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RF Electronics Chapter 7: RF Filters Page 253 2022, C. J. Kikkert, James Cook University, ISBN 978-0-6486803-9-0. Figure 7.69. Coupling coefficient versus tapping point for different line impedances. This design technique is also described by the author in [13]. When the percentage bandwidth of the filter becomes greater than 20%, the coupling gaps for interdigital filters become too small to be produced using readily available technology. As a result, a different coupling technique is required. It is possible to couple two resonators using a quarter-wavelength long transmission line as shown in figure 7.70. The coupling can be varied by changing the tapping point. When this is done, graphs similar to figure 7.61 are produced by the circuit of figure 7.68 and from equation 7.30 the coupling coefficient can be determined as a function of tapping point as shown in figure 7.69, since the spacing between the peaks and the bandwidth are known. Example 7.4: 1 GHz, 500 MHz Bandwidth Filter The coupling coefficients shown in figure 7.69 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. Equations 4 and 5 give the normalized Q values and coupling coefficients as: Normalised De-normalised for 50% Bandwidth q 1 = q n =0.618 Q 1 = Q n =1.236 k 12 = k 45 = 1 K 12 = K 45 = 0.5 k 23 = k 34 = 0.5559 K 23 = K 34 = 0.278 Figure 7.69 shows that different transmission line impedances should be used for different coupling coefficients in order to obtain realistic tapping points. For the filter, 50 transmission lines are used for the input and output resonators, which require the highest coupling coefficients of 0.5. For the other resonators, 36 transmission lines, which have lower losses, are used. Interpolating the tapping points from figure. 7.69, results in the following normalised tapping points, TXLine results in the following resonator line lengths: RF Electronics: Design and Simulation 253 www.cadence.com/go/awr