Contents. ! Transmission Lines! The Smith Chart! Vector Network Analyser (VNA) ! Measurements. ! structure! calibration! operation
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2 Contents! Transmission Lines! The Smith Chart! Vector Network Analyser (VNA)! structure! calibration! operation! Measurements Göran Jönsson, EIT Network Analysis 2!
3 Waves on Lines! If the wavelength to be considered is significantly greater compared to the size of the circuit the voltage will be independent of the location. amplitude! >> d d! distance but this is not true at short wavelengths = high frequencies t! T! v(t,z)! The velocity of the wave is v =! T =! " f Z S! z!! " m [ ] = v f = 300 f [ MHz] v S (t)! Transmission line! simulation Göran Jönsson, EIT Network Analysis 3! Z L! The voltage or the current is a function of both time and distance
4 Travelling Voltage Wave on a Lossless Line t! T! v(t,s)! direction of propagation!" z! v + (t,z) + v + (t,z) = V + 0 cos(!t " #z + $ + 0 ) = Re V + j(!t "#z) %& 0 e ' (! where V + = the complex amplitude of v + 0 = V + 0 e j! 0 + (t,z) at z = 0 Göran Jönsson, EIT Network Analysis 4!
5 Reflection Coefficient! Definition:! = reflected voltage wave incident voltage wave = V " e # z V + e "# z V L! V L + Z S! v S (t)! Transmission line + V L! Z L! z! Göran Jönsson, EIT Network Analysis 5!
6 Reflection Coefficient! At an arbitrary location d at the line the reflection coefficient is! d =! L e "2# d =! L e "2$d "2 j%d e! d! L Z S! v S (t)! Z 0! + V L! Z L! z! d! Göran Jönsson, EIT Network Analysis 6!
7 ! Reflection Coefficient Polar diagram! d =! L e "2# d =! L e "2$d "2 j%d e Implies a rotation in the polar!-plane Lossless transmission line Lossy transmission line Göran Jönsson, EIT Network Analysis 7!
8 Conversion of Reflection Coefficient to Impedance! d,z d! L,Z L Z S! v S (t)! Z 0! Z L! z! d!! d = Z d " Z 0 Z d + Z 0 # Z d = Z 0 1+! d 1"! d Göran Jönsson, EIT Network Analysis 8!
9 Reflection Coefficient Load Impedance! Z L = Z 0 1+! L 1"! L! L = Z L " Z 0 Z L + Z 0! = 0 " Z = Z 0! = 1 " Z = #! = "1 # Z = 0 Göran Jönsson, EIT Network Analysis 9!
10 Standing-Wave Ratio SWR =! = V max V min = I max = 1+ " I min 1# " Göran Jönsson, EIT Network Analysis 10!
11 The Smith Chart The chart was invented by Phillip Smith in the early 1930-ties Transform between!- and Z-plane positive reactance! inductive positive resistance negative reactance! capacitive Göran Jönsson, EIT Network Analysis 11!
12 The Smith Chart p + jq = r!1+ jx r +1+ jx Göran Jönsson, EIT Network Analysis 12!
13 The Smith Chart Circles! Constant resistance lines! resistance circles! Constant reactance lines! reactance circles Göran Jönsson, EIT Network Analysis 13!
14 Example of Smith Chart Usage Conversion impedance! admittance z = 1 y!( y) = 1 y "1 1 y +1 = = " y "1 y +1 = = "! z ( ) = e j#!( z)! Series connection! Addition of resistance:!motion at constant reactance circle! Addition of reactance:!motion at constant resistance circle Göran Jönsson, EIT Network Analysis 14!
15 ! Model: Definition of S-parameters S 21 a 1 b 2-port 2 b S S a2 S 12! Definition: " b 1 = s 11! a 1 + s 12! a 2 # $ b 2 = s 21! a 1 + s 22! a 2! # "# or in matrix format: b 1 b 2 $ & %& =! s 11 s 12 # s 21 s "# 22 $! & # %& "# a 1 a 2 $ & %& S 11 = b 1 a 1 a 2 =0 S 21 = b 2 a 1 a 2 =0 S 12 = b 1 a 2 a 1 =0 S 22 = b 2 a 2 a 1 =0 IMPORTANT! The definition utilizes 50" as reference impedance Göran Jönsson, EIT Network Analysis 15!
16 Measurement of S-parameters! S S 21! out! in! L S 11 2-port S 22 S 12! in = S 11 + S 12 S 21! L 1" S 22! L = S 11! L =0! out = S 22 + S 12 S 21! S 1" S 11! S = S 22!S =0 The S-parameters are easily measured if the ports are terminated by the reference impedance Z 0 = 50" (! L respectively! S = 0) S 11 = b 1 a 1 a 2 =0 S 21 = b 2 a 1 a 2 =0 S 12 = b 1 a 2 a 1 =0 S 22 = b 2 a 2 a 1 =0 Göran Jönsson, EIT Network Analysis 16!
17 Scalar Network Analysis! Characterising the Device Under Test properties! Spectrum analyser + sweep generator! frequency sweep! amplitude sweep only magnitude measurement, DUT no phase information Göran Jönsson, EIT Network Analysis 17!
18 Vector Network Analysis! Characterising the Device Under Test properties! Network Analyser! frequency sweep! amplitude sweep! complete information! amplitude! phase a 1! b 1! DUT b 2! a 2! Göran Jönsson, EIT Network Analysis 18!
19 Soft Keys 4 channels select measurement, diagram etc. Calibration Start- stop frequency Sweep settings Marker settings PRESET Göran Jönsson, EIT Network Analysis 19!
20 The Vector Network Analyser Structure Network analyser with S-parameter test set Directional coupler Channel b 2 b 2! Splitter Port 2 Receiver and display Port 1 DUT Saw tooth generator VCO signal generator receiver Reference a 1 a 1! b 1! a 1! a 2! b 2! display Channel b 1 b 1! Modern network analysers are often equipped with four receivers which provides more efficient methods for calibration. S-parameter test set Göran Jönsson, EIT Network Analysis 20! DUT splitter directional coupler
21 Calibration!! Attenuation and phase shift in the test cables must be compensated Calibrated reference planes are therefore created where the device under test is connected Test cable Calibrated reference plane DUT Test cable Göran Jönsson, EIT Network Analysis 21!
22 Calibration! Calibrated reference planes will be created where the DUT is to be connected Through Open Short TOSM Through measurements at known references correction data may be determined Test cable Match 50 "# Test cable 50 "# Calibrated reference planes Göran Jönsson, EIT Network Analysis 22!
23 Calibration TOSM - Classical Full Two-Port Calibration F o r w a r d m e a s u r e m e n t a 1 b 1 e r r o r t w o - p o r t A 1 F S 11 A S F 12 A F S 2 2 A a 1 b 1 X F D U T S 21 S 1 1 S 2 2 S 1 2 b 2 a 2 e r r o r t w o - p o r t B S F 12 B b F 2 S 22 B Extension of the one port error model by 3 additional error terms for forward direction yields 6 error terms. Adding a similar model for reverse direction yields the classical!!12-term error model (TOSM) i d e a l t w o - p o r t n e t w o r k a n a l y z e r!load matches R e v e r s e m e a s u r e m e n t!transmission losses of receiver e r r o r t w o - p o r t A a 1 D U T S 21 b 2 e r r o r t w o - p o r t B S R 12 B b 2!Device independent crosstalks R S 22 A S 1 1 S 2 2 R S 22 B R S 11 B b 1 a 2 S R 12 A b 1 S 1 2 a 2 1 X R i d e a l t w o - p o r t n e t w o r k a n a l y z e r Göran Jönsson, EIT Network Analysis 23!
24 Be careful about torn connectors!! The wear and tear when connectors are connected and disconnected may result in measurement errors.! always check that the connectors are clean! only turn the socket or the nut! the contact pin may never spin round! always use a torque wrench! the connector may never be fastened by other tools if you tighten up to hard the thread is harmed! Test cables and connectors for professional use are only used for a limited period until they will be exchanged or reconditioned. Göran Jönsson, EIT Network Analysis 24!
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