Next  |  Prev  |  Up  |  Top  |  Index  |  JOS Index  |  JOS Pubs  |  JOS Home  |  Search

### Reflectance of an Impedance

Let denote the driving-point impedance of an arbitrary continuous-time LTI system. Then, by definition, where and denote the Laplace transforms of the applied force and resulting velocity, respectively. The wave variable decomposition in Eq.(C.74) gives (C.75)

We may call the reflectance of impedance relative to . For example, if a transmission line with characteristic impedance were terminated in a lumped impedance , the reflection transfer function at the termination, as seen from the end of the transmission line, would be .

We are working with reflectance for force waves. Using the elementary relations Eq.(C.73), i.e., and , we immediately obtain the corresponding velocity-wave reflectance: Next  |  Prev  |  Up  |  Top  |  Index  |  JOS Index  |  JOS Pubs  |  JOS Home  |  Search

[How to cite this work]  [Order a printed hardcopy]  [Comment on this page via email]
{"ft_lang_label":"__label__en","ft_lang_prob":0.7702463,"math_prob":0.89223564,"size":927,"snap":"2023-40-2023-50","text_gpt3_token_len":230,"char_repetition_ratio":0.115926325,"word_repetition_ratio":0.20779221,"special_character_ratio":0.2286947,"punctuation_ratio":0.13095239,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9684736,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58],"im_url_duplicate_count":[null,null,null,3,null,null,null,8,null,3,null,null,null,3,null,3,null,null,null,3,null,null,null,3,null,2,null,null,null,2,null,2,null,null,null,2,null,null,null,3,null,7,null,null,null,null,null,null,null,null,null,7,null,2,null,2,null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-09-22T00:50:36Z\",\"WARC-Record-ID\":\"<urn:uuid:bb8a4d4f-3c3f-45b7-9aff-c37ccdc295b8>\",\"Content-Length\":\"17955\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:6d638c96-ee88-4b2d-8cdb-88afc2d7efb3>\",\"WARC-Concurrent-To\":\"<urn:uuid:63672e88-ccdc-4466-8ad2-ab07bf14073e>\",\"WARC-IP-Address\":\"171.64.197.141\",\"WARC-Target-URI\":\"https://ccrma.stanford.edu/~jos/pasp/Reflectance_Impedance.html\",\"WARC-Payload-Digest\":\"sha1:VFHKGGBDJ2P73SQAKVRIBKSBG5PVRALI\",\"WARC-Block-Digest\":\"sha1:Z6PWUJCXUTDQTCQFBWPNNWAWZWDWGVFY\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233506320.28_warc_CC-MAIN-20230922002008-20230922032008-00750.warc.gz\"}"}