Presentation to: ANAMET

Improved Measurement of Passive Intermodulation Products

James Miall

Date: March 2004

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

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?

How do you measure PIM?Huber + Suhner’s PIM Measuring System

TX1(f1)

TX2(f2)

PA1

PA2 Filter Combiner

TX

RX

Duplexer

DUT

Cable Load

LNA(IM3)

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

Intermodulation Distortion: Traditional Theory

To calculate from first principles the expected input power (Pi) dependence of the intermodulation distortion power consider a passive device the I(V) characteristic can be expressed in a Taylor series expansion:

)(!3

121)0()( 43

3

32

2

2

0

VOVdV

IdVdV

IdVdVdIIVI

V

δδδδ +⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛+⎟

⎠⎞

⎜⎝⎛+=

=

where the reciprocal of the coefficient of the second term is just the ohmic resistance R ( )

0/1

==

VdVdIR

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…

Slide from J. Gallup and L. Hao

3rd Order PIM

If a PIM producing artefact is modelled as having response

i(t) = a1·u(t) + a2·u2(t) + a3·u3(t)

where: u(t) = u1·cos(ω1·t) + u2·cos(ω2·t)

then the 3rd order intermodulation products of interest are given by

uIM3(t) = k·[ u12·u2·cos(2ω1·t - ω2·t) + u1·u2

2·cos(2ω2·t- ω1·t) ]

with ω1 = 1867MHz and ω2 = 1821MHz then IM3 products at 1775MHzand 1913MHz are produced

GSM 1800 Band – 1710-1785MHz & 1805-1880MHz

System Calibration & Uncertainties

System was calibrated against Impedance and Power standards

PIM MeasurementSystem

N-7/16Adaptor

Standard Thermistor

StepAttenuator

Measurement Plane

Reference Thermistor30dB

20dB coupler20dB

3dB

Synthesizer(1775MHz)

Amplifier

PIM MeasurementSystem

N-7/16Adaptor

Standard Thermistor

StepAttenuator

Measurement Plane

Reference Thermistor30dB

20dB coupler20dB

3dB

Synthesizer(1775MHz)

Amplifier

Calibration of the Receive Path (i.e. spectrum analyser/LNA/filter etc.) assembly as a power meter

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

Mismatch between signal generator and measurement port

Resolution of spectrum analyser

Frequency Terms:

Random Terms:

Connection repeatabilityChange in PIM with amount of cable bending

Difference between Coaxial Connections:

Signal generator and amplifier frequency drift

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.

Change in PIM with applied power of 1 frequency (1867MHz) with

other frequency (1821MHz) at constant level (20.19W)

2.5

2.9

3.3

3.7

4.1

4.5

0 5 10 15 20 25 30 35

Power Level of 1867MHz signal /W

Mea

sure

d PI

M /n

W

uIM3(t) = k·[ u12·u2·cos(2ω1·t - ω2·t) + u1·u2

2·cos(2ω2·t- ω1·t) ]

Effect of Heating

The system power was turned on and the PIM level measured every 15s for 600s.

Change in Measured PIM with System Heating

2.5

3

3.5

4

4.5

5

5.5

0 100 200 300 400 500 600Time /s

PIM

leve

l /nW

PIM levelsingle exponential fit

Response shows more than 1 time constant but implies that in the long time constant object:

PIM = a·e-Time / b + c where: a = 1.778 nW, b = 206.4 s, c = 2.745 nW

Possible relation - (Change in PIM) α 1 / (Change in Temperature)

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·log10(1+10−x/20) Error− (dB) = 20·log10(1−10−x/20)

-10-9-8-7-6-5-4-3-2-101234567

0 5 10 15 20 25 30 35 40

(True PIM) - (System PIM) dB

Erro

r (dB

)

(Sys+DUT) dB

(Sys-DUT) dB This becomes an increasingly important part of the uncertainty budget as the PIM in the DUT becomes lower

System Linearity

Signal Generators and Amplifiers are not linear.

Need to measure power at DUT separately for both input paths

Linearity of Power Amplifiers

0

5

10

15

20

25

30

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 .9

Power Supplied to Amplifier (as indicated on Signal Generator) /mW

Pow

er a

t Mea

sure

men

t Por

t /W

Linearity of PIM Measurement System (ref lev 0dBm on Spectrum Analyser)

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0 20 40 60 80 100

Attenuation of Input Signal /dB

Diff

eren

ce b

etw

een

Syst

em R

espo

nse

and

Inpu

t Sig

nal L

evel

(ref

eren

ced

to 2

5dB

valu

e) /d

B

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

An Uncertainty Budget for Measuring -110dB Device

There are two dominant contributions

1. Connection Repeatability – getting repeatable connections is a difficult job even with torque spanners

2. Scalar Subtraction Error

Uncertainty Source Divisor U(xi)% u(xi)% Calibration of the rig 2 0.657 0.329Short term drift in rig 1.732 0.100 0.058Mismatch between TS and DUTPIM 1.414 0.030 0.021Connection repeatability 2 5.586 2.793Signal generator drift*2 and PA drift*2 2 0.500 0.250Typical random effects 1 0.100 0.100System PIM - DUT PIM 1.414 17.600 12.445Combined standard uncertainty 11.626Expanded uncertainty (k = 2) 23.251

Final Scalar Results

110dB standard (ser: 403002) = (-109.8 ± 1.11) dB

80dB standard (ser: 401002) = (-78.2 ± 0.35) dB

80dB standard (ser: 401001) = (-77.0 ± 0.62) dB

Measurement port connected directly to cable load = (-124.9 ± 1.6) dB

110dB standard (ser: 403002) = (-109.8 ± 0.47) dB

80dB standard (ser: 401002) = (-78.2 ± 0.32) dB

80dB standard (ser: 401001) = (-77.0 ± 0.60) dB

Results showing just the connection uncertainty

Results showing the full uncertainty

Vector PIM Measurement

With a set of low PIM spacers it should be possible to separate the various PIM contributions (other than connections)

Uncorrected System PIM

Actual System

PIM

Cable Load PIM

Imag

Uncorrected System PIM

Actual System

PIM

Cable Load PIM

Imag

Uncorrected DUT

System

Cable Load

DUT

DUT & Cable Load

Real

ImagUncorrected

DUT

System

Cable Load

DUT

DUT & Cable Load

Real

Imag

Establishing the Internal System PIM and Cable Load PIM

A DUT PIM measurement showing PIM contributions and spacer measurements

Measured = Internal + Connection1 + DUT + Connection2 + Cable Load

Vector PIM Measurement (improved setup)

The improved setup involved more amplification and filtering to try to lower the noise floor at the VVM to enable lower signal level measurements

1821MHz

1867MHz Power Amplif iers Combiner

Duplexer

TX

RX

DUT

Cable Load

FilterLNA

Original Dev ices

40dB AmplifierFilter

1750MHz-1950MHz

H&S Rece ive Band Filter

Vector Volt

Meter

1821MHz

1867MHz Power Amplif iers Combiner

Duplexer

TX

RX

DUT

Cable Load

FilterLNA

Original Dev ices

40dB AmplifierFilter

1750MHz-1950MHz

H&S Rece ive Band Filter

Vector Volt

Meter

The Vector Voltmeter frequency reference and phase locking connections are missing

Initial Test of Principle

Do ‘low PIM’ adaptor combinations provide a reasonable phase shift?

Relationship between physical length of offsets and phase of measured PIM

-100

0

100

200

300

400

500

600

700

800

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

Offset /m

Pha

se /°

Measurements

Best-fit straight line

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

Initial Circle Fitting

Measurements of complex PIM of 80dB standard offset by low PIM spacers (axes show measured voltage in 50ohm line)

-0.0015

-0.001

-0.0005

0

0.0005

0.001

0.0015

-0.0015 -0.001 -0.0005 0 0.0005 0.001 0.0015

MeasurementsBest FitCentre

Circle’s were fitted using Kasa’s method. This minimizes the sum of the 4th

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.

Uncertainty on centre > N2

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

Measurements of system PIM with several low PIM spacers

0

0.2

0.4

0.6

0.8

1

-1 -0.5 0 0.5

PIM (Re) /mV

PIM

(Im

) /m

V

System PIMAd1 + Ad2Ad1 + Ad2 + Ad3 + Ad4Ad1 + Ad7 + Ad2System Average

Circle Fitting to 110dB Item

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

Circle Fitting to offset 110dB standard

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

PIM (Re) /mV

PIM

(Im

) /m

VBes t Fit to Means

Mean DataWeighted Best FitData

Ad1 + Ad2 + 110dB - expected 8deg - actual 24degAd1 + Ad2 + Ad3 + Ad4 + 110dB - expected 16deg - actual 14degAd1 + Ad7 + Ad2 + 110dB - very different to expectedAd5 + Ad6 + Ad3 + Ad4 - expected 8deg from above- actual 8.5deg

Circle Fitting to 80dB Item

80dB 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)

80dB PIM Standard Circle Fitting

-40

-30

-20

-10

0

10

20

30

40

-40 -20 0 20 40

PIM (Re) /mV

PIM

(Im

) /m

VBest FitDataCentreWeighted FitMeans

Ad5 + Ad6 + Ad3 + Ad4 + 80dB expected = 56deg, measured = 61degAd1 + Ad7 + Ad2 + 80dB expected = 179deg, measured = 174degAd1 + Ad7 + Ad8 + Ad2 + 80dB expected = 6deg, measured = 12degAd3 + Ad4 + Ad1 + Ad7 + Ad2 + 80dB expected = 189deg, measured = 193degAd1+Ad3+Ad4+Ad10+Ad9+Ad2+80dB expected = -58deg, measured –55deg

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 moresuitable equipment to get results that actually have lower uncertainties