A transistor with \u00df = 100 is biased to operate at a dc collector current of 0.4 mA. Find the values of 8m, ra, and re. Repeat for a bias current of 40 u A. ^ Hide Answer 16 mA\/V, 6.25 k2,61.9 ; 1.6 mA\/V, 6.25 k2, 618.8 22<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n To solve this problem, we need to find the values of ( r_e ), ( r_a ), and ( \\beta ) for a transistor biased at two different collector currents: ( 0.4 \\, \\text{mA} ) and ( 40 \\, \\mu\\text{A} ). The quantities ( r_e ), ( r_a ), and ( \\beta ) are key parameters in the small-signal analysis of a transistor.<\/p>\n\n\n\n For a bias current of ( 0.4 \\, \\text{mA} ), the values of the small-signal parameters are:<\/p>\n\n\n\n For a bias current of ( 40 \\, \\mu\\text{A} ), the values are:<\/p>\n\n\n\n These results highlight how the emitter resistance and transconductance change with varying collector currents, while the output resistance remains constant for both conditions.<\/p>\n","protected":false},"excerpt":{"rendered":" A transistor with \u00df = 100 is biased to operate at a dc collector current of 0.4 mA. Find the values of 8m, ra, and re. Repeat for a bias current of 40 u A. ^ Hide Answer 16 mA\/V, 6.25 k2,61.9 ; 1.6 mA\/V, 6.25 k2, 618.8 22 The Correct Answer and Explanation is […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-191459","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/191459","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=191459"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/191459\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=191459"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=191459"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=191459"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Given Data:<\/h3>\n\n\n\n
\n
Small-Signal Parameters:<\/h3>\n\n\n\n
\n
The emitter resistance ( r_e ) is given by the formula:
[
r_e = \\frac{V_T}{I_C}
]
where ( V_T ) is the thermal voltage, typically around 26 mV at room temperature. For ( I_C = 0.4 \\, \\text{mA} ):
[
r_e = \\frac{26 \\, \\text{mV}}{0.4 \\, \\text{mA}} = 65 \\, \\Omega
] For ( I_C = 40 \\, \\mu\\text{A} ):
[
r_e = \\frac{26 \\, \\text{mV}}{40 \\, \\mu\\text{A}} = 650 \\, \\Omega
]<\/li>\n\n\n\n
The output resistance is typically assumed to be large in small-signal analysis for a transistor, especially in a common-emitter configuration. Thus, we can assume ( r_a ) to be large, typically in the order of a few k\u03a9, unless otherwise specified. In this case, we are given that ( r_a ) is approximately 6.25 k\u03a9<\/strong> for both biasing conditions.<\/li>\n\n\n\n
The transconductance ( g_m ) is the rate of change of the collector current with respect to the base-emitter voltage and is given by:
[
g_m = \\frac{I_C}{V_T}
] For ( I_C = 0.4 \\, \\text{mA} ):
[
g_m = \\frac{0.4 \\, \\text{mA}}{26 \\, \\text{mV}} = 15.38 \\, \\text{mA\/V}
] For ( I_C = 40 \\, \\mu\\text{A} ):
[
g_m = \\frac{40 \\, \\mu\\text{A}}{26 \\, \\text{mV}} = 1.538 \\, \\text{mA\/V}
]<\/li>\n<\/ol>\n\n\n\nConclusion:<\/h3>\n\n\n\n
\n
\n