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RF Electronics Chapter 7: RF Filters Page 247 2022, C. J. Kikkert, James Cook University, ISBN 978-0-6486803-9-0. Example 7.3: 1 GHz, 70 MHz Bandpass Filter Design a 5-resonator filter with a 70 MHz bandwidth centred at 1 GHz, using a RO4003 substrate for the PCB. The required k and q values can be obtained from table 7.1, the relevant part of which is shown in table 7.4. The design procedure used here is also described in [13, 14]. Table 7.4. Butterworth response, K and Q value filter table, from Zverev [1], pp 341. n q0 I. L. q 1 q n k 12 k 23 k 34 k 45 5 INF. 0.000 0.6180 0.6180 1.0000 0.5559 0.5559 1.0000 32.361 1.045 0.4001 1.5527 1.4542 0.6946 0.5285 0.6750 32.361 1.045 0.5662 0.7261 1.0947 0.5636 0.5800 0.8106 16.180 2.263 0.3990 1.8372 1.4414 0.6886 0.5200 0.6874 16.180 2.263 0.5777 0.7577 1.0711 0.5408 0.6160 0.7452 10.787 3.657 0.4036 2.0825 1.4088 0.6750 0.5080 0.7066 10.787 3.657 0.5927 0.7869 1.0408 0.5144 0.6520 0.6860 8.090 5.265 0.4111 2.3118 1.3670 0.6576 0.4927 0.7290 8.090 5.265 0.6100 0.8157 1.0075 0.4844 0.6887 0.6278 Notice that the k and q values vary depending on the losses. One could guess the losses to be about 2 dB and use the corresponding k and q values. Note that for each value of insertion loss, there are two sets of k and q values. Since the tap coupling is normally used and the tapping points only cover a limited range, it is desirable to select the table values where the difference between the q values is small. Alternately, the design is done assuming no losses, so that equations 4 and 5 can be used. After the design is completed, any variations in k and q values required to accommodate the losses can be achieved by optimisation. That process is implemented here. The lossless q values are thus q 1 = q n = 0.6180, resulting in Q 1 = Q n = 0.6180*1e9/70e6 = 8.828. The bandwidth, without loading due to adjacent resonators is given by equation 9.4.1 in Zverev [1] for the first and last resonator respectively as: 1 3 3 1 Resonator q BW Filter dB dB Eqn. 7.29a n dB dB q BW Filter n 3 3 Resonator Eqn. 7.29b In our design the filter BW 3dB is 70 MHz, 3dB is thus 70/0.618 MHz = 113.2 MHz. For this filter, q 1 = q n and the input and output tapping points are the same. The tapping point can be determined using Cadence AWR DE and the two-resonator circuit of figure 7.60. To prevent the second resonator from influencing the tuning of the tapping point, a very large coupling gap is used and the resonance of the coupled resonator is placed far away from the centre frequency by disabling all the possible elements as shown in figure 7.60. To measure the voltage of the input resonator, a high impedance (1 MΩ) port (port 2) is connected to the resonator. The signal at port 2 is then the voltage at the top of resonator and has the correct frequency response for determining the loading RF Electronics: Design and Simulation 247 www.cadence.com/go/awr

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