Contents. Transmission Lines The Smith Chart Vector Network Analyser (VNA) ü structure ü calibration ü operation. Measurements

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2 Contents Transmission Lines The Smith Chart Vector Network Analyser (VNA) ü structure ü calibration ü operation Measurements Göran Jönsson, EIT Vector 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] simulation v S (t) Transmission line! Göran Jönsson, EIT Vector 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 + 0 e j(!t!"z) $ % where V + = the complex amplitude of v + 0 = V + 0 e j! 0 + (t,z) at z = 0 Göran Jönsson, EIT Vector 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 Vector 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 Vector Network Analysis 6

7 Reflection Coefficient Implies a rotation in the polar!-plane Polar diagram!d =! L e "2!d =! L e "2"d "2 j#d e Lossless transmission line Lossy transmission line Göran Jönsson, EIT Vector Network Analysis 7

8 Conversion of Reflection Coefficient to Impedance Γ d,z d Γ L,Z L Z S v S (t) Z 0 Z L z d Γ d = Z d Z 0 Z d + Z 0 Z d = Z 0 1+ Γ d 1 Γ d Göran Jönsson, EIT Vector Network Analysis 8

9 Reflection Coefficient Load Impedance Γ Z L = Z 0 1+ Γ L 1 Γ L Γ L = Z L Z 0 Z L + Z 0 Γ = 0 Z = Z 0 Γ = 1 Z = Γ = 1 Z = 0 Göran Jönsson, EIT Vector Network Analysis 9

10 Standing-Wave Ratio SWR =! = V max V min = I max = 1+ " I min 1# " Göran Jönsson, EIT Vector 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 Vector Network Analysis 11

12 The Smith Chart p + jq = r!1+ jx r +1+ jx Göran Jönsson, EIT Vector Network Analysis 12

13 The Smith Chart Circles Constant resistance lines " resistance circles Constant reactance lines " reactance circles Göran Jönsson, EIT Vector 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 Vector Network Analysis 14

15 Definition of S-parameters Model: a x!"#$%#&'$(")*+' b x!",'-.'%('& )*+' 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 Vector Network Analysis 15

16 Measurement of S-parameters! S! in! L S 21! out 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 Vector 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 Vector 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 2 DUT b 1 a 2 Göran Jönsson, EIT Vector Network Analysis 18

19 Soft Keys 4 channels select measurement, diagram etc. Calibration Start- stop frequency Sweep settings Marker settings PRESET Göran Jönsson, EIT Vector 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 DUT splitter directional coupler Göran Jönsson, EIT Vector Network Analysis 20

21 Calibration Attenuation and phase shift in the test cables must be compensated Calibrated reference planes are therefore created where the device under test will be connected Test cable Calibrated reference plane DUT Test cable Göran Jönsson, EIT Vector Network Analysis 21

22 Before the Calibration Before you proceed with the calibration you must 1. Connect the test cables to be used After the calibration you are not allowed to change anything concerning the test cables, adding adapters etc. 2. Set/check the frequency range If the range is increased the calibration will be turned off and you need to recalibrate. If the span is decreased the analyser will interpolate the calibration data (CAI). 3. Set/check the SOURCE POWER For linear measurements of active devices you normally need to reduce the SOURCE POWER to avoid compression. If you forget any of these items you probably must redo the calibration Göran Jönsson, EIT Vector Network Analysis 22

23 Calibration Calibrated reference planes will be created where the DUT is to be connected Through TOSM Open Short!*+,-.*%/"'#-+"0 /"1$# '$%21,31% +"4"+"1&"#%&,++"&0 $5,1 6'$'%&'1%("% 6"$"+/51"6!"#$%&'()" Match 50! 50! 50! Calibrated reference planes!"#$%&'()" Göran Jönsson, EIT Vector Network Analysis 23

24 Calibration TOSM - Classical Full Two-Port Calibration Forward measurement X F error two-port A 1 a 1 DUT S 21 b 2 error two-port B S F 12B a 1 F F S 11A S 22A S 11 S 22 F S 22B b 2 b 1 S F 12A b 1 S 12 a 2 ideal two-port network analyzer R everse measurement 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) Load matches error two-port A a 1 DUT S 21 b 2 error two-port B S R 12B b 2 Transmission losses of receiver b 1 R S 22A S R 12A b 1 S 11 S 22 S 12 a 2 R S 22B 1 R S 11B a 2 Device independent crosstalks X R ideal two-port network analyzer Göran Jönsson, EIT Vector Network Analysis 24

25 Standard Connectors BNC - 4 GHz outer diameter: 14.3 mm N - 11 GHz outer diameter: 20.2 mm SMA - 18 GHz outer diameter: 8.25 mm 56 Ncm Göran Jönsson, EIT Vector Network Analysis 25

26 Precision Microwave Coaxial Connectors Göran Jönsson, EIT Vector Network Analysis 26

27 Precision Connectors To connect an SMA male to a 3.5 mm female, use 56 Ncm 3.5 mm male to a SMA female, use 90 Ncm Connectors in each of the shaded areas have the same size outer conductor and therefore can safely be mated together! 3.5 mm - 34 GHz - 90 Ncm 2.92 mm or Type K - 40 GHz - 90 Ncm 2.4 mm - 50 GHz - 90 Ncm SMA or or mm or Type V - 70 GHz - 90 Ncm Photograph 1.0 mm GHz - 56 Ncm Göran Jönsson, EIT Vector Network Analysis 27

28 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 Do Not Allow to Rotate only turn the socket or the nut the contact pin may never spin round only use your thumb and index finger or a torque wrench the connector may never be fastened by other tools if you tighten up to hard the thread is harmed Outer conductor and threads starting to engage. Rotate Coupling Nut Only Test cables and connectors for professional use are only used for a limited period until they will be exchanged or reconditioned. Göran Jönsson, EIT Vector Network Analysis 28