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! distance but this is not true at short wavelengths = high frequencies t! v(t,z)! T! The velocity of the wave is Transmission line simulation Göran Jönsson, EIT 2009-11-16 Network Analysis 3! The voltage or the current is a function of both time and distance Contents Travelling Voltage Wave on a Lossless Line Transmission Lines The Smith Chart Vector Network Analyser (VNA)! structure! calibration! operation Measurements v(t,s)! t! T! direction of propagation!" +! where = the complex amplitude of v + (t,z) at z = 0 Göran Jönsson, EIT 2009-11-16 Network Analysis 2! Göran Jönsson, EIT 2009-11-16 Network Analysis 4!
Reflection Coefficient Reflection Coefficient Implies a rotation in the polar!-plane Definition: Polar diagram Lossless transmission line Lossy transmission line Transmission line + V L! Göran Jönsson, EIT 2009-11-16 Network Analysis 5! Göran Jönsson, EIT 2009-11-16 Network Analysis 7! Reflection Coefficient At an arbitrary location d at the line the reflection coefficient is Conversion of Reflection Coefficient to Impedance Z 0! d! Z 0! + V L! d! Göran Jönsson, EIT 2009-11-16 Network Analysis 6! Göran Jönsson, EIT 2009-11-16 Network Analysis 8!
Reflection Coefficient Load Impedance 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 2009-11-16 Network Analysis 9! Göran Jönsson, EIT 2009-11-16 Network Analysis 11! Standing-Wave Ratio The Smith Chart Göran Jönsson, EIT 2009-11-16 Network Analysis 10! Göran Jönsson, EIT 2009-11-16 Network Analysis 12!
The Smith Chart Circles Definition of S-parameters Model: Constant resistance lines! resistance circles 2-port or in matrix format: Definition: Constant reactance lines! reactance circles IMPORTANT! The definition utilizes 50" as reference impedance Göran Jönsson, EIT 2009-11-16 Network Analysis 13! Göran Jönsson, EIT 2009-11-16 Network Analysis 15! Example of Smith Chart Usage Measurement of S-parameters 2-port Conversion impedance! admittance Series connection! Addition of resistance: motion at constant reactance circle! Addition of reactance: motion at constant resistance circle The S-parameters are easily measured if the ports are terminated by the reference impedance Z 0 = 50" (! L respectively! S = 0) Göran Jönsson, EIT 2009-11-16 Network Analysis 14! Göran Jönsson, EIT 2009-11-16 Network Analysis 16!
Scalar Network Analysis Characterising the Device Under Test properties Spectrum analyser + sweep generator! frequency sweep! amplitude sweep Soft Keys 4 channels select measurement, diagram etc. Start- stop frequency Sweep settings Marker settings only magnitude measurement, no phase information PRESET Göran Jönsson, EIT 2009-11-16 Network Analysis 17! Göran Jönsson, EIT 2009-11-16 Network Analysis 19! Vector Network Analysis The Vector Network Analyser Structure Characterising the Device Under Test properties Network Analyser! frequency sweep! amplitude sweep! complete information amplitude phase Network analyser with S-parameter test set Channel b 2 Receiver and display b 2! Splitter Saw tooth generator VCO Directional coupler Port 2 Port 1 a 1! b 2! b 1! a 2! Göran Jönsson, EIT 2009-11-16 Network Analysis 18! Reference a 1 Channel b 1 a 1! b 1! signal generator S-parameter test set receiver b 1! a 1! a 2! b 2! Modern network analysers are often equipped directional with four receivers which provides more coupler efficient methods for calibration. Göran Jönsson, EIT 2009-11-16 Network Analysis 20! display splitter
Attenuation and phase shift in the test cables must be compensated Calibrated reference planes are therefore created where the device under test is connected TOSM - Classical Full Two-Port 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 e r r o r t w o - p o r t B b 2 R S 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 Calibrated reference plane b 1 R S 12 A b S 12 1 a 2 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 1 a 2 Göran Jönsson, EIT 2009-11-16 Network Analysis 21! Göran Jönsson, EIT 2009-11-16 Network Analysis 23! Be careful about torn connectors! Calibrated reference planes will be created where the is to be connected Through Open Short TOSM Through measurements at known references correction data may be determined 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 Match 50 "# 50 "# Calibrated reference planes s and connectors for professional use are only used for a limited period until they will be exchanged or reconditioned. Göran Jönsson, EIT 2009-11-16 Network Analysis 22! Göran Jönsson, EIT 2009-11-16 Network Analysis 24!