Improved Measurement of Passive Intermodulation Products

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1 Presentation to: ANAMET Improved Measurement of Passive Intermodulation Products James Miall Date: March 2004

2 Introduction PIM = Passive InterModulation IMD = InterModulation Distortion PIM is mixing of two or more different frequency signals at non-linearities in passive components such as cables or filters All the PIM production mechanisms are not fully understood but PIM can be caused by Poor / point mechanical contacts Ferrous content of conductors in the RF path Oxidisation of conductor surfaces Thermal effects

3 Why is PIM a Problem? Telecommunications systems will generally have a transmit and receive band which cover different frequency ranges. The Transmit power level can be 40dBm+ but the Receive path will often be sensitive enough to pick up signals 100dB+ below this It is very important that there are no TX out of band emissions as they will easily be enough to cause RX desensitisation (increased signal-to-noise ratio, decrease system capacity, degraded call quality etc.) The system can be designed to filter out the IM from active components (amplifiers etc.) but what about the PIM from the last filter or the cable connecting the duplexer to the antenna?

4 How do you measure PIM? TX Huber + Suhner s PIM Measuring System TX1(f 1 ) PA1 RX DUT TX2(f 2 ) PA2 Filter Combiner Duplexer LNA(IM3) Cable Load Spectrum Analyser Huber + Suhner s Reflected PIM Measurement System consists of 2 separate frequency sources and amplifiers (~20W each) Filter Combiner Duplexer DUT and Cable Load to absorb TX power LNA + more filtering (not shown) Spectrum Analyser

5 Slide from J. Gallup and L. Hao Intermodulation Distortion: Traditional Theory To calculate from first principles the expected input power (P i ) dependence of the intermodulation distortion power consider a passive device the I(V) characteristic can be expressed in a Taylor series expansion: I ( V ) = I (0) + di dv V = d I 2 1 d I 3 δ V + δv δv dv + 3! dv O( δv 4 ) where the reciprocal of the coefficient of the second term is just the ohmic resistance R 1/( ) R = di dv V = 0 All higher order terms generate non-linear behaviour and hence lead to mixing and harmonic generation. For many unbiased passive systems the I(V) characteristic is symmetric about V = 0, thus I(V) = -I(-V). In this case the third term on the right of the Taylor expansion will be zero. The lowest order non-linear term is now the third order term. But many passive systems do NOT satisfy these conditions so the dependence of IMD level on input power is not necessarily cubic

6 3 rd Order PIM If a PIM producing artefact is modelled as having response i(t) = a 1 u(t) + a 2 u 2 (t) + a 3 u 3 (t) where: u(t) = u 1 cos(ω 1 t) + u 2 cos(ω 2 t) then the 3 rd order intermodulation products of interest are given by u IM3 (t) = k [ u 12 u 2 cos(2ω 1 t - ω 2 t) + u 1 u 22 cos(2ω 2 t- ω 1 t) ] with ω 1 = 1867MHz and ω 2 = 1821MHz then IM3 products at 1775MHz and 1913MHz are produced GSM 1800 Band MHz & MHz

7 System Calibration & Uncertainties System was calibrated against Impedance and Power standards Calibration of the Receive Path (i.e. spectrum analyser/lna/filter etc.) assembly as a power meter Synthes izer (1775MHz) Amplifier 20dB coupler 30dB 20dB Reference Thermistor Standard Thermistor Step Atte nuator 3dB PIM Measurement System Measurement Plane N-7/16 Adaptor

8 System Calibration & Uncertainties System was calibrated against Impedance and Power standards Power at DUT terms: Uncertainty on measurement using power meter & sensor Mismatch between measurement port and DUT Signal generator and amplifier level drift Power at Spectrum Analyser Terms: Non-linearity of duplexer, filter and LNA Non-linearity of spectrum analyser Signal generator power reading uncertainty Frequency Terms: Signal generator and amplifier frequency drift Mismatch between signal generator and measurement port Resolution of spectrum analyser Random Terms: Difference between Coaxial Connections: Connection repeatability Change in PIM with amount of cable bending

9 Input Power Dependence of PIM produced PIM level will vary differently with changes in level of the two input frequencies. Non-linear dependence in graph is due to system heating. Data was taken by slowly increasing the power level. Measured PIM /nw Change in PIM with applied power of 1 frequency (1867MHz) w ith other frequency (1821MHz) at constant level (20.19W) Powe r Leve l of 1867MHz signal /W u IM3 (t) = k [ u 12 u 2 cos(2ω 1 t - ω 2 t) + u 1 u 22 cos(2ω 2 t- ω 1 t) ]

10 Effect of Heating Change in Measured PIM with System Heating The system power was turned on and the PIM level measured every 15s for 600s. PIM level /nw PIM level single exponential fit Time /s Response shows more than 1 time constant but implies that in the long time constant object: PIM = a e -Time / b + c where: a = nw, b = s, c = nw Possible relation - (Change in PIM) α 1 / (Change in Temperature)

11 Error Due to Scalar Measurement of Vector Quantities The measurement of vector PIM, which is a vector quantity using only a scalar detector (spectrum analyser) introduces additional errors. The 2 limits of this for the totally in phase and 180º out of phase cases are given by the formulæ: Error + (db) = 20 log 10 (1+10 x/20 ) Error (db) = 20 log 10 (1 10 x/20 ) Error (db) (Sys+DUT) db (Sys-DUT) db (True PIM) - (System PIM) db This becomes an increasingly important part of the uncertainty budget as the PIM in the DUT becomes lower

12 System Linearity 30 Linea rity of Powe r Amplifiers Signal Generators and Amplifiers are not linear. Need to measure power at DUT separately for both input paths Power at Measurement Port /W Pow er Supplied to Amplifier (as indicate d on Signal Genera tor) /mw Linearity of PIM Measurement System (ref lev 0dBm on Spectrum Analyser) Difference between System Response and Input Signal Level (referenced to 25dB value) /db Attenuation of Input Signal /db LNA, filters and Spectrum Analyser are reasonably linear until input power level becomes too low. Calibration at a few power levels close to required level should be sufficient

13 An Uncertainty Budget for Measuring -110dB Device Uncertainty Source Divisor U(xi)% u(xi)% Calibration of the rig Short term drift in rig Mismatch between TS and DUTPIM Connection repeatability Signal generator drift*2 and PA drift* Typical random effects System PIM - DUT PIM Combined standard uncertainty Expanded uncertainty (k = 2) There are two dominant contributions 1. Connection Repeatability getting repeatable connections is a difficult job even with torque spanners 2. Scalar Subtraction Error

14 Final Scalar Results Results showing just the connection uncertainty Measurement port connected directly to cable load 110dB standard (ser: ) 80dB standard (ser: ) 80dB standard (ser: ) = ( ± 1.6) db = ( ± 0.47) db = (-78.2 ± 0.32) db = (-77.0 ± 0.60) db Results showing the full uncertainty 110dB standard (ser: ) 80dB standard (ser: ) 80dB standard (ser: ) = ( ± 1.11) db = (-78.2 ± 0.35) db = (-77.0 ± 0.62) db

15 Vector PIM Measurement Measured = Internal + Connection1 + DUT + Connection2 + Cable Load Syste m Imag Actual System PIM Uncorrected System PIM Cable Load PIM Imag Uncorrected DUT Cable Load DUT DUT & Cable Load Rea l Establishing the Internal System PIM and Cable Load PIM With a set of low PIM spacers it should be possible to separate the various PIM contributions (other than connections) A DUT PIM measurement showing PIM contributions and spacer measurements

16 Vector PIM Measurement (improved setup) 1821MHz 1867MHz Filter 1750MHz- 1950MHz Power Amplifiers LNA 40dB Amplifier Co mb iner Original Dev ices Filter TX Duplexer RX DUT Cable Load The improved setup involved more amplification and filtering to try to lower the noise floor at the VVM to enable lower signal level measurements H&S Rece ive Band Filter Vector Volt Meter The Vector Voltmeter frequency reference and phase locking connections are missing

17 Initial Test of Principle Do low PIM adaptor combinations provide a reasonable phase shift? PIM a x + b where: a = 5194 º/m x = offset (m) b = -40.3º PIM spacers have ε 1.5 Which is somewhere between air and Teflon filled coax Phase / Relationship between physical length of offsets and phase of measure d PIM Measurements Best-fit straight line Offset /m

18 Initial Circle Fitting Circle s were fitted using Kasa s method. This minimizes the sum of the 4 th powers of the difference between the data and fitted circle (not least-squares) Provides a good estimate for the circle centre and radius provided that the circle radius is large compared to the error on each point. 2 Uncertainty on centre > N Measurements of complex PIM of 80dB standard offset by low PIM spacers (axes show measured voltage in 50ohm line) Measurements Best Fit Centre

19 System PIM Measuring the system PIM was difficult as some of the low PIM spacers were not much lower in PIM than the system itself Error bars show 2 * StDev without reconnection. Connection repeatability also of similar size to system PIM PIM (Im) /mv Measurements of system PIM with several low PIM spacers 1 System PIM Ad1 + Ad2 Ad1 + Ad7 + Ad2 0.8 System Average PIM (Re) /mv Ad1 + Ad2 + Ad3 + Ad4

20 Circle Fitting to 110dB Item Circle Fitting to offset 110dB standard 2 Available low PIM phase shifts gave very poor set of data so higher PIM airlines were also used Weighted best fit weights contribution of each point according to inverse of variance PIM (Im) /mv Bes t Fit to Means Mean Data -2.5 Weighted Best Fit PIM (Re) /mv Data Ad1 + Ad dB - expected 8deg - actual 24deg Ad1 + Ad2 + Ad3 + Ad dB - expected 16deg - actual 14deg Ad1 + Ad7 + Ad dB - very different to expected Ad5 + Ad6 + Ad3 + Ad4 - expected 8deg from above- actual 8.5deg

21 Circle Fitting to 80dB Item 80dB PIM Standard Circle Fitting dB results came out very well as all the low PIM spacers (including airlines) and the connections had much lower PIM levels than this (Phase is not necessarily consistent between graphs) PIM (Im) /mv PIM (Re) /mv Best Fit Data Cent re Weighted Fit Means Ad5 + Ad6 + Ad3 + Ad4 + 80dB expected = 56deg, measured = 61deg Ad1 + Ad7 + Ad2 + 80dB expected = 179deg, measured = 174deg Ad1 + Ad7 + Ad8 + Ad2 + 80dB expected = 6deg, measured = 12deg Ad3 + Ad4 + Ad1 + Ad7 + Ad2 + 80dB expected = 189deg, measured = 193deg Ad1+Ad3+Ad4+Ad10+Ad9+Ad2+80dB expected = -58deg, measured 55deg

22 Conclusions 1) Scalar Measurements are fine for higher power PIM measurements but uncertainties increase rapidly at low power levels 2) There are a lot of potential pitfalls! 3) Vector Measurements show promise but require some work with more suitable equipment to get results that actually have lower uncertainties

IMPACT OF POWER VARIATION ON 3RD ORDER PASSIVE INTERMODULATION OF COAXIAL RF-CABLES AND THEIR CONNECTORS

IMPACT OF POWER VARIATION ON 3RD ORDER PASSIVE INTERMODULATION OF COAXIAL RF-CABLES AND THEIR CONNECTORS Hartmut Gohdes RFS kabelmetal, Division of kabelmetal electro GmbH, D-30179 Hannover, Germany Abstract