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An Introduction to S-parameters

An Introduction to S-parameters. Copyright © Polar Instruments 2014.

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An Introduction to S-parameters

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  1. An Introduction to S-parameters Copyright © Polar Instruments 2014

  2. Whilst reading through this document you may find it useful to have access to the Polar Si9000e PCB Transmission Line Field Solver, as this will aid your understanding of S-parameters. Evaluation licenses are available from our offices, contact details can be found on slide 43. Copyright © Polar Instruments 2014

  3. S-parameters are a useful method for representing a circuit as a “black box” Copyright © Polar Instruments 2014

  4. S-parameters are a useful method for representing a circuit as a “black box” The external behaviour of thisblack box can be predicted without any regard for the contents of the black box. Copyright © Polar Instruments 2014

  5. S-parameters are a useful method for representing a circuit as a “black box” The external behaviour of thisblack box can be predicted without any regard for the contents of the black box. This black box could contain anything:a resistor, a transmission line or an integrated circuit. Copyright © Polar Instruments 2014

  6. A “black box” or network may have any number of ports. This diagram shows a simple network with just 2 ports. Copyright © Polar Instruments 2014

  7. A “black box” or network may have any number of ports. This diagram shows a simple network with just 2 ports. Note : A port is a terminal pair of lines. Copyright © Polar Instruments 2014

  8. S-parameters are measured by sending a single frequency signal into the network or “black box” and detecting what waves exit from each port. Power, voltage and currentcan be considered to be in the form of waves travellingin both directions. Copyright © Polar Instruments 2014

  9. S-parameters are measured by sending a single frequency signal into the network or “black box” and detecting what waves exit from each port. Power, voltage and currentcan be considered to be in the form of waves travellingin both directions. For a wave incident on Port 1,some part of this signal reflects back out of that port and some portion of the signal exits other ports. Copyright © Polar Instruments 2014

  10. I have seen S-parameters described as S11, S21, etc. Can you explain? First lets look at S11. S11 refers to the signalreflected at Port 1 for the signal incident at Port 1. Copyright © Polar Instruments 2014

  11. I have seen S-parameters described as S11, S21, etc. Can you explain? First lets look at S11. S11 refers to the signalreflected at Port 1 for the signal incident at Port 1.Scattering parameter S11is the ratio of the two waves b1/a1. Copyright © Polar Instruments 2014

  12. I have seen S-parameters described as S11, S21, etc. Can you explain? Now lets look at S21. S21 refers to the signalexiting at Port 2 for the signal incident at Port 1.Scattering parameter S21is the ratio of the two waves b2/a1. Copyright © Polar Instruments 2014

  13. I have seen S-parameters described as S11, S21, etc. Can you explain? Now lets look at S21. S21 refers to the signalexiting at Port 2 for the signal incident at Port 1.Scattering parameter S21is the ratio of the two waves b2/a1. S21? Surely that should be S12?? Copyright © Polar Instruments 2014

  14. I have seen S-parameters described as S11, S21, etc. Can you explain? Now lets look at S21. S21 refers to the signalexiting at Port 2 for the signal incident at Port 1.Scattering parameter S21is the ratio of the two waves b2/a1. S21? Surely that should be S12??S21 is correct! S-parameter convention always refers to the responding port first! Copyright © Polar Instruments 2014

  15. Copyright © Polar Instruments 2014

  16. I have seen S-parameters described as S11, S21, etc. Can you explain? A linear network can be characterised by a set of simultaneous equationsdescribing the exiting waves from each port in terms of incident waves. S11 = b1 / a1 S12 = b1 / a2 S21 = b2 / a1 S22 = b2 / a2 Note again how the subscript follows the parameters in the ratio (S11=b1/a1, etc...) Copyright © Polar Instruments 2014

  17. Copyright © Polar Instruments 2014

  18. S-parameters are complex (i.e. they have magnitude and angle) because both the magnitude and phase of the input signal are changed by the network. (This is why they are sometimes referred to as complex scattering parameters). Copyright © Polar Instruments 2014

  19. These four S-parameters actually contain eight separate numbers: the real and imaginary parts (or the modulus and the phase angle) of each of the four complex scattering parameters. Copyright © Polar Instruments 2014

  20. Quite often we refer to the magnitude only as it is of the most interest.How much gain (or loss) you get is usually more important than how muchthe signal has been phase shifted. Copyright © Polar Instruments 2014

  21. What do S-parameters depend on? S-parameters depend upon the networkand the characteristic impedances of the source and load used to measure it, and the frequency measured at.i.e.if the network is changed, the S-parameters change. if the frequency is changed, the S-parameters change. if the load impedance is changed, the S-parameters change. if the source impedance is changed, the S-parameters change. Copyright © Polar Instruments 2014

  22. What do S-parameters depend on? S-parameters depend upon the networkand the characteristic impedances of the source and load used to measure it, and the frequency measured at.i.e.if the network is changed, the S-parameters change. if the frequency is changed, the S-parameters change. if the load impedance is changed, the S-parameters change. if the source impedance is changed, the S-parameters change. In the Si9000e the source and load impedance default is 50 Ohms, although this is configurable. Copyright © Polar Instruments 2014

  23. What do S-parameters depend on? S-parameters depend upon the networkand the characteristic impedances of the source and load used to measure it, and the frequency measured at.i.e.if the network is changed, the S-parameters change. if the frequency is changed, the S-parameters change. if the load impedance is changed, the S-parameters change. if the source impedance is changed, the S-parameters change. Copyright © Polar Instruments 2014

  24. A little math… This is the matrix algebraic representationof 2 port S-parameters: Some matrices are symmetrical. A symmetrical matrix has symmetry about the leading diagonal. Copyright © Polar Instruments 2014

  25. A little math… This is the matrix algebraic representationof 2 port S-parameters: Some matrices are symmetrical. A symmetrical matrix has symmetry about the leading diagonal. In the case of a 2-port network, that means that S21 = S12 and interchanging the input and output ports does not change the transmission properties. Copyright © Polar Instruments 2014

  26. A little math… This is the matrix algebraic representationof 2 port S-parameters: Some matrices are symmetrical. A symmetrical matrix has symmetry about the leading diagonal. In the case of a symmetrical 2-port network, that means that S21 = S12 and interchanging the input and output ports does not change the transmission properties.A transmission line is an example of a symmetrical 2-port network. Copyright © Polar Instruments 2014

  27. A little math… Parameters along the leading diagonal,S11 & S22, of the S-matrix are referred to as reflection coefficients because they refer to the reflection occurring at one port only. Copyright © Polar Instruments 2014

  28. A little math… Parameters along the leading diagonal,S11 & S22, of the S-matrix are referred to as reflection coefficients because they refer to the reflection occurring at one port only. Off-diagonal S-parameters, S12, S21, are referred to as transmission coefficients because they refer to what happens from one port to another. Copyright © Polar Instruments 2014

  29. Larger networks: A Network may have any number of ports. Copyright © Polar Instruments 2014

  30. Larger networks: A Network may have any number of ports. The S-matrix for an n-port network contains n2 coefficients (S-parameters), each one representing a possible input-output path. Copyright © Polar Instruments 2014

  31. Larger networks: A Network may have any number of ports. The S-matrix for an n-port network contains n2 coefficients (S-parameters), each one representing a possible input-output path. The number of rows and columns in an S-parameters matrix is equal to the number of ports. Copyright © Polar Instruments 2014

  32. Larger networks: A Network may have any number of ports. The S-matrix for an n-port network contains n2 coefficients (S-parameters), each one representing a possible input-output path. The number of rows and columns in an S-parameters matrix is equal to the number of ports. For the S-parameter subscripts “ij”, “j” is the port that is excited (the input port) and “i” is the output port. Copyright © Polar Instruments 2014

  33. Larger networks: Yes i for output j for input — logical ;-) A Network may have any number of ports. The S-matrix for an n-port network contains n2 coefficients (S-parameters), each one representing a possible input-output path. The number of rows and columns in an S-parameters matrix is equal to the number of ports. For the S-parameter subscripts “ij”, “j” is the port that is excited (the input port) and “i” is the output port. Copyright © Polar Instruments 2014

  34. Larger networks: A Network may have any number of ports. The S-matrix for an n-port network contains n2 coefficients (S-parameters), each one representing a possible input-output path. The number of rows and columns in an S-parameters matrix is equal to the number of ports. For the S-parameter subscripts “ij”, “j” is the port that is excited (the input port) and “i” is the output port. Copyright © Polar Instruments 2014

  35. Copyright © Polar Instruments 2014

  36. Sum up… • S-parameters are a powerful way to describe an electrical network • S-parameters change with frequency / load impedance / source impedance / network • S11 is the reflection coefficient • S21 describes the forward transmission coefficient (responding port 1st!) • S-parameters have both magnitude and phase information • Sometimes the gain (or loss) is more important than the phase shift and the phase information may be ignored • S-parameters may describe large and complex networks • If you would like to learn more please consider evaluating the Polar Si9000e PCB Transmission Line Field Solver. A 5 step process to generate, plot and export S-parameters is included in the following slides. Copyright © Polar Instruments 2014

  37. Using Polar Si9000e Field Solver to generate, plot and export S-parameters Step 1: Select the transmission line structure and enter the parameters Copyright © Polar Instruments 2014

  38. Using Polar Si9000e Field Solver to generate, plot and export S-parameters Step 2: Switch to the Frequency Dependent tab and enter the frequency range Copyright © Polar Instruments 2014

  39. Using Polar Si9000e Field Solver to generate, plot and export S-parameters Step 3: Select Calculate to generate S-parameters and plot graph Copyright © Polar Instruments 2014

  40. Using Polar Si9000e Field Solver to generate, plot and export S-parameters Step 4: The S-parameter data may be plotted in a number of useful ways Copyright © Polar Instruments 2014

  41. Touchstone Excel .CSV Using Polar Si9000e Field Solver to generate, plot and export S-parameters Step 5: The same S-parameter data may be exported to a number of formats Copyright © Polar Instruments 2014

  42. Touchstone Excel .CSV Using Polar Si9000e Field Solver to generate, plot and export S-parameters Step 5: The same S-parameter data may be exported to a number of formats Copyright © Polar Instruments 2014

  43. Polar Atlas Si Insertion loss test system may be used to extract Sdd 21 with either the IPC TM 650 SPP method or IPC TM 650 SET2DIL method Copyright © Polar Instruments 2014

  44. Polar Atlas Si is also capable of extracting phase and effective Er at frequency Copyright © Polar Instruments 2014

  45. Further reading: Agilent papers http://www.sss-mag.com/pdf/an-95-1.pdf http://www.sss-mag.com/pdf/AN154.pdf National Instruments paper http://zone.ni.com/devzone/nidzgloss.nsf/webmain/D2C4FA88321195FE8625686B00542EDB?OpenDocument Other links: http://www.sss-mag.com http://www.microwaves101.com/index.cfm http://www.reed-electronics.com/tmworld/article/CA187307.html http://en.wikipedia.org/wiki/S-parameters Online lecture OLL-140 Intro to S-parameters - Eric Bogatin Online lecture OLL-141 S11 & Smith charts - Eric Bogatin www.bethesignal.com Copyright © Polar Instruments 2014

  46. For more information: Contact Polar now: Phone USA / Canada / MexicoKen Taylor ( 503) 356 5270 Asia / Pacific Terence Chew +65 6873 7470 Japan japan@polarinstruments.asia +81 45 339 0155 UK / EuropeNeil Chamberlain +44 23 9226 9113 Germany / Austria / Switzerland Hermann Reischer +43 7666 20041-0 www.polarinstruments.com Copyright © Polar Instruments 2014

  47. Copyright © Polar Instruments 2014

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