MAXIMUM AVERAGE POWER TRANSFER
To obtain the maximum average power transferred from a source to a load, the load impedance should be chosen equal to the conjugate of the Thevenin equivalent impedance representing the reminder of the network. This means that the load impedance must be solved using the thevenin’s theorem
The formulas to solve for ZL:
STEPS IN SOLVING THE ZL AND POWER TRANSFER
1. Solve the load impedance (ZL) using the Thevenin’s theorem. Short the voltage source and open the current source.
2. Solve the Vth where Zl parallel to it, this means that the ZL is not concluded to solve the Vth.
3. The ZL must be in rectangular form . Used only the real part ( Rth +/- jXth)
4. The RL is equal to the conjugate of Zth. (see in formula)
5. Solve the power using the formula below:
where: Vth=Voc
(Click the image to enlarge)
The maximum average power transfer is a method to identify the maximum impedance load that is needed in the given ac circuit. This can be solve using thevenin’s theorem.
EFFECTIVE OR RMS VALUE
The effective or root mean square(RMS) value of a periodic current is the DC value that delivers the same average power to a resistor as the periodic current.
IN SINUSOID
The Root Mean Square (RMS) value of a sinusoidal voltage or current is equal to the maximum value divided by square root of 2.
APPARENT AND COMPLEX POWER
- Real power (P) [Unit: W]
- Reactive power (Q) [Unit: VAR]
- Complex power (S) [Unint :VA]
- Apparent Power (|S|)
Real power (P) is equal to the Voltage magnitude times Current magnitude time cos(angle of v -angle o i).
P=VrmsIrmscos(Av-Ai)
Reactive power (Q)= to Ssin(angle v-angle i)
Apparent power is the power that is “appears” to flow to the load. (S= |Vrms||Irms|)
Complex power (solve in polar form) = Vrms(Irms)*. note * is the conjugate or the angle will be in opposite sign.
or S = P + jQ (if converted in rectangular)
where P is the real power and Q is the reactive power.
power factor(pf) = P/S = cos(angle v-angle i)
Example (Click to enlarge)
USING THE POWER TRIANGLE
The power triangle graphically shows the relationship between real (P), reactive (Q) and apparent power (S).
Example: Find the complex power of the three loads
Solution:
Using the power triangle, it is more easily to solve the given problems and if you know how to used trigonometric functions then the problem is a piece of cake to you. But first things to do in solving the problem is to understand it, what is asked and what method is easily to solve the given problem
FranCircuit 2 