superposition of ac and dc sources

Superposition of

AC and DC Sources Presented by:

M. Hammad WaseemL1F14BSEE0033

November 30, 2015

Contents of Presentation• What is Superposition?• Usage of Superposition.• Steps of Superposition with dc independent

sources.• Example 1 - Using two independent DC sources.• Steps of superposition with ac and dc sources.• Example 2 - Using AC and DC sources in RC

circuit.

What is Superposition? • The voltage across a component is the

algebraic sum of the voltage across the component due to each independent source acting upon it.

• The current flowing through a component is the algebraic sum of the current flowing through component due to each independent source acting upon it.

Usage of Superposition• Separating the contributions of the DC and AC

independent sources. Example:

To determine the performance of an amplifier, we calculate the DC voltages and currents to establish the bias point. The AC signal is usually what will be amplified. A generic amplifier has a constant DC operating point, but the AC signal’s amplitude and frequency will vary depending on the application.

Usage of Superposition (Cont.)Superposition can be used to reduce the complexity

of a circuit so that the voltages and currents in the circuit can be determined easily.To turn off a voltage source, replace it with a short circuit.To turn off a current source, replace it with an open

circuit.Polarity of voltage across components and direction of

currents through the components must be the same during each iteration through the circuit.

The total of the currents and voltages from each iteration is the solution when all sources are active in the circuit

Steps of Superposition with DC Independent Sources

• Turn off all independent sources except one.• Redraw circuit.• Solve for the voltages and currents in the new circuit.• Turn off the active independent source and turn on one

of the other independent sources.• Repeat Steps 2 and 3.• Continue until you have turned on each of the

independent sources in the original circuit.• To find the total voltage across each component and

the total current flowing, add the contributions from each of the voltages and currents found in Step 3.

Example 1 Using two independent DC sources:

• Since we have two sources of power in this circuit, we will have to calculate two sets of values for voltage drops and/or currents, one for the circuit with only the 28 volt battery in effect and one for the circuit with only the 7 volt battery in effect.

Example 1(Cont.) For 28 V battery:

Example 1 (Cont.)• Analyzing the circuit with only the 28 volt battery, we

obtain the following values for voltage and current:

• For 7 V battery:

Example 1(Cont.)

• Analyzing the circuit with only the 7 volt battery, we obtain another set of values for voltage and current:

Example 1(Cont.)• Applying these superimposed voltage figures to the

circuit, the end result looks something like this:

• Superimposed current figures like this:

Example 1(Cont.)• Table of Voltages with polarities:

Example 1(Cont.)• Table of Currents with directions:

Steps of Superposition with AC and DC Sources

• Turn off AC voltage source except DC voltage source.• Redraw the circuit.• In RC circuit, capacitor act as an open for DC voltage

source whereas in RL circuit inductor act as closed for DC voltage source.

• Calculate and measured DC voltages across capitor(or inductor) and resistor.

• For DC source, if we use RC circuit then voltage across capacitor is equal to DC supply voltage, and voltage across resistor is zero. Else if we use RL circuit then voltage across inductor is zero, and voltage across resistor is equal to dc supply voltage.

Steps of Superposition with AC and DC sources (Cont.)

• Now turn on AC voltage source and turn off DC voltage source.• Repeat step 2.• In RC circuit, capacitor act as short for AC voltage source

whereas in RL circuit, inductor act as open for AC voltage source.

• Calculate and measured AC voltages across capacitor(or inductor) and resistor.

• For ac source, if we use RC circuit then voltage across resistor is equal to AC supply voltage, and voltage across capacitor is zero. Else if we use RL circuit then voltage across resistor is zero, and voltage across inductor is equal to AC supply voltage.

• Superimposed both the sources and check AC and DC voltages across capacitor(or inductor) and resistor with the help of oscilloscope in AC coupling and DC coupling.

Example 2:Using AC and DC sources in RC circuit:

fig a fig b• In fig b, we remove the ac voltage source.• We calculate and measure DC voltages across

capacitors and resistors.

Example 2(Cont.):• To calculate voltage across capacitor: Apply KVL in fig b Vs=Vc+VR

As VR=0 VS=VC+0 Vc=Vs=2 V• To calculate voltage across resistor: Vs=Vc+VR

As VC=VS

VS=Vs+VR

VR=Vs-Vs VR=0 V

Example 2(Cont.)• We measured voltage across resistor and voltage

across capacitor with the help of Digital Voltmeter in which we set knob in dc voltage state.

• Now turn on AC voltage source and turn off DC voltage source in fig b.

fig c

Example 2(Cont.)• To calculate voltage across capacitor: Vs=Vc+VR

As VR=VS

VS=Vc+Vs Vc=Vs-Vs Vc=0 V• To calculate voltage across resistor: Vs=Vc+VR

As Vc=0 V VS=0+VR

VR=Vs=1 V

Example 2 (Cont.)Table

VC DC

VC AC

VR DC

VR AC

Calculated Values

2 V 0 V 0 V 1 V

Measured Values

2 V 0 V 0 V 1.02 V

Frequency(f) = 10 kHz

Thank You