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RF Electronics Chapter 7: RF Filters Page 233 2022, C. J. Kikkert, James Cook University, ISBN 978-0-6486803-9-0. response and the group delay has peaks at the passband edges, similar to figure 7.2. Like the Bessel type filter of figure 7.31, the group delay is bigger at the lower corner frequency than the upper corner frequency. Like the other capacitive coupled filters, the attenuation at higher frequencies (220 MHz) is far less than the attenuation at lower frequencies (100 MHz). The measured frequency response of the filter is close to the calculated response shown in figure 7.39. Cauer-Chebyshev Bandpass filters Cauer-Chebyshev filters have zeros in the stopband resulting in equal ripples in the stopband as well as having ripples in the passband. It is more difficult to include zeros in the stopband of coupled resonator RF filters, as this requires coupling between adjacent resonators. It is also possible to include zeros of transmission by including open circuited stubs of one-quarter wavelength at the appropriate frequency. Such stubs are normally used to suppress the unwanted passbands occurring at the second and third harmonic of the passband frequency. In other RF filters, transmission zeros are placed at frequencies that must be rejected, such as the transmission frequency in the receive input of a diplexer. In these cases an equal stopband ripple design as specified by the Cauer-Chebyshev filters is not implemented. Parallel Coupled-Line Filters This filter type is also known as a Stripline filter. For this filter, the design equations 7.11 to 7.14 can be used. However, one can also use the generalised coupled resonator filter equations shown in equations 29 and 30 and applied to the interdigital filter design example on page 170. The filter parameters a(i) and the resulting even and odd mode Characteristic impedances are given as: c F q BW a 1 2 ) 0 ( Eqn. 7.11 1 , 2 ) ( i i c k F BW i a Eqn. 7.12 ) ) ( ) ( 1 ( 2 i a i a Z Z in oo Eqn. 7.13 ) ) ( ) ( 1 ( 2 i a i a Z Z in oe Eqn. 7.14 In these expressions BW is the bandwidth of the filter, F c is the centre frequency, q 1 , q n are the normalised input and output loaded Q values and k i,i+1 is the coupling coefficient between the i th and the (i+1) th resonator as obtained from filter tables. Example 7.1: 1 GHz, 70 MHz Bandwidth Filter Design a 4-resonator filter with a bandwidth of 70 MHz and a centre frequency of 1 GHz. The attenuation should be as low as possible in the passband. The input and output impedances should be 50 Ω. The filter is made using 0.82 mm thick RO4003 substrate with 35 micron copper. A Butterworth filter type is selected for the initial design. Equations 7.4 and 7.5 can thus be used for obtaining the K and Q values, or they can be taken from table 7.1 to give: RF Electronics: Design and Simulation 233 www.cadence.com/go/awr

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