Question $1$

$($a$)$ A diode has the current$-$voltage equation $\backslash ($ I$\_\{$D$\}=5\backslash$times $10^\{-9\}\backslash$left$[\backslash$exp $\backslash$left$(20$ V$\_\{$D$\}\backslash$right$)-1\backslash$right$]\backslash$mathrm$\{$A$\}\backslash ).$

i$.$ Derive an expression for the diode small$-$signal resistance and determine its value for $\backslash ($ V$\_\{$D$\}=0\mathrm{.}8\backslash$mathrm$\{$~V$\}\backslash ).$

$(6$ marks$)$

ii$.$ A $20$ mV peak$-$to$-$peak sinewave voltage is added to the diode bias voltage of $0\mathrm{.}8$ V $.$ Determine the diode AC power dissipation.

$($b$)$ The Zener in the regulator of Fig. $1$ requires a minimum current of $10$ mA under all conditions.

i$.$ The supply voltage $\backslash ($ E $\backslash )$ can vary between $10$ V and $15$ V and the load current can vary between $0$ and $50$ mA $.$ Determine the maximum allowed value of the resistor $\backslash ($ R $\backslash )$ and its minimum power rating.

$(12$ marks$)$

ii$.$ Determine the Th$$venin resistance of the circuit looking out from the Zener terminals in the case where $\backslash ($ E$=10\backslash$mathrm$\{$~V$\},$ R $\backslash )$ is equal to the value calculated in part $($i$)$ and the load current is $50$ mA $.$

$(4$ marks$)$

Fig. $1.$ Regulator.