3 Design of Rf and Microwave Filters

Design of RF and Microwave Filters2009

Microwave & Millimeter-wave Lab.

*Contents

1. Introduction ; types of Filters 2. Characterization of Filters 3. Approximate Design Methods 4. Lowpass Prototype Network 5. Impedance Scaling and Frequency Mapping 6. Immittance Inverters


*1. Introduction 1.1 Types of Filters A. Lowpass Filters B. Highpass Filters

C. Bandpass Filters D. Bandstop Filters


*2. Filter Characterization(1) Two-port Network ;

Fig. 1 Two-port Network


*2. Filter Characterization(2) Fig. 2 Characteristics of ideal bandpass filter Characteristics of ideal bandpass filters ; not realizable approximation required


*2. Filter Characterization(3) Practical specifications ;1) Passband ; lower cutoff frequency - upper cutoff frequency 2) Insertion loss : ; must be as small as possible 3) Return Loss : ; degree of impedance matching 4) Ripple ; variation of insertion loss within the passband


*2. Filter Characterization(4) 5) Group delay

; time to required to pass the filter 6) Skirt frequency characteristics ; depends on the system specifications 7) Power handling capability


*3. Approximate Design Methods 1) based on Amplitude characteristics A. Image parameter method B. Insertion loss method a) J-K inverters b) Unit element - Kuroda identity 2) based on Linear Phase characteristics


*3.1 Filter design(the insertion loss method) Definition of Power Loss Ratio (PLR) ; impedance matching as well as frequency selectivity Fig. 3 General filter network network synthesis procedures are required


*3.1 Filter Design(2)Approximation methods : 1) Maximally Flat (Butterworth) response 2) Chebyshev response 3) Elliptic Function response


*3.2 Approximation Methods A. Maximally flat response Where, ; passband tolerance ; order of filterUsually degree of freedom=1 (order N)Fig. 4 Comparison Between Maximally Flat and Chebyshev response

1

1.5

0.5

1

0

c

PLR

Chebyshev

Maximally flat


*3.2 Approximation Methods(2)B. Chebyshev response : equal ripple response in the passband : Chebyshev Polynomial of order


*3.2 Approximation Methods(3)Fig. 5 Chebyshev and Elliptic Function response; ripple (0.01 dB, 0.1 dB, etc.); order of filter degree of freedom=2 (ripple and order)


*3.2 Approximation Methods(4)C. Elliptic Function response equal ripple passband in both passband and stopband

: stopband minimum attenuation : transmission zero at stopband

degree of freedom=3 (order N, ripple, transmission zero at stopband )


*4. Lowpass Prototype Filter ; normalized to 1 Fig. 5 Lowpass prototype


*4. Lowpass Prototype Filter(2) Maximally Flat response ;

Equal Ripple response ;


*4. Lowpass Prototype Filter(3)Table1. Element values for Butterworth and chebyshev filters

TypeElement NoButterworth0.1 dB rippleChebyshev0.5 dB rippleChebyshev10.61801.14681.705821.61801.37121.229632.00001.97502.540841.61801.37121.229650.61801.14681.7058


*5. Impedance and freq. mapping5.1 Impedance Scaling

Impedance level 50 ; same reflection coefficient maintained series branch(impedance) elements ; shunt branch(admittance) elements ;


*5. Impedance and freq. mapping(2)5.2 Frequency Expansion

cutoff frequency 1 lowpass cutoff frequency

mapping function ;

series and shunt branch elements ;


*5. Impedance and freq. mapping(3)Fig. 6 Various mapping relations derived from lowpass prototype network


*5.3 Lowpass to Highpass transformation(lowpass cutoff freq. 1 highpass cutoff freq. ) mapping function ; series branch(impedance) elements ;

shunt branch(admittance) elements ; Fig. 7 Highpass filter derived from lowpass prototype 5. Impedance and freq. mapping(4)


*5.4 Lowpass to bandpass transformation (low cutoff freq. , high cutoff freq. ) mapping function ;

5. Impedance and freq. mapping(5)


*series branch element : impedance

shunt branch element : admittance

Fig. 8 Bandpass filter derived from thelowpass prototype 5. Impedance and freq. mapping(6)


*Example : Design a bandpass filter having a 0.5dB equal-ripple response, with N=3. The f0 is 1GHz, bandwidth is 10%, and the input and output impedance 50.

step 1 : from the element values of lowpass prtotype (0.5dB ripple Chebyshev)

step 2 : apply impedance scaling 5. Impedance and freq. mapping(7)


*step 3 : apply bandpass transformation 5. Impedance and freq. mapping(8)


*5.5 Lowpass to bandstop transformation (low cutoff freq. , high cutoff freq. ) mapping function ;

inverse of bandpass mapping function5. Impedance and freq. mapping(9)


*series branch element : admittance

shunt branch element : impedance

Fig. 9 Bandstop network derived from thelowpass prototype 5. Impedance and freq. mapping(10)


*5.6 Immitance Inverters K ; impedance inverter J ; admittance inverterex. simplest form of inverter : /4 transformer series LC J-inverter + shunt LC shunt LC K-inverter + series LC Fig. 10 Immitance inverter 5. Impedance and freq. mapping(11)


*5.7 Bandpass filters using J-, K-inverters Fig. 11 Equivalent Network for lowpass prototype and bandpass network Reflection coefficient ;lowpass :bandpass :If (mapping relation) 5. Impedance and freq. mapping(12)


*Fig. 12 Lowpass network and bandpass network 5. Impedance and freq. mapping(13)


*From the partial fraction expansion including bandpass mapping relation

: fractional bandwidth, : center freq.

In the same manner, J-inverter values are derived as 5. Impedance and freq. mapping(14)


*Typical immittance inverters ; Fig. 13 Impedance(K-) inverters 5. Impedance and freq. mapping(15)


*Fig. 14 Admittance(J-) inverters 5. Impedance and freq. mapping(16)


*6. LC filters, Distributed filters 6.1 LC filters A. C-coupled bandpass filters Fig. 14 Bandpass filter network using ideal J-inverters Fig. 15 Bandpass filter network containing practical inverters


*Fig. 16 Inverter of first and last stages By equating the real and imaginary part of and6. LC filters, Distributed filters(2)


*B. L-coupled bandpass filter Fig.17 C-coupled Bandpass filter Fig.18 L-coupled Bandpass filter 6. LC filters, Distributed filters(3)


*Design a LC bandpass filter. The f0 is 2.8 GHz, bandwidth is 500 MHz, and the input and output impedance 50. step 1 : from the element values of lowpass prototypestep 2 : apply impedance scaling step 3 : apply bandpass transformation using J-invertersStep 4 : simulation6. LC filters, Distributed filters(4)


*Simulated results:6. LC filters, Distributed filters(3)


* Step 5 : Realization

Insertion loss < 3.1 dBRetrun loss > 15.5 dBAttenuation @ 3.3 GHz : 15 dB


* Step 6. improvement

C-couplingLC filterL-couplingLC filter+=


*Measured results27 dB


*6.2 Distributed filters At microwave frequencies :

Resonators made of Lumped elements are lossy(low Q) or bulky Distributed Resonators

Distributed resonators ; quarter-wavelength or half-wavelength transmission lines such as microstrip lines, coaxial lines and waveguides 6. LC filters, Distributed filters(3)


*A. Combline filters : cellular base stations as well as portable phone

Fig. 19 (a) Top view of Combline FilterFig. 19 (b) Side view of Combline Filter6. LC filters, Distributed filters(3)

Select box and type. Control handles change width & height of box.

Fig. 17(b) Side View of Combline Filter

tuning screw

L

conductor


* Instead of lumped element inductors distributed inductors (L < /4) are used.

Overall equivalent circuit :Fig. 20 Coupled lineFig. 21 Equivalent circuit of Fig.20Fig. 22 Equivalent circuit of Fig. 19

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3 Design of Rf and Microwave Filters