If a diode at 300°K with a constant bias current of 100μA has a forward voltage of 700mV across it, what will the voltage drop across this s

Question

If a diode at 300°K with a constant bias current of 100μA has a forward voltage of 700mV across it, what will the voltage drop across this same diode be if the bias current is increased to 1mA? g

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Neala 3 years 2021-08-07T21:03:43+00:00 1 Answers 9 views 0

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  1. Verity
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    2021-08-07T21:05:14+00:00
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    Answer:

    the voltage drop across this same diode will be 760 mV

    Explanation:

    Given that:

    Temperature T = 300°K

    current I_1 = 100 μA

    current I_2 = 1 mA

    forward voltage V_r = 700 mV = 0.7 V

    To objective is to find the voltage drop across this same diode  if the bias current is increased to 1mA.

    Using the formula:

    I = I_o \begin {pmatrix} e^{\dfrac{V_r}{nv_T}-1} \end {pmatrix}

    I_1 = I_o \begin {pmatrix} e^{\dfrac{V_r}{nv_T}-1} \end {pmatrix}

    where;

    V_r = 0.7

    I_1 = I_o \begin {pmatrix} e^{\dfrac{0.7}{nv_T}-1} \end {pmatrix}

    I_2 = I_o \begin {pmatrix} e^{\dfrac{V_r'}{nv_T}-1} \end {pmatrix}

    \dfrac{I_1}{I_2} = \dfrac{ I_o \begin {pmatrix} e^{\dfrac{0.7}{nv_T}-1} \end {pmatrix} }{ I_o \begin {pmatrix} e^{\dfrac{V_r'}{nv_T}-1} \end {pmatrix} }

    \dfrac{100 \ \mu A}{1 \ mA} = \dfrac{ \begin {pmatrix} e^{\dfrac{0.7}{nv_T}-1} \end {pmatrix} }{ \begin {pmatrix} e^{\dfrac{V_r'}{nv_T}-1} \end {pmatrix} }

    Suppose n = 1

    V_T = \dfrac{T}{11600} \\ \\ V_T = \dfrac{300}{11600} \\ \\ V_T = 25. 86 \ mV

    Then;

    e^{\dfrac{V_r'}{nv_T}-1} = 10 \begin {pmatrix} e ^{\dfrac{ 0.7} { nV_T} -1} \end {pmatrix}

    e^{\dfrac{V_r'}{nv_T}-1} = 10 \begin {pmatrix} e ^{\dfrac{ 0.7} { 25.86} -1} \end {pmatrix}

    e^{\dfrac{V_r'}{nv_T}-1} = 5.699 \times 10^{12}

    {e^\dfrac{V_r'}{nv_T}} = 5.7 \times 10^{12}

    {\dfrac{V_r'}{nv_T}} =log_{e ^{5.7 \times 10^{12}}}

    {\dfrac{V_r'}{nv_T}} =29.37

    V_r'=29.37 \times nV_T

    V_r'=29.37 \times 25.86

    V_r'=759.5 \ mV

    Vr' \simeq 760 mV

    Thus, the voltage drop across this same diode will be 760 mV

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