Chapter 1Introduction

Bandpass filters are essential building blocks in communication system designs. It can reduce the harmonic and spurious emissions for transmitters, and may improve the rejection of interferences for receivers. The rapid growth in commercial microwave technology, varies of microwave communication system had been developed. Hence, Microstrip filters play important roles in many RF or microwave applications. Emerging applications such as wireless communications continue to challenge RF/microwave filters with ever more stringent requirements higher performance, smaller size, lighter weight, and lower cost.

Figure 1: Microstrip Bandpass Filters

Figure 2: Fractal based microstrip bandpass filter

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Chapter 2Low Cost Wideband Microstrip Bandpass

Filters

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.

2.1 Common form of Filters

The most common forms of filter are Parallel Coupled Line Filters, Interdigital Filters, Coupled Coaxial Line Cavity Filters and LC filters.

2.1.1. Parallel Coupled Line Filters

Parallel Coupled Line Filters 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 3: 7.5% Bandwidth Parallel Coupled Line Filter.

A hairpin filter has folded resonators as shown in Fig. 3. 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.

2.1.2 Interdigital Filters

Interdigital Filters use quarter wavelength resonators, grounded on opposite ends for adjacent resonators, with electromagnetic coupling between the resonators. Fig. 4 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 and Martin have presented design equations for such filters with bandwidths up to 10%. Some commercial manufacturers make interdigital filters with bandwidths up to 33% BW.

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Figure 4: 7% Bandwidth Interdigital Filter

2.1.3 Coupled Coaxial Line Cavity Filters

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

2.1.4 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.

2.2 Direct coupled transmission line resonator filters

This paper describes a new design technique for the design of direct coupled transmission line filters with large andwidths. In these filters quarter wavelength resonators are direct coupled using quarter wavelength transmission lines. Fig. 5 shows a microstrip layout for a two-resonator filter, used for determining the coupling coefficients.

Figure 5: Two-resonator filter used for determining the coupling coefficients.

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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.

Figure 6: 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. 6. 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 realization of the two-resonator Direct Coupled Transmission Line Resonator Filter shown in Fig. 3. The third network is a realization of the same filter, using ideal transmission lines. The circuit diagram used in the computer simulation is shown in Fig. 7.

Figure 7: 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. 7. For a Butterworth filter of order n, the k and q values can be obtained from filter tables in Zverev or from the following expressions:

(1)

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Equation 9.4.3 in Zverev shows how the coupling coefficient can be measured from the frequency difference between the peaks of Fig. 8 as:

(2)

Where K12 is the coupling coefficient, k12 is the normalized coupling coefficient, Δfp 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. 8. In the simulation, the tapping point for the ideal transmission line resonator is set and the tapping point for the microstrip circuit and the coupling coefficient for the transformer coupled resonator are varied to ensure that the same coupling coefficient is obtained.

Figure 8: Frequency response for determining coupling coefficients.

Fig. 9 shows the resulting coupling coefficients plotted versus transmission line normalized 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.

Figure 9: Coupling coefficients for the three different resonator circuits.

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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 modeled. 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. 10. It can be seen that high coupling factors require high impedance transmission lines.

Figure 10: Coupling Coefficient versus Normalized 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 11: Coupling Coefficient variation with unequal tapping on adjacent resonators.

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Fig. 11 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:

(3)

2.3. Filter design example

The coupling coefficients shown in Fig. 10 and 11 can now be applied to the design of a wideband filter. As an example the design of a 5 resonator Butterworth band pass 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 =0.618k12 = k45 = 1k23 = k34 = 0.5559

Since the % bandwidth is 50%, de-normalizing results in:

Q1= Qn =0.309K12 = K45 = 0.5K23 = 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 normalized tapping points:

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

Figure: 12. Filter layout for initial tap values.

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Entering those values in the Microwave Office circuit schematic of the filter, results in the initial filter layout shown in Fig. 12, with the corresponding frequency response shown in Fig. 13. To highlight differences between the 750 MHz and 1250 MHz, corner frequency specifications and frequency response obtained from the computer simulation and an optimization mask is superimposed on Fig. 11. In addition an optimization mask for a -1 dB attenuation from 780 Hz 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 13: Frequency response for initial filter.

2.4. 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 optimizer constraints on S11 to be less than -20 dB and carrying out the first stage of the optimization process of the filter to meet this return loss as well as the pass band specifications results in the following tapping points:

Resonator 1 50Ω Tap = 0.5147Resonator 2 36Ω Tap = 0.5969Resonator 3 36Ω Tap = 0.4304Resonator 1 36Ω Tap = 0.5969Resonator 1 50Ω Tap = 0.5147

The resulting frequency response of the filter after this first stage of optimization is shown in Fig. 14.

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Figure 14: Frequency response of the filter after stage 1 optimization.

For a wideband filter implementation like this, the spurious 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 minimize 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 pass band at 1 GHz more than just having a second harmonic stub. The hairpin filter of Fig. 3 incorporates both second and third harmonic, open circuit stubs according to these principles.

Figure 15: Frequency response for harmonic suppression open circuit stub filters.

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The harmonic suppression stubs are now incorporated in the optimized filter design of Fig. 14. 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 pass band. The second stage of the optimization involves optimizing the combined filter, and adjust the resonators lengths, tapping points, harmonic stubs and output line lengths, to provide the correct pass band, stop band and harmonic performance and the correct input match in the pass band. The optimization limits are those shown in Fig. 14 with the addition of -55 dB stop band attenuation in the region of 1.8 GHz to 2.5 GHz. The optimization cost function versus resonator lengths and tapping points is a very nonlinear multidimensional function, with many local minima. A single optimization technique will thus not provide the optimum answer and in practice it is necessary to change optimization levels, weights and strategy in order to obtain the best result. In most instances having a more severe optimization limit than required and later relaxing that limit may help the optimization achieve a satisfactory result. Sometimes if the optimization cost function is not decreasing, easing the optimization limit may result in further progress in the optimization cost function. By having the harmonic stubs included in the design the -20 dB optimization limit on S11, shown in Fig. 14 cannot be achieved for this design and an S11 optimization limit of -15 dB is more realizable. The final step in the filter design is to change the layout from a simple design as shown in Fig. 12, to a more compact and easier to manufacture design. To achieve this, the three tiered ground level shown in Fig. 12 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. 3. This final layout should also ensure that the input and output connectors are in the correct location for mounting the filter. Fig. 16 is a photograph of the final filter.

Figure 16: The 750 to 1250 MHz Filter Realization.

Fig. 17 shows the frequency response of the final filter after optimization, it also shows the final optimization 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. 17. 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. 3 or the inter digital filter of Fig. 4. It should be noted that the right most

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resonator is significantly larger than the other resonators. This is required to compensate for the effects of the harmonic stubs on the pass band response.

Figure 17: Simulated and Measured Frequency response for final filter.

At higher frequencies the coupling lines cannot be bent as shown in fig. 16. As a result the ground line must be adjusted in height as shown in fig. 18, which is a 3.5 GHz filter with a1 GHz pass band. The red squares show the feed-through connections between the top and the bottom ground planes.

Figure 18: Layout of a 3-4 GHz band pass filter.

Figure 19: Simulated and Measured Frequency response for 3-4GHz filter.

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Fig.19 shows the simulated and measured frequency response of the filter with the layout of figure 18. It can be seen that there is an excellent agreement between the actual and the designed performance in the pass band. In the stop band, 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 minimized. The design technique presented here uses micro strip 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.

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Chapter 3Design Technique for Microstrip Filters

Most communication systems require an RF front end, where RF filters and low noise amplifiers perform analogue signal processing. Microstrip RF filters are commonly used in receivers and transmitters operating in the 800 MHz to 30 GHz frequency range. The two most common types used are the parallel coupled line filter and the interdigital filter. A hairpin filter is a variation of the parallel coupled line filter, where the resonators are bent into a hairpin shape in order to achieve a more convenient aspect ratio. The design of these filters is well known and generally involves the use of empirical relations. Microwave RF filters are designed using either low pass filter equations with suitable transformations or using coupled resonators design procedures. In this paper a novel technique is presented for determining the PCB layout required for the end resonator loading and coupling factors for any stripline or microstrip realization. The design technique presented here is based on the adjustment procedure for helical filters, described in Zverev. This book contains tables for normalized coupling (k) and normalized loaded Q (q) values and gives the following equations for these for Butterworth filters:

3.1. Design Procedure

Four filters with a centre frequency of 1 GHz and a 75 MHz bandwidth are designed using this technique.

Figure 20 shows the resulting inter digital filter.

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Figure 20: 1GHz inter digital filter.

Figure 21: Test circuit for determining the required coupling gaps and resonator loading.

Figure 21 shows the Microwave Office realization of a coupled line structure, using two resonators. The structure corresponds to the first two resonators of the interdigital filter if figure 20. The author has simulated many microstrip-line filters using Microwave Office and ADS with both circuit simulation and electromagnetic simulation. The author has found that all give accurate results, however the circuit simulation from Microwave Office gave the best agreement with the measurements on the actual filters produced and as a result that circuit simulation is used throughout this paper. Circuit simulation also has the advantage of being much faster. The resonator of figure 21 is made up of different coupled line sections, the length Lct of one of these is made variable to enable the input tapping point, and thus the loaded Q of the first resonator, to be varied. An equation is used for the other coupled line length, to permit independent control of the input tapping point as well as the centre frequency by varying the total length of the resonator. To determine the resonator loaded Q and set the correct tapping point, the coupling distance between the coupled resonator sections (Scrc) is made large and the coupled resonator is split into two unconnected parts by disabling TL5 and TL9, to ensure that this coupled resonator does not effect the end resonator, as shown in figure 22. An end-effect, ground connection and T section is used to allow the model to be realized accurately. The resonator line width is a compromise between filter size, radiation losses and resistive losses. A resonator line width of 3 mm is chosen for these designs.

Figure 22: Test circuit for determining the resonator loading.

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For helical filters, the adjustment of the loaded Q values for the end resonators involves the measurement of the 3 dB bandwidth of the field in the end resonator. During simulation of a microstrip filter, this loaded resonator bandwidth can be obtained by measured the voltage at the top of the resonator, (Port 2 of figure 20). Equation (3) shows the relationship between the 3dB bandwidth of this voltage and the loaded normalized q of the end resonators of the filter as:

For a 5 resonator filter, equations (1) and (2) or filter tables give q0 = qn = 0.6180, k12 = k45 = 1.0 and k23 = k34 = 0.5559. From equation (3), the 3 dB resonator voltage bandwidth should thus be 121 MHz. The input tapping point and the line length are then tuned to achieve the orrect bandwidth and centre frequency. When Lct = 9.7 mm and Lcr = 45.3 mm, the frequency response of figure 22 is obtained. From Zverev, when observing the fields inside the end resonator of a helical filter, a double humped response as shown in the blue curve in figure 23 results, with the distance between the peaks being related to the coupling coefficients as follows:

Figure 23: Frequency sweep of loaded end resonator of figure 2.

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Figure 24: Frequency sweep of coupling test circuit.

This equation can also be used to determine the coupling gaps required. For the required filter k12 = k45 = 1.0, so that a distance between the peaks of 75 MHz is required. For the coupling between the inner resonators, k23 = k34 = 0.5559, corresponding to a 41.7 MHz distance between the peaks as shown in figure 5 is required. In figure 2, elements TL5 and TL9 are enabled to determine the required coupling gaps (Scsc) by observing the voltage at port 2. Scsc is tuned to obtain the frequency response shown in figure 5. In order to make the peaks of the response as sharp as possible and thus allow an accurate determination of the peak values, the tapping point is made as small as possible. In addition, there will be minima in the S11 plot shown in red in figure 5. The S11 plot is sharper and provides more precise but slightly different frequency spacing. As shown in figure 5, a 1.8 mm coupling gap results in a frequency spacing of 42.8 MHz when S11 is used and 49 MHz when the resonator voltage is used. The result from S11 is close enough to the required 41.7 MHz. The coupling for a 100 MHz frequency difference requires a 1.15mm coupling gap. Minor errors in the coupling gaps are not critical, as these values are used for the starting values for the filter optimization process, which then results in the final filter parameters. The same design process can be applied for other filter types. The test circuits must be adapted for the different layouts. The combline filter layout is similar to that of the interdigital filter, however all the grounded connections are on the same side. The input tapping is the same as the interdigital filter, but the coupling gaps are 0.2 mm for the outer resonators and 1.8 mm for the inner resonators. The coupling gaps for the outer esonators are thus a lot smaller and that may limit the practicality of the filter. For the hairpin filter, the required tapping point is 3.7 mm from the start of the hairpin bend and coupling gaps of 0.45mm are required for the outer resonators and gaps of 0.95 mm are required for the inner resonators. The test circuit for determining the tapping points for direct coupled filters is outlined. Using the procedure above, tapping points of 9.7 mm is required for the outer resonators and tapping points of 4 mm are required for the other resonators. For the direct coupled filter, the coupling lines are chosen to be 12.5% of a wavelength. This length has been found to give a reasonable stopband performance, whilst maintaining reasonable coupling tapping points.

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3.2 Filter comparison

Figure 25: Circuit schematic for inter digital filter.

Once the coupling factors and tapping points have been determined, they are entered into the schematic circuit for each of the filter types. Figure 25 shows the schematic for the 5 resonator inter digital filter. Figure 26 shows the frequency response for the 4 different filter types, with the tapping points and coupling gaps indicated above. It can be seen that the initial performance of the filters is close to specification. To complete the design procedure, the filters are optimized to provide the fine tuning required to fully meet the design specification. In addition some manufacturing constraints can be included. For instance for the filters designed here, the minimum coupling gap size was set at 0.5 mm, which is larger than the coupling gap of 0.2 mm calculated for the combline filter types, with the tapping points and coupling gaps indicated above. It can be seen that the initial performance of the filters is close to specification. To complete the design procedure, the filters are optimized to provide the fine tuning required to fully meet the design specification. In addition some manufacturing constraints can be included. For instance for the filters designed here, the minimum coupling gap size was set at 0.5 mm, which is larger than the coupling gap of 0.2 mm calculated for the combline filter.

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Figure 26: Frequency response of filters from design calculations.

The optimization goals should be kept as simple as possible to maximize the speed of the optimization. The corner frequencies of the filter are specified by setting three optimization goals as shown in figures 26 and 27.

Figure 27: Interdigital filter after optimization.

The insertion loss of the filter is close to 1 dB, so that the filter is to have less than 4 dB attenuation from 962.5 MHz to 1037.5 MHz, and more attenuation elsewhere. In addition an optimization goal with S11 to be less than - 25 dB from 980 MHz to 1020 MHz is added, to ensure that the filter has the lowest possible attenuation in the passband. For the interdigital filter, the frequency response after optimization is shown in figure 8. The same optimization process is applied to the other 3 filters. Figure 28 shows the passband response of the 4 filters after optimization. Figure 29 shows the frequency response of these filters over a wide frequency range. The hairpin filter has high stopband attenuation for frequencies less than the second harmonic, but has a harmonic response at that frequency. The direct coupled filter has high stopband attenuation but has little attenuation at the third harmonic frequency. The combline and interdigital filters have smaller harmonic responses but have less stopband

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attenuation. The filter type to be used will thus depend on the stopband specifications. The direct coupled filter allows larger bandwidths to be realized than the other filters.

Figure 28: Comparison of filters, passband after optimization.

Figure 29: Comparison of filters, stopband after optimization.

3.3. Filter measurements

The 4 filters with the simulated performance shown in Figures 28 and 29 were built. Figure 20 shows the photograph of the interdigital. Figure 30 shows the combline filter, figure 31 shows the hairpin filter and figure 32 shows the direct coupled filter. The interdigital filter is 42 x 60 mm in size, the combline filter is 41 x 60 mm, the direct coupled filter is 75 x 60 mm and the hairpin filter is 78 x 70 mm. The photographs are reproduced to approximately the same scale

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Figure 30: 1GHz combline filter.

Figure 31: 1 GHz hairpin filter.

Figure 32: 1 GHz direct coupled filter.

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Figures 33 to 34 show the measured frequency response of the filters. There is a remarkable agreement between the calculated and measured performance. The measured passband centre frequency of the combline, interdigital and direct coupled filters is 20 MHz or 2% lower than the design value. The resonators are thus 0.8 mm, or the substrate thickness, too long. This additional length is due to the via connecting the grounded end of the resonator to the bottom ground-plane. A second realization of those filters can take this effect into consideration to produce the correct centre frequency.

Figure 33: Interdigital filter frequency response.

Figure 34: Combline filter frequency response.

Figure 35: Hairpin filter frequency response.

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Figure 36: Direct coupled filter frequency response.

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Chapter 4Conclusion

In this paper we describe microstrip bandpass filters, different types of low cost wideband microstrip bandpass filters and a design technique for designing wideband direct coupled resonator filters. 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 inter digital filter, so that one-iteration filter designs can be produced reliably. By comparing Fig. 3, 4 and 16, it can be seen that the Direct Coupled Transmission Line Resonator Filters are larger than the inter digital 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. Finally we describe a design procedure that can be used to design any coupled resonator filter, whose layout can be simulated. Four different filters are designed, each with a similar passband response, but a very different out of band response. This allows the appropriate RF filters to be selected, such that unwanted RF signals are filtered out effectively. This design technique can be used to design new filters topologies, which can provide cost effective analogue signal processing by the receiver front end. One example would be a filter with some hairpin resonators, to achieve high stopband attenuation, coupled to interdigital resonators to remove the harmonic responses from the hairpin filter. The measured filter performances closely match those obtained by computer simulation.

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References

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[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.

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

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