Question #187244

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Expert's answer

Since the voltage across the diode is "V_D=0.7V", the current through the loop is obtained by using the relation for the current "I_D=\\frac{V_{DD}-V_D}{R}"

To begin the iteration, we assume that "V_D=0.7V"

Substituting the values "V_{DD}= 1V, R=1k \\Omega; V_D=0.7V" in the relation for the current gives,

"I_D=\\frac{V_{DD}-V_D}{R}=\\frac{1-0.7}{1000}=0.3mA"

From the relation for the diode current, I_{D} given by "I_D=I_se^{\\frac{V_D}{V_T}}" , we get the relation for V_{D} as "V = 0.025 \\ln({\\frac{I_D}{I_S}})"

Substituting the values I_{D}= 0.3mA, I_{S}=10^{-12}mA in the relation for the voltage gives "V_D = 0.025 \\ln({\\frac{I_D}{I_S}})= 0.025 \\ln({\\frac{0.3}{10^{-12}}})=0.66V"

Now find the current by substituting the values V_{D}= 0.66V; V_{DD}= 1 and R = 1"k\\Omega" in the relation "I_D= {\\frac{V_{DD}-V_D}{R}}= {\\frac{1-0.66}{1000}}=0.3392 A"

On substituting the value of I_{D}= 0.34 mA and /, = 10^{-12}mA in the relation for the voltage, "V=0.025 \\ln \\frac{I_D}{I_S}" , we get the value for voltage, V.

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