Maximum Power Transfer Theorem Calculus-Based Proof Dr. Mahmood A. - PowerPoint PPT Presentation

Maximum Power Transfer Theorem Calculus-Based Proof Dr. Mahmood A. Hameed ECSE Department Rensselaer Polytechnic Institute Intro to ECSE

⇒ Power Delivered to Load Resistor Is = Rst RL IT RL ' . I , = Is RL LIL PL VL = = + - s " C r . . = - , - Rs 2 Rs - + RL 't I 28 November M. Hameed 2020

⇒ ⇒ ⇒ Maximize Power Delivered to Load Resistor min { Rp÷+Rct2Rs } Z Max { K } - b- PL = - Rps÷ + Ritz Rs - dir Dr Eto DRL - ' 2 Rs - I Rs -Rp÷ Re Re = - I o + = %max= R÷ ! zrs = rsII÷r Rs R , = fits = 28 November M. Hameed 2020

Matlab Demonstration 3552 Maximum Power Transfer Theorem uh 0.6 %% Initialize circuit parameters av ¥ #k Vs = 9; %Constant Source Voltage Rs = 35; %Constant Source Resistance 0.5 RL = 1:100; %Variable Load Resistor to %% Determine Current through each resistor (all same) Power absorbed by load resistor, PL, [watts] 0.4 I = Vs./(Rs+RL); %Application of Ohm's Law %% Determine power absorbed by load resistor 0.3 PL = (I.^2).*(RL); %P = VI = I^2R = V^2/R %% Plot power absorbed by resistor as a function of load resistance 0.2 plot(RL,PL,'LineWidth',3,'color','k'); hold on; xlabel('Load Resistance, RL, [ohms]'); 0.1 ylabel('Power absorbed by load resistor, PL, [watts]') title('Maximum Power Transfer Theorem'); grid on; 0 0 10 20 30 35 40 50 60 70 80 90 100 Load Resistance, RL, [ohms] 28 November M. Hameed 2020