射频电路设计基础课件

1 1射射频电路路设计基基础1射频电路设计基础23B.RF Microwave Filters3B.RF Microwave Filters31.0 Basic Filter Theory1.0 Basic Filter Theory4IntroductionAn ideal filter is a linear 2-port network that provides perfect transmission of signal for frequencies in a certain passband region,infinite attenuation for frequencies in the stopband region,and a linear phase response in the passband(to reduce signal distortion).The goal of filter design is to approximate the ideal requirements within acceptable tolerance with circuits or systems consisting of real components.IntroductionAn ideal filter is5Categorization of FiltersLow pass filter(LPF),high pass filter(HPF),bandpass filter(BPF),bandstop filter(BSF),arbitrary type,etc.In each category,the filter can be further divided into active and passive types.In an active filter,there can be amplification of the signal power in the passband region;a passive filter do not provide power amplification in the passband.Filters used in electronics can be constructed from resistors,inductors,capacitors,transmission line sections,and resonating structures(e.g.,piezoelectric crystal,Surface Acoustic Wave(SAW)devices,mechanical resonators,etc.).An active filter may contain a transistor,FET,and an op-amp.FilterLPFBPFHPFActivePassiveActivePassiveCategorization of FiltersLow p6Filter Frequency ResponseFrequency response implies the behavior of the filter with respect to steady-state sinusoidal excitation(e.g.,energizing the filter with a sine voltage or current source and observing its output).There are various approaches to displaying the frequency response:Transfer function H()(the traditional approach)Attenuation factor A()S-parameters,e.g.,s21()Others,such as ABCD parameters,etc.Filter Frequency ResponseFrequ7Filter Frequency Response(contd)Low pass filter(passive)Filter H()V1()V2()ZLcA()/dB0c31020304050(1.1b)(1.1a)c|H()|1Transfer functionArg(H()Complex valueReal valueFilter Frequency Response(con8Filter Frequency Response(contd)Low pass filter(passive)continued.For the impedance matched system,using s21 to observe the filter response is more convenient,as this can be easily measured using a vector network analyzer(VNA).ZcZcZcTransmission lineis optionalc20log|s21()|0 dBArg(s21()FilterZcZcZcVsa1b2Complex valueFilter Frequency Response(con9Low pass filter(passive)continued.Filter Frequency Response(contd)A()/dB0c31020304050 Filter H()V1()V2()ZLPassbandStopbandTransition bandCut-off frequency(3 dB)Low pass filter(passive)cont10High pass filter(passive)Filter Frequency Response(contd)A()/dB0c31020304050c|H()|1Transfer functionStopbandPassbandHigh pass filter(passive)Filt11Filter Frequency Response(contd)Bandpass filter(passive)Bandstop filterA()/dB401330201002o1|H()|1Transfer function2oA()/dB401330201002o1|H()|1Transfer function2oFilter Frequency Response(con12Basic Filter Synthesis ApproachesImage Parameter Method.ZoZoZoZoZo Filter Zo H1()H2()Hn()ZoZo Consider a filter to be a cascade of linear 2-port networks.Synthesize or realize each 2-port network,so that the combine effect gives the required frequency response.The image impedance seen at the input and output of each network is maintained.The combinedresponseResponse ofa singlenetworkBasic Filter Synthesis Approac13Basic Filter Synthesis Approaches(contd)Insertion Loss Method.Filter ZoZoUse the RCLM circuit synthesis theorem to come up with a resistive terminatedLC network that can produce theapproximate response.ZoIdealApproximate with rational polynomialfunction|H()|We can also use Attenuation Factor or|s21|for this.Approximate ideal filter responsewith polynomial function:Basic Filter Synthesis Approac14Our ScopeOnly concentrate on passive LC and stripline filters.Filter synthesis using the Insertion Loss Method(ILM).The Image Parameter Method(IPM)is more efficient and suitable for simple filter designs,but has the disadvantage that arbitrary frequency response cannot be incorporated into the design.Our ScopeOnly concentrate on p152.0 Passive LC Filter Synthesis Using the Insertion Loss Method2.0 Passive LC Filter Synthesi16Insertion Loss Method(ILM)The insertion loss method(ILM)enables a systematic way to design and synthesize a filter with various frequency responses.The ILM method also enables a filter performance to be improved in a straightforward manner,at the expense of a higher order filter.A rational polynomial function is used to approximate the ideal|H()|,A(),or|s21()|.Phase information is totally ignored.Ignoring phase simplifies the actual synthesis method.An LC network is then derived which will produce this approximated response.The attenuation A()can be cast into power attenuation ratio,called the Power Loss Ratio,PLR,which is related to A()2.Insertion Loss Method(ILM)The17More on ILMThere is a historical reason why phase information is ignored.Original filter synthesis methods are developed in the 1920s60s,for voice communication.The human ear is insensitive to phase distortion,thus only the magnitude response(e.g.,|H()|,A()is considered.Modern filter synthesis can optimize a circuit to meet both magnitude and phase requirements.This is usually done using computer optimization procedures with goal functions.ExtraMore on ILMThere is a historic18Power Loss Ratio(PLR)PLR large,high attenuationPLR close to 1,low attenuationFor example,a low passfilter response is shownbelow:ZLVsLossless2-port network1ZsPAPinPLPLR(f)Low pass filter PLRf10Low attenuationHighattenuationfc(2.1a)Power Loss Ratio(PLR)PLR larg19PLR and s21In terms of incident and reflected waves,assuming ZL=Zs=ZC.ZcVsLossless2-port networkZcPAPinPLa1b1b2(2.1b)PLR and s21In terms of inciden20PLR for the Low Pass Filter(LPF)Since|1()|2 is an even function of,it can be written in terms of 2 as:PLR can be expressed as:Various types of polynomial function in can be used for P().The requirement is that P()must either be an odd or even function.Among the classical polynomial functions are:Maximally flat or Butterworth functionsEqual ripple or Chebyshev functionsElliptic functionMany,many more(2.2)(2.3a)(2.3b)This is also knownas Characteristic PolynomialThe characteristics we need from P()2 for LPF:P()2 0 for 1 for cPLR for the Low Pass Filter(L21Characteristic Polynomial FunctionsMaximally flat or Butterworth:Equal ripple or Chebyshev:Bessel or linear phase:N=order of theCharacteristicPolynomial P()(2.4a)(2.4b)(2.4c)Characteristic Polynomial Func22Examples of PLR for the Low Pass FilterPLR of the low pass filter using 4th order polynomial functions(N=4)Butterworth,Chebyshev(ripple factor=1),and Bessel.Normalized to c=1 rad/s,k=1.ButterworthChebyshevBesselPLRIdealIf we convert into dB,this ripple is equal to3 dBk=1Examples of PLR for the Low Pa23Examples of PLR for the Low Pass Filter(contd)PLR of the low pass filter using the Butterworth characteristic polynomial,normalized to c=1 rad/s,k=1.N=2N=6N=4N=5N=3N=7Conclusion:The type of polynomialfunction and the orderdetermine the attenuation rate in the stopband.Examples of PLR for the Low Pa24Characteristics of Low Pass Filters Using Various Polynomial Functions Butterworth:Moderately linear phase response,slow cutoff,smooth attenuation in the passband.Chebyshev:Bad phase response,rapid cutoff for a similar order,contains ripple in the passband.May have impedance mismatch for N even.Bessel:Good phase response,linear.Very slow cutoff.Smooth amplitude response in the passband.Characteristics of Low Pass Fi25Low Pass Prototype DesignA lossless linear,passive,reciprocal network that can produce the insertion loss profile for the low pass filter is the LC ladder network.Many researchers have tabulated the values for the L and C for the low pass filter with cut-off frequency c=1 rad/s,that works with the source and load impedance Zs=ZL=1.This low pass filter is known as the Low Pass Prototype(LPP).As the order N of the polynomial P increases,the required element also increases.The no.of elements=N.L1=g2L2=g4C1=g1C2=g3RL=gN+11L1=g1L2=g3C1=g2C2=g4RL=gN+1g0=1Dual of eachotherLow Pass Prototype DesignA los26Low Pass Prototype Design(contd)The LPP is the building block from which real filters may be constructed.Various transformations may be used to convert it into a high pass,bandpass,or other filter of arbitrary center frequency and bandwidth.The following slides show some sample tables for designing LPP for Butterworth and Chebyshev amplitude response of PLR.Low Pass Prototype Design(con27Table for the Butterworth LPP DesignSee Example 2.1 in the following slides on how the constant values g1,g2,g3,etc.,are obtained.Table for the Butterworth LPP 28Table for the Chebyshev LPP DesignRipple factor 20log10=0.5 dBRipple factor 20log10=3.0 dBTable for the Chebyshev LPP De29Table for the Maximally-Flat Time Delay LPP DesignTable for the Maximally-Flat T30Example 2.1:Finding the Constants for the LPP DesignandThusTherefore we can compute the power loss ratio as:P()2RRVsCLRjLRVs1/jCV1Consider a simple case of a 2nd order low pass filter:ExtraExample 2.1:Finding the Const3031ExtraPLR can be written in terms of polynomial of 2:For Butterworth response with k=1,c=1:(E1.1)(E1.2)Comparing equations(E1.1)and(E1.2):Setting R=1 for the Low Pass Prototype(LPP):(E1.3)(E1.4)Thus from equation(E1.4):Using(E1.3)Compare this result withN=2 in the table for the LPP Butterworth response.This direct brute forceapproach can beextended to N=3,4,5Example 2.1:Finding the Constants for the LPP Design(contd)ExtraPLR can be written in ter3132Example 2.1:VerificationExtraExample 2.1:VerificationExtra33Example 2.1:Verification(contd)Extra3 dB at 160 mHz(milliHertz!),which is equivalent to 1 rad/sPower loss ratioversus frequencyExample 2.1:Verification(con34Impedance Denormalization and Frequency Transformation of LPPOnce the LPP filter is designed,the cut-off frequency c can be transformed to other frequencies.Furthermore the LPP can be mapped to other filter types such as high pass,bandpass,and bandstop.This frequency scaling and transformation entails changing the value and configuration of the elements of the LPP.Finally the impedance presented by the filter at the operating frequency can also be scaled,from unity to other values;this is called impedance denormalization.Let Zo be the new system impedance value.The following slide summarizes the various transformation from the LPP filter.Impedance Denormalization and 35Impedance Denormalization and Frequency Transformation of LPP(contd)LPP to Low PassLPP to High PassLPP toBandpassLPP toBandstopNote that the inductor always multiplies with Zo while the capacitor divides with Zo(2.5a)(2.5b)LCCenter frequencyFractional bandwidthImpedance Denormalization and 36Summary of Passive LC Filter Design Flow Using the ILM MethodStep 1:From the requirements,determine the order and type of approximation functions to use.Insertion loss(dB)in the passband?Attenuation(dB)in the stopband?Cut-off rate(dB/decade)in the transition band?Tolerable ripple?Linearity of phase?Step 2:Design a normalized low pass prototype(LPP)using the L and C elements.L1=g2L2=g4C1=g1C2=g3RL=gN+11|H()|011Summary of Passive LC Filter D37Summary of Passive Filter Design Flow Using the ILM Method(contd)Step 3:Perform frequency scaling,and denormalize the impedance.Step 4:Choose suitable lumped components,or transform the lumped circuit design into distributed realization.|H()|011250Vs15.916pF0.1414pF79.58nH0.7072nH0.7072nH15.916pF50RLAll uses the microstrip stripline circuitSummary of Passive Filter Desi38Filter vs.Impedance Transformation NetworkIf we ponder carefully,the sharp observer will notice that the filter can be considered as a class of impedance transformation network.In the passband,the load is matched to the source network,much like a filter.In the stopband,the load impedance is highly mismatched from the source impedance.However,the procedure described here only applies to the case when both load and source impedance are equal and real.ExtraFilter vs.Impedance Transform39Example 2.2A:LPF Design Butterworth ResponseDesign a 4th order Butterworth low pass filter,Rs=RL=50,fc=1.5 GHz.L1=0.7654HL2=1.8478HC1=1.8478FC2=0.7654FRL=1 g0=1L1=4.061 nHL2=9.803 nHC1=3.921 pFC2=1.624 pFRL=50 g0=1/50Steps 1&2:LPPStep 3:Frequency scalingand impedance denormalizationExample 2.2A:LPF Design But40Design a 4th order Chebyshev low pass filter,0.5 dB ripple factor,Rs=50,fc=1.5 GHz.Example 2.2B:LPF Design Chebyshev ResponseL1=1.6703HL2=2.3661HC1=1.1926FC2=0.8419FRL=1.9841 g0=1L1=8.861 nHL2=12.55 nHC1=2.531 pFC2=1.787 pFRL=99.2 g0=1/50Steps 1&2:LPPStep 3:Frequency scalingand impedance denormalizationDesign a 4th order Chebyshev l41Example 2.2(contd)ChebyshevButterworth|s21|Ripple is roughly 0.5 dBArg(s21)ChebyshevButterworthBetter phaselinearity for ButterworthLPF in the passbandComputer simulation resultusing AC analysis(ADS2003C)Note:Equation used in Data Display of ADS2003Cto obtain a continuous phase display with the built-infunction phase().Example 2.2(contd)ChebyshevB42Example 2.3:BPF Design Design a bandpass filter with Butterworth(maximally flat)response.N=3Center frequency fo=1.5 GHz3 dB Bandwidth=200 MHz or f1=1.4 GHz,f2=1.6 GHzImpedance=50 Example 2.3:BPF Design Design43Example 2.3(contd)From table,design the low pass prototype(LPP)for 3rd order Butterworth response,c=1.Zo=1g1 1.000Fg3 1.000Fg2 2.000Hg4120oSimulated resultusing PSpiceVoltage across g4Steps 1&2:LPPExample 2.3(contd)From table44Example 2.3(contd)LPP to bandpass transformationImpedance denormalization50 Vs15.916 pF0.1414 pF79.58 nH0.7072 nH0.7072 nH15.916 pF50 RLStep 3:Frequency scalingand impedance denormalizationExample 2.3(contd)LPP to ban45Example 2.3(contd)Simulated result using PSpice:Voltage across RLExample 2.3(contd)Simulated 46All Pass FilterThere is also another class of filter known as the All Pass Filter(APF).This type of filter does not produce any attenuation in the magnitude response,but provides phase response in the band of interest.APF is often used in conjunction with LPF,BPF,HPF,etc.,to compensate for phase distortion.ExtraZo BPF APF f0|H(f)|1fArg(H(f)Example of the APF responsef|H(f)|10fArg(H(f)f0|H(f)|1fArg(H(f)Linearphase inpassbandNonlinearphase in passbandAll Pass FilterThere is also a47Example 2.4:Practical RF BPF Design Using SMD Discrete ComponentsExample 2.4:Practical RF BPF 48Example 2.4(contd)BPF synthesisusing synthesistool E-synof ADS2003CExample 2.4(contd)BPF synthe49Example 2.4(contd)|s21|/dBArg(s21)/degreeMeasuredSimulatedMeasurement is performed with theAgilent 8753ES Vector NetworkAnalyzer,using Full OSL calibration Example 2.4(contd)|s21|/dBAr503.0 Microwave Filter Realization Using Stripline Structures3.0 Microwave Filter Realizati513.1 Basic Approach3.1 Basic Approach52Filter Realization Using Distributed Circuit ElementsLumped-element filter realization using surface mounted inductors and capacitors generally works well at lower frequencies(at UHF,say 3 GHz),the passive filter is usually realized using distributed circuit elements such as transmission line sections.Here we will focus on stripline microwave circuits.Filter Realization Using Distr53Filter Realization Using Distributed Circuit Elements(contd)Recall in the study of Terminated Transmission Line Circuit that a length of terminated Tline can be used to approximate an inductor and a capacitor.This concept forms the basis of transforming the LC passive filter into distributed circuit elements.ZoZoZc,lLZc,lCZc,Zc,Zc,ZoZoFilter Realization Using Distr54Filter Realization Using Distributed Circuit Elements(contd)This approach is only an approximation.There will be deviation between the actual LC filter response and those implemented with terminated Tline.Also,the frequency response of the distributed circuit filter is periodic.Other issues are shown below.Zc,Zc,Zc,ZoZoHow do we implement a series Tlineconnection?(only practical for certain Tline configuration)Connection of physicallength cannot beignored at themicrowave region,comparable to Thus some theorems are used to facilitate the transformation of the LCcircuit into stripline microwave circuits.Chief among these are the KurodasIdentities(See Appendix 1)Filter Realization Using Distr55More on Approximating L and C with Terminated Tline:Richards TransformationZc,lLZin(3.1.1a)Zc,lCZin(3.1.1b)For LPP design,a further requirement isthat:(3.1.1c)Wavelength atcut-off frequencyHere,instead of fixing Zc and tuning l to approach an L or C,we allow Zc to be a variable too.More on Approximating L and C 56Example 3.1:LPF Design Using StriplineDesign a 3rd order Butterworth low pass filter,Rs=RL=50,fc=1.5 GHz.Steps 1&2:LPPStep 3:Convert to TlinesZc=0.500Zc=1.0001 Zc=1.0001 Zo=1 g1 1.000Hg3 1.000Hg2 2.000Fg41Length=c/8for all Tlinesat =1 rad/sExample 3.1:LPF Design Using 57Example 3.1(contd)Length=c/8for all Tlinesat =1 rad/sStep 4:Add an extra Tline on the series connection and apply Kurodas 2nd Identity.Zc=0.500Zc=1.0001 Zc=1.0001 Zc=1.0Zc=1.0Extra TlineExtra Tlinen2Z1=2lZ2=1Similar operation isperformed hereYcExample 3.1(contd)Length=58Example 3.1(contd)Zc=0.5001 1 Zc=2.0Zc=2.0Zc=2.000Zc=2.000After applying Kurodas 2nd IdentityLength=c/8for all Tlinesat =1 rad/sSince all Tlines have similar physicallength,this approach to stripline filterimplementation is also known as Commensurate Line Approach.Example 3.1(contd)Zc=0.5001 59Example 3.1(contd)Zc=2550 50 Zc=100Zc=100Zc=100Zc=100Length=c/8for all Tlines atf=fc=1.5 GHz Zc/8 1.5 GHz/mm W/mm 50 13.45 2.8525 12.77 8.00100 14.23 0.61Microstrip line using double-sided FR4 PCB(r=4.6,H=1.57 mm)Step 5:Impedance and frequency denormalizationHere we multiply allimpedance with Zo=50We can work out the correct width W given theimpedance,dielectric constant,and thickness.From W/H ratio,the effective dielectric constanteff can be determined.Use this together withfrequency at 1.5 GHz to find the wavelength.Example 3.1(contd)Zc=2550 560Example 3.1(contd)Step 6:The layout(top view)Example 3.1(contd)Step 6:Th61Example 3.1(contd)Simulated resultsExample 3.1(contd)Simulated 62Conclusions for Section 3.1 Further tuning is needed to optimize the frequency response.The method illustrated is good for the low pass and bandstop filter implementation.For high pass and bandpass,other approaches are needed.Conclusions for Section 3.1 Fu633.2 Further Implementations3.2 Further Implementations64Realization of LPF Using the Step-Impedance ApproachA relatively easy way to implement LPF using stripline components.Using alternating sections of high and low characteristic impedance Tlines to approximate the alternating L and C elements in an LPF.Performance of this approach is marginal as it is an approximation,where a sharp cutoff is not required.As usual,beware of parasitic passbands!Realization of LPF Using the S65Equivalent Circuit of a Transmission Line Section Z11 Z12 Z11 Z12Z12lZc(3.2.1a)(3.2.1b)(3.2.1c)Ideal lossless TlineT-network equivalent circuitPositive reactancePositivesusceptanceEquivalent Circuit of a Transm66Approximation for High and Low ZCWhen l /2,the series element can be thought of as an inductor and the shunt element can be considered a capacitor.For l 1:For l /4 and Zc=ZL 1:jX/2jBjX/2X ZH lB YLlWhen Zc 1l 1l /4 Z11-Z12 Z11-Z12Z12Approximation for High and Low67Approximation for High and Low ZC(contd)Note that l /2 implies a physically short Tline.Thus a short Tline with high Zc(e.g.,ZH)approximates an inductor.A short Tline with low Zc(e.g.,ZL)approximates a capacitor.The ratio of ZH/ZL should be as high as possible.Typical values:ZH=100 to 150,ZL=10 to 15.(3.2.2a)(3.2.2b)Approximation for High and Low68Example 3.2:Mapping an LPF Circuit into a Step Impedance Tline NetworkFor instance,consider the LPF Design Example 2.2A(Butterworth).Let us use the microstrip line.Since a microstrip Tline with low Zc is wide and a Tline with high Zc is narrow,the transformation from circuit to physical layout would be as follows:L1=4.061 nHL2=9.803 nHC1=3.921 pFC2=1.624 pFRL=50 g0=1/50Example 3.2:Mapping an LPF Ci69Example 3.2:Physical Realization o