RF Connector Guide - FC Lane

RF TheoryINTRODUCTION TO BASIC RF THEORY1.2CONSTRUCTION AND FUNCTION OF RF LINESCoaxial lines represent the most efficient method of transmitting signals from a source (Figure 3) via a RF lineto a termination. The most commonly used method is that of cable assemblies, where the distance between thesource and the termination is the assembly length.Direction of PropagationSource (load)TerminationConnector PairsFigure 3Direction of propagation along a RF lineThe most important factor in connector selection is the RF cable chosen, as this usually will set the minimum connector specifications such as physical size, performance, etc. The connectors chosen must have an electricalspecification (in terms of, for example: power) equal to, if not better than the specified cable. Cable and connectors (i.e. the complete assembly) will both contribute to losses and variations in the system.The purpose of RF lines is to guide RF signals from a source to a termination with minimal losses and changes1.2.1Types of RF LinesCoaxial lineFigure 4Two-wire lineWaveguideMicro-strip lineVarious types of RF linesHUBER SUHNER CONNECTOR GUIDE11

INTRODUCTION TO BASIC RF THEORY1.2.2A Typical RF LineOuter ConductorDielectric (Insulator)Inner Conductor (Centre Contact)Figure 5Construction of a RF lineDue to the concentric inner and outer conductor construction, the coaxial line is well protected against outsideinfluences.The signals will be transmitted in TEM-mode (Transversal Electric and Magnetic field) until the upper frequencylimit, the so-called cut-off frequency (refer to Chapter 1.2.6 on page 18), is reached. The mechanical constructionof the RF line determines this point. Basically, the smaller the mechanical dimensions the higher the frequencies.No fields exist in the direction of propagation of the energy.(Transversal means the electric and the magnetic field lines are perpendicular to the cable axis).The greater part of electrical properties are independent of the frequency, e.g. impedance and velocity of propagation. Only the attenuation loss increases at higher frequencies, caused by skin effect and dielectric losses. (Forexplanation of RF expressions refer to the Glossary).1.2.3Electromagnetic Field along a RF LineThe voltage and the current lines propagate in different ways within the RF line. The voltage waves (electric fieldlines) pulsate from the surface of the inner conductor towards the inner diameter of the outer conductor (seeFigure 6).HEdFigure 612DCross section view: Electric and magnetic fields inside the RF lineHUBER SUHNER CONNECTOR GUIDE

RF TheoryINTRODUCTION TO BASIC RF THEORYThe current propagates along the RF line causing a circular pulsating magnetic field around the inner conductorwith the greatest intensity near its surface (refer to Figure 7 and Figure 8). The current creates a magnetic field,whereas the voltage causes an electric field inside the line.EHi VFigure 7The electric and magnetic fields in a RF lineAs references basic RF equations are included in this chapter, so that the relationship between connector factorscan be shown.The equations for calculation of the electric field and magnetic field are: Electric field E (volts metre)E u 1rln Dd Magnetic field H (amperes metre)(1)H i 1r2 π(2)D Inside diameter of outer conductord Outer diameter of inner conductoru Voltage between inner and outer conductors (the so-called instantaneous potentialdifference across the line)i Current on the inner or outer conductors (the so-called instantaneous current)ErFigure 8Electric field strength increases towards the inner conductorThe maximum field strength is most intense at the surface of the inner conductor. It will decrease with increasingelectrical distance.A longitudinal section view shows another view of the propagating voltage and current (refer to Figure 9 below).HUBER SUHNER CONNECTOR GUIDE13

INTRODUCTION TO BASIC RF THEORYabcdeElectric FieldHVMagnetic FieldCurrents uia’b’c’ d’VoltagesIncident Voltage uIncident Current ie’Direction of PropagationFigure 9Longitudinal section view of travelling voltage and current (idealized)The incident voltages and current travel together along the line at the same instant14HUBER SUHNER CONNECTOR GUIDE

RF TheoryINTRODUCTION TO BASIC RF THEORY1.2.4Resistances and Reactances in a RF LineLiRiCLiGLoFigure 10Ro Inductance of the inner conductorLo Inductance of the outer conductorRi Resistance of the inner conductorRo Resistance of the outer conductorC Capacitance between the conductorsG Conductance of the insulationEquivalent circuit of RF lineIf the inductances Li and Lo and the resistances Ri and Ro are added up and the entire circuit is defined per unitlength, the following equivalent circuit model results:L’1ZoR’C’L’G’ Inductance per unit lengthR’ Resistance per unit lengthC’ Capacitance per unit lengthG’ Conductance per unit length2Figure 11Equivalent circuit with L and R defined per unit lengthImpedance Z0 impedance between 1 and 2, source and termination (Figure 11).Z0 R′ j2πfL′G′ j2πfC′(3)At higher frequencies 2 π f L’ is larger than R’At higher frequencies 2 π f C’ is larger than G’j factor indicating a phase difference of 90 At higher frequencies R’ and G’ have no influence on the impedanceHUBER SUHNER CONNECTOR GUIDE15

INTRODUCTION TO BASIC RF THEORY1.2.5Impedance of the RF LineIf the dielectric is not solid but air, the waves propagate at the velocity of light c.c 1(4) ε 0 m 0(ε0 and m0 are described on page 20)With a solid dielectric, the characteristic impedance of a standard transmission line is normally expressed asZ0 R jωLG jωc(5)where ω 2πf and f is the frequency under consideration. j is the standard “operator” used in circuit analysisto indicate a phase difference of 90 .The impedance of a coaxial line can also be determined by the ratio of diameters (refer to Figure 13) and thedielectric constant εr.Z 377Ω ln D 60Ω ln D 138Ω log D ε r ε rddd2π ε r1.2.5.1(6)Characteristic Impedance of a low-loss Line at High FrequenciesIn a practical microwave circuit it is frequently possible to assume that a line is lossless (lossless line), i.e. that Rand G are both zero whereupon the impedance is more simply expressed as:Z0 L’16 Cable inductance per unit length C′L′(7)C’ Cable capacitance per unit lengthHUBER SUHNER CONNECTOR GUIDE

RF TheoryINTRODUCTION TO BASIC RF THEORYor:Characteristic Impedance Electric field strength[ohm] Z 0 EHMagnetic field strength(8)The ratio of the voltage to the current, (the electric and the magnetic field, respectively) in atravelling wave is constant, a property of the transmission line determined by the characteristic impedance, whichis the same at any reference plane anywhere on the line, provided that the RF line is homogeneous (see Figure 12below).Line with a high impedance:strong magnetic fieldpoor magnetic field strengthFigure 12Line with a low impedance:strong electric fieldpoor electric field strengthDifferent field strengthsd Diameter of the inner conductorD Inside diameter of the outer conductorεr Dielectric constant of the insulation materialThe cable inductance L’ is determined by the ratio . DdDThe cable capacitance C’ is determined by the ratiodand the dielectric constant εr of the insulation material.Figure 13Diameters of inner and outer conductors The impedance of a transmission (coaxial) line is determined by theratio of outer conductor diameter to inner conductor diameterand by the dielectric constant εr of the insulation material The impedance is independent of the line length and frequency(at approximately 1 MHz)HUBER SUHNER CONNECTOR GUIDE17

INTRODUCTION TO BASIC RF THEORYImpedanceAirεr 1Foam PEεr 1.5PTFEεr 2.05PEεr 2.2850Ω2.302.783.303.5275Ω3.494.636.006.60Table 2DDiameter ratios d of various εr50 Ω lineεr 2.28Figure 1475 Ω lineεr 2.28Different impedances caused by different insulator diameters A reduction of the inner conductor diameter increases impedance An increasing dielectric constant reduces impedance1.2.6Cut-off FrequencyAs mentioned in Chapter 1.2.2, the upper frequency limit is also called the cut-off frequency and can be approximated by:c 300’000 km/sfc 2 c(D d) π ε r(9)The cut-off frequency is the frequency at which other waves than TEM waves can take place, i.e. a field component in the direction of propagation appears, causing significant changes in the characteristics of the RF line (e.g.resonances).18HUBER SUHNER CONNECTOR GUIDE

RF TheoryINTRODUCTION TO BASIC RF THEORY1.2.7Wavelength and Frequency1.4 GHz30 cm (11.81 in.)GeneratorTermination30 cm (11.81 in.)1 GHzλ1 30 cm (11.81 in.)λ12 GHzλ2 15 cm (5.91 in.)λ2λ3 7.5 cm (2.95 in.)4 GHzλ3Figure 15Frequency and wavelengthThe wavelength becomes shorter as the frequency increasesHUBER SUHNER CONNECTOR GUIDE19

INTRODUCTION TO BASIC RF THEORY1.2.7.1Relationship between Frequency and WavelengthThe frequency and the wavelength are interdependent, a fact expressed by the following formulas:v λ f and v c give ε rv Velocity of propagationλ Wavelengthf Frequencyεr Dielectric constant1.2.8(10)λ cf ε r(11)Velocity of PropagationThe transmission of the electromagnetic energy is not attached to a medium, but can evolve in free space (seeChapter 1.2.3 on page 12). The energy propagates at the velocity of light in air (metres per second).v c ε 1xm00(12)The approximate value is:c 300.000 km/s (186411 miles/s)m0 Magnetic permeability of the medium (4.TT.10–7 Henry/m)ε0 Electric permittivity (8.854.10–12 Farad/m)In a line, the velocity of propagation v is dependent on the dielectric constant εr of the insulation material.Thereby, the following relationship applies.v c ε r20(13)HUBER SUHNER CONNECTOR GUIDE

RF TheoryINTRODUCTION TO BASIC RF THEORY1.2.8.1Influence of Dielectric Material on the Velocity of PropagationAir εr 1.01 GHz30 cm (11.81 in.)1 nsecFoam PE εr 1.51 GHz24.5 cm (9.64 in.)1 nsecTeflon PTFE εr 2.051 GHz21 cm (8.27 in.)1 nsecPE εr 2.281 GHz20 cm (7.87 in.)Figure 161 nsecWave propagation in various materials Every insulation material except air reduces the velocity of propagation Every insulation material except air reduces the wavelength Both effects increase along with the dielectric constantHUBER SUHNER CONNECTOR GUIDE21

INTRODUCTION TO BASIC RF THEORY1.3REFLECTIONSAn example of a line with several discontinuities (steps): 50 Ω–Figure 17Change of impedance as a result of discontinuities (mated connector pair)A discontinuity on a RF line is a location where the impedance of the line changesDiscontinuities can be a result of e.g.– Changes in conductor diameters– Change in insulator diameter– Change in interface dimensions– Space between parts (gaps)1.3.1Reflected Wave (Voltage)A discontinuity can also be the short end itself in a short circuit, where there is total reflection.UincidentUreflectedShortFigure 18Short circuitThe travelling incident voltage meets another voltage of Uincident at the short.The reflected wave has the opposite voltage magnitude of Ureflected, thus the sum is zero.22HUBER SUHNER CONNECTOR GUIDE

RF TheoryINTRODUCTION TO BASIC RF THEORYLow ImpedanceHigh ImpedanceFigure 19StepDiscontinuity as a result of lower impedance (smaller insulator diameter)The travelling wave arrives at the step with a magnitude of e.g. 7 V. The voltage must change because the impedance changes at the discontinuity. A fraction of the voltage will then bereflected (refer to Figure 19).The incident current will be reflected as well as the incident voltage, because the currentand the voltage follow each other along the line1.3.2Reflection from Various Discontinuities100% reflection of the voltage and currentShort reflected voltage changes thepolarity 180 phase shift100% reflection of voltage and currentOpen-circuit reflected voltage does notchange the polarity No phase shiftFigure 20Reflection and shift by short and open circuitA phase always will be zero at the source (reference).HUBER SUHNER CONNECTOR GUIDE23

INTRODUCTION TO BASIC RF THEORYPartially reflected voltage 180 phase shiftthat isZ1 Z2Partially reflected voltage No phase shiftthat isFigure 21Z1 Z2Phase shift as consequence of discontinuitiesforward wavetransmitted wavereflected waveFigure 22Waves reflected and transmitted at a discontinuity– Every discontinuity creates a reflecting wave– On a line with a discontinuity, 2 travelling waves are propagating:The transmitted wave will continue forward and the reflected wave will return to the source.RF line without discontinuities Matched lineRF line with discontinuities Mismatched lineThe extent of the mismatch or discontinuity will be determined by the quantity of the arisingreflections.24HUBER SUHNER CONNECTOR GUIDE

RF TheoryINTRODUCTION TO BASIC RF THEORY1.3.3Terms for Definition of the Mismatch1.3.3.1Reflection Coefficient ΓUforwardUfurtherUbackFigure 23Reflected wavesΓ U reflectedU forward(14)The reflection coefficient (factor) is the ratio of the reflected voltage to the forward voltage. For practical examples of reflection measurement, please refer to Chapter 4.The reflection factor is usually expressed in %:Γ U reflectedx 100%U forwardThe coefficient expresses the amount or what percentage of the forward voltage is reflected.Ideal lineΓ 0(The factor should be as low as possible)Γ 0%Short or open circuitΓ 1Γ 100 %Note: It is possible that Ureflected (Uback) is higher than Uforward. This occurs when the impedance increases aftera discontinuity (refer to Chapter 3.2 on page 63). This only applies to the voltage, the power will be lower.HUBER SUHNER CONNECTOR GUIDE25

INTRODUCTION TO BASIC RF THEORY1.3.3.2Return Loss RLR L 20logU forward[dB]U reflected(15)R L 20log 1Γ- further is:(16)The return loss is a logarithmic measure of the reflection coefficient.Normally, the return loss is related to the power and not to the voltage.The return loss is expressed in [dB] (decibel) and indicates the ratio of the transmitted power tothe reflected power:Ideal line RL [dB](High return loss no reflection)Short and open circuit RL 0 [dB]The return loss should be as high as possibleThe return loss can also be defined when the impedance, before and after the discontinuity, isdiffferent:R L 20logZ1Figure 2426(17)Z2Change of impedanceReturn lossTable 3Z2 Z1Z2 – Z1Reflected power in [%]Reflected voltage in [%]0 dB100 %100 %3 dB50 %70 %6 dB25 %50 %10 dB10 %31.5 %20 dB1%10 %30 dB0.1 %3.1 %Comparison of return loss to reflected power and voltageHUBER SUHNER CONNECTOR GUIDE

RF TheoryINTRODUCTION TO BASIC RF THEORY1.3.3.3Voltage Standing Wave Ratio VSWRAlong a mismatched line, two travelling waves will propagate:One wave travels forward and the other is reflected. Both waves will have the same frequency. When the voltageis measured at a point of the line, a voltmeter will indicate the sum of the voltages of both travelling waves atthis particular point:Usum Uforward UreflectedUsum (s,t) Ufor (s,t) Uref (s,t)s distance [mm]t time [s](18)This means that the travelling waves are added. It can be shown that this resulting wave does not actually travelalong the line, but stands still. In other words: at any reference plane (points), there will always be a maximumor a minimum voltage. This wave is called a standing wave.VSWR U forward U reflectedU forward U refelctedVSWR (19)When Ureflected Γ x Uforward:U forward ΓxU forwardU forward–ΓxU forward(20)Umax Uforward UreflectedUmin Uforward - Ureflected(22)VSWR U maxU min(21)VSWR 1 Γ1 Γ(23)The standing wave ratio is the ratio of the measurable maximum voltage to the minimumvoltage along a homogeneous RF line ( λ ):Ideal lineVSWR 1.0Short circuit or open circuitVSWR HUBER SUHNER CONNECTOR GUIDE(The VSWR should be as low as possible)27

INTRODUCTION TO BASIC RF THEORYStanding Waves:Total reflection:VSWR U max U minHigh reflectionModerate reflectionLow reflectionNo reflectionVSWR Figure 2528U max 1U minVarious standing wavesHUBER SUHNER CONNECTOR GUIDE

RF TheoryINTRODUCTION TO BASIC RF THEORY1.3.4Comparison between Γ, RL and VSWRReflection Coefficient(24)(27)(30)Table 4VSWRΓ U reflectedU forwardΓ 1R alog 20VSWR 1Γ VSWR 1Return Loss(25)U U reflectedVSWR forwardU forward–U reflected(26)(28)(29)VSWR 1 Γ1–ΓR (31)alog 20 1VSWR Ralog 20 –1RL 20logU forwardU reflectedRL 20log 1Γ(32)VSWR 1RL 20logVSWR 1 Relationship between Γ, RL and VSWR (equations 24 through 32)ΓVSWRReturn Lossnot matchedpoorly matchedmatchedwell matchedvery well matchedFigure 26Table of comparison of magnitudes (refer also to the table in the formula booklet)HUBER SUHNER CONNECTOR GUIDE29

INTRODUCTION TO BASIC RF THEORY1.3.5Reflection from two or more DiscontinuitiesWave 2 forwardWave 1 forwardWave transmittedA reflectedSum A BB reflectedD Distance betweendiscontinuitiesDAFigure 27BReflections from several discontinuitiesOn lines with two or several discontinuities, two or more reflected travelling waves will propagate (see Figure 17in Chapter 1.3 on page 22).The absolute reflected signal is the sum of the reflected individual signals.A reflected1B reflectedSum A B2Total reflection Areflected BreflectedFigure 2830Two reflected waves (1) equivalent to total reflection (2)HUBER SUHNER CONNECTOR GUIDE

RF TheoryINTRODUCTION TO BASIC RF THEORYWith two or several discontinuities, the magnitude of the total reflected signals depends on the distance (e.g. inwavelengths) between the discontinuities.Connector AConnector BCable lengthΓThe reflected signals sum upl ¡ frequencyReflected signals cancel each other outFigure 29Reflected signals spread over cable length1.4ATTENUATION LOSS OF RF LINESL’R’Energy inEnergy outPinFigure 30C’G’PoutAttenuation loss (loss of energy) through the cableThe attenuation (or transmission) loss indicates how much energy is lost during the transmission of the signalthrough the RF line (Figure 30).The three following factors influence these quantities:–The electrical energy will partly be converted into thermal energy (heat), caused by the copper loss(skin effect) and the dielectric losses.–Reflected energy is lost in transmitting direction.–Leakage (poor shielding) causes radiative losses of the electrical energy.HUBER SUHNER CONNECTOR GUIDE31

INTRODUCTION TO BASIC RF THEORY1.4.1Determination of the Attenuation LossAttenuation α 10 l

INTRODUCTION TO BASIC RF THEORY 10 HUBER SUHNER CONNECTOR GUIDE High frequency begins where currents and voltages become frequency dependent or where the wavelength becomes important (λ length of component) 1.1.1 Band Designations Abbreviations used: VLF very low frequency LF low frequency MF medium frequency RF high frequency VHF very high .