Experiement 4

• Objectives: To verify the thevenin theorem. To verify nortons theorem. To verify maximum power transfer theorem. To simplify the complex network 5. To prove that the value is the same by any method. 1. 2. 3. 4.

• Equipment: 1. 2. 3. 4. 5. 6.

Digital multimeter DMM. Wires. Bread board. Resistors. Power supply Resistor box.

• Contents: 1. Thevenin's theorem. 2. Norton's theorem. 3. Maximum power transfer theorem. • Theory:  Thevenin theorem state that any two terminal circuit with linear

element can represented by a circuit containing Vth & Rth connected in serie where: Vth = Vo.c & Rth is the equavelent resistance of the dead cirduit.  Nortons theorem state that the equavelant circuit can

represented by an independent current source Is.c in parallel with Rth. where Is.c =V o.c /Rth.  Maximum power transfer theorem state that the maximum

power transferred when RL = Rth., Pmax = (Vo.c/2)*(Is.c/2) • Calculation & data analysis: • Thevinen theorem: We connect the circuit shown in figure 4.1 and then measure the Vo.c through A B and the equivalent resistance & the short circuit current.

And fill the table 4.1: Equivalent voltage V measured 16.8 Table 4.1

calculated 16.73

Equivalent resistance Ω measured calculated 2235 2221

Equivalent current (Is.c) mA measured calculated 7.57 7.53

IT = ∑V / ∑R = 10/10100 = 0.99 mA. Vo.c = -It*3300 + 20 = 16.733 v. Rth = (3300//6800) = 22.44K/10.1K = 2221Ω. Is.c = Vth/Rth = 16.733/2221 = 7.53 mA. Then we connect the Equivalent thevenin circuit with the 2.2K resistor shown in figure 4.2 and measure the load current and the load voltage, shown in table 4.2. Load voltage (V) measured 8.2 Table 2.4

Load current (mA)

calculated 8.33

measured 3.55

calculated 3.78

IL = Vth /(Rth+RL) = 16.733/4421 = 3.78 mA.. VL = IL*RL = 3.78*10^-3*2200 = 8.33 v. • Norton's theorem: We connect the circuit shown in figure 4.3 and measure the load current & voltage and fill the table 4.3 Equivalent source Equivalent current resistance(Ω) (mA) 7.54

2221

Load voltage (v) measure d 8.35

Table 4.3 IL = Is.c*2200/(Rth+2200) = 3.78 mA

Calculated 8.33

Load current (mA) measure d 3.79

calculated 3.78

VL = IL*2200 = 8.33 v • Maximum power transfer theorem: We connect the circuit shown in figure 4.4 & measure the value of V for every load & fill the table 4.4 Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Table 4.4

Decade Resistance(Ω) 100 200 400 600 800 1000 1300 1600 1900 2000 2100 2200 2300 2400 2500

Load voltage Load current (v) (mA) 0.73 7.3 1.4 7 2.57 6.425 3.57 5.95 4.44 5.55 5.21 5.21 6.2 4.769 7 4.375 7.73 4.068 7.95 3.975 8.15 3.88 8.35 3.79 8.49 3.691 8.6 3.583 8.73 3.492

Load power (mW) 5.329 9.8 16.51 21.24 24.642 27.144 29.57 30.625 31.448 31.6 31.629 31.692 31.339 30.813 30.485

I1 = V1/100 = 7.3 mA P1 = I1*V1 = 0.73*7.3 = 5.329 mW I2 = V2/100 = 7 mA P2 = I2*V2 = 1.4*7 = 9.8 mW I3 = V3/100 = 6.425 mA P1 = I3*V3 = 6.425*2.57 = 16.51 mW I4 = V4/100 = 5.95 mA P4 = I4*V4 = 5.95*3.57 = 21.24 mW I5 = V5/100 = 5.55 mA P1 = I5*V5 = 4.44*5.55 = 24.642 mW I6 = V6/100 = 5.21 mA P6 = I6*V6 = 5.21*5.21 = 27.144 mW I7 = V7/100 = 4.769 mA P7 = I7*V7 = 6.2*4.769 = 29.57 mW I8 = V8/100 = 4.375 mA P8 = I8*V8 = 7*4.375 = 30.625 mW I9 = V9/100 = 4.068 mA P1 = I9*V9 = 7.73*4.068 = 31.448 mW

I10 = V10/100 = 3.975 mA P10 = I10*V10 = 7.95*3.975 = 31.6 mW I11 = V11/100 = 3.88 mA P11 = I11*V11 = 8.15*3.88 = 31.629 mW I12 = V12/100 = 3.79 mA P12 = I12*V12 = 8.35*3.79 = 31.692 mW I13 = V13/100 = 3.691 mA P13 = I13*V13 = 8.49*3.691 = 31.339 mW I14 = V14/100 = 3.583 mA P14 = I14*V14 = 8.6*3.583 = 30.813 mW I15 = V15/100 = 3.492 mA P15 = I15*V15 = 8.73*3.492 = 30.485 mW Then we plot P versus RL & found that the maximum power transfer when RL = 2.2KΩ, shown in figure 4.5. •

Conclusions: 1. we see that the maximum power transfer when RL = Rth

2. we see that the same current & the same voltage a cross 2.2K resistor through thevenin or Norton' thevenin 3. there is a percentage error between thevenin Norton & measured values. 4. it's easy to simplify the comlex circuits by thevenin or Norton.

• Circuit connection & simulation:

Figure 4.1

Figure 4.2

Figure 4.3

Figure 4.4

R-P charactarestic

P(mW)

40 30 20 10 0 0

1000

Figure 4.5

2000 R(ohm)

3000