Question

Consider the diode circuit shown below. The diode, D, obeys the current-voltage characteristic \(I_D = I_s(\exp(V_D/nV_T) - 1)\). The circuit is biased so that voltage \(V>0\) and current \(I<0\). If you had to design this circuit to transfer maximum power from the current source (\(I_1\)) to a resistive load (not shown) at the output, what values for R1 and R2 would you choose? A. Small \(R_1\), B. Large \(R_1\), C. Small \(R_2\), D. Large \(R_2\). Choose the correct answer from the options given below:

• A. A and C
• B. B and C
• C. A and D
• D. B and D

Hint:

For maximizing power transfer efficiency (i.e., delivering the most power from a source to a load), you need to minimize power losses in any parallel (shunt) paths. This is achieved by making the shunt resistances as high as possible.

Answer 1

The Correct Option is D

Step 1: Define the objective.The goal is to maximize the power transferred from the current source \(I_1\) to the load resistor \(R_L\) at the output, where voltage (V) and current (I) are measured. This is a power delivery maximization problem.
Step 2: Analyze current flow.The source current \(I_1\) enters a central node and divides into these paths:

Diode (current \(I_D\)).
Resistor \(R_1\) (current \(I_{R1}\)).
Resistor \(R_2\) (current \(I_{R2}\)).
External load (current \(-I\)).
Applying Kirchhoff's Current Law (KCL): \(I_1 = I_D + I_{R1} + I_{R2} + (-I)\).
Step 3: Identify power dissipation.The source \(I_1\) generates power that distributes across components. Load power is \(P_L = V(-I)\). Internal losses are \(P_{loss} = P_{diode} + P_{R1} + P_{R2}\). Maximize \(P_L\) by minimizing \(P_{loss}\).
Step 4: Minimize losses in R1 and R2.The resistors dissipate power as \(P_{R1} = V^2/R_1\) and \(P_{R2} = V^2/R_2\). To reduce this dissipation, minimize currents \(I_{R1} = V/R_1\) and \(I_{R2} = V/R_2\). Therefore, \(R_1\) and \(R_2\) should be maximized. Higher \(R_1\) and \(R_2\) provide high impedance, preventing current \(I_1\) from being diverted from the load.
Step 5: Design conclusion.To maximize load current (and power), shunt paths through \(R_1\) and \(R_2\) should have high resistance. Thus, choose large values for \(R_1\) and \(R_2\), corresponding to options B and D.