{'fraction_non_alphanumeric': 0.014326647564469915, 'fraction_numerical': 0.0014326647564469914, 'mean_word_length': 5.185840707964601, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Synthesis of 2-CRF Section Filter without External Elements

This paper presents the synthesis and circuit transformation for fourth-order filters based on two CRF sections. The synthesized network selects the input and output electro-acoustic couplings and defines the position of the four eigen modes excited in the topology. These values can be related with the physical dimensions of the structure. This is the area and layer configuration and thicknesses. The synthesis method reveals the existence of multiple solutions for a given filter response, which give rise to a different degree of miniaturization. Final simulated illustrative designs will be outlined to verify the synthesis method.