The analysis of a transistor network resulted in the reduced equivalent in Fig. 9.92. a. Find the load resistance that will result in maximum power transfer to the load, and find the maximum power delivered. b. If the load were changed to 68 kΩ, would you expect a fairly high level of power

Question

The analysis of a transistor network resulted in the reduced equivalent in Fig. 9.92.

a. Find the load resistance that will result in maximum power transfer to the load, and find the maximum power delivered.
b. If the load were changed to 68 kΩ, would you expect a fairly high level of power transfer to the load based on the results of part (a)? What would the new power level be? Is your initial assumption verified?
c. If the load were changed to 8.2 kΩ, would you expect a fairly high level of power transfer to the load based on the results of part (a)? What would the new power level be? Is your initial assumption verified?

Accepted Answer

a. Replacing the current source by an open-circuit equivalent results in

[latex]R_{Th} = R_s = 40 kΩ[/latex]

Restoring the current source and finding the open-circuit voltage at the output terminals results in

[latex]E_{Th} = V_{oc} = IR_s = (10 mA)(40 kΩ) = 400 V[/latex]

For maximum power transfer to the load,

[latex]R_L = R_{Th} = 40 k\Omega[/latex]

with a maximum power level of

[latex]P_{L_{max}}=\frac{E^{2}_{Th}}{4R_{Th}}=\frac{(400V)^2}{4(40 kΩ)}=1W [/latex]

b. Yes, because the 68 kΩ load is greater (note Fig. 9.86) than the 40 kΩ load, but relatively close in magnitude.

[latex]I_L=\frac{E_{Th}}{R_{Th}+R_L}=\frac{400V}{40 kΩ + 68 kΩ}=\frac{400}{108 kΩ}≅ 3.7 mA\[0.5cm] P_L=I^{2}_{L}R_L=(3.7 mA)^2 (68 kΩ) ≅ 0.93 W [/latex]

Yes, the power level of 0.93 W compared to the 1 W level of part (a) verifies the assumption.

c. No, 8.2 kΩ is quite a bit less (note Fig. 9.86) than the 40 kΩ value.

[latex]I_L=\frac{E_{Th}}{R_{Th}+R_L}=\frac{400V}{40 kΩ + 8.2 kΩ}=\frac{400}{48.2 kΩ}≅ 8.3 mA\[0.5cm] P_L=I^{2}_{L}R_L=(8.3 mA)^2 (8.2 kΩ) ≅ 0.57 W [/latex]

Yes, the power level of 0.57 W compared to the 1 W level of part (a) verifies the assumption

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