{"id":47474,"date":"2025-07-02T12:23:09","date_gmt":"2025-07-02T12:23:09","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=47474"},"modified":"2025-07-02T12:23:10","modified_gmt":"2025-07-02T12:23:10","slug":"when-the-drain-and-gate-of-a-mosfet-are-connected-together-a-two-terminal-device-known-as-a-diode-connected-transistor-results","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/when-the-drain-and-gate-of-a-mosfet-are-connected-together-a-two-terminal-device-known-as-a-diode-connected-transistor-results\/","title":{"rendered":"When the drain and gate of a MOSFET are connected together, a two terminal device known as a \\”diode-connected transistor\\” results."},"content":{"rendered":"\n
When the drain and gate of a MOSFET are connected together, a two terminal device known as a \\\"diode-connected transistor\\\" results.<\/pre>\n\n\n\n
\"\"<\/figure>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n
Here is the step-by-step derivation for the given relationships.<\/p>\n\n\n\n
Part a: The i-v relationship<\/h3>\n\n\n\n
The problem asks to show that the current-voltage (i-v) relationship for a diode-connected MOSFET is given by:
i = (1\/2) * k’ * (W\/L) * (v – |Vt|)^2<\/p>\n\n\n\n
    \n
  1. Circuit Configuration:<\/strong>\u00a0In a diode-connected configuration, the drain and gate terminals of the MOSFET are connected. This means the gate-to-source voltage (v_GS) is equal to the drain-to-source voltage (v_DS). Let’s call this common voltage\u00a0v, so\u00a0v_GS = v_DS = v.<\/li>\n\n\n\n
  2. Operating Region:<\/strong>\u00a0A MOSFET operates in the saturation region when\u00a0v_GS > |Vt|\u00a0and\u00a0v_DS \u2265 v_GS – |Vt|.\n
      \n
    • The first condition,\u00a0v > |Vt|, ensures the transistor is turned on and conducting current.<\/li>\n\n\n\n
    • Let’s check the second condition. Substituting\u00a0v_GS = v\u00a0and\u00a0v_DS = v, the inequality becomes\u00a0v \u2265 v – |Vt|. This simplifies to\u00a00 \u2265 -|Vt|, which is always true since the threshold voltage\u00a0|Vt|\u00a0is a positive value.<\/li>\n\n\n\n
    • Therefore, whenever the diode-connected transistor is on (i.e.,\u00a0v > |Vt|), it is guaranteed to be operating in the saturation region.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
    • Saturation Current Equation:<\/strong>\u00a0The standard equation for the drain current\u00a0i_D\u00a0of a MOSFET in saturation is:
      i_D = (1\/2) * k’ * (W\/L) * (v_GS – |Vt|)^2
      Here,\u00a0k’\u00a0is the process transconductance parameter,\u00a0W\/L\u00a0is the aspect ratio of the transistor, and\u00a0Vt\u00a0is the threshold voltage.<\/li>\n\n\n\n
    • Final Derivation:<\/strong>\u00a0By substituting our circuit’s conditions (i = i_D\u00a0and\u00a0v = v_GS) into the saturation equation, we directly obtain the required i-v relationship:
      i = (1\/2) * k’ * (W\/L) * (v – |Vt|)^2<\/li>\n<\/ol>\n\n\n\n
      Part b: The incremental resistance<\/h3>\n\n\n\n
      The problem asks to show that the incremental resistance r at a bias point v = |Vt| + V_ov is given by:
      r = 1 \/ [\u2202i\/\u2202v] = 1 \/ (k’ * (W\/L) * V_ov)<\/p>\n\n\n\n
        \n
      1. Definition of Incremental Resistance:<\/strong>\u00a0The incremental resistance\u00a0r\u00a0is defined as the inverse of the slope of the i-v curve at a specific operating point. Mathematically,\u00a0r = 1 \/ (\u2202i\/\u2202v).<\/li>\n\n\n\n
      2. Differentiate the i-v Relationship:<\/strong>\u00a0We start with the equation derived in Part (a) and differentiate the current\u00a0i\u00a0with respect to the voltage\u00a0v:
        \u2202i\/\u2202v = d\/dv [ (1\/2) * k’ * (W\/L) * (v – |Vt|)^2 ]
        Using the chain rule for differentiation, we get:
        \u2202i\/\u2202v = (1\/2) * k’ * (W\/L) * 2 * (v – |Vt|)^(2-1) * (d\/dv(v – |Vt|))
        \u2202i\/\u2202v = k’ * (W\/L) * (v – |Vt|)<\/li>\n\n\n\n
      3. Apply the Bias Point:<\/strong>\u00a0The expression is evaluated at the given bias point. The overdrive voltage,\u00a0V_ov, is defined as the amount by which the gate-source voltage exceeds the threshold voltage:\u00a0V_ov = v_GS – |Vt|.
        Since\u00a0v_GS = v\u00a0in this circuit, we have\u00a0V_ov = v – |Vt|.<\/li>\n\n\n\n
      4. Final Derivation:<\/strong>\u00a0We can substitute\u00a0V_ov\u00a0into our expression for the derivative:
        \u2202i\/\u2202v = k’ * (W\/L) * V_ov
        Finally, we find the incremental resistance\u00a0r\u00a0by taking the reciprocal of this expression:
        r = 1 \/ (\u2202i\/\u2202v) = 1 \/ (k’ * (W\/L) * V_ov)<\/li>\n<\/ol>\n\n\n\n
        \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"
        When the drain and gate of a MOSFET are connected together, a two terminal device known as a \\”diode-connected transistor\\” results. The Correct Answer and Explanation is: Here is the step-by-step derivation for the given relationships. Part a: The i-v relationship The problem asks to show that the current-voltage (i-v) relationship for a diode-connected MOSFET […]<\/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-47474","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/47474","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=47474"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/47474\/revisions"}],"predecessor-version":[{"id":47477,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/47474\/revisions\/47477"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=47474"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=47474"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=47474"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}