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simulate this circuit – Schematic created using CircuitLab
I'm really unsure how to start with this. The instructions said to find Vin such that Vout will be 0.5Vin. The only given is Vd = 0.7 and Rd = 5 ohms. I tried to do a KVL equation but then I don't know what the current is since Vin is not given.
Additional info: Diode model that is used is the constant voltage drop model with resistance of Rd=5 ohms and forward voltage of 0.7
An explicit model to be used for the diode is missing in the original question, however the diode parameters provided (\$V_d\$ and \$R_d\$) point towards using a piece-wise linear model for the diode. Therefore, your circuit should be redrawn as follows.
simulate this circuit – Schematic created using CircuitLab
Assuming \$V_{out} > V_d\$, the ideal diode has a forward bias and acts as a short-circuit. Voltage equations: $$ \frac{V_{out}-V_i}{R_1}+\frac{V_{out}-V_d}{R_d}=0 $$ With the additional constraint \$V_{out} = 0.5V_i\$: $$ \frac{-0.5V_i}{R_1}+\frac{0.5V_i-V_d}{R_d}=0 $$ $$ 0.5\left(\frac{1}{R_d}-\frac{1}{R_1}\right)V_i=\frac{V_d}{R_d} $$ $$ V_i=2\frac{V_d}{R_d\left(\frac{1}{R_d}-\frac{1}{R_1}\right)} $$ Checking numerically if the forward bias assumption holds true: $$ V_i=\frac{1.4}{5(0.2-0.1)}=\frac{1.4}{0.5}=2.8 $$ $$ V_{out}=0.5V_i=1.4 > V_d $$
