{"id":858,"date":"2014-11-14T01:13:40","date_gmt":"2014-11-13T23:13:40","guid":{"rendered":"http:\/\/blog.the-leviathan.ch\/?p=858"},"modified":"2015-01-04T03:26:52","modified_gmt":"2015-01-04T01:26:52","slug":"current-mirror","status":"publish","type":"post","link":"https:\/\/blog.the-leviathan.ch\/?p=858","title":{"rendered":"Current mirror"},"content":{"rendered":"

Given, a complicated darlington circuitry:
\n\"darlington\"<\/a>
\nWe now replace the darlington pairs with single NPN transistors by defining: $$I_C=I_B \\cdot a$$ with $$a=(\\beta+1)\\cdot\\beta$$ and $$I_E=I_B \\cdot b$$ with $$b=(\\beta+1)^2$$
\n\"darlington_replacement\"<\/a><\/p>\n

Now we set:
\n$$I_{KD} = I_{B1} + I_{C3} = I_{B1} + I_{B3} \\cdot a$$ and $$I_{RL}=I_{C4}=I_{B4}\\cdot a$$ and $$I_{B2}=I_{B5}$$ and $$I_{KD} + I_{C1} + I_{RL} = I_{E5} + I_{E2} $$
\n$$I_{KD} + I_{B1} \\cdot a + I_{RL} = I_{B5} \\cdot b + I_{B2} \\cdot b = 2\\cdot I_{B5}\\cdot b = 2\\cdot I_{B2}\\cdot b$$
\n$$\\Rightarrow I_{RL}=- a \\cdot I_{KD} – I_{KD} + a^2 \\cdot I_{B3} + 2 \\cdot b \\cdot I_{B2}$$<\/p>\n

And resolve the current equation:
\n$$I_{B3} \\cdot b = I_{E3} = I_{C5}+I_{B2}+I_{B5}$$
\n$$=I_{C5}+2 \\cdot I_{B2}$$
\n$$=I_{C5}+2 \\cdot I_{B5}$$
\n$$=a \\cdot I_{B5}+2 \\cdot I_{B5}=(a+2)\\cdot I_{B5}=(a+2)\\cdot I_{B2}$$<\/p>\n

$$\\Rightarrow I_{B2} = I_{B5} = \\frac{1}{a+2} \\cdot I_{E3} =\\frac{b}{a+2} \\cdot I_{B3}$$
\n$$I_{E1} = I_{B1} \\cdot b = I_{B3}+I_{B4}$$<\/p>\n

$$I_{C2} = I_{B2} \\cdot a$$
\n$$= I_{E4}=I_{B4} \\cdot b$$<\/span><\/span><\/span><\/span><\/span><\/span><\/span>
\n$$\\Rightarrow I_{B4} = \\frac{a}{b}\\cdot I_{B2}=\\frac{a}{b}\\cdot\\frac{b}{a+2} \\cdot I_{B3}$$<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

$$I_{RL}=\\frac{a^2 b}{a^2 b + 2 a b +2}$$<\/p>\n","protected":false},"excerpt":{"rendered":"

Given, a complicated darlington circuitry: We now replace the darlington pairs with single NPN transistors by defining: $$I_C=I_B \\cdot a$$ with $$a=(\\beta+1)\\cdot\\beta$$ and $$I_E=I_B \\cdot b$$ with $$b=(\\beta+1)^2$$ Now we set: $$I_{KD} = I_{B1} + I_{C3} = I_{B1} + I_{B3} \\cdot a$$ and $$I_{RL}=I_{C4}=I_{B4}\\cdot a$$ and $$I_{B2}=I_{B5}$$ and $$I_{KD} + I_{C1} + I_{RL} = I_{E5} … Continue reading Current mirror<\/span> →<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-858","post","type-post","status-publish","format-standard","hentry","category-daily"],"_links":{"self":[{"href":"https:\/\/blog.the-leviathan.ch\/index.php?rest_route=\/wp\/v2\/posts\/858","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.the-leviathan.ch\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.the-leviathan.ch\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.the-leviathan.ch\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.the-leviathan.ch\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=858"}],"version-history":[{"count":63,"href":"https:\/\/blog.the-leviathan.ch\/index.php?rest_route=\/wp\/v2\/posts\/858\/revisions"}],"predecessor-version":[{"id":957,"href":"https:\/\/blog.the-leviathan.ch\/index.php?rest_route=\/wp\/v2\/posts\/858\/revisions\/957"}],"wp:attachment":[{"href":"https:\/\/blog.the-leviathan.ch\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=858"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.the-leviathan.ch\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=858"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.the-leviathan.ch\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=858"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}