A designer needs to back$-$light a display, and believes $9$ LEDs are required. Each LED needs $2$V at $10$ mA$.$ The load is to be switched on$/$off by a $3\mathrm{.}3$V digital logic device, such that VLH and Vi$\_$L are as indicated below. Neither terminal of the load needs to be grounded, so a single NPN transistor is proposed as driver. Find the resistor values below such that the LEDs are on as specified $($saturated NPN$)$ when the logic device output is high and off when the logic device output is low. Show calculations verifying the required off$-$state Vbe and the required on$-$state base current and the required LED current. Note: Brute force analysis requires simultaneous solution of $2$ nonlinear equations to determine R$4$ and Rs$.$ This is do$-$able but tedious $-$ and sometimes there is no solution. Suggestion for this problem determine R$4$ for the on$-$state without RS$,$ then reduce the calculated value of R$4$ by $20\%,$ then determine R$5$ for the off state analysis. Then re$-$check the $"$on state". In the real world there is often some iteration anyway, given that you must pick from standard resistor values. D$1$ D$2$ D$3$ R$1?$ D D$5$ D D$6$ D D$7$ Vin is output of $3\mathrm{.}3$V logic gate Vilmin $-2\mathrm{.}8$V$,$ Vilmax$\mathrm{.}6$ Vbe on$-0\mathrm{.}7.$ Vbe$\_$off$-0\mathrm{.}45,$ Sat beta$-10.$ Veesat $-03$ Vled un$-2$V$,$ ILED $-10$ mA R$2$ D D D $?$ Vi R$4$ Q$1$ Vino D$4$ D$8$ D$9?2$N$3904$ R$312$ R$5$ D D D