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

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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


slide-1
SLIDE 1

Maximum Power Transfer Theorem Calculus-Based Proof

  • Dr. Mahmood A. Hameed

ECSE Department Rensselaer Polytechnic Institute

Intro to ECSE

slide-2
SLIDE 2
  • M. Hameed

28 November 2020

Power Delivered to Load Resistor

Is

=

Rst RL

+

LIL

PL

=

VL

. I ,

=

IT RL

= Is

'

RL

  • s

"

  • C

,

r

. .

=

  • Rs
  • I

+ RL 't

2 Rs

slide-3
SLIDE 3
  • M. Hameed

28 November 2020

Maximize Power Delivered to Load Resistor

Z

PL

  • b-

Max { K }

=

min { Rp÷+Rct2Rs}

Rps÷

+ Ritz Rs

  • dir

Eto

Dr

DRL

2

  • Rp÷

+

I

=

Re

  • =

Rs

'

Re

  • I Rs

R ,

=

Rs

%max= R÷!zrs

= rsII÷r

=

fits

slide-4
SLIDE 4
  • M. Hameed

%% Initialize circuit parameters Vs = 9; %Constant Source Voltage Rs = 35; %Constant Source Resistance RL = 1:100; %Variable Load Resistor %% Determine Current through each resistor (all same) I = Vs./(Rs+RL); %Application of Ohm's Law %% Determine power absorbed by load resistor PL = (I.^2).*(RL); %P = VI = I^2R = V^2/R %% Plot power absorbed by resistor as a function of load resistance plot(RL,PL,'LineWidth',3,'color','k'); hold on; xlabel('Load Resistance, RL, [ohms]'); ylabel('Power absorbed by load resistor, PL, [watts]') title('Maximum Power Transfer Theorem'); grid on;

28 November 2020

Matlab Demonstration

10 20 30 40 50 60 70 80 90 100

Load Resistance, RL, [ohms]

0.1 0.2 0.3 0.4 0.5 0.6

Power absorbed by load resistor, PL, [watts] Maximum Power Transfer Theorem

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uh

av¥#k

to

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