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: Understand the goal. The objective is to transfer the maximum possible power from the current source \(I_1\) to an external load resistor \(R_L\) connected at the output terminals (where V and I are measured). This is a problem of maximizing power delivery efficiency.
Step 2: Analyze the current paths. The current \(I_1\) from the source flows into the central node. From there, it splits into several paths:

Through the diode (current \(I_D\)).
Through resistor \(R_1\) (current \(I_{R1}\)).
Through resistor \(R_2\) (current \(I_{R2}\)).
To the external load (current \(-I\)).
According to KCL, \(I_1 = I_D + I_{R1} + I_{R2} + (-I)\).
Step 3: Identify power losses. The power generated by the source \(I_1\) is distributed among all the components. The power delivered to the load is \(P_L = V(-I)\). The power lost or consumed by the internal components is \(P_{loss} = P_{diode} + P_{R1} + P_{R2}\). To maximize \(P_L\), we must minimize \(P_{loss}\).
Step 4: Determine how to minimize losses in R1 and R2. The power dissipated in the resistors is \(P_{R1} = V^2/R_1\) and \(P_{R2} = V^2/R_2\). To minimize this power dissipation, the currents \(I_{R1} = V/R_1\) and \(I_{R2} = V/R_2\) must be minimized. This means that the resistances \(R_1\) and \(R_2\) should be as large as possible. Large values of \(R_1\) and \(R_2\) create high impedance paths that prevent the source current \(I_1\) from being shunted away from the load.
Step 5: Conclude the design choice. To maximize the current (and thus power) delivered to the external load, the shunt paths through \(R_1\) and \(R_2\) must have very high resistance. Therefore, we should choose a large \(R_1\) and a large \(R_2\). This corresponds to options B and D.