[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-657428-105":59,"doc-detail-657428-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","block-diagrams-transfer-function-examples-feedback-loops","Block Diagrams - Transfer Function Examples - Feedback Loops","","Explains how block diagrams represent linear systems using transfer functions defined as output divided by input. Derives transfer functions through worked examples: a second-order system using Laplace transforms, cascaded systems where transfer functions multiply, and parallel systems where transfer functions add. Includes a bonus feedback loop section defining open-loop and closed-loop systems, using algebra to obtain Y/F = W/(1 + gW) and applying Black’s formula to compute the closed-loop transfer function for a circuit.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/block-diagrams-transfer-function-examples-feedback-loops/657428/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/block-diagrams-transfer-function-examples-feedback-loops/657428.png","ImageObject",300,407,{"name":92,"@type":93},"lilac","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-10-26",true,{"@type":102,"interactionType":103,"userInteractionCount":81},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How is the transfer function defined in the block diagrams?","Question",{"text":112,"@type":113},"The transfer function is described as output/input, i.e., W(s) = output divided by input in the Laplace-frequency domain.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What happens to transfer functions for cascaded systems?",{"text":117,"@type":113},"For cascaded systems, the overall transfer function equals the product of the individual transfer functions: output/input = W2(s)·W1(s).",{"name":119,"@type":110,"acceptedAnswer":120},"How is the closed-loop transfer function computed for a feedback loop?",{"text":121,"@type":113},"Using algebra and Black’s formula, the closed-loop transfer function is output/input = W/(1 + gW). For the provided open-loop W(s), substituting into this formula yields the closed-loop rational expression.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},657428,1793074120,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":81,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":24,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":144},3985747861865,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","Block Diagrams  \n1. Introduction  \nWe discussed some simple block diagrams when we introduced the notions of system, input, and output back in unit 1. Here, we will include the transfer function in the diagram and show how to use them to compute the transfer function of more complicated systems.  \nAs we do this, it will be useful to keep in mind the desciption of the transfer function as output/input.  \n2. Simple Examples  \nExample 1. Suppose we have the system m..x + bx. + kx = f (t), with input f (t) and output x(t) . The Laplace transform converts this all to functions and equations in the frequency variable s. The transfer function for this system is W (s) = 1/(ms2 + bs + k) . We can write the relation between input and output as  \ninput F (s) 􀀠 output X (s) = W (s)F (s) As a block diagram we can represent the system by  \nFig. 1. Block diagram for a system with transfer function W (s) .  \nSometimes we write the formula for the transfer function in the box  \nrepresenting the system. For the above example this would look like  \nF (s)  \n\n| 1 |\n| --- |\n| ms2 + bs + k |\n\nX (s)  \nFig. 2. Block diagram giving the formula for the transfer function. Example 2. (Cascading systems) Consider the cascaded system  \np 1(D)x = f , p 2(D)y = x, rest IC.  \nThe input to the cascade is f and the output is y. The first equation takes the input f and outputs x. This is the input to the second equation, which ouputs y.  \nThis is easy to solve on the frequency side. Let W1 (s) = 1/p 1(s) and W2 (s) = 1/p 2(s) be the transfer functions for the two differential equations. Considering the two equations separately we have  \nX (s) = W1 (s) · F(s) and Y (s) = W2 (s) · X(s) .  \nIt follows immediately that Y (s) = W2 (s) · W1 (s) · F(s) . Therefore the transfer function for the cascade is  \noutput/input = Y (s)/F (s) = W2 (s) · W1 (s) . In other words, for cascaded systems the transfer functions multiply.  \nRepresenting this as block diagrams we have two equivalent diagrams  \nF (s)  \nW1 (s)  \nX (s)  \nW2 (s)  \nY (s)  \nF (s)  \nW1 (s)W2 (s)  \nY (s)  \nFig. 3. Equivalent block diagrams for a cascaded system.  \nExample 3. (Parallel systems) Suppose that we have a system consisting of two systems in parallel as shown in the block diagram.  \nFig. 4. Systems in parallel.  \nFind the transfer function for the entire system.  \nSolution. The plus sign in the circle indicates the two signals coming into the junction should be added. The split near the start indicates the input F (s) go into each system.  \nThe way to figure out the transfer function is to name the outputs of each individual system.  \nFig. 5. System with intermediate outputs labeled.  \nFor each system we know output = transfer function × input. Thus, X1 = W1 · F, X2 = W2 · F, Y = X1 + X2. So, we easily compute  \nY = X1 + X2 = W1 · F + W2 · F = (W1 + W2) · F. Therefore the transfer function is W1 + W2.  \n3. Feedback Loops  \nThis is a bonus section. You will not see it in the problems or tests.  \nMany systems use feedback loops. That is, the output of the system is monitored and used to modify the input. It is very hard to control a system without a feedback loop.  \nSuppose we start with a system with transfer function W (s) .  \nand modify it to have the feedback loop shown  \nThe original system is known as the open loop system and the corresponding system with feedback is known as the closed loop system.  \nWe’ve labeled the outputs from each system element. The symbol ×g means the input is scaled by g, that is apply a gain of g to the input. The symbol ∑ means the two inputs are combined; the plus and minus signs indicate to add or subtract the corresponding input.  \nThe method of finding the transfer function is the same as in the previous examples. A bit of algebra gives  \nV = F −gY, Y = W · V ⇒ Y = W (F −gY) ⇒ Y = ~~1 ~~W · F.  \nAs usual, the transfer function is output/input = Y /F = W / (1 + gW) . This formula is one case of what is often called Black’s formula  \nExample 4. Suppose we have an open loop","cbCaibLzmkPZsVpT","https://ap.wps.com/l/cbCaibLzmkPZsVpT","pdf",208383,"English","# 1. Introduction\n# 2. Simple Examples\n## Example 1\n## Example 2 (Cascading systems)\n## Example 3 (Parallel systems)\n# 3. Feedback Loops\n## Black’s formula\n## Example 4","[{\"question\":\"How is the transfer function defined in the block diagrams?\",\"answer\":\"The transfer function is described as output/input, i.e., W(s) = output divided by input in the Laplace-frequency domain.\"},{\"question\":\"What happens to transfer functions for cascaded systems?\",\"answer\":\"For cascaded systems, the overall transfer function equals the product of the individual transfer functions: output/input = W2(s)·W1(s).\"},{\"question\":\"How is the closed-loop transfer function computed for a feedback loop?\",\"answer\":\"Using algebra and Black’s formula, the closed-loop transfer function is output/input = W/(1 + gW). For the provided open-loop W(s), substituting into this formula yields the closed-loop rational expression.\"}]","Block Diagrams - Transfer Function Examples - Feedback Loops | PDF",1792979028,13]