A non-ideal Si-based pn junction diode is tested by sweeping the bias applied across its terminals from -5 V to +5 V. The effective thermal voltage, V_{T}, for the diode is measured to be (29 \pm 2) {mV}. The resolution of the voltage source in the measurement range is 1 {mV}. The percentage uncertainty (rounded off to 2 decimal places) in the measured current at a bias voltage of 0.02 {V} is

Correct Answer is : 4.70 - 4.80

GATE Electrical Engineering (EE) 2020 Solved Paper

Question : 42 of 65

Marks: +1, -0

A non-ideal Si-based pn junction diode is tested by sweeping the bias applied across its terminals from

-5 V

+5 V

. The effective thermal voltage,

V_{T}

, for the diode is measured to be

(29 ± 2) {mV}

. The resolution of the voltage source in the measurement range is

1 {mV}

. The percentage uncertainty (rounded off to 2 decimal places) in the measured current at a bias voltage of

0.02 {V}

Solution:

I=I O^{e}

V_{T}=29 ± 2 m V

\ln (\;{I}/{I_{0}})=\;{V_{D}}/{η V_{T}}

\ln I-\ln I_{0}=\;{V_{D}}/{η V_{T}}

Differentiating partiality with respect

+0 {V}_{ {T}}

\;{∂ {I}}/{ {I}}=0+\;{ {V}_{ {D}}}/{η}(\;{-1}/{ {V}_{ {T}}^{2}}) × ∂ {V}_{ {T}}

\;{∂ {I}}/{ {I}}=\;{- {IV}_{0}}/{ {V}_{ {T}}^{2}}

η=1

Resultant uncertainty

{W}_{\;\text "res "\;}= {W}_{ {I}} √{(\;{∂ {I}}/{∂ {V}_{ {T}}})^{2} × {W}_{ {v}}^{2}=± \;{∂ {I}}/{∂ {V}_{ {T}}} × {W}_{ {v}}}

{w}_{\;\text "res "\;}= {W}_{ {I}}=± \;{ {IV}_{0}}/{ {V}_{ {T}}^{2}} {w}_{ {V}}

{W}_{ {I}}=± \;{ {IV}_{0}}/{ {V}_{ {T}}^{2}} {w}_{ {v}} ± \;{ {I} × 0.02}/{(0.029)^{2}} × 0.02

=± 0.0475 {I}

\;{ {W}_{ {I}}}/{ {I}}=± 0.0475 × 100=± 7.75 \%

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