will produce four signals, two AM and two PM of average power γ 2 /... Open at page → 15 Page 15 7 3 Description of the noise standard The block diagram of the noise standard at 5 MHz, 10 MHz, and 100 MHz is shown in Figure 2. The detailed description of this noise standard can be found in [2]. The noise standard ha... Open at page → 16 Page 16 8 The modulated output has precisely equal PM and AM noise, since there is no phase coherence between the signal and the noise, as described in 2.2.3 and [12]. The power spectral density (PSD) of the SSB PM noise, [L(f)... Open at page → 17 Page 17 9 4 Measurement setup for calibration of the PM/AM noise standard To measure ()fL at multiple offset frequencies, f, a digital fast Fourier transform (FFT) spectrum analyzer is used to take advantage of its speed, high d... Open at page → 18 Page 18 10 5 Calibration procedure at NIST The offset generator and the PM/AM noise standard are turned on and allowed to stabilize for at least 24 hours. The offset signal generator is connected to the LO port of the down-conve... Open at page → 19 Page 19 11 5.3 Measurement of the noise power spectral density down-converted from both the upper and the lower sidebands The carrier power of the PM/AM standard is then turned OFF and the noise is turned ON. The frequency of th... Open at page → 20 Page 20 12 5.4 Measurement of the noise floor power spectral density The carrier power of the PM/AM noise standard is turned OFF and the noise is turned OFF. The frequency of the offset generator kept at ν0. Next, a noise floor... Open at page → 21 Page 21 13 6 Measurement equation L(f) in Eq. (16) represents a ratio of power measurements performed at radio frequency (rf). A higher order correction, Kβ, due to the small angle modulation approximation is introduced and Eq.... Open at page → 22 Page 22 14 The same SNR is assumed for both V Beat- and V Beat+ measurements. The logarithmic form of Eq. (19) is given by: ( ) ( ) ( ) ( ) ( ) ( )( ) 2 ,2 , 2 , 2 2 , , 10log 10log 10log 1 1 10log 10log 1 10log(2 ). NoiseOff M... Open at page → 23 Page 23 15 7 Estimation of uncertainty Normalizing the PSD to a 1 Hz bandwidth and rewriting the measurement Eq. (19) gives ( ) () () ( ) ( )( ) 2 2 , , 2 2 , , 1 . 12 1 NoiseOn M NoiseOff M NL RF BW Beat M Beat M V f V f f K K... Open at page → 24 Page 24 16 The individual multipliers of (23) are ( ) 2 2 4 , , 22 2 2 , , , 4 NoiseOn M NoiseOn M NoiseOn M NoiseOn M NoiseOff M V V V V V  ∂ =   ∂ − L L (25) ( ) 2 2 4 , , 22 2 2 , , , 4 NoiseOff M NoiseOff M NoiseOff... Open at page → 25 Page 25 17 2 2 2 2 21 ,σ σ σ σ −   = + = +      NoiseOn N FFTAve SR SR NoiseN (33) 2 2 2 2 22 1 . Beat B FFTAve SR SR Beat N SNR σ σ σ σ −   = + = +      (34) N Noise and N Beat are the number of FFT averages use... Open at page → 26 Page 26 18 8 Uncertainty budget As stated in the Introduction, the AM and PM noise of the noise standard are usually measured two times at NIST, once before sending it (“out” measurement) to the customer and a second time after... Open at page → 27 Page 27 19 By use of Table 1 and Eq. (32) the expanded fractional uncertainty for values shown in this example is ± 11.5 % or ± 0.5 dB for n set equal to 6. It should be noted that this calibration standard creates equal amount... Open at page → 28 Page 28 20 9 Validation of the measurement To further validate the calibration method, we use two different approaches. In the first approach, the noise of the standard is measured with different PM noise measurement systems and... Open at page → 29 Page 29 21 Appendix A. Verification of the baseband measurement equation The phase noise, L(f) and amplitude noise, S α(f) generated by the PM/AM noise standard is given by ( ) ( ) [ ] [ ] 0 0 Noise ( - ) + Noise ( + )1 1 . [dBc... Open at page → 30 Page 30 22 When the signals from the offset generator and the noise standard are mixed, two sidebands at 0 fν± are translated to a baseband frequency at f. The folded double-sideband down- conversion is represented by Eq. (A4) a... Open at page → 31 Page 31 23 measurement. The upper and lower sideband gains are factored out into a single term and simplified by a first order Taylor expansion when both sidebands are approximately equal as follows: ( ) + O when , 2 + = + + = +... Open at page → 32 Page 32 24 2 ( ) . ( ) LVL noise NL LVL carrier g P K g P   =    (A11) K RF is the ratio of the effective power gain between noise and carrier power measurements. Ideally, this number should be unity; however, it is affect... Open at page → 33 Page 33 25 Appendix B. Measurement of correction factors, K NL, KRF, KBW and K β (i) Set-up for measuring nonlinearity of the down-converter and the FFT analyzer – K NL As discussed earlier, K NL is defined as the change in gain... Open at page → 34 Page 34 26 These measurements are repeated for all the specified offset frequencies ( ±f ) at each of the three carrier frequencies. Because the mixer is operating in linear mode, K NL should ideally be equal to 1. The maximum o... Open at page → 35 Page 35 27 (iv) Calculation of small angle modulation correction factor – Kβ Kβ is a correction to the small angle modulation approximation used to calculate L(f ) from a single sideband power ratio. An effective peak phase modu... Open at page → 36 Page 36 28 Appendix C. Error of signal power measurements in the presence of background noise Consider the fast Fourier transform (FFT) of a signal of amplitude A and frequency f, such that the signal occurs in a single-frequenc... Open at page → 37 Page 37 29 2 2 1 1 . N i i M S N σ = = +∑ (C8) If the noise power is known, it can be subtracted off and the measurement of the average signal power reported as 2 2 11 . N i i M S N σ = − =∑ (C9) Apart from the propagation of er... Open at page → 38 Page 38 30 2 2 2 1( ) . 2 x P x dx e dx σ πσ − = (C18) The fourth moment is 2 2 4 4 42 3 . 2 σ σ πσ ∞ − −∞ = =∫ x x x e dx (C19) Thus the error is 4 4 4 2 23 2 ; 2 σ σ σ σ = − = = E N N N E N (C20) The measurement of signal powe... Open at page → 39 Page 39 31 REFERENCES [1] “Calibration Services User Guide,” http://ts.nist.gov/MeasurementServices/Calibrations/pm_am_noise.cfm#pm_am. [Online]. Available: http://ts.nist.gov/MeasurementServices/Calibrations/pm_am_noise.cfm#pm_... Open at page → 40 Page 40 32 Errata 1. p. 15, Equation (24) should be changed to () ( ) ( ) () () () () ( ) 22 2 2 2 2 ,,22 ,, 222 2 2 2 2 2 2 2 22 ,2 ,, L LL L L L L LL NoiseOn M NoiseOff M NoiseOn M NoiseOff M C NL RF BW NL RF BW Beat M Beat M... 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