Your RF Cable, the unknown Entity

Transcription

1 HAM RADIO 2018 Your RF Cable, the unknown Entity PROF. DR. THOMAS BAIER DG8SAQ Hochschule Ulm University of Applied Sciences Prittwitzstrasse Ulm Thanks to: Dan Maguire AC6A HAM RADIO Ferdinand Sigloch DB2SG

2 Program Cable Types und Characteristics Physics Measurement Methods Analysis Methods HAM RADIO

3 Cable Types unsymmetric Inner Conductor Dielektric (ε r ) Screen = Outer Conductor Coaxial ine Conductor Ribbon/Insulator Conductor Twin-ead HAM RADIO

4 Propagation velocity c ength l pulse moves with velocity c t 0 c < c 0 = vacuum speed of light t Propagation time: Propagation velocity: Velocity factor: HAM RADIO c VF l / c / c 0

5 ine Impedance Z I Z Z U Z Termination with line impedance Z U I HAM RADIO

6 Measuring with Pulse Generator: Pulse Reflectometry (1) Z Z Z high impedance scope sees outgoing and returning pulses HAM RADIO

7 Pulse Reflectometry (2) variable termination Test object: 18,3m RG58 C/U HAM RADIO

8 Pulse Reflectometry (3) generator pulse 2 2l 2l c VF c 470 Ω termination pulse reflected at cable end 0 no reflection when terminated with Z short circuit termination HAM RADIO

9 Pulse Reflectometry (4) Z Z HAM RADIO

10 Pulse Reflectometry (5) propagation time forth and back 2 185ns 2l 218,3m VF 8 2 c0 185ns310 m/s 0,659 one way time 92,5ns HAM RADIO

11 More accurate Measurements using a Vector Network Analyzer S S21 11 Reflection 1 2 DUT Transmission DUT : DEVICE UNDER TEST = Cable HAM RADIO

12 Advantages of Vectorial Network Analysis accurate, high dynamic range flexible: Measuring in Frequency Domain ω Attenuation Match ine Impedance Group Delay Time Domain t Pulse Response Step Response HAM RADIO

13 Insertion oss and ine Impedance of 18.3m RG58 C/U Antenna Cable calibration plane measure S 21 und S 11 HAM RADIO

14 Time Domain Analysis using Fourier- Transform (DG8SAQ VNWA Software) input data to be transformed Pulse response windowing function: velocity faktor Dämpfung ablesbar HAM RADIO time resolution plotting range Propagation time is doubled for reflect signals (S 11 ) amplitude resolution improves

15 Propagation Delay from Pulse Response of S 21 Measurement τ : 8dB average attenuation 18,3m cable length windowing functions: Hamming Blackman Propagation time 92,8ns HAM RADIO

16 S 11 of open ended Cable in Time Domain: Time Domain Reflectometry = TDR again 18,3m length reflections at both ends: Input Output signal travels forth and back In contrast to pulse generator experiment, here we only see reflected signals. HAM RADIO

17 TDR sees more: Cable Extension + Antenna (S 11 ) 2τ : cable extended by 22,8m-18,3m = 4,5m adapter antenna reflection of adapter HAM RADIO

18 RG58 C/U in Frequency Domain: Open Questions: Propagation delay and VF depend on frequency, i.e. dispersion!? We need a mathematical model! Oscillations in S 11? HAM RADIO

19 Modelling (1) Relevant properties Side effects Capacitance dielectric loss Resistance dc, skin effekt Inductance skin effekt HAM RADIO

20 Modelling (2) A Coax is a Rod Capacitor C ' C 20r l ln( r / r) 2 1 r 1 r 1 = 0.45mm r 2 = 1.5mm ε r = 2.25 Data of RG58 C/U From APP GROUP r r 2 Polyethylen Wikipedia C ' C can be measured l 104 pf/m HAM RADIO

21 Modelling (3) Capacitance can be measured Open RG58 C/U measured 102 pf/m HAM RADIO

22 Modelling (4) Dielektrikum ist komplex, d.h. verlustbehaftet r r' j r '' r'(1 jtan( )) YC j C0 r jc0 r '( 1 j tan( )) j CC tan( ) possibly additional dc conductivity G 0 : YC j C f 2 Ctan( ) G oss ω = 2π f 0 δ=loss angle C 0 = capacitance without dielectric C C r 0 Y j C f G G C PO G P0 0 HAM RADIO

23 Modelling (5) A few Dielectrics S G PO Hz m aus ineare Elemente der Höchstfrequenztechnik, Prof. Bächthold, ETH Zürich S Hz m PE is an excellent insulator G 0 0 HAM RADIO

24 Modelling (6) Resistance and Inductance per ength R ' R l Cu 25mΩ/m 1 r 2 1 (center conductor only) r 1 = 0.45mm r 2 = 1.5mm µ r = 1 l l 2 r r 241nH/m 0 ' ln( 2 / 1) (high frequency limit, no B-field inside conductors) R can also be measured HAM RADIO

25 Shorted Coax is a Resistor at low Frequency calculated 25mΩ/m: braided inner conductor Sn-plated outer conductor also lossy 49mΩ/m, also measured with Ohm-meter at dc: 35mΩ/m inner conductor + 14mΩ /m outer conductor HAM RADIO

26 Skin Effect low frequency current uniformly distributed over conductor cross section R ' R l 1 r Cu 2 1 high frequency R ' r 1 1 r 1 Cu 1 2 r current confined to surface 2 1 f δ = penetration depth = skin depth HAM RADIO f 1 Cu 0

27 Skin Effect in round homogeneous Wire Result of Maxwells Equations Impedance per ength (Theory) We ll work with this formula! skin depth dc resistance per length HAM RADIO

28 Measurement in Shunt Configuration DUT: Piece of Copper Wire to VNWA TX any kind of T-adapter to VNWA RX Shunt configuration for high sensitivity at low impedance levels! DUT = 10cm 0.35mm Cuwire meander to keep inductance low HAM RADIO

29 VNWA Optimizer Tool Simulation vs. Measurement optimizer result: =10.9cm d=0.29mm HAM RADIO

30 Inductance vs. Magnetic Field Energie energy stored in inductance = E = energy stored in magnetic field I ' l space I space 2 B dv 2 2 I E B dv 0 0 cross section 2 BdF Every space segment carrying B-field adds to inductance value! (cylinder symmetry) HAM RADIO

31 Inductance low frequency B B B s a i s i a high frequency B s 0 0 B a B i i s a 0 0 a ' r a 0 2 ln l 2 r1 241nH/m (RG58) For both cases identical! i s 0 nh ' 50 8 m nh ' 6 m (RG58) i s ' ' r 2 f 1 HAM RADIO ' ' ' ' decreases with increasing frequency f! i a s identical f Cu decreases with increasing frequency f

32 Induktivitätsmessung am kurzgeschlossenen Koaxkabel calculated a = ( )nH/m=298nH/m i + a + s = 314 nh/m low frequency case HAM RADIO

33 Simple Skin Effect Modell for inner Impedance: Round Wire with Radius r exact solution (complicated) Z i, exact 0 x J0( x) R 2 J ( x) r 0 x (1 j) (1 j) f R iasy, 0R0' 4 f i ' asymptotic solution, poor at low frequencies 2 0R 0 Z i,joh R 0 j f 2 R j 2 R f skin Excellent compromise, simple! R ' Johnson, High Speed Signal Propagation, Prentice Hall, 2011 HAM RADIO

34 Now we know all individual Effects! Capacitance Resistance Inductance Effect in Cable? HAM RADIO

35 Some RF Transmission ine Theory: Infinitely short ine with ength dx dx = Inductance per ength [H/m] R = Wire Resistance per ength [Ω/m] C = Capacitance per ength [F/m] G = Isolator Conductance per ength [S/m] du( x) ( R' j') I( x) dx di( x) ( G ' jc') U( x) dx mit ( R' j')( G' jc' ) Z R' j' G ' jc' U( x) acosh( x) bsinh( x) Z- and S-Matrix of ine HAM RADIO

36 Useful Results: High Frequency imit (i.e. ω is large) R and G may be neglected with respect to ωc and ω : j j j jc j C c C VF 0 C C 0 1 VF Also in this limit: ' C ' Z const Thus, and C can be expressed by Z and VF: Z 1 C C VF Z C VF 0 0 HAM RADIO

37 and C may be computed from Z and VF! Example RG58: Z VF 50 0, pf C Z C VF m/s 0,66 m 0 Z 50 nh C VF 310m/s0,66 m 0 high freq. limit! HAM RADIO

38 Why 50Ω? High frequency limit: ' C ' r ln 20r ln( r / r) r1 2 1 Z ' 60 r ln 2 C' r r 1 r 1 r r 2 Voltage drop on outer and inner conductor: R i R a 1 r11 r2 1 r2 r11 U Z ln r r r ln r r Thicker cables have lower loss! attenuation function Voltage divider R i R a oad Z ine impedance and attenuation function only depend on r 2 /r 1 radius ratio! HAM RADIO

39 This is why 50Ω: Minimum oss! attenuation function owest loss for r 2 /r 1 = Ω für ε r = 2.25 radius ratio r 2 /r 1 HAM RADIO

40 Model Summary R G j R j2r f j skin jcg f G j C 0 PO 0 a Z ( R' j' )( G' jc' ) R ' G' j' jc ' l I 1 I 2 U 1 U 2 U 1 Z cosh( ) 1 l I1 U 2 sinh( l) 1 cosh( l) I 2 Z-matrix, may be converted to S-matrix HAM RADIO

41 Conversion to S-Matrix S Tor 1 ij Tor 2 S R S T z Z Z with Z reference impedance, i.e e ( z 2z 1) z 2z 1 2 l 2 2 R z e T 2 2 l ( 1) ( 1) 4z e l HAM RADIO

42 Special Case Example Z = Z 0 i.e. z =1 z Z Z 1 0 2l 2 2 2l 2 2 l l l e ( z 2z 1) z 2z 1e 4 R ( z 1) ( e 1) 0 T 4z e 4e R T 4e l S 0 S e l e 2 l matched loss delay HAM RADIO

43 Useful Equation to calculate ine Impedance from measured S ij Z Z S S 12S S11 S21 12S11 e Z 0 = reference impedance (i.g. 50Ω) ( z 1)( S ( z 1) z 1) ( 1)( ( 1) 1) 2 l 11 A z S11 z z What do we do now with all that math? HAM RADIO wiki/file:man-scratching-head.gif

44 Zplots-Software by Dan Maguire AC6A: Transmission ine Theory and Modell built-in. A ine analysis HAM RADIO

45 Analysis of RG58 C/U using ZPlots measurement and deduced model model parameters HAM RADIO

46 Model Parameter from ZPlots 0 line impedance (RF limit) velocity faktor (RF limit) length mω R 0 k0xz0(nom) m x Z0(nom) mω R skin k Hz m Hz 6 x S G PO k Z (nom) Hz m Hz using x 2 ln(10) ft 20 m VNWA can simulate this... HAM RADIO

47 VNWA Virtual Demo Device Setup R 0 R skin G 0 G PO HAM RADIO l 0 (nom) Z (nom) VF

48 Parameter Extraktion and Model works fine! S 21 0,5dB / S 11 5dB / measurement (Mem*) vs. simulation (Sij) here cable not ideal, but match > 30dB, so no practical problem Gruppenlaufzeit ( S21) 2ns/ HAM RADIO

49 So far so good!??? HAM RADIO

50 The Twin-ead actually is a 4-Port Device Port 1 Port 3 Port 2 Port 4 but in push-pull operation it is a 2-port Port 1 Port 2 HAM RADIO

51 Scattering Parameters do possess Symmetries cable mirror symmetric w.r.t. half length S S cable reciprocal device S S with just two independent S-parameters S 21 and S 11 can be determined with two reflection measurements Γ x, Γ y using two different cable terminations (x, y e.g. Short, oad) S S S x x y SxxS y ( ) S S S S, S y, y y x x y x y ( x y) (S xsy) ( xsy-1) ( y Sx-1) ( ) S S S S y x x y x y reflection coefficient termination x or y reflection coefficient cable with termination x or y HAM RADIO x 470Ω y Short

52 How to measure a balanced oad using a single-ended VNA? via 2-port measurement! Port 1 Z Z11 Z22 Z21 Z12 measured Z-Matrix elements Z 2 1 If both ports are identical: Z 2 ( Z Z ) Port 2 Z 2 2 can be computed from measured S ij with VNWA custom functions s_dm or s_dm_sym HAM RADIO

53 6,2m Twin-ead from 2-Port Measurement S 11 S 21 S 11 renormalized to 380Ω S 11 symmetric load of 470Ω Interference caused by unsymmetric operation Z : Marking says 450Ω Measurement 380Ω oad ok! HAM RADIO

54 Better: Reflection Measurement using BAUN and symmetric Calibration Symmetric SO-Standards must have been characterized beforehand via 2-port measurements! 1:4 BAUN 100Ω resistors Symmetric Short standard DUT to VNWA TX Port calibration plane HAM RADIO

55 Simulation Model identical with Coax Model! measurement vs. simulation VNWA optimizer: VF=0,887 Z =382Ω!!! Sales Brochure: Twin-ead" 450 Ohm version, black, UV-resistant, velocity faktor v/c = 0,905 HAM RADIO

56 Huge Collection of Cable Parameters: TDetails by Dan AC6A VF=0,902 Z =395Ω HAM RADIO

57 Insertion oss from simulated Impedance Match to Z = 382Ω? matched measurement vs. matched model S 21 0,1 db measurements not perfect! S 11 model reliable? measurement with BAUN, simulation with parameters from VNWA optimizer/zplots HAM RADIO

58 Alternate Method to obtain Insertion oss from Reflection Measurements (RG58) 2dB S 21 open short 6dB vs. 12dB open short oszillations in Counter-phase example RG58 VNWA Z 0 =Z cable Open or Short Double propagation path means double loss practically identical! S 21 from transmission measurement reflection coefficients Γ from reflection measurements (S 11 ) HAM RADIO

59 Also works for Twin-ead! 0,1 db S21 simulation model open short open short oszillations counter-phase S21 measured Model simulation not bad at all! HAM RADIO

60 RF-Cables: Our Achievements Underlying physics understood Realistic cable models for simulations Measurement methods for coaxial cables Measurement methods for twin-leads Analysis methods (Zplots, Optimizer) HAM RADIO

61 Vielen Dank für Ihr Interesse! HAM RADIO