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Designing Low Cost Wideband Microstrip Bandpass Filters

Conference Paper · December 2005

DOI: 10.1109/TENCON.2005.301311 · Source: IEEE Xplore

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Tencon 2005, Paper 1568965073, Kikkert, Designing Low Cost Wideband Microstrip Bandpass Filters

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Designing Low Cost Wideband Microstrip Bandpass Filters

Cornelis Jan Kikkert Electrical and Computer Engineering, School of Engineering

James Cook University Townsville, Australia, 4811 Keith.Kikkert@jcu.edu.au

Abstract—The design of RF filters where the bandwidth is much greater than 10% of the centre frequency is difficult to implement, since conventional filter design techniques such as those for coupled line or interdigital filters are applicable to filters with less than 10% bandwidth. This paper describes a design technique for designing wideband RF filters and illustrates this with the design of a 5 resonator filter with a 50% bandwidth at a centre frequency of 1 GHz. The design technique produces filters with a remarkable accuracy, so that one-iteration filter designs can be produced reliably.

I. INTRODUCTION Most RF filters are narrowband filters, with bandwidths less

than 10% of the centre frequency and are designed as coupled resonator filters using a wide variety of filter topologies [1, 2], the most common forms being:

A: Parallel Coupled Line Filters [1, 2, 3], use half wavelength long resonators, with electromagnetic coupling between quarter wavelength sections to produce the filtering. They are often made using microstrip or stripline circuits resulting in a low cost filter.

Figure 1. 7.5% Bandwidth Parallel Coupled Line Filter.

A hairpin filter has folded resonators as shown in Fig. 1. This filter has a 1 GHz centre frequency and 75 MHz bandwidth and was designed by the author. Harmonic suppression stubs are included. For wideband filters, the spacing between the resonators becomes too small for the filter to be manufactured reliably.

B: Interdigital Filters [1,2], use quarter wavelength resonators, grounded on opposite ends for adjacent resonators, with electromagnetic coupling between the resonators. Fig. 2 shows a 1 GHz, 70 MHz bandwidth interdigital filter designed by the author. Often these filters are made using round rods in a rectangular cavity. Dishal [4] and Martin [5] have presented design equations for such filters with bandwidths up to 10%. Some commercial manufacturers [6] make interdigital filters with bandwidths up to 33% BW.

Figure 2. 7% Bandwidth Interdigital Filter

C: Coupled Coaxial Line Cavity Filters, use quarter wavelength coaxial lines, located inside a cavity. Adjacent cavities are coupled by apertures in adjoining walls. Such filters are commonly used in narrowband high power applications. Helical Filters [7] are a variation of this type of filter. The bandwidth of these filters is limited by the size of the coupling apertures, which has to be less than the size of the wall joining the two cavities to be coupled. In some

Tencon 2005, Paper 1568965073, Kikkert, Designing Low Cost Wideband Microstrip Bandpass Filters

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Coaxial Line Cavity filters, the cavities are coupled using coupling loops and sometimes these coupling loops are connected using transmission lines.

D: LC filters. Since Inductors and Capacitors have relatively high losses at RF frequencies, LC filters are not normally used for RF bandpass filters above 100 MHz. At UHF frequencies LC filters are used for low pass or high pass filters.

II. DIRECT COUPLED TRANSMISSION LINE RESONATOR FILTERS

This paper describes a new design technique for the design of direct coupled transmission line filters with large bandwidths. In these filters quarter wavelength resonators are direct coupled using quarter wavelength transmission lines. Fig. 3 shows a microstrip layout for a two-resonator filter, used for determining the coupling coefficients.

Figure 3. Two-resonator filter used for determining the coupling coefficients.

To use this type of filter in a design, the coupling coefficients must be determined as the tapping point is varied. This can be done using computer simulation using Microwave Office [8].

1 2

1 2

3 4MUC2ID=M1L1=Lr nHR1=0 OhmL2=Lr nHR2=0 OhmK1_2=0.5

CAPID=C1C=Cr pF

CAPID=C2C=Cr pF

PORTP=1Z=5e3 Ohm

PORTP=2Z=5e3 Ohm

Cr=1e12/(25*wr2)

twopi=6.283wr2=twopi*1e9*frM

Lr=25*1e9/wr2

frM=0.8938

Figure 4. Mutually coupled LC two resonator filter.

To obtain confidence in the results, three different networks are simulated. The first one is a two-resonator LC network using a mutual coupling shown in Fig. 4. Models for ideal components are used in the computer simulation, thus removing any limitations of practical LC filters. By definition,

the coupling coefficient K1_2 should agree very closely with the value of the coupling coefficient measured by other techniques. The second network is a microstrip realisation of the two-resonator Direct Coupled Transmission Line Resonator Filter shown in Fig. 3. The third network is a realisation of the same filter, using ideal transmission lines. The circuit diagram used in the computer simulation is shown in Fig. 5.

TLINID=TL1Z0=Zres OhmEL=LLT1 DegF0=1 GHz

TLINID=TL2Z0=Zres OhmEL=LLt-LLT1 DegF0=1 GHz

TLINID=TL3Z0=50 OhmEL=90 DegF0=1 GHz

TLINID=TL4Z0=Zres OhmEL=LLT2 DegF0=1 GHz

TLINID=TL5Z0=Zres OhmEL=LLt-LLT2 DegF0=1 GHz

PORTP=1Z=5000 Ohm

PORTP=2Z=5000 Ohm

Zres=25

LLt=90*FLtLLT1=CLt*LLt*(1-Ldel)LLT2=CLt*LLt*(1+Ldel)

Ldel=0.9CLt=0.4FLt=1

Figure 5. Two-resonator filter using ideal transmission lines.

To determine the coupling coefficient of the resonators, the tapping point is varied by changing CLt in Fig. 5. For a Butterworth filter of order n, the k and q values can be obtained from filter tables in Zverev [7] or from the following expressions:

nSin

nSinqq n 2

22

)12(20ππ

=−

==

(1)

niSin

niSin

kij

2)12(

2)12(2

1ππ +−

=

Equation 9.4.3 in Zverev [7] shows how the coupling coefficient can be measured from the frequency difference between the peaks of Fig. 6 as:

00

31212 f

ff

BWkK pdB ∆== (2)

Where K12 is the coupling coefficient, k12 is the normalised coupling coefficient as obtained from (1), ∆fp is the frequency difference between the peaks, f0 is the centre frequency and BW3dB is the actual filter bandwidth. A typical plot obtained from the computer simulation is shown in Fig. 6. In the simulation, the tapping point for the ideal transmission line resonator is set and the tapping point for the microstrip circuit

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and the coupling coefficient for the transformer coupled resonator are varied to ensure that the same coupling coefficient is obtained.

Figure 6. Frequency response for determining coupling coefficients.

Fig. 7 shows the resulting coupling coefficients plotted versus transmission line normalised tapping point and transformer mutual coupling coefficient. The resonator transmission line has a 25 Ω impedance. There is virtually no difference between the ideal transmission line resonator and the microstrip resonator. There is also a good agreement between the coupling coefficient set as a parameter in the mutually coupled transformer model and that obtained using (1).

Figure 7. Coupling coefficients for the three different resonator circuits.

For practical filter layouts, it is desirable that the tapping points are not to be too close to the grounded end of the resonators. The tapping-point distance should be much greater than the line width of the coupling transmission line; otherwise the T junction joining the coupling line to the resonator cannot be accurately modelled. This can be achieved by varying the characteristic impedances of the resonators. The variation of coupling factor with transmission line impedance is shown in Fig. 8. It can be seen that high coupling factors require high impedance transmission lines.

Figure 8. Coupling Coefficient versus Normalised Tapping Point as a function of transmission line impedance.

For a practical filter, there will be several resonators, each being coupled to the next one. As a result each resonator will have two T sections with coupling lines connected to it. During the final stages of the design process, the tapping points are optimized to obtain the required filter specification. It is likely that during the optimization, some of the tapping points on the resonator may need to slide past each other. To avoid this layout limitation, both the tapping points for each resonator are made the same, so that a cross connection can be used. As a result the tapping points for the adjacent resonators will be different.

Figure 9. Coupling Coefficient variation with unequal tapping on adjacent resonators.

Fig. 9 is a plot of the variation of the coupling coefficient as the average tapping point value is kept the same but the difference between the tapping points on the adjacent resonators is varied. It can be seen that varying the tapping points between adjacent resonators reduces the coupling.

This graph can be reasonably approximated by:

2Re )(2.0 TapTapTap Averagequired ∆+= (3)

Tencon 2005, Paper 1568965073, Kikkert, Designing Low Cost Wideband Microstrip Bandpass Filters

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III. FILTER DESIGN EXAMPLE The coupling coefficients shown in Fig. 8 and 9 can now be

applied to the design of a wideband filter. As an example the design of a 5 resonator Butterworth bandpass filter with a lower 3 dB cut-off frequency of 750 MHz and an upper cut off frequency of 1250 MHz is chosen the filter will thus have a 50% bandwidth.

Equation (1) can be used to determine the normalized Q values and coupling coefficients as:

q1= qn =0.618 k12 = k45 = 1 k23 = k34 = 0.5559 Since the % bandwidth is 50%, de-normalising results in:

Q1= Qn =0.309 K12 = K45 = 0.5 K23 = K34 = 0.278 For the filter, 50 Ω transmission lines are used for the input

and output resonators, which require the highest coupling coefficients of 0.5. For the other resonators, 36 Ω transmission lines are used. Interpolating the tapping points from Fig. 8 and using (3), results in the following normalised tapping points:

Resonator 1 50Ω Tap = 0.487 Resonator 2 36Ω Tap = 0.614 Resonator 3 36Ω Tap = 0.426 Resonator 1 36Ω Tap = 0.614 Resonator 1 50Ω Tap = 0.487

Figure 10. Filter layout for initial tap values.

Entering those values in the Microwave Office circuit schematic of the filter, results in the initial filter layout shown in Fig. 10, with the corresponding frequency response shown in Fig. 11. To highlight differences between the 750 MHz and 1250 MHz, corner frequency specifications and frequency-response obtained from the computer simulation and an optimisation mask is superimposed on Fig. 11. In addition an optimisation mask for a –1 dB attenuation from 780 MHz to 1220 MHz is shown. It can be seen that the design procedure results in a filter that has a bandwidth that closely matches the design specifications, but whose centre frequency is 3.5% low. This difference is due to the end effect of the open circuit resonators not being taken into account in the above calculations.

Figure 11. Frequency response for initial filter.

IV. FINE TUNING THE FILTER To shift the centre frequency, the length of all the

resonators is changed slightly using the ‘tuning simulation’ capability of Microwave Office. In addition, it is desirable to fine tune the filter to obtain the lowest insertion loss. This is best achieved by ensuring that the filter has a low return loss. Setting the optimiser constraints on S11 to be less than -20 dB and carrying out the first stage of the optimisation process of the filter to meet this return loss as well as the passband specifications results in the following tapping points:

Resonator 1 50Ω Tap = 0.5147 Resonator 2 36Ω Tap = 0.5969 Resonator 3 36Ω Tap = 0.4304 Resonator 1 36Ω Tap = 0.5969 Resonator 1 50Ω Tap = 0.5147 The resulting frequency response of the filter after this first

stage of optimisation is shown in Fig. 12.

Figure 12. Frequency response of the filter after stage 1 optimisation.

For a wideband filter implementation like this, the spurious

Tencon 2005, Paper 1568965073, Kikkert, Designing Low Cost Wideband Microstrip Bandpass Filters

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response at the harmonics, particularly that at 2 GHz is unacceptable. To provide better attenuation at those frequencies, stubs need to be added to the filter. Those stubs will distort the frequency response of the filter. In order to minimise the effect of the stubs on the centre frequency of the filter, it is desirable to use two sets of stubs and vary the spacing between the two sets of stubs to provide a low return loss at the centre frequency of the filter. In addition it is desirable to make the harmonic stubs slightly different lengths, to widen the bandwidth over which good harmonic attenuation is obtained. Fig. 13 shows the frequency response of two harmonic stub filters, one having second harmonic suppression only and the other one having both second and third harmonic suppression. It can be seen that having both second and third harmonic stubs distorts the passband at 1 GHz more than just having a second harmonic stub. The hairpin filter of Fig. 1 incorporates both second and third harmonic, open circuit stubs according to these principles.

Figure 13. Frequency response for harmonic suppression open circuit stub filters.

The harmonic suppression stubs are now incorporated in the optimized filter design of Fig. 12. For this design a stop band attenuation of 50 dB from 1.8 GHz to 2.5 GHz is required and the filter performance above 2.5 GHz is not important. As a result only second harmonic stubs are used, since that causes less distortion to the filter passband.

The second stage of the optimisation involves optimising the combined filter, and adjust the resonators lengths, tapping points, harmonic stubs and output line lengths, to provide the correct passband, stopband and harmonic performance and the correct input match in the passband. The optimisation limits are those shown in Fig. 12 with the addition of a -55 dB stopband attenuation in the region of 1.8 GHz to 2.5 GHz.

The optimisation cost function versus resonator lengths and tapping points is a very nonlinear multidimensional function, with many local minima. A single optimisation technique will thus not provide the optimum answer and in practice it is necessary to change optimisation levels, weights and strategy

in order to obtain the best result. In most instances having a more severe optimisation limit than required and later relaxing that limit may help the optimisation achieve a satisfactory result. Sometimes if the optimisation cost function is not decreasing, easing the optimisation limit may result in further progress in the optimisation cost function. By having the harmonic stubs included in the design the -20 dB optimisation limit on S11, shown in Fig. 12 cannot be achieved for this design and an S11 optimisation limit of -15 dB is more realisable.

The final step in the filter design is to change the layout from a simple design as shown in Fig. 10, to a more compact and easier to manufacture design. To achieve this, the three tiered ground level shown in Fig. 10 is made one level and the coupling transmission lines are folded and bent in order to take up as little space as possible, while connecting to the resonators at the correct tapping points. In addition the harmonic stubs may be folded as shown in Fig. 1. This final layout should also ensure that the input and output connectors are in the correct location for mounting the filter. Fig. 14 is a photograph of the final filter.

Figure 14. The 750 to 1250 MHz Filter Realisation.

Fig. 15 shows the frequency response of the final filter after optimisation, it also shows the final optimisation limits used. To determine the reliability of the design technique, 4 filters were constructed. The measured frequency response of those filters are also shown in Fig. 15. It can be seen that the design technique results in highly repeatable filters, whose measured performance agrees remarkably with the results from computer simulation. The agreement between the measured and simulated results for these filters is much better than those for the hairpin filter of Fig. 1 or the interdigital filter of Fig. 2. It should be noted that the right most resonator is significantly larger than the other resonators. This is required to compensate for the effects of the harmonic stubs on the passband response.

Tencon 2005, Paper 1568965073, Kikkert, Designing Low Cost Wideband Microstrip Bandpass Filters

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Figure 15. Simulated and Measured Frequency response for final filter.

At higher frequencies the coupling lines cannot be bent as shown in fig. 14. As a result the ground line must be adjusted in height as shown in fig. 16, which is a 3.5 GHz filter with a 1 GHz passband. The red squares show the feed-through connections between the top and the bottom groundplanes.

Figure 16. Layout of a 3-4 GHz bandpass filter.

Figure 17. Simulated and Measured Frequency response for 3-4GHz filter.

Fig.17 shows the simulated and measured frequency response of the filter with the layout of figure 16. It can be seen that there is an excellent agreement between the actual and the designed performance in the passband. In the stopband, there is less isolation than expected, due to radiation between the input and output transmission lines. Placing

microwave absorber in strategic places ensured that this radiation was minimised.

The design technique presented here uses microstrip resonators to illustrate the design principles and result in a low cost filter. The same design technique can however be used for direct coupled resonators filters using transmission lines resonators in other forms, such as coaxial cables or coaxial cavity resonators.

V. CONCLUSION A design technique for designing wideband direct coupled

resonator filters has been presented. The design technique presented here is also applicable to narrower band filters. Since the filter design is based on resonators coupled using transmission lines, the accuracy of the simulation is much better than those designs which rely on electromagnetic radiation, like the hairpin filter or the interdigital filter, so that one-iteration filter designs can be produced reliably. By comparing Fig. 1, 2 and 14, it can be seen that the Direct Coupled Transmission Line Resonator Filters are larger than the interdigital or parallel coupled line filters. Direct coupled transmission line resonator filters are thus the best filter type to use when space is not an issue, but where accuracy is important or where wide bandwidths are required.

ACKNOWLEDGMENT The author acknowledges the assistance of Applied Wave

Research Inc. for providing Microwave Office at a discounted price. Without the analysis and optimisation capability of this software, the design would have not been possible. The technical staff at James Cook University is acknowledged for their help in fabrication the filters.

REFERENCES [1] G. Matthaei, L. Young, and E. M. T. Jones, Microwave Filters,

Impedance-Matching Networks, and Coupling Structures. Boston, MA: Artech House, 1980. pp.583-650.

[2] D. Pozar, Microwave Engineering , Third Edition, Wiley, 2005. pp. 416-438.

[3] N. G. Toledo, “Practical Techniques For Designing Microstrip Tapped Hairpin Resonator Filters On Fr4 Laminates” Available: http://wireless.asti.dost.gov.ph/sitebody/techpapers/hairpin_pej.DOC.

[4] M. Dishal, “A Simple Design Procedure for Small Percentage Bandwidth Round Rod Interdigital Filters” MTT, Vol 13, No5, Sep 1965, pp 696 – 698.

[5] P. Martin, “Design Equations for Tapped Round Rod Combline and Interdigital Bandpass Filters”, Nov 2002. Available: http://www.rfshop.com.au/C&IDES.DOC.

[6] K&L Microwave , 9IR20-7500/X2000-O/O Wide Band Interdigital Filter, Available: http://www.klmicrowave.com/bulletin2004/August/PDF/9IR20.pdf.

[7] A. I. Zverev, Handbook of Filter Synthesis, Wiley, 1967, Helical Filters pp 499-521, k and q Filter Tables, p 341, Eqn. 9.4.3 pp 517.

[8] Microwave Office, Product details available: http://appwave.com/products/.

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